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+ļ»æProject Gutenberg's A Text-Book of Astronomy, by George C. Comstock
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Text-Book of Astronomy
+
+Author: George C. Comstock
+
+Release Date: January 3, 2011 [EBook #34834]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY ***
+
+
+
+
+Produced by Chris Curnow, Iris Schimandle, Lindy Walsh and
+the Online Distributed Proofreading Team at
+http://www.pgdp.net
+
+
+
+
+
+
+
+
+
+                      TWENTIETH CENTURY TEXT-BOOKS
+
+
+                                EDITED BY
+                     A. F. NIGHTINGALE, PH.D., LL.D.
+            FORMERLY SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO
+
+
+
+                 [Illustration: A TOTAL SOLAR ECLIPSE.
+    After Burckhalter's photographs of the eclipse of May 28, 1900.]
+
+
+
+                      TWENTIETH CENTURY TEXT-BOOKS
+
+
+                             A TEXT-BOOK OF
+                               ASTRONOMY
+
+                                   BY
+                           GEORGE C. COMSTOCK
+
+
+                DIRECTOR OF THE WASHBURN OBSERVATORY AND
+                     PROFESSOR OF ASTRONOMY IN THE
+                        UNIVERSITY OF WISCONSIN
+
+
+                             [Illustration]
+
+
+                                NEW YORK
+                        D. APPLETON AND COMPANY
+                                  1903
+
+
+
+                            COPYRIGHT, 1901
+                       BY D. APPLETON AND COMPANY
+
+
+
+
+PREFACE
+
+
+The present work is not a compendium of astronomy or an outline course
+of popular reading in that science. It has been prepared as a text-book,
+and the author has purposely omitted from it much matter interesting as
+well as important to a complete view of the science, and has endeavored
+to concentrate attention upon those parts of the subject that possess
+special educational value. From this point of view matter which permits
+of experimental treatment with simple apparatus is of peculiar value and
+is given a prominence in the text beyond its just due in a well-balanced
+exposition of the elements of astronomy, while topics, such as the
+results of spectrum analysis, which depend upon elaborate apparatus, are
+in the experimental part of the work accorded much less space than their
+intrinsic importance would justify.
+
+Teacher and student are alike urged to magnify the observational side of
+the subject and to strive to obtain in their work the maximum degree of
+precision of which their apparatus is capable. The instruments required
+are few and easily obtained. With exception of a watch and a protractor,
+all of the apparatus needed may be built by any one of fair mechanical
+talent who will follow the illustrations and descriptions of the text.
+In order that proper opportunity for observations may be had, the study
+should be pursued during the milder portion of the year, between April
+and November in northern latitudes, using clear weather for a direct
+study of the sky and cloudy days for book work.
+
+The illustrations contained in the present work are worthy of as careful
+study as is the text, and many of them are intended as an aid to
+experimental work and accurate measurement, e. g., the star maps, the
+diagrams of the planetary orbits, pictures of the moon, sun, etc. If the
+school possesses a projection lantern, a set of astronomical slides to
+be used in connection with it may be made of great advantage, if the
+pictures are studied as an auxiliary to Nature. Mere display and scenic
+effect are of little value.
+
+A brief bibliography of popular literature upon astronomy may be found
+at the end of this book, and it will be well if at least a part of these
+works can be placed in the school library and systematically used for
+supplementary reading. An added interest may be given to the study if
+one or more of the popular periodicals which deal with astronomy are
+taken regularly by the school and kept within easy reach of the
+students. From time to time the teacher may well assign topics treated
+in these periodicals to be read by individual students and presented to
+the class in the form of an essay.
+
+The author is under obligations to many of his professional friends who
+have contributed illustrative matter for his text, and his thanks are in
+an especial manner due to the editors of the Astrophysical Journal,
+Astronomy and Astrophysics, and Popular Astronomy for permission to
+reproduce here plates which have appeared in those periodicals, and to
+Dr. Charles Boynton, who has kindly read and criticised the proofs.
+
+                                                  GEORGE C. COMSTOCK.
+
+  UNIVERSITY OF WISCONSIN, _February, 1901_.
+
+
+
+
+CONTENTS
+
+
+ CHAPTER                                                        PAGE
+    I.--DIFFERENT KINDS OF MEASUREMENT                             1
+          The measurement of angles and time.
+
+   II.--THE STARS AND THEIR DIURNAL MOTION                        10
+          Finding the stars--Their apparent motion--
+          Latitude--Direction of the meridian--Sidereal
+          time--Definitions.
+
+  III.--FIXED AND WANDERING STARS                                 29
+          Apparent motion of the sun, moon, and
+          planets--Orbits of the planets--How to find
+          the planets.
+
+   IV.--CELESTIAL MECHANICS                                       46
+          Kepler's laws--Newton's laws of motion--The law
+          of gravitation--Orbital motion--Perturbations--
+          Masses of the planets--Discovery of Neptune--
+          The tides.
+
+    V.--THE EARTH AS A PLANET                                     70
+          Size--Mass--Precession--The warming of the
+          earth--The atmosphere--Twilight.
+
+   VI.--THE MEASUREMENT OF TIME                                   86
+          Solar and sidereal time--Longitude--The
+          calendar--Chronology.
+
+  VII.--ECLIPSES                                                 101
+          Their cause and nature--Eclipse limits--Eclipse
+          maps--Recurrence and prediction of eclipses.
+
+ VIII.--INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE     121
+          The clock--Radiant energy--Mirrors and lenses--
+          The telescope--Camera--Spectroscope--Principles
+          of spectrum analysis.
+
+   IX.--THE MOON                                                 150
+          Numerical data--Phases--Motion--Librations--Lunar
+          topography--Physical condition.
+
+    X.--THE SUN                                                  178
+          Numerical data--Chemical nature--Temperature--
+          Visible and invisible parts--Photosphere--Spots--
+          FaculƦ--Chromosphere--Prominences--Corona--The
+          sun-spot period--The sun's rotation--Mechanical
+          theory of the sun.
+
+   XI.--THE PLANETS                                              212
+          Arrangement of the solar system--Bode's law--
+          Physical condition of the planets--Jupiter--
+          Saturn--Uranus and Neptune--Venus--Mercury--
+          Mars--The asteroids.
+
+  XII.--COMETS AND METEORS                                       251
+          Motion, size, and mass of comets--Meteors--Their
+          number and distribution--Meteor showers--Relation
+          of comets and meteors--Periodic comets--Comet
+          families and groups--Comet tails--Physical nature
+          of comets--Collisions.
+
+ XIII.--THE FIXED STARS                                          291
+          Number of the stars--Brightness--Distance--Proper
+          motion--Motion in line of sight--Double stars--
+          Variable stars--New stars.
+
+  XIV.--STARS AND NEBULƆ                                         330
+          Stellar colors and spectra--Classes of stars--
+          Clusters--NebulƦ--Their spectra and physical
+          condition--The Milky Way--Construction of the
+          heavens--Extent of the stellar system.
+
+   XV.--GROWTH AND DECAY                                         358
+          Logical bases and limitations--Development of the
+          sun--The nebular hypothesis--Tidal friction--Roche's
+          limit--Development of the moon--Development of stars
+          and nebulƦ--The future.
+
+        APPENDIX                                                 383
+
+        INDEX                                                    387
+
+
+
+
+LIST OF LITHOGRAPHIC PLATES
+
+
+                                                         FACING PAGE
+    I.--Northern Constellations                                  124
+   II.--Equatorial Constellations                                190
+  III.--Map of Mars                                              246
+   IV.--The Pleiades                                             344
+        Protractor                       _In pocket at back of book_
+
+
+
+
+LIST OF FULL-PAGE ILLUSTRATIONS
+
+
+                                                         FACING PAGE
+  A Total Solar Eclipse                               _Frontispiece_
+  The Harvard College Observatory, Cambridge, Mass.               24
+  Isaac Newton                                                    46
+  Galileo Galilei                                                 52
+  The Lick Observatory, Mount Hamilton, Cal.                      60
+  The Yerkes Observatory, Williams Bay, Wis.                     100
+  The Moon, one day after First Quarter                          150
+  William Herschel                                               234
+  Pierre Simon Laplace                                           364
+
+
+
+
+ASTRONOMY
+
+
+
+
+CHAPTER I
+
+DIFFERENT KINDS OF MEASUREMENT
+
+
+1. ACCURATE MEASUREMENT.--Accurate measurement is the foundation of
+exact science, and at the very beginning of his study in astronomy the
+student should learn something of the astronomer's kind of measurement.
+He should practice measuring the stars with all possible care, and
+should seek to attain the most accurate results of which his instruments
+and apparatus are capable. The ordinary affairs of life furnish abundant
+illustration of some of these measurements, such as finding the length
+of a board in inches or the weight of a load of coal in pounds and
+measurements of both length and weight are of importance in astronomy,
+but of far greater astronomical importance than these are the
+measurement of angles and the measurement of time. A kitchen clock or a
+cheap watch is usually thought of as a machine to tell the "time of
+day," but it may be used to time a horse or a bicycler upon a race
+course, and then it becomes an instrument to measure the amount of time
+required for covering the length of the course. Astronomers use a clock
+in both of these ways--to tell the time at which something happens or is
+done, and to measure the amount of time required for something; and in
+using a clock for either purpose the student should learn to take the
+time from it to the nearest second or better, if it has a seconds hand,
+or to a small fraction of a minute, by estimating the position of the
+minute hand between the minute marks on the dial. Estimate the fraction
+in tenths of a minute, not in halves or quarters.
+
+EXERCISE 1.--If several watches are available, let one person tap
+sharply upon a desk with a pencil and let each of the others note the
+time by the minute hand to the nearest tenth of a minute and record the
+observations as follows:
+
+    2h. 44.5m.  First tap.   2h. 46.4m.  1.9m.
+    2h. 44.9m.  Second tap.  2h. 46.7m.  1.8m.
+    2h. 46.6m.  Third tap.   2h. 48.6m.  2.0m.
+
+The letters h and m are used as abbreviations for hour and minute. The
+first and second columns of the table are the record made by one
+student, and second and third the record made by another. After all the
+observations have been made and recorded they should be brought together
+and compared by taking the differences between the times recorded for
+each tap, as is shown in the last column. This difference shows how much
+faster one watch is than the other, and the agreement or disagreement of
+these differences shows the degree of accuracy of the observations. Keep
+up this practice until tenths of a minute can be estimated with fair
+precision.
+
+2. ANGLES AND THEIR USE.--An angle is the amount of opening or
+difference of direction between two lines that cross each other. At
+twelve o'clock the hour and minute hand of a watch point in the same
+direction and the angle between them is zero. At one o'clock the minute
+hand is again at XII, but the hour hand has moved to I, one twelfth part
+of the circumference of the dial, and the angle between the hands is one
+twelfth of a circumference. It is customary to imagine the circumference
+of a dial to be cut up into 360 equal parts--i. e., each minute space of
+an ordinary dial to be subdivided into six equal parts, each of which
+is called a degree, and the measurement of an angle consists in finding
+how many of these degrees are included in the opening between its sides.
+At one o'clock the angle between the hands of a watch is thirty degrees,
+which is usually written 30Ā°, at three o'clock it is 90Ā°, at six o'clock
+180Ā°, etc.
+
+A watch may be used to measure angles. How? But a more convenient
+instrument is the protractor, which is shown in Fig. 1, applied to the
+angle _A B C_ and showing that _A B C_ = 85Ā° as nearly as the protractor
+scale can be read.
+
+The student should have and use a protractor, such as is furnished with
+this book, for the numerous exercises which are to follow.
+
+[Illustration: FIG. 1.--A protractor.]
+
+EXERCISE 2.--Draw neatly a triangle with sides about 100 millimeters
+long, measure each of its angles and take their sum. No matter what may
+be the shape of the triangle, this sum should be very nearly
+180Ā°--exactly 180Ā° if the work were perfect--but perfection can seldom
+be attained and one of the first lessons to be learned in any science
+which deals with measurement is, that however careful we may be in our
+work some minute error will cling to it and our results can be only
+approximately correct. This, however, should not be taken as an excuse
+for careless work, but rather as a stimulus to extra effort in order
+that the unavoidable errors may be made as small as possible. In the
+present case the measured angles may be improved a little by adding
+(algebraically) to each of them one third of the amount by which their
+sum falls short of 180Ā°, as in the following example:
+
+            Measured angles.    Correction.  Corrected angles.
+                 Ā°                   Ā°              Ā°
+  A            73.4               + 0.1           73.5
+  B            49.3               + 0.1           49.4
+  C            57.0               + 0.1           57.1
+              -----                              -----
+  Sum         179.7                              180.0
+  Defect      + 0.3
+
+This process is in very common use among astronomers, and is called
+"adjusting" the observations.
+
+[Illustration: FIG. 2.--Triangulation.]
+
+3. TRIANGLES.--The instruments used by astronomers for the measurement
+of angles are usually provided with a telescope, which may be pointed at
+different objects, and with a scale, like that of the protractor, to
+measure the angle through which the telescope is turned in passing from
+one object to another. In this way it is possible to measure the angle
+between lines drawn from the instrument to two distant objects, such as
+two church steeples or the sun and moon, and this is usually called the
+angle between the objects. By measuring angles in this way it is
+possible to determine the distance to an inaccessible point, as shown in
+Fig. 2. A surveyor at _A_ desires to know the distance to _C_, on the
+opposite side of a river which he can not cross. He measures with a tape
+line along his own side of the stream the distance _A B_ = 100 yards and
+then, with a suitable instrument, measures the angle at _A_ between the
+points _C_ and _B_, and the angle at _B_ between _C_ and _A_, finding _B
+A C_ = 73.4Ā°, _A B C_ = 49.3Ā°. To determine the distance _A C_ he draws
+upon paper a line 100 millimeters long, and marks the ends _a_ and _b_;
+with a protractor he constructs at _a_ the angle _b a c_ = 73.4Ā°, and at
+_b_ the angle _a b c_ = 49.3Ā°, and marks by _c_ the point where the two
+lines thus drawn meet. With the millimeter scale he now measures the
+distance _a c_ = 90.2 millimeters, which determines the distance _A C_
+across the river to be 90.2 yards, since the triangle on paper has been
+made similar to the one across the river, and millimeters on the one
+correspond to yards on the other. What is the proposition of geometry
+upon which this depends? The measured distance _A B_ in the surveyor's
+problem is called a base line.
+
+EXERCISE 3.--With a foot rule and a protractor measure a base line and
+the angles necessary to determine the length of the schoolroom. After
+the length has been thus found, measure it directly with the foot rule
+and compare the measured length with the one found from the angles. If
+any part of the work has been carelessly done, the student need not
+expect the results to agree.
+
+[Illustration: FIG. 3.--Finding the moon's distance from the earth.]
+
+In the same manner, by sighting at the moon from widely different parts
+of the earth, as in Fig. 3, the moon's distance from us is found to be
+about a quarter of a million miles. What is the base line in this case?
+
+4. THE HORIZON--ALTITUDES.--In their observations astronomers and
+sailors make much use of the _plane of the horizon_, and practically any
+flat and level surface, such as that of a smooth pond, may be regarded
+as a part of this plane and used as such. A very common observation
+relating to the plane of the horizon is called "taking the sun's
+altitude," and consists in measuring the angle between the sun's rays
+and the plane of the horizon upon which they fall. This angle between a
+line and a plane appears slightly different from the angle between two
+lines, but is really the same thing, since it means the angle between
+the sun's rays and a line drawn in the plane of the horizon toward the
+point directly under the sun. Compare this with the definition given in
+the geographies, "The latitude of a point on the earth's surface is its
+angular distance north or south of the equator," and note that the
+latitude is the angle between the plane of the equator and a line drawn
+from the earth's center to the given point on its surface.
+
+A convenient method of obtaining a part of the plane of the horizon for
+use in observation is as follows: Place a slate or a pane of glass upon
+a table in the sunshine. Slightly moisten its whole surface and then
+pour a little more water upon it near the center. If the water runs
+toward one side, thrust the edge of a thin wooden wedge under this side
+and block it up until the water shows no tendency to run one way rather
+than another; it is then level and a part of the plane of the horizon.
+Get several wedges ready before commencing the experiment. After they
+have been properly placed, drive a pin or tack behind each one so that
+it may not slip.
+
+5. TAKING THE SUN'S ALTITUDE. EXERCISE 4.--Prepare a piece of board 20
+centimeters, or more, square, planed smooth on one face and one edge.
+Drive a pin perpendicularly into the face of the board, near the middle
+of the planed edge. Set the board on edge on the horizon plane and turn
+it edgewise toward the sun so that a shadow of the pin is cast on the
+plane. Stick another pin into the board, near its upper edge, so that
+its shadow shall fall exactly upon the shadow of the first pin, and with
+a watch or clock observe the time at which the two shadows coincide.
+Without lifting the board from the plane, turn it around so that the
+opposite edge is directed toward the sun and set a third pin just as the
+second one was placed, and again take the time. Remove the pins and draw
+fine pencil lines, connecting the holes, as shown in Fig. 4, and with
+the protractor measure the angle thus marked. The student who has
+studied elementary geometry should be able to demonstrate that at the
+mean of the two recorded times the sun's altitude was equal to one half
+of the angle measured in the figure.
+
+[Illustration: FIG. 4.--Taking the sun's altitude.]
+
+When the board is turned edgewise toward the sun so that its shadow is
+as thin as possible, rule a pencil line alongside it on the horizon
+plane. The angle which this line makes with a line pointing due south is
+called the sun's _azimuth_. When the sun is south, its azimuth is zero;
+when west, it is 90Ā°; when east, 270Ā°, etc.
+
+EXERCISE 5.--Let a number of different students take the sun's altitude
+during both the morning and afternoon session and note the time of each
+observation, to the nearest minute. Verify the setting of the plane of
+the horizon from time to time, to make sure that no change has occurred
+in it.
+
+6. GRAPHICAL REPRESENTATIONS.--Make a graph (drawing) of all the
+observations, similar to Fig. 5, and find by bisecting a set of chords
+_g_ to _g_, _e_ to _e_, _d_ to _d_, drawn parallel to _B B_, the time at
+which the sun's altitude was greatest. In Fig. 5 we see from the
+intersection of _M M_ with _B B_ that this time was 11h. 50m.
+
+The method of graphs which is here introduced is of great importance in
+physical science, and the student should carefully observe in Fig. 5
+that the line _B B_ is a scale of times, which may be made long or
+short, provided only the intervals between consecutive hours 9 to 10, 10
+to 11, 11 to 12, etc., are equal. The distance of each little circle
+from _B B_ is taken proportional to the sun's altitude, and may be upon
+any desired scale--e. g., a millimeter to a degree--provided the same
+scale is used for all observations. Each circle is placed accurately
+over that part of the base line which corresponds to the time at which
+the altitude was taken. Square ruled paper is very convenient, although
+not necessary, for such diagrams. It is especially to be noted that from
+the few observations which are represented in the figure a smooth curve
+has been drawn through the circles which represent the sun's altitude,
+and this curve shows the altitude of the sun at every moment between 9
+A. M. and 3 P. M. In Fig. 5 the sun's altitude at noon was 57Ā°. What was
+it at half past two?
+
+[Illustration: FIG. 5.--A graph of the sun's altitude.]
+
+7. DIAMETER OF A DISTANT OBJECT.--By sighting over a protractor, measure
+the angle between imaginary lines drawn from it to the opposite sides of
+a window. Carry the protractor farther away from the window and repeat
+the experiment, to see how much the angle changes. The angle thus
+measured is called "the angle subtended" by the window at the place
+where the measurement was made. If this place was squarely in front of
+the window we may draw upon paper an angle equal to the measured one and
+lay off from the vertex along its sides a distance proportional to the
+distance of the window--e. g., a millimeter for each centimeter of real
+distance. If a cross line be now drawn connecting the points thus found,
+its length will be proportional to the width of the window, and the
+width may be read off to scale, a centimeter for every millimeter in the
+length of the cross line.
+
+The astronomer who measures with an appropriate instrument the angle
+subtended by the moon may in an entirely similar manner find the moon's
+diameter and has, in fact, found it to be 2,163 miles. Can the same
+method be used to find the diameter of the sun? A planet? The earth?
+
+
+
+
+CHAPTER II
+
+THE STARS AND THEIR DIURNAL MOTION
+
+
+8. THE STARS.--From the very beginning of his study in astronomy, and as
+frequently as possible, the student should practice watching the stars
+by night, to become acquainted with the constellations and their
+movements. As an introduction to this study he may face toward the
+north, and compare the stars which he sees in that part of the sky with
+the map of the northern heavens, given on Plate I, opposite page 124.
+Turn the map around, upside down if necessary, until the stars upon it
+match the brighter ones in the sky. Note how the stars are grouped in
+such conspicuous constellations as the Big Dipper (Ursa Major), the
+Little Dipper (Ursa Minor), and Cassiopeia. These three constellations
+should be learned so that they can be recognized at any time.
+
+_The names of the stars._--Facing the star map is a key which contains
+the names of the more important constellations and the names of the
+brighter stars in their constellations. These names are for the most
+part a Greek letter prefixed to the genitive case of the Latin name of
+the constellation. (See the Greek alphabet printed at the end of the
+book.)
+
+9. MAGNITUDES OF THE STARS.--Nearly nineteen centuries ago St. Paul
+noted that "one star differeth from another star in glory," and no more
+apt words can be found to mark the difference of brightness which the
+stars present. Even prior to St. Paul's day the ancient Greek
+astronomers had divided the stars in respect of brightness into six
+groups, which the modern astronomers still use, calling each group a
+_magnitude_. Thus a few of the brightest stars are said to be of the
+first magnitude, the great mass of faint ones which are just visible to
+the unaided eye are said to be of the sixth magnitude, and intermediate
+degrees of brilliancy are represented by the intermediate magnitudes,
+second, third, fourth, and fifth. The student must not be misled by the
+word magnitude. It has no reference to the size of the stars, but only
+to their brightness, and on the star maps of this book the larger and
+smaller circles by which the stars are represented indicate only the
+brightness of the stars according to the system of magnitudes. Following
+the indications of these maps, the student should, in learning the
+principal stars and constellations, learn also to recognize how bright
+is a star of the second, fourth, or other magnitude.
+
+10. OBSERVING THE STARS.--Find on the map and in the sky the stars
+Ī± UrsƦ Minoris, Ī± UrsƦ Majoris, Ī² UrsƦ Majoris. What geometrical
+figure will fit on to these stars? In addition to its regular name,
+Ī± UrsƦ Minoris is frequently called by the special name Polaris, or
+the pole star. Why are the other two stars called "the Pointers"? What
+letter of the alphabet do the five bright stars in Cassiopeia suggest?
+
+EXERCISE 6.--Stand in such a position that Polaris is just hidden behind
+the corner of a building or some other vertical line, and mark upon the
+key map as accurately as possible the position of this line with respect
+to the other stars, showing which stars are to the right and which are
+to the left of it. Record the time (date, hour, and minute) at which
+this observation was made. An hour or two later repeat the observation
+at the same place, draw the line and note the time, and you will find
+that the line last drawn upon the map does not agree with the first one.
+The stars have changed their positions, and with respect to the vertical
+line the Pointers are now in a different direction from Polaris.
+Measure with a protractor the angle between the two lines drawn in the
+map, and use this angle and the recorded times of the observation to
+find how many degrees per hour this direction is changing. It should be
+about 15Ā° per hour. If the observation were repeated 12 hours after the
+first recorded time, what would be the position of the vertical line
+among the stars? What would it be 24 hours later? A week later? Repeat
+the observation on the next clear night, and allowing for the number of
+whole revolutions made by the stars between the two dates, again
+determine from the time interval a more accurate value of the rate at
+which the stars move.
+
+The motion of the stars which the student has here detected is called
+their "diurnal" motion. What is the significance of the word diurnal?
+
+In the preceding paragraph there is introduced a method of great
+importance in astronomical practice--i. e., determining something--in
+this case the rate per hour, from observations separated by a long
+interval of time, in order to get a more accurate value than could be
+found from a short interval. Why is it more accurate? To determine the
+rate at which the planet Mars rotates about its axis, astronomers use
+observations separated by an interval of more than 200 years, during
+which the planet made more than 75,000 revolutions upon its axis. If we
+were to write out in algebraic form an equation for determining the
+length of one revolution of Mars about its axis, the large number,
+75,000, would appear in the equation as a divisor, and in the final
+result would greatly reduce whatever errors existed in the observations
+employed.
+
+Repeat Exercise 6 night after night, and note whether the stars come
+back to the same position at the same hour and minute every night.
+
+[Illustration: FIG. 6. The plumb-line apparatus.]
+
+[Illustration: FIG. 7. The plumb-line apparatus.]
+
+11. THE PLUMB-LINE APPARATUS.--This experiment, and many others, may be
+conveniently and accurately made with no other apparatus than a plumb
+line, and a device for sighting past it. In Figs. 6 and 7 there is
+shown a simple form of such apparatus, consisting essentially of a board
+which rests in a horizontal position upon the points of three screws
+that pass through it. This board carries a small box, to one side of
+which is nailed in vertical position another board 5 or 6 feet long to
+carry the plumb line. This consists of a wire or fish line with any
+heavy weight--e. g., a brick or flatiron--tied to its lower end and
+immersed in a vessel of water placed inside the box, so as to check any
+swinging motion of the weight. In the cover of the box is a small hole
+through which the wire passes, and by turning the screws in the
+baseboard the apparatus may be readily leveled, so that the wire shall
+swing freely in the center of the hole without touching the cover of the
+box. Guy wires, shown in the figure, are applied so as to stiffen the
+whole apparatus. A board with a screw eye at each end may be pivoted to
+the upright, as in Fig. 6, for measuring altitudes; or to the box, as in
+Fig. 7, for observing the time at which a star in its diurnal motion
+passes through the plane determined by the plumb line and the center of
+the screw eye through which the observer looks.
+
+The whole apparatus may be constructed by any person of ordinary
+mechanical skill at a very small cost, and it or something equivalent
+should be provided for every class beginning observational astronomy. To
+use the apparatus for the experiment of Ā§ 10, it should be leveled, and
+the board with the screw eyes, attached as in Fig. 7, should be turned
+until the observer, looking through the screw eye, sees Polaris exactly
+behind the wire. Use a bicycle lamp to illumine the wire by night. The
+apparatus is now adjusted, and the observer has only to wait for the
+stars which he desires to observe, and to note by his watch the time at
+which they pass behind the wire. It will be seen that the wire takes the
+place of the vertical edge of the building, and that the board with the
+screw eyes is introduced solely to keep the observer in the right place
+relative to the wire.
+
+12. A SIDEREAL CLOCK.--Clocks are sometimes so made and regulated that
+they show always the same hour and minute when the stars come back to
+the same place, and such a timepiece is called a sidereal clock--i. e.,
+a star-time clock. Would such a clock gain or lose in comparison with an
+ordinary watch? Could an ordinary watch be turned into a sidereal watch
+by moving the regulator?
+
+[Illustration: FIG. 8.--Photographing the circumpolar stars.--BARNARD.]
+
+13. PHOTOGRAPHING THE STARS.--EXERCISE 7.--For any student who uses a
+camera. Upon some clear and moonless night point the camera, properly
+focused, at Polaris, and expose a plate for three or four hours. Upon
+developing the plate you should find a series of circular trails such as
+are shown in Fig. 8, only longer. Each one of these is produced by a
+star moving slowly over the plate, in consequence of its changing
+position in the sky. The center indicated by these curved trails is
+called the pole of the heavens. It is that part of the sky toward which
+is pointed the axis about which the earth rotates, and the motion of the
+stars around the center is only an apparent motion due to the rotation
+of the earth which daily carries the observer and his camera around this
+axis while the stars stand still, just as trees and fences and telegraph
+poles stand still, although to the passenger upon a railway train they
+appear to be in rapid motion. So far as simple observations are
+concerned, there is no method by which the pupil can tell for himself
+that the motion of the stars is an apparent rather than a real one, and,
+following the custom of astronomers, we shall habitually speak as if it
+were a real movement of the stars. How long was the plate exposed in
+photographing Fig. 8?
+
+14. FINDING THE STARS.--On Plate I, opposite page 124, the pole of the
+heavens is at the center of the map, near Polaris, and the heavy trail
+near the center of Fig. 8 is made by Polaris. See if you can identify
+from the map any of the stars whose trails show in the photograph. The
+brighter the star the bolder and heavier its trail.
+
+Find from the map and locate in the sky the two bright stars Capella and
+Vega, which are on opposite sides of Polaris and nearly equidistant from
+it. Do these stars share in the motion around the pole? Are they visible
+on every clear night, and all night?
+
+Observe other bright stars farther from Polaris than are Vega and
+Capella and note their movement. Do they move like the sun and moon? Do
+they rise and set?
+
+In what part of the sky do the stars move most rapidly, near the pole or
+far from it?
+
+How long does it take the fastest moving stars to make the circuit of
+the sky and come back to the same place? How long does it take the slow
+stars?
+
+15. RISING AND SETTING OF THE STARS.--A study of the sky along the lines
+indicated in these questions will show that there is a considerable part
+of it surrounding the pole whose stars are visible on every clear night.
+The same star is sometimes high in the sky, sometimes low, sometimes to
+the east of the pole and at other times west of it, but is always above
+the horizon. Such stars are said to be circumpolar. A little farther
+from the pole each star, when at the lowest point of its circular path,
+dips for a time below the horizon and is lost to view, and the farther
+it is away from the pole the longer does it remain invisible, until, in
+the case of stars 90Ā° away from the pole, we find them hidden below the
+horizon for twelve hours out of every twenty-four (see Fig. 9). The sun
+is such a star, and in its rising and setting acts precisely as does
+every other star at a similar distance from the pole--only, as we shall
+find later, each star keeps always at (nearly) the same distance from
+the pole, while the sun in the course of a year changes its distance
+from the pole very greatly, and thus changes the amount of time it
+spends above and below the horizon, producing in this way the long days
+of summer and the short ones of winter.
+
+[Illustration: FIG. 9.--Diurnal motion of the northern constellations.]
+
+How much time do stars which are more than 90Ā° from the pole spend above
+the horizon?
+
+We say in common speech that the sun rises in the east, but this is
+strictly true only at the time when it is 90Ā° distant from the
+pole--i. e., in March and September. At other seasons it rises north or
+south of east according as its distance from the pole is less or greater
+than 90Ā°, and the same is true for the stars.
+
+16. THE GEOGRAPHY OF THE SKY.--Find from a map the latitude and
+longitude of your schoolhouse. Find on the map the place whose latitude
+is 39Ā° and longitude 77Ā° west of the meridian of Greenwich. Is there any
+other place in the world which has the same latitude and longitude as
+your schoolhouse?
+
+The places of the stars in the sky are located in exactly the manner
+which is illustrated by these geographical questions, only different
+names are used. Instead of latitude the astronomer says _declination_,
+in place of longitude he says _right ascension_, in place of meridian he
+says _hour circle_, but he means by these new names the same ideas that
+the geographer expresses by the old ones.
+
+Imagine the earth swollen up until it fills the whole sky; the earth's
+equator would meet the sky along a line (a great circle) everywhere 90Ā°
+distant from the pole, and this line is called the _celestial equator_.
+Trace its position along the middle of the map opposite page 190 and
+notice near what stars it runs. Every meridian of the swollen earth
+would touch the sky along an hour circle--i. e., a great circle passing
+through the pole and therefore perpendicular to the equator. Note that
+in the map one of these hour circles is marked 0. It plays the same part
+in measuring right ascensions as does the meridian of Greenwich in
+measuring longitudes; it is the beginning, from which they are reckoned.
+Note also, at the extreme left end of the map, the four bright stars in
+the form of a square, one side of which is parallel and close to the
+hour circle, which is marked 0. This is familiarly called the Great
+Square in Pegasus, and may be found high up in the southern sky whenever
+the Big Dipper lies below the pole. Why can it not be seen when Ursa
+Major is above the pole?
+
+Astronomers use the right ascensions of the stars not only to tell in
+what part of the sky the star is placed, but also in time reckonings, to
+regulate their sidereal clocks, and with regard to this use they find
+it convenient to express right ascension not in degrees but in hours,
+24 of which fill up the circuit of the sky and each of which is equal
+to 15Ā° of arc, 24 Ɨ 15 = 360. The right ascension of Capella is
+5h. 9m. = 77.2Ā°, but the student should accustom himself to using it
+in hours and minutes as given and not to change it into degrees. He
+should also note that some stars lie on the side of the celestial
+equator toward Polaris, and others are on the opposite side, so that the
+astronomer has to distinguish between north declinations and south
+declinations, just as the geographer distinguishes between north
+latitudes and south latitudes. This is done by the use of the + and -
+signs, a + denoting that the star lies north of the celestial equator,
+i. e., toward Polaris.
+
+[Illustration: FIG. 10.--From a photograph of the Pleiades.]
+
+Find on Plate II, opposite page 190, the Pleiades (Plēadēs),
+R. A. = 3h. 42m., Dec. = +23.8Ā°. Why do they not show on Plate I,
+opposite page 124? In what direction are they from Polaris? This is one
+of the finest star clusters in the sky, but it needs a telescope to
+bring out its richness. See how many stars you can count in it with the
+naked eye, and afterward examine it with an opera glass. Compare what
+you see with Fig. 10. Find Antares, R. A. = 16h. 23m. Dec. = -26.2Ā°. How
+far is it, in degrees, from the pole? Is it visible in your sky? If so,
+what is its color?
+
+Find the R. A. and Dec. of Ī± UrsƦ Majoris; of Ī² UrsƦ Majoris; of
+Polaris. Find the Northern Crown, _Corona Borealis_, R. A. = 15h. 30m.,
+Dec. = +27.0Ā°; the Beehive, _PrƦsepe_, R. A. = 8h. 33m., Dec. = +20.4Ā°.
+
+These should be looked up, not only on the map, but also in the sky.
+
+17. REFERENCE LINES AND CIRCLES.--As the stars move across the sky in
+their diurnal motion, they carry the framework of hour circles and
+equator with them, so that the right ascension and declination of each
+star remain unchanged by this motion, just as longitudes and latitudes
+remain unchanged by the earth's rotation. They are the same when a star
+is rising and when it is setting; when it is above the pole and when it
+is below it. During each day the hour circle of every star in the
+heavens passes overhead, and at the moment when any particular hour
+circle is exactly overhead all the stars which lie upon it are said to
+be "on the meridian"--i. e., at that particular moment they stand
+directly over the observer's geographical meridian and upon the
+corresponding celestial meridian.
+
+An eye placed at the center of the earth and capable of looking through
+its solid substance would see your geographical meridian against the
+background of the sky exactly covering your celestial meridian and
+passing from one pole through your zenith to the other pole. In Fig. 11
+the inner circle represents the terrestrial meridian of a certain
+place, _O_, as seen from the center of the earth, _C_, and the outer
+circle represents the celestial meridian of _O_ as seen from _C_, only
+we must imagine, what can not be shown on the figure, that the outer
+circle is so large that the inner one shrinks to a mere point in
+comparison with it. If _C P_ represents the direction in which the
+earth's axis passes through the center, then _C E_ at right angles to it
+must be the direction of the equator which we suppose to be turned
+edgewise toward us; and if _C O_ is the direction of some particular
+point on the earth's surface, then _Z_ directly overhead is called the
+_zenith_ of that point, upon the celestial sphere. The line _C H_
+represents a direction parallel to the horizon plane at _O_, and _H C P_
+is the angle which the axis of the earth makes with this horizon plane.
+The arc _O E_ measures the latitude of _O_, and the arc _Z E_ measures
+the declination of _Z_, and since by elementary geometry each of these
+arcs contains the same number of degrees as the angle _E C Z_, we have
+the
+
+_Theorem._--The latitude of any place is equal to the declination of its
+zenith.
+
+_Corollary._--Any star whose declination is equal to your latitude will
+once in each day pass through your zenith.
+
+[Illustration: FIG. 11.--Reference lines and circles.]
+
+18. LATITUDE.--From the construction of the figure
+
+    āˆ  _E C Z_ + āˆ  _Z C P_ = 90Ā°
+    āˆ  _H C P_ + āˆ  _Z C P_ = 90Ā°
+
+from which we find by subtraction and transposition
+
+    āˆ  _E C Z_ = āˆ  _H C P_
+
+and this gives the further
+
+_Theorem._--The latitude of any place is equal to the elevation of the
+pole above its horizon plane.
+
+An observer who travels north or south over the earth changes his
+latitude, and therefore changes the angle between his horizon plane and
+the axis of the earth. What effect will this have upon the position of
+stars in his sky? If you were to go to the earth's equator, in what part
+of the sky would you look for Polaris? Can Polaris be seen from
+Australia? From South America? If you were to go from Minnesota to
+Texas, in what respect would the appearance of stars in the northern sky
+be changed? How would the appearance of stars in the southern sky be
+changed?
+
+[Illustration: FIG. 12.--Diurnal path of Polaris.]
+
+EXERCISE 8.--Determine your latitude by taking the altitude of Polaris
+when it is at some one of the four points of its diurnal path, shown in
+Fig. 12. When it is at _1_ it is said to be at upper culmination, and
+the star Ī¶ UrsƦ Majoris in the handle of the Big Dipper will be
+directly below it. When at _2_ it is at western elongation, and the star
+Castor is near the meridian. When it is at _3_ it is at lower
+culmination, and the star Spica is on the meridian. When it is at _4_ it
+is at eastern elongation, and Altair is near the meridian. All of these
+stars are conspicuous ones, which the student should find upon the map
+and learn to recognize in the sky. The altitude observed at either _2_
+or _4_ may be considered equal to the latitude of the place, but the
+altitude observed when Polaris is at the positions marked _1_ and _3_
+must be corrected for the star's distance from the pole, which may be
+assumed equal to 1.3Ā°.
+
+The plumb-line apparatus described at page 12 is shown in Fig. 6
+slightly modified, so as to adapt it to measuring the altitudes of
+stars. Note that the board with the screw eye at one end has been
+transferred from the box to the vertical standard, and has a screw eye
+at each end. When the apparatus has been properly leveled, so that the
+plumb line hangs at the middle of the hole in the box cover, the board
+is to be pointed at the star by sighting through the centers of the two
+screw eyes, and a pencil line is to be ruled along its edge upon the
+face of the vertical standard. After this has been done turn the
+apparatus halfway around so that what was the north side now points
+south, level it again and revolve the board about the screw which holds
+it to the vertical standard, until the screw eyes again point to the
+star. Rule another line along the same edge of the board as before and
+with a protractor measure the angle between these lines. Use a bicycle
+lamp if you need artificial light for your work. The student who has
+studied plane geometry should be able to prove that one half of the
+angle between these lines is equal to the altitude of the star.
+
+After you have determined your latitude from Polaris, compare the result
+with your position as shown upon the best map available. With a little
+practice and considerable care the latitude may be thus determined
+within one tenth of a degree, which is equivalent to about 7 miles. If
+you go 10 miles north or south from your first station you should find
+the pole higher up or lower down in the sky by an amount which can be
+measured with your apparatus.
+
+19. THE MERIDIAN LINE.--To establish a true north and south line upon
+the ground, use the apparatus as described at page 13, and when Polaris
+is at upper or lower culmination drive into the ground two stakes in
+line with the star and the plumb line. Such a meridian line is of great
+convenience in observing the stars and should be laid out and
+permanently marked in some convenient open space from which, if
+possible, all parts of the sky are visible. June and November are
+convenient months for this exercise, since Polaris then comes to
+culmination early in the evening.
+
+20. TIME.--What is _the time_ at which school begins in the morning?
+What do you mean by "_the time_"?
+
+The sidereal time at any moment is the right ascension of the hour
+circle which at that moment coincides with the meridian. When the hour
+circle passing through Sirius coincides with the meridian, the sidereal
+time is 6h. 40m., since that is the right ascension of Sirius, and in
+astronomical language Sirius is "_on the meridian_" at 6h. 40m. sidereal
+time. As may be seen from the map, this 6h. 40m. is the right ascension
+of Sirius, and if a clock be set to indicate 6h. 40m. when Sirius
+crosses the meridian, it will show sidereal time. If the clock is
+properly regulated, every other star in the heavens will come to the
+meridian at the moment when the time shown by the clock is equal to the
+right ascension of the star. A clock properly regulated for this purpose
+will gain about four minutes per day in comparison with ordinary clocks,
+and when so regulated it is called a sidereal clock. The student should
+be provided with such a clock for his future work, but one such clock
+will serve for several persons, and a nutmeg clock or a watch of the
+cheapest kind is quite sufficient.
+
+[Illustration: THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.]
+
+EXERCISE 9.--Set such a clock to sidereal time by means of the transit
+of a star over your meridian. For this experiment it is presupposed that
+a meridian line has been marked out on the ground as in Ā§ 19, and the
+simplest mode of performing the experiment required is for the observer,
+having chosen a suitable star in the southern part of the sky, to place
+his eye accurately over the northern end of the meridian line and to
+estimate as nearly as possible the beginning and end of the period
+during which the star appears to stand exactly above the southern end of
+the line. The middle of this period may be taken as the time at which
+the star crossed the meridian and at this moment the sidereal time is
+equal to the right ascension of the star. The difference between this
+right ascension and the observed middle instant is the error of the
+clock or the amount by which its hands must be set back or forward in
+order to indicate true sidereal time.
+
+A more accurate mode of performing the experiment consists in using the
+plumb-line apparatus carefully adjusted, as in Fig. 7, so that the line
+joining the wire to the center of the screw eye shall be parallel to the
+meridian line. Observe the time by the clock at which the star
+disappears behind the wire as seen through the center of the screw eye.
+If the star is too high up in the sky for convenient observation, place
+a mirror, face up, just north of the screw eye and observe star, wire
+and screw eye by reflection in it.
+
+The numerical right ascension of the observed star is needed for this
+experiment, and it may be measured from the star map, but it will
+usually be best to observe one of the stars of the table at the end of
+the book, and to obtain its right ascension as follows: The table gives
+the right ascension and declination of each star as they were at the
+beginning of the year 1900, but on account of the precession (see
+Chapter V), these numbers all change slowly with the lapse of time, and
+on the average the right ascension of each star of the table must be
+increased by one twentieth of a minute for each year after 1900--i. e.,
+in 1910 the right ascension of the first star of the table will be
+0h. 38.6m. + (10/20)m. = 0h. 39.1m. The declinations also change
+slightly, but as they are only intended to help in finding the star on
+the star maps, their change may be ignored.
+
+Having set the clock approximately to sidereal time, observe one or two
+more stars in the same way as above. The difference between the observed
+time and the right ascension, if any is found, is the "correction" of
+the clock. This correction ought not to exceed a minute if due care has
+been taken in the several operations prescribed. The relation of the
+clock to the right ascension of the stars is expressed in the following
+equation, with which the student should become thoroughly familiar:
+
+    A = T Ā± U
+
+_T_ stands for the time by the clock at which the star crossed the
+meridian. _A_ is the right ascension of the star, and _U_ is the
+correction of the clock. Use the + sign in the equation whenever the
+clock is too slow, and the - sign when it is too fast. _U_ may be found
+from this equation when _A_ and _T_ are given, or _A_ may be found when
+_T_ and _U_ are given. It is in this way that astronomers measure the
+right ascensions of the stars and planets.
+
+Determine _U_ from each star you have observed, and note how the several
+results agree one with another.
+
+21. DEFINITIONS.--To define a thing or an idea is to give a description
+sufficient to identify it and distinguish it from every other possible
+thing or idea. If a definition does not come up to this standard it is
+insufficient. Anything beyond this requirement is certainly useless and
+probably mischievous.
+
+Let the student define the following geographical terms, and let him
+also criticise the definitions offered by his fellow-students: Equator,
+poles, meridian, latitude, longitude, north, south, east, west.
+
+Compare the following astronomical definitions with your geographical
+definitions, and criticise them in the same way. If you are not able to
+improve upon them, commit them to memory:
+
+_The Poles_ of the heavens are those points in the sky toward which the
+earth's axis points. How many are there? The one near Polaris is called
+the north pole.
+
+_The Celestial Equator_ is a great circle of the sky distant 90Ā° from
+the poles.
+
+_The Zenith_ is that point of the sky, overhead, toward which a plumb
+line points. Why is the word overhead placed in the definition? Is there
+more than one zenith?
+
+_The Horizon_ is a great circle of the sky 90Ā° distant from the zenith.
+
+_An Hour Circle_ is any great circle of the sky which passes through the
+poles. Every star has its own hour circle.
+
+_The Meridian_ is that hour circle which passes through the zenith.
+
+_A Vertical Circle_ is any great circle that passes through the zenith.
+Is the meridian a vertical circle?
+
+_The Declination_ of a star is its angular distance north or south of
+the celestial equator.
+
+_The Right Ascension_ of a star is the angle included between its hour
+circle and the hour circle of a certain point on the equator which is
+called the _Vernal Equinox_. From spherical geometry we learn that this
+angle is to be measured either at the pole where the two hour circles
+intersect, as is done in the star map opposite page 124, or along the
+equator, as is done in the map opposite page 190. Right ascension is
+always measured from the vernal equinox in the direction opposite to
+that in which the stars appear to travel in their diurnal motion--i. e.,
+from west toward east.
+
+_The Altitude_ of a star is its angular distance above the horizon.
+
+_The Azimuth_ of a star is the angle between the meridian and the
+vertical circle passing through the star. A star due south has an
+azimuth of 0Ā°. Due west, 90Ā°. Due north, 180Ā°. Due east, 270Ā°.
+
+What is the azimuth of Polaris in degrees?
+
+What is the azimuth of the sun at sunrise? At sunset? At noon? Are these
+azimuths the same on different days?
+
+_The Hour Angle_ of a star is the angle between its hour circle and the
+meridian. It is measured from the meridian in the direction in which the
+stars appear to travel in their diurnal motion--i. e., from east toward
+west.
+
+What is the hour angle of the sun at noon? What is the hour angle of
+Polaris when it is at the lowest point in its daily motion?
+
+22. EXERCISES.--The student must not be satisfied with merely learning
+these definitions. He must learn to see these points and lines in his
+mind as if they were visibly painted upon the sky. To this end it will
+help him to note that the poles, the zenith, the meridian, the horizon,
+and the equator seem to stand still in the sky, always in the same place
+with respect to the observer, while the hour circles and the vernal
+equinox move with the stars and keep the same place among them. Does the
+apparent motion of a star change its declination or right ascension?
+What is the hour angle of the sun when it has the greatest altitude?
+Will your answer to the preceding question be true for a star? What is
+the altitude of the sun after sunset? In what direction is the north
+pole from the zenith? From the vernal equinox? Where are the points in
+which the meridian and equator respectively intersect the horizon?
+
+
+
+
+CHAPTER III
+
+FIXED AND WANDERING STARS
+
+
+23. STAR MAPS.--Select from the map some conspicuous constellation that
+will be conveniently placed for observation in the evening, and make on
+a large scale a copy of all the stars of the constellation that are
+shown upon the map. At night compare this copy with the sky, and mark in
+upon your paper all the stars of the constellation which are not already
+there. Both the original drawing and the additions made to it by night
+should be carefully done, and for the latter purpose what is called the
+method of allineations may be used with advantage--i. e., the new star
+is in line with two already on the drawing and is midway between them,
+or it makes an equilateral triangle with two others, or a square with
+three others, etc.
+
+A series of maps of the more prominent constellations, such as Ursa
+Major, Cassiopea, Pegasus, Taurus, Orion, Gemini, Canis Major, Leo,
+Corvus, Bootes, Virgo, Hercules, Lyra, Aquila, Scorpius, should be
+constructed in this manner upon a uniform scale and preserved as a part
+of the student's work. Let the magnitude of the stars be represented on
+the maps as accurately as may be, and note the peculiarity of color
+which some stars present. For the most part their color is a very pale
+yellow, but occasionally one may be found of a decidedly ruddy
+hue--e. g., Aldebaran or Antares. Such a star map, not quite complete,
+is shown in Fig. 13.
+
+So, too, a sharp eye may detect that some stars do not remain always of
+the same magnitude, but change their brightness from night to night,
+and this not on account of cloud or mist in the atmosphere, but from
+something in the star itself. Algol is one of the most conspicuous of
+these _variable stars_, as they are called.
+
+[Illustration: FIG. 13.--Star map of the region about Orion.]
+
+24. THE MOON'S MOTION AMONG THE STARS.--Whenever the moon is visible
+note its position among the stars by allineations, and plot it on the
+key map opposite page 190. Keep a record of the day and hour
+corresponding to each such observation. You will find, if the work is
+correctly done, that the positions of the moon all fall near the curved
+line shown on the map. This line is called the ecliptic.
+
+After several such observations have been made and plotted, find by
+measurement from the map how many degrees per day the moon moves. How
+long would it require to make the circuit of the heavens and come back
+to the starting point?
+
+On each night when you observe the moon, make on a separate piece of
+paper a drawing of it about 10 centimeters in diameter and show in the
+drawing every feature of the moon's face which you can see--e. g., the
+shape of the illuminated surface (phase); the direction among the stars
+of the line joining the horns; any spots which you can see upon the
+moon's face, etc. An opera glass will prove of great assistance in this
+work.
+
+Use your drawings and the positions of the moon plotted upon the map to
+answer the following questions: Does the direction of the line joining
+the horns have any special relation to the ecliptic? Does the amount of
+illuminated surface of the moon have any relation to the moon's angular
+distance from the sun? Does it have any relation to the time at which
+the moon sets? Do the spots on the moon when visible remain always in
+the same place? Do they come and go? Do they change their position with
+relation to each other? Can you determine from these spots that the moon
+rotates about an axis, as the earth does? In what direction does its
+axis point? How long does it take to make one revolution about the axis?
+Is there any day and night upon the moon?
+
+Each of these questions can be correctly answered from the student's own
+observations without recourse to any book.
+
+25. THE SUN AND ITS MOTION.--Examine the face of the sun through a
+smoked glass to see if there is anything there that you can sketch.
+
+By day as well as by night the sky is studded with stars, only they can
+not be seen by day on account of the overwhelming glare of sunlight, but
+the position of the sun among the stars may be found quite as
+accurately as was that of the moon, by observing from day to day its
+right ascension and declination, and this should be practiced at noon on
+clear days by different members of the class.
+
+EXERCISE 10.--The right ascension of the sun may be found by observing
+with the sidereal clock the time of its transit over the meridian. Use
+the equation in Ā§ 20, and substitute in place of _U_ the value of the
+clock correction found from observations of stars on a preceding or
+following night. If the clock gains or loses _with respect to sidereal
+time_, take this into account in the value of _U_.
+
+EXERCISE 11.--To determine the sun's declination, measure its altitude
+at the time it crosses the meridian. Use either the method of Exercise
+4, or that used with Polaris in Exercise 8. The student should be able
+to show from Fig. 11 that the declination is equal to the sum of the
+altitude and the latitude of the place diminished by 90Ā°, or in an
+equation
+
+    Declination = Altitude + Latitude - 90Ā°.
+
+If the declination as found from this equation is a negative number it
+indicates that the sun is on the south side of the equator.
+
+The right ascension and declination of the sun as observed on each day
+should be plotted on the map and the date, written opposite it. If the
+work has been correctly done, the plotted points should fall upon the
+curved line (ecliptic) which runs lengthwise of the map. This line, in
+fact, represents the sun's path among the stars.
+
+Note that the hours of right ascension increase from 0 up to 24, while
+the numbers on the clock dial go only from 0 to 12, and then repeat 0 to
+12 again during the same day. When the sidereal time is 13 hours, 14
+hours, etc., the clock will indicate 1 hour, 2 hours, etc., and 12 hours
+must then be added to the time shown on the dial.
+
+If observations of the sun's right ascension and declination are made
+in the latter part of either March or September the student will find
+that the sun crosses the equator at these times, and he should determine
+from his observations, as accurately as possible, the date and hour of
+this crossing and the point on the equator at which the sun crosses it.
+These points are called the equinoxes, Vernal Equinox and Autumnal
+Equinox for the spring and autumn crossings respectively, and the
+student will recall that the vernal equinox is the point from which
+right ascensions are measured. Its position among the stars is found by
+astronomers from observations like those above described, only made with
+much more elaborate apparatus.
+
+Similar observations made in June and December show that the sun's
+midday altitude is about 47Ā° greater in summer than in winter. They show
+also that the sun is as far north of the equator in June as he is south
+of it in December, from which it is easily inferred that his path, the
+ecliptic, is inclined to the equator at an angle of 23Ā°.5, one half of
+47Ā°. This angle is called the obliquity of the ecliptic. The student may
+recall that in the geographies the torrid zone is said to extend 23Ā°.5
+on either side of the earth's equator. Is there any connection between
+these limits and the obliquity of the ecliptic? Would it be correct to
+define the torrid zone as that part of the earth's surface within which
+the sun may at some season of the year pass through the zenith?
+
+EXERCISE 12.--After a half dozen observations of the sun have been
+plotted upon the map, find by measurement the rate, in degrees per day,
+at which the sun moves along the ecliptic. How many days will be
+required for it to move completely around the ecliptic from vernal
+equinox back to vernal equinox again? Accurate observations with the
+elaborate apparatus used by professional astronomers show that this
+period, which is called a _tropical year_, is 365 days 5 hours 48
+minutes 46 seconds. Is this the same as the ordinary year of our
+calendars?
+
+26. THE PLANETS.--Any one who has watched the sky and who has made the
+drawings prescribed in this chapter can hardly fail to have found in the
+course of his observations some bright stars not set down on the printed
+star maps, and to have found also that these stars do not remain fixed
+in position among their fellows, but wander about from one constellation
+to another. Observe the motion of one of these planets from night to
+night and plot its positions on the star map, precisely as was done for
+the moon. What kind of path does it follow?
+
+Both the ancient Greeks and the modern Germans have called these bodies
+wandering stars, and in English we name them planets, which is simply
+the Greek word for wanderer, bent to our use. Besides the sun and moon
+there are in the heavens five planets easily visible to the naked eye
+and, as we shall see later, a great number of smaller ones visible only
+in the telescope. More than 2,000 years ago astronomers began observing
+the motion of sun, moon, and planets among the stars, and endeavored to
+account for these motions by the theory that each wandering star moved
+in an orbit about the earth. Classical and mediƦval literature are
+permeated with this idea, which was displaced only after a long struggle
+begun by Copernicus (1543 A. D.), who taught that the moon alone of
+these bodies revolves about the earth, while the earth and the other
+planets revolve around the sun. The ecliptic is the intersection of the
+plane of the earth's orbit with the sky, and the sun appears to move
+along the ecliptic because, as the earth moves around its orbit, the sun
+is always seen projected against the opposite side of it. The moon and
+planets all appear to move near the ecliptic because the planes of their
+orbits nearly coincide with the plane of the earth's orbit, and a narrow
+strip on either side of the ecliptic, following its course completely
+around the sky, is called the _zodiac_, a word which may be regarded as
+the name of a narrow street (16Ā° wide) within which all the wanderings
+of the visible planets are confined and outside of which they never
+venture. Indeed, Mars is the only planet which ever approaches the edge
+of the street, the others traveling near the middle of the road.
+
+[Illustration: FIG. 14.--The apparent motion of a planet.]
+
+27. A TYPICAL CASE OF PLANETARY MOTION.--The Copernican theory,
+enormously extended and developed through the Newtonian law of
+gravitation (see Chapter IV), has completely supplanted the older
+Ptolemaic doctrine, and an illustration of the simple manner in which it
+accounts for the apparently complicated motions of a planet among the
+stars is found in Figs. 14 and 15, the first of which represents the
+apparent motion of the planet Mars through the constellations Aries and
+Pisces during the latter part of the year 1894, while the second shows
+the true motions of Mars and the earth in their orbits about the sun
+during the same period. The straight line in Fig. 14, with cross ruling
+upon it, is a part of the ecliptic, and the numbers placed opposite it
+represent the distance, in degrees, from the vernal equinox. In Fig. 15
+the straight line represents the direction from the sun toward the
+vernal equinox, and the angle which this line makes with the line
+joining earth and sun is called the earth's longitude. The imaginary
+line joining the earth and sun is called the earth's radius vector, and
+the pupil should note that the longitude and length of the radius vector
+taken together show the direction and distance of the earth from the
+sun--i. e., they fix the relative positions of the two bodies. The same
+is nearly true for Mars and would be wholly true if the orbit of Mars
+lay in the same plane with that of the earth. How does Fig. 14 show that
+the orbit of Mars does not lie exactly in the same plane with the orbit
+of the earth?
+
+EXERCISE 13.--Find from Fig. 15 what ought to have been the apparent
+course of Mars among the stars during the period shown in the two
+figures, and compare what you find with Fig. 14. The apparent position
+of Mars among the stars is merely its direction from the earth, and this
+direction is represented in Fig. 14 by the distance of the planet from
+the ecliptic and by its longitude.
+
+[Illustration: FIG. 15.--The real motion of a planet.]
+
+The longitude of Mars for each date can be found from Fig. 15 by
+measuring the angle between the straight line _S V_ and the line drawn
+from the earth to Mars. Thus for October 12th we may find with the
+protractor that the angle between the line _S V_ and the line joining
+the earth to Mars is a little more than 30Ā°, and in Fig. 14 the position
+of Mars for this date is shown nearly opposite the cross line
+corresponding to 30Ā° on the ecliptic. Just how far below the ecliptic
+this position of Mars should fall can not be told from Fig. 15, which
+from necessity is constructed as if the orbits of Mars and the earth lay
+in the same plane, and Mars in this case would always appear to stand
+exactly on the ecliptic and to oscillate back and forth as shown in Fig.
+14, but without the up-and-down motion there shown. In this way plot in
+Fig. 14 the longitudes of Mars as seen from the earth for other dates
+and observe how the forward motion of the two planets in their orbits
+accounts for the apparently capricious motion of Mars to and fro among
+the stars.
+
+[Illustration: FIG. 16.--The orbits of Jupiter and Saturn.]
+
+28. THE ORBITS OF THE PLANETS.--Each planet, great or small, moves in
+its own appropriate orbit about the sun, and the exact determination of
+these orbits, their sizes, shapes, positions, etc., has been one of the
+great problems of astronomy for more than 2,000 years, in which
+successive generations of astronomers have striven to push to a still
+higher degree of accuracy the knowledge attained by their predecessors.
+Without attempting to enter into the details of this problem we may say,
+generally, that every planet moves in a plane passing through the sun,
+and for the six planets visible to the naked eye these planes nearly
+coincide, so that the six orbits may all be shown without much error as
+lying in the flat surface of one map. It is, however, more convenient to
+use two maps, such as Figs. 16 and 17, one of which shows the group of
+planets, Mercury, Venus, the earth, and Mars, which are near the sun,
+and on this account are sometimes called the inner planets, while the
+other shows the more distant planets, Jupiter and Saturn, together with
+the earth, whose orbit is thus made to serve as a connecting link
+between the two diagrams. These diagrams are accurately drawn to scale,
+and are intended to be used by the student for accurate measurement in
+connection with the exercises and problems which follow.
+
+In addition to the six planets shown in the figures the solar system
+contains two large planets and several hundred small ones, for the most
+part invisible to the naked eye, which are omitted in order to avoid
+confusing the diagrams.
+
+29. JUPITER AND SATURN.--In Fig. 16 the sun at the center is encircled
+by the orbits of the three planets, and inclosing all of these is a
+circular border showing the directions from the sun of the
+constellations which lie along the zodiac. The student must note
+carefully that it is only the directions of these constellations that
+are correctly shown, and that in order to show them at all they have
+been placed very much too close to the sun. The cross lines extending
+from the orbit of the earth toward the sun with Roman numerals opposite
+them show the positions of the earth in its orbit on the first day of
+January (_I_), first day of February (_II_), etc., and the similar lines
+attached to the orbits of Jupiter and Saturn with Arabic numerals show
+the positions of those planets on the first day of January of each year
+indicated, so that the figure serves to show not only the orbits of the
+planets, but their actual positions in their orbits for something more
+than the first decade of the twentieth century.
+
+The line drawn from the sun toward the right of the figure shows the
+direction to the vernal equinox. It forms one side of the angle which
+measures a planet's longitude.
+
+[Illustration: FIG. 17.--The orbits of the inner planets.]
+
+EXERCISE 14.--Measure with your protractor the longitude of the earth on
+January 1st. Is this longitude the same in all years? Measure the
+longitude of Jupiter on January 1, 1900; on July 1, 1900; on September
+25, 1906.
+
+Draw neatly on the map a pencil line connecting the position of the
+earth for January 1, 1900, with the position of Jupiter for the same
+date, and produce the line beyond Jupiter until it meets the circle of
+the constellations. This line represents the direction of Jupiter from
+the earth, and points toward the constellation in which the planet
+appears at that date. But this representation of the place of Jupiter in
+the sky is not a very accurate one, since on the scale of the diagram
+the stars are in fact more than 100,000 times as far off as they are
+shown in the figure, and the pencil mark does not meet the line of
+constellations at the same intersection it would have if this line were
+pushed back to its true position. To remedy this defect we must draw
+another line from the sun parallel to the one first drawn, and its
+intersection with the constellations will give very approximately the
+true position of Jupiter in the sky.
+
+EXERCISE 15.--Find the present positions of Jupiter and Saturn, and look
+them up in the sky by means of your star maps. The planets will appear
+in the indicated constellations as very bright stars not shown on the
+map.
+
+Which of the planets, Jupiter and Saturn, changes its direction from the
+sun more rapidly? Which travels the greater number of miles per day?
+When will Jupiter and Saturn be in the same constellation? Does the
+earth move faster or slower than Jupiter?
+
+The distance of Jupiter or Saturn from the earth at any time may be
+readily obtained from the figure. Thus, by direct measurement with the
+millimeter scale we find for January 1, 1900, the distance of Jupiter
+from the earth is 6.1 times the distance of the sun from the earth, and
+this may be turned into miles by multiplying it by 93,000,000, which is
+approximately the distance of the sun from the earth. For most purposes
+it is quite as well to dispense with this multiplication and call the
+distance 6.1 astronomical units, remembering that the astronomical unit
+is the distance of the sun from the earth.
+
+EXERCISE 16.--What is Jupiter's distance from the earth at its nearest
+approach? What is the greatest distance it ever attains? Is Jupiter's
+least distance from the earth greater or less than its least distance
+from Saturn?
+
+On what day in the year 1906 will the earth be on line between Jupiter
+and the sun? On this day Jupiter is said to be in _opposition_--i. e.,
+the planet and the sun are on opposite sides of the earth, and Jupiter
+then comes to the meridian of any and every place at midnight. When the
+sun is between the earth and Jupiter (at what date in 1906?) the planet
+is said to be in _conjunction_ with the sun, and of course passes the
+meridian with the sun at noon. Can you determine from the figure the
+time at which Jupiter comes to the meridian at other dates than
+opposition and conjunction? Can you determine when it is visible in the
+evening hours? Tell from the figure what constellation is on the
+meridian at midnight on January 1st. Will it be the same constellation
+in every year?
+
+
+30. MERCURY, VENUS, AND MARS.--Fig. 17, which represents the orbits of
+the inner planets, differs from Fig. 16 only in the method of fixing the
+positions of the planets in their orbits at any given date. The motion
+of these planets is so rapid, on account of their proximity to the sun,
+that it would not do to mark their positions as was done for Jupiter and
+Saturn, and with the exception of the earth they do not always return to
+the same place on the same day in each year. It is therefore necessary
+to adopt a slightly different method, as follows: The straight line
+extending from the sun toward the vernal equinox, _V_, is called the
+prime radius, and we know from past observations that the earth in its
+motion around the sun crosses this line on September 23d in each year,
+and to fix the earth's position for September 23d in the diagram we have
+only to take the point at which the prime radius intersects the earth's
+orbit. A month later, on October 23d, the earth will no longer be at
+this point, but will have moved on along its orbit to the point marked
+30 (thirty days after September 23d). Sixty days after September 23d it
+will be at the point marked 60, etc., and for any date we have only to
+find the number of days intervening between it and the preceding
+September 23d, and this number will show at once the position of the
+earth in its orbit. Thus for the date July 4, 1900, we find
+
+    1900, July 4 - 1899, September 23 = 284 days,
+
+and the little circle marked upon the earth's orbit between the numbers
+270 and 300 shows the position of the earth on that date.
+
+In what constellation was the sun on July 4, 1900? What zodiacal
+constellation came to the meridian at midnight on that date? What other
+constellations came to the meridian at the same time?
+
+The positions of the other planets in their orbits are found in the same
+manner, save that they do not cross the prime radius on the same date in
+each year, and the times at which they do cross it must be taken from
+the following table:
+
+                      TABLE OF EPOCHS
+
+  -----------------------------------------------------------
+    A. D. | Mercury.   |  Venus.   |   Earth.   |  Mars.
+  --------+------------+-----------+------------+------------
+  Period  | 88.0 days. |224.7 days.|365.25 days.| 687.1 days.
+   1900   | Feb. 18th. | Jan. 11th.| Sept. 23d. | April 28th.
+   1901   | Feb. 5th.  | April 5th.| Sept. 23d. |   ...
+   1902   | Jan. 23d.  | June 29th.| Sept. 23d. | March 16th.
+   1903   | April 8th. | Feb. 8th. | Sept. 23d. |   ...
+   1904   | March 25th.| May 3d.   | Sept. 23d. | Feb. 1st.
+   1905   | March 12th.| July 26th.| Sept. 23d. | Dec. 19th.
+   1906   | Feb. 27th. | March 8th.| Sept. 23d. |   ...
+   1907   | Feb. 14th. | May 31st. | Sept. 23d. | Nov. 6th.
+   1908   | Feb. 1st.  | Jan. 11th.| Sept. 23d. |   ...
+   1909   | Jan. 18th. | April 4th.| Sept. 23d. | Sept. 23d.
+   1910   | Jan. 5th.  | June 28th.| Sept. 23d. |   ...
+  -----------------------------------------------------------
+
+The first line of figures in this table shows the number of days that
+each of these planets requires to make a complete revolution about the
+sun, and it appears from these numbers that Mercury makes about four
+revolutions in its orbit per year, and therefore crosses the prime
+radius four times in each year, while the other planets are decidedly
+slower in their movements. The following lines of the table show for
+each year the date at which each planet first crossed the prime radius
+in that year; the dates of subsequent crossings in any year can be found
+by adding once, twice, or three times the period to the given date, and
+the table may be extended to later years, if need be, by continuously
+adding multiples of the period. In the case of Mars it appears that
+there is only about one year out of two in which this planet crosses the
+prime radius.
+
+After the date at which the planet crosses the prime radius has been
+determined its position for any required date is found exactly as in the
+case of the earth, and the constellation in which the planet will appear
+from the earth is found as explained above in connection with Jupiter
+and Saturn.
+
+The broken lines in the figure represent the construction for finding
+the places in the sky occupied by Mercury, Venus, and Mars on July 4,
+1900. Let the student make a similar construction and find the positions
+of these planets at the present time. Look them up in the sky and see if
+they are where your work puts them.
+
+31. EXERCISES.--The "evening star" is a term loosely applied to any
+planet which is visible in the western sky soon after sunset. It is easy
+to see that such a planet must be farther toward the east in the sky
+than is the sun, and in either Fig. 16 or Fig. 17 any planet which
+viewed from the position of the earth lies to the left of the sun and
+not more than 50Ā° away from it will be an evening star. If to the right
+of the sun it is a morning star, and may be seen in the eastern sky
+shortly before sunrise.
+
+What planet is the evening star _now_? Is there more than one evening
+star at a time? What is the morning star now?
+
+Do Mercury, Venus, or Mars ever appear in opposition? What is the
+maximum angular distance from the sun at which Venus can ever be seen?
+Why is Mercury a more difficult planet to see than Venus? In what month
+of the year does Mars come nearest to the earth? Will it always be
+brighter in this month than in any other? Which of all the planets comes
+nearest to the earth?
+
+The earth always comes to the same longitude on the same day of each
+year. Why is not this true of the other planets?
+
+The student should remember that in one respect Figs. 16 and 17 are not
+altogether correct representations, since they show the orbits as all
+lying in the same plane. If this were strictly true, every planet would
+move, like the sun, always along the ecliptic; but in fact all of the
+orbits are tilted a little out of the plane of the ecliptic and every
+planet in its motion deviates a little from the ecliptic, first to one
+side then to the other; but not even Mars, which is the most erratic in
+this respect, ever gets more than eight degrees away from the ecliptic,
+and for the most part all of them are much closer to the ecliptic than
+this limit.
+
+
+
+
+CHAPTER IV
+
+CELESTIAL MECHANICS
+
+
+32. THE BEGINNINGS OF CELESTIAL MECHANICS.--From the earliest dawn of
+civilization, long before the beginnings of written history, the motions
+of sun and moon and planets among the stars from constellation to
+constellation had commanded the attention of thinking men, particularly
+of the class of priests. The religions of which they were the guardians
+and teachers stood in closest relations with the movements of the stars,
+and their own power and influence were increased by a knowledge of them.
+
+[Illustration: ISAAC NEWTON (1643-1727).]
+
+Out of these professional needs, as well as from a spirit of scientific
+research, there grew up and flourished for many centuries a study of the
+motions of the planets, simple and crude at first, because the
+observations that could then be made were at best but rough ones, but
+growing more accurate and more complex as the development of the
+mechanic arts put better and more precise instruments into the hands of
+astronomers and enabled them to observe with increasing accuracy the
+movements of these bodies. It was early seen that while for the most
+part the planets, including the sun and moon, traveled through the
+constellations from west to east, some of them sometimes reversed their
+motion and for a time traveled in the opposite way. This clearly can not
+be explained by the simple theory which had early been adopted that a
+planet moves always in the same direction around a circular orbit having
+the earth at its center, and so it was said to move around in a small
+circular orbit, called an epicycle, whose center was situated upon
+and moved along a circular orbit, called the deferent, within which the
+earth was placed, as is shown in Fig. 18, where the small circle is the
+epicycle, the large circle is the deferent, _P_ is the planet, and _E_
+the earth. When this proved inadequate to account for the really
+complicated movements of the planets, another epicycle was put on top of
+the first one, and then another and another, until the supposed system
+became so complicated that Copernicus, a Polish astronomer, repudiated
+its fundamental theorem and taught that the motions of the planets take
+place in circles around the sun instead of about the earth, and that the
+earth itself is only one of the planets moving around the sun in its own
+appropriate orbit and itself largely responsible for the seemingly
+erratic movements of the other planets, since from day to day we see
+them and observe their positions from different points of view.
+
+[Illustration: FIG. 18.--Epicycle and deferent.]
+
+33. KEPLER'S LAWS.--Two generations later came Kepler with his three
+famous laws of planetary motion:
+
+I. Every planet moves in an ellipse which has the sun at one of its
+foci.
+
+II. The radius vector of each planet moves over equal areas in equal
+times.
+
+III. The squares of the periodic times of the planets are proportional
+to the cubes of their mean distances from the sun.
+
+These laws are the crowning glory, not only of Kepler's career, but of
+all astronomical discovery from the beginning up to his time, and they
+well deserve careful study and explanation, although more modern
+progress has shown that they are only approximately true.
+
+EXERCISE 17.--Drive two pins into a smooth board an inch apart and
+fasten to them the ends of a string a foot long. Take up the slack of
+the string with the point of a lead pencil and, keeping the string drawn
+taut, move the pencil point over the board into every possible position.
+The curve thus traced will be an ellipse having the pins at the two
+points which are called its foci.
+
+In the case of the planetary orbits one focus of the ellipse is vacant,
+and, in accordance with the first law, the center of the sun is at the
+other focus. In Fig. 17 the dot, inside the orbit of Mercury, which is
+marked _a_, shows the position of the vacant focus of the orbit of Mars,
+and the dot _b_ is the vacant focus of Mercury's orbit. The orbits of
+Venus and the earth are so nearly circular that their vacant foci lie
+very close to the sun and are not marked in the figure. The line drawn
+from the sun to any point of the orbit (the string from pin to pencil
+point) is a _radius vector_. The point midway between the pins is the
+_center_ of the ellipse, and the distance of either pin from the center
+measures the _eccentricity_ of the ellipse.
+
+Draw several ellipses with the same length of string, but with the pins
+at different distances apart, and note that the greater the eccentricity
+the flatter is the ellipse, but that all of them have the same length.
+
+If both pins were driven into the same hole, what kind of an ellipse
+would you get?
+
+The Second Law was worked out by Kepler as his answer to a problem
+suggested by the first law. In Fig. 17 it is apparent from a mere
+inspection of the orbit of Mercury that this planet travels much faster
+on one side of its orbit than on the other, the distance covered in ten
+days between the numbers 10 and 20 being more than fifty per cent
+greater than that between 50 and 60. The same difference is found,
+though usually in less degree, for every other planet, and Kepler's
+problem was to discover a means by which to mark upon the orbit the
+figures showing the positions of the planet at the end of equal
+intervals of time. His solution of this problem, contained in the second
+law, asserts that if we draw radii vectors from the sun to each of the
+marked points taken at equal time intervals around the orbit, then the
+area of the sector formed by two adjacent radii vectores and the arc
+included between them is equal to the area of each and every other such
+sector, the short radii vectores being spread apart so as to include a
+long arc between them while the long radii vectores have a short arc. In
+Kepler's form of stating the law the radius vector is supposed to travel
+with the planet and in each day to sweep over the same fractional part
+of the total area of the orbit. The spacing of the numbers in Fig. 17
+was done by means of this law.
+
+For the proper understanding of Kepler's Third Law we must note that the
+"mean distance" which appears in it is one half of the long diameter of
+the orbit and that the "periodic time" means the number of days or years
+required by the planet to make a complete circuit in its orbit.
+Representing the first of these by _a_ and the second by _T_, we have,
+as the mathematical equivalent of the law,
+
+    a^{3} Ć· T^{2} = C
+
+where the quotient, _C_, is a number which, as Kepler found, is the same
+for every planet of the solar system. If we take the mean distance of
+the earth from the sun as the unit of distance, and the year as the unit
+of time, we shall find by applying the equation to the earth's motion,
+_C_ = 1. Applying this value to any other planet we shall find in the
+same units, _a_ = _T_^{2/3}, by means of which we may determine the
+distance of any planet from the sun when its periodic time, _T_, has
+been learned from observation.
+
+EXERCISE 18.--Uranus requires 84 years to make a revolution in its
+orbit. What is its mean distance from the sun? What are the mean
+distances of Mercury, Venus, and Mars? (See Chapter III for their
+periodic times.) Would it be possible for two planets at different
+distances from the sun to move around their orbits in the same time?
+
+A circle is an ellipse in which the two foci have been brought together.
+Would Kepler's laws hold true for such an orbit?
+
+34. NEWTON'S LAWS OF MOTION.--Kepler studied and described the motion of
+the planets. Newton, three generations later (1727 A. D.), studied and
+described the mechanism which controls that motion. To Kepler and his
+age the heavens were supernatural, while to Newton and his successors
+they are a part of Nature, governed by the same laws which obtain upon
+the earth, and we turn to the ordinary things of everyday life as the
+foundation of celestial mechanics.
+
+Every one who has ridden a bicycle knows that he can coast farther upon
+a level road if it is smooth than if it is rough; but however smooth and
+hard the road may be and however fast the wheel may have been started,
+it is sooner or later stopped by the resistance which the road and the
+air offer to its motion, and when once stopped or checked it can be
+started again only by applying fresh power. We have here a familiar
+illustration of what is called
+
+THE FIRST LAW OF MOTION.--"Every body continues in its state of rest or
+of uniform motion in a straight line except in so far as it may be
+compelled by force to change that state." A gust of wind, a stone, a
+careless movement of the rider may turn the bicycle to the right or the
+left, but unless some disturbing force is applied it will go straight
+ahead, and if all resistance to its motion could be removed it would go
+always at the speed given it by the last power applied, swerving neither
+to the one hand nor the other.
+
+When a slow rider increases his speed we recognize at once that he has
+applied additional power to the wheel, and when this speed is slackened
+it equally shows that force has been applied against the motion. It is
+force alone which can produce a change in either velocity or direction
+of motion; but simple as this law now appears it required the genius of
+Galileo to discover it and of Newton to give it the form in which it is
+stated above.
+
+35. THE SECOND LAW OF MOTION, which is also due to Galileo and Newton,
+is:
+
+"Change of motion is proportional to force applied and takes place in
+the direction of the straight line in which the force acts." Suppose a
+man to fall from a balloon at some great elevation in the air; his own
+weight is the force which pulls him down, and that force operating at
+every instant is sufficient to give him at the end of the first second
+of his fall a downward velocity of 32 feet per second--i. e., it has
+changed his state from rest, to motion at this rate, and the motion is
+toward the earth because the force acts in that direction. During the
+next second the ceaseless operation of this force will have the same
+effect as in the first second and will add another 32 feet to his
+velocity, so that two seconds from the time he commenced to fall he will
+be moving at the rate of 64 feet per second, etc. The column of figures
+marked _v_ in the table below shows what his velocity will be at the end
+of subsequent seconds. The changing velocity here shown is the change of
+motion to which the law refers, and the velocity is proportional to the
+time shown in the first column of the table, because the amount of force
+exerted in this case is proportional to the time during which it
+operated. The distance through which the man will fall in each second is
+shown in the column marked _d_, and is found by taking the average of
+his velocity at the beginning and end of this second, and the total
+distance through which he has fallen at the end of each second, marked
+_s_ in the table, is found by taking the sum of all the preceding values
+of _d_. The velocity, 32 feet per second, which measures the change of
+motion in each second, also measures the _accelerating force_ which
+produces this motion, and it is usually represented in formulƦ by the
+letter _g_. Let the student show from the numbers in the table that the
+accelerating force, the time, _t_, during which it operates, and the
+space, _s_, fallen through, satisfy the relation
+
+    s = 1/2 gt^{2},
+
+which is usually called the law of falling bodies. How does the table
+show that _g_ is equal to 32?
+
+            TABLE
+
+    _t_   _v_   _d_   _s_
+
+     0      0     0     0
+     1     32    16    16
+     2     64    48    64
+     3     96    80   144
+     4    128   112   256
+     5    160   144   400
+    etc.  etc.  etc.  etc.
+
+If the balloon were half a mile high how long would it take to fall to
+the ground? What would be the velocity just before reaching the ground?
+
+[Illustration: GALILEO GALILEI (1564-1642).]
+
+Fig. 19 shows the path through the air of a ball which has been struck
+by a bat at the point _A_, and started off in the direction _A B_ with a
+velocity of 200 feet per second. In accordance with the first law of
+motion, if it were acted upon by no other force than the impulse given
+by the bat, it should travel along the straight line _A B_ at the
+uniform rate of 200 feet per second, and at the end of the fourth second
+it should be 800 feet from _A_, at the point marked 4, but during these
+four seconds its weight has caused it to fall 256 feet, and its actual
+position, 4', is 256 feet below the point 4. In this way we find its
+position at the end of each second, 1', 2', 3', 4', etc., and drawing a
+line through these points we shall find the actual path of the ball
+under the influence of the two forces to be the curved line _A C_. No
+matter how far the ball may go before striking the ground, it can not
+get back to the point _A_, and the curve _A C_ therefore can not be a
+part of a circle, since that curve returns into itself. It is, in fact,
+a part of a _parabola_, which, as we shall see later, is a kind of orbit
+in which comets and some other heavenly bodies move. A skyrocket moves
+in the same kind of a path, and so does a stone, a bullet, or any other
+object hurled through the air.
+
+[Illustration: FIG. 19.--The path of a ball.]
+
+36. THE THIRD LAW OF MOTION.--"To every action there is always an equal
+and contrary reaction; or the mutual actions of any two bodies are
+always equal and oppositely directed." This is well illustrated in the
+case of a man climbing a rope hand over hand. The direct force or action
+which he exerts is a downward pull upon the rope, and it is the reaction
+of the rope to this pull which lifts him along it. We shall find in a
+later chapter a curious application of this law to the history of the
+earth and moon.
+
+It is the great glory of Sir Isaac Newton that he first of all men
+recognized that these simple laws of motion hold true in the heavens as
+well as upon the earth; that the complicated motion of a planet, a
+comet, or a star is determined in accordance with these laws by the
+forces which act upon the bodies, and that these forces are essentially
+the same as that which we call weight. The formal statement of the
+principle last named is included in--
+
+37. NEWTON'S LAW OF GRAVITATION.--"Every particle of matter in the
+universe attracts every other particle with a force whose direction is
+that of a line joining the two, and whose magnitude is directly as the
+product of their masses, and inversely as the square of their distance
+from each other." We know that we ourselves and the things about us are
+pulled toward the earth by a force (weight) which is called, in the
+Latin that Newton wrote, _gravitas_, and the word marks well the true
+significance of the law of gravitation. Newton did not discover a new
+force in the heavens, but he extended an old and familiar one from a
+limited terrestrial sphere of action to an unlimited and celestial one,
+and furnished a precise statement of the way in which the force
+operates. Whether a body be hot or cold, wet or dry, solid, liquid, or
+gaseous, is of no account in determining the force which it exerts,
+since this depends solely upon mass and distance.
+
+The student should perhaps be warned against straining too far the
+language which it is customary to employ in this connection. The law of
+gravitation is certainly a far-reaching one, and it may operate in every
+remotest corner of the universe precisely as stated above, but
+additional information about those corners would be welcome to
+supplement our rather scanty stock of knowledge concerning what happens
+there. We may not controvert the words of a popular preacher who says,
+"When I lift my hand I move the stars in Ursa Major," but we should not
+wish to stand sponsor for them, even though they are justified by a
+rigorous interpretation of the Newtonian law.
+
+The word _mass_, in the statement of the law of gravitation, means the
+quantity of matter contained in the body, and if we represent by the
+letters _mĀ“_ and _mĀ“Ā“_ the respective quantities of matter contained in
+the two bodies whose distance from each other is _r_, we shall have, in
+accordance with the law of gravitation, the following mathematical
+expression for the force, _F_, which acts between them:
+
+    F = k {mĀ“mĀ“Ā“/r^{2}}.
+
+This equation, which is the general mathematical expression for the law
+of gravitation, may be made to yield some curious results. Thus, if we
+select two bullets, each having a mass of 1 gram, and place them so that
+their centers are 1 centimeter apart, the above expression for the force
+exerted between them becomes
+
+    F = k {(1 Ɨ 1)/1^{2}} = k,
+
+from which it appears that the coefficient _k_ is the force exerted
+between these bodies. This is called the gravitation constant, and it
+evidently furnishes a measure of the specific intensity with which one
+particle of matter attracts another. Elaborate experiments which have
+been made to determine the amount of this force show that it is
+surprisingly small, for in the case of the two bullets whose mass of 1
+gram each is supposed to be concentrated into an indefinitely small
+space, gravity would have to operate between them continuously for more
+than forty minutes in order to pull them together, although they were
+separated by only 1 centimeter to start with, and nothing save their own
+inertia opposed their movements. It is only when one or both of the
+masses _mĀ“_, _mĀ“Ā“_ are very great that the force of gravity becomes
+large, and the weight of bodies at the surface of the earth is
+considerable because of the great quantity of matter which goes to make
+up the earth. Many of the heavenly bodies are much more massive than the
+earth, as the mathematical astronomers have found by applying the law of
+gravitation to determine numerically their masses, or, in more popular
+language, to "weigh" them.
+
+The student should observe that the two terms mass and weight are not
+synonymous; mass is defined above as the quantity of matter contained in
+a body, while weight is the force with which the earth attracts that
+body, and in accordance with the law of gravitation its weight depends
+upon its distance from the center of the earth, while its mass is quite
+independent of its position with respect to the earth.
+
+By the third law of motion the earth is pulled toward a falling body
+just as strongly as the body is pulled toward the earth--i. e., by a
+force equal to the weight of the body. How much does the earth rise
+toward the body?
+
+38. THE MOTION OF A PLANET.--In Fig. 20 _S_ represents the sun and _P_ a
+planet or other celestial body, which for the moment is moving along the
+straight line _P 1_. In accordance with the first law of motion it would
+continue to move along this line with uniform velocity if no external
+force acted upon it; but such a force, the sun's attraction, is acting,
+and by virtue of this attraction the body is pulled aside from the line
+_P 1_.
+
+Knowing the velocity and direction of the body's motion and the force
+with which the sun attracts it, the mathematician is able to apply
+Newton's laws of motion so as to determine the path of the body, and a
+few of the possible orbits are shown in the figure where the short cross
+stroke marks the point of each orbit which is nearest to the sun. This
+point is called the _perihelion_.
+
+Without any formal application of mathematics we may readily see that
+the swifter the motion of the body at _P_ the shorter will be the time
+during which it is subjected to the sun's attraction at close range, and
+therefore the force exerted by the sun, and the resulting change of
+motion, will be small, as in the orbits _P 1_ and _P 2_.
+
+On the other hand, _P 5_ and _P 6_ represent orbits in which the
+velocity at _P_ was comparatively small, and the resulting change of
+motion greater than would be possible for a more swiftly moving body.
+
+What would be the orbit if the velocity at _P_ were reduced to nothing
+at all?
+
+What would be the effect if the body starting at _P_ moved directly away
+from _1_?
+
+[Illustration: FIG. 20.--Different kinds of orbits.]
+
+The student should not fail to observe that the sun's attraction tends
+to pull the body at _P_ forward along its path, and therefore increases
+its velocity, and that this influence continues until the planet reaches
+perihelion, at which point it attains its greatest velocity, and the
+force of the sun's attraction is wholly expended in changing the
+direction of its motion. After the planet has passed perihelion the
+sun begins to pull backward and to retard the motion in just the same
+measure that before perihelion passage it increased it, so that the
+two halves of the orbit on opposite sides of a line drawn from the
+perihelion through the sun are exactly alike. We may here note the
+explanation of Kepler's second law: when the planet is near the sun it
+moves faster, and the radius vector changes its direction more rapidly
+than when the planet is remote from the sun on account of the greater
+force with which it is attracted, and the exact relation between the
+rates at which the radius vector turns in different parts of the orbit,
+as given by the second law, depends upon the changes in this force.
+
+When the velocity is not too great, the sun's backward pull, after a
+planet has passed perihelion, finally overcomes it and turns the planet
+toward the sun again, in such a way that it comes back to the point _P_,
+moving in the same direction and with the same speed as before--i. e.,
+it has gone around the sun in an orbit like _P 6_ or _P 4_, an ellipse,
+along which it will continue to move ever after. But we must not fail to
+note that this return into the same orbit is a consequence of the last
+line in the statement of the law of gravitation (p. 54), and that, if
+the magnitude of this force were inversely as the cube of the distance
+or any other proportion than the square, the orbit would be something
+very different. If the velocity is too great for the sun's attraction to
+overcome, the orbit will be a hyperbola, like _P 2_, along which the
+body will move away never to return, while a velocity just at the limit
+of what the sun can control gives an orbit like _P 3_, a parabola, along
+which the body moves with _parabolic velocity_, which is ever
+diminishing as the body gets farther from the sun, but is always just
+sufficient to keep it from returning. If the earth's velocity could be
+increased 41 per cent, from 19 up to 27 miles per second, it would have
+parabolic velocity, and would quit the sun's company.
+
+The summation of the whole matter is that the orbit in which a body
+moves around the sun, or past the sun, depends upon its velocity and if
+this velocity and the direction of the motion at any one point in the
+orbit are known the whole orbit is determined by them, and the position
+of the planet in its orbit for past as well as future times can be
+determined through the application of Newton's laws; and the same is
+true for any other heavenly body--moon, comet, meteor, etc. It is in
+this way that astronomers are able to predict, years in advance, in what
+particular part of the sky a given planet will appear at a given time.
+
+It is sometimes a source of wonder that the planets move in ellipses
+instead of circles, but it is easily seen from Fig. 20 that the planet,
+_P_, could not by any possibility move in a circle, since the direction
+of its motion at _P_ is not at right angles with the line joining it to
+the sun as it must be in a circular orbit, and even if it were
+perpendicular to the radius vector the planet must needs have exactly
+the right velocity given to it at this point, since either more or less
+speed would change the circle into an ellipse. In order to produce
+circular motion there must be a balancing of conditions as nice as is
+required to make a pin stand upon its point, and the really surprising
+thing is that the orbits of the planets should be so nearly circular as
+they are. If the orbit of the earth were drawn accurately to scale, the
+untrained eye would not detect the slightest deviation from a true
+circle, and even the orbit of Mercury (Fig. 17), which is much more
+eccentric than that of the earth, might almost pass for a circle.
+
+[Illustration: FIG. 21. An impossible orbit.]
+
+The orbit _P 2_, which lies between the parabola and the straight line,
+is called in geometry a hyperbola, and Newton succeeded in proving from
+the law of gravitation that a body might move under the sun's attraction
+in a hyperbola as well as in a parabola or ellipse; but it must move in
+some one of these curves; no other orbit is possible.[1] Thus it would
+not be possible for a body moving under the law of gravitation to
+describe about the sun any such orbit as is shown in Fig. 21. If the
+body passes a second time through any point of its orbit, such as _P_ in
+the figure, then it must retrace, time after time, the whole path that
+it first traversed in getting from _P_ around to _P_ again--i. e., the
+orbit must be an ellipse.
+
+  [1] The circle and straight line are considered to be special cases
+      of these curves, which, taken collectively, are called the conic
+      sections.
+
+Newton also proved that Kepler's three laws are mere corollaries from
+the law of gravitation, and that to be strictly correct the third law
+must be slightly altered so as to take into account the masses of the
+planets. These are, however, so small in comparison with that of the
+sun, that the correction is of comparatively little moment.
+
+39. PERTURBATIONS.--In what precedes we have considered the motion of a
+planet under the influence of no other force than the sun's attraction,
+while in fact, as the law of gravitation asserts, every other body in
+the universe is in some measure attracting it and changing its motion.
+The resulting disturbances in the motion of the attracted body are
+called _perturbations_, but for the most part these are insignificant,
+because the bodies by whose disturbing attractions they are caused are
+either very small or very remote, and it is only when our moving planet,
+_P_, comes under the influence of some great disturbing power like
+Jupiter or one of the other planets that the perturbations caused by
+their influence need to be taken into account.
+
+The problem of the motion of three bodies--sun, Jupiter, planet--which
+must then be dealt with is vastly more complicated than that which we
+have considered, and the ablest mathematicians and astronomers have not
+been able to furnish a complete solution for it, although they have
+worked upon the problem for two centuries, and have developed an immense
+amount of detailed information concerning it.
+
+[Illustration: THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.]
+
+In general each planet works ceaselessly upon the orbit of every other,
+changing its size and shape and position, backward and forward in
+accordance with the law of gravitation, and it is a question of serious
+moment how far this process may extend. If the diameter of the earth's
+orbit were very much increased or diminished by the perturbing action of
+the other planets, the amount of heat received from the sun would be
+correspondingly changed, and the earth, perhaps, be rendered unfit
+for the support of life. The tipping of the plane of the earth's orbit
+into a new position might also produce serious consequences; but the
+great French mathematician of a century ago, Laplace, succeeded in
+proving from the law of gravitation that although both of these changes
+are actually in progress they can not, at least for millions of years,
+go far enough to prove of serious consequence, and the same is true for
+all the other planets, unless here and there an asteroid may prove an
+exception to the rule.
+
+The precession (Chapter V) is a striking illustration of a perturbation
+of slightly different character from the above, and another is found in
+connection with the plane of the moon's orbit. It will be remembered
+that the moon in its motion among the stars never goes far from the
+ecliptic, but in a complete circuit of the heavens crosses it twice,
+once in going from south to north and once in the opposite direction.
+The points at which it crosses the ecliptic are called the _nodes_, and
+under the perturbing influence of the sun these nodes move westward
+along the ecliptic about twenty degrees per year, an extraordinarily
+rapid perturbation, and one of great consequence in the theory of
+eclipses.
+
+[Illustration: FIG. 22.--A planet subject to great perturbations by
+Jupiter.]
+
+40. WEIGHING THE PLANETS.--Although these perturbations can not be
+considered dangerous, they are interesting since they furnish a method
+for weighing the planets which produce them. From the law of gravitation
+we learn that the ability of a planet to produce perturbations depends
+directly upon its mass, since the force _F_ which it exerts contains
+this mass, _mĀ“_, as a factor. So, too, the divisor _r^{2}_ in the
+expression for the force shows that the distance between the disturbing
+and disturbed bodies is a matter of great consequence, for the smaller
+the distance the greater the force. When, therefore, the mass of a
+planet such as Jupiter is to be determined from the perturbations it
+produces, it is customary to select some such opportunity as is
+presented in Fig. 22, where one of the small planets, called asteroids,
+is represented as moving in a very eccentric orbit, which at one point
+approaches close to the orbit of Jupiter, and at another place comes
+near to the orbit of the earth. For the most part Jupiter will not exert
+any very great disturbing influence upon a planet moving in such an
+orbit as this, since it is only at rare intervals that the asteroid and
+Jupiter approach so close to each other, as is shown in the figure. The
+time during which the asteroid is little affected by the attraction of
+Jupiter is used to study the motion given to it by the sun's
+attraction--that is, to determine carefully the undisturbed orbit in
+which it moves; but there comes a time at which the asteroid passes
+close to Jupiter, as shown in the figure, and the orbital motion which
+the sun imparts to it will then be greatly disturbed, and when the
+planet next comes round to the part of its orbit near the earth the
+effect of these disturbances upon its apparent position in the sky will
+be exaggerated by its close proximity to the earth. If now the
+astronomer observes the actual position of the asteroid in the sky, its
+right ascension and declination, and compares these with the position
+assigned to the planet by the law of gravitation when the attraction of
+Jupiter is ignored, the differences between the observed right
+ascensions and declinations and those computed upon the theory of
+undisturbed motion will measure the influence that Jupiter has had upon
+the asteroid, and the amount by which Jupiter has shifted it, compared
+with the amount by which the sun has moved it--that is, with the motion
+in its orbit--furnishes the mass of Jupiter expressed as a fractional
+part of the mass of the sun.
+
+There has been determined in this manner the mass of every planet in the
+solar system which is large enough to produce any appreciable
+perturbation, and all these masses prove to be exceedingly small
+fractions of the mass of the sun, as may be seen from the following
+table, in which is given opposite the name of each planet the number by
+which the mass of the sun must be divided in order to get the mass of
+the planet:
+
+    Mercury      7,000,000 (?)
+    Venus          408,000
+    Earth          329,000
+    Mars         3,093,500
+    Jupiter          1,047.4
+    Saturn           3,502
+    Uranus          22,800
+    Neptune         19,700
+
+It is to be especially noted that the mass given for each planet
+includes the mass of all the satellites which attend it, since their
+influence was felt in the perturbations from which the mass was derived.
+Thus the mass assigned to the earth is the combined mass of earth and
+moon.
+
+41. DISCOVERY OF NEPTUNE.--The most famous example of perturbations is
+found in connection with the discovery, in the year 1846, of Neptune,
+the outermost planet of the solar system. For many years the motion of
+Uranus, his next neighbor, had proved a puzzle to astronomers. In
+accordance with Kepler's first law this planet should move in an ellipse
+having the sun at one of its foci, but no ellipse could be found which
+exactly fitted its observed path among the stars, although, to be sure,
+the misfit was not very pronounced. Astronomers surmised that the small
+deviations of Uranus from the best path which theory combined with
+observation could assign, were due to perturbations in its motion
+caused by an unknown planet more remote from the sun--a thing easy to
+conjecture but hard to prove, and harder still to find the unknown
+disturber. But almost simultaneously two young men, Adams in England and
+Le Verrier in France, attacked the problem quite independently of each
+other, and carried it to a successful solution, showing that if the
+irregularities in the motion of Uranus were indeed caused by an unknown
+planet, then that planet must, in September, 1846, be in the direction
+of the constellation Aquarius; and there it was found on September 23d
+by the astronomers of the Berlin Observatory whom Le Verrier had invited
+to search for it, and found within a degree of the exact point which the
+law of gravitation in his hands had assigned to it.
+
+This working backward from the perturbations experienced by Uranus to
+the cause which produced them is justly regarded as one of the greatest
+scientific achievements of the human intellect, and it is worthy of note
+that we are approaching the time at which it may be repeated, for
+Neptune now behaves much as did Uranus three quarters of a century ago,
+and the most plausible explanation which can be offered for these
+anomalies in its path is that the bounds of the solar system must be
+again enlarged to include another disturbing planet.
+
+42. THE SHAPE OF A PLANET.--There is an effect of gravitation not yet
+touched upon, which is of considerable interest and wide application in
+astronomy--viz., its influence in determining the shape of the heavenly
+bodies. The earth is a globe because every part of it is drawn toward
+the center by the attraction of the other parts, and if this attraction
+on its surface were everywhere of equal force the material of the earth
+would be crushed by it into a truly spherical form, no matter what may
+have been the shape in which it was originally made. But such is not the
+real condition of the earth, for its diurnal rotation develops in every
+particle of its body a force which is sometimes called _centrifugal_,
+but which is really nothing more than the inertia of its particles,
+which tend at every moment to keep unchanged the direction of their
+motion and which thus resist the attraction that pulls them into a
+circular path marked out by the earth's rotation, just as a stone tied
+at the end of a string and swung swiftly in a circle pulls upon the
+string and opposes the constraint which keeps it moving in a circle. A
+few experiments with such a stone will show that the faster it goes the
+harder does it pull upon the string, and the same is true of each
+particle of the earth, the swiftly moving ones near the equator having a
+greater centrifugal force than the slow ones near the poles. At the
+equator the centrifugal force is directly opposed to the force of
+gravity, and in effect diminishes it, so that, comparatively, there is
+an excess of gravity at the poles which compresses the earth along its
+axis and causes it to bulge out at the equator until a balance is thus
+restored. As we have learned from the study of geography, in the case of
+the earth, this compression amounts to about 27 miles, but in the larger
+planets, Jupiter and Saturn, it is much greater, amounting to several
+thousand miles.
+
+But rotation is not the only influence that tends to pull a planet out
+of shape. The attraction which the earth exerts upon the moon is
+stronger on the near side and weaker on the far side of our satellite
+than at its center, and this difference of attraction tends to warp the
+moon, as is illustrated in Fig. 23 where _1_, _2_, and _3_ represent
+pieces of iron of equal mass placed in line on a table near a horseshoe
+magnet, _H_. Each piece of iron is attracted by the magnet and is held
+back by a weight to which it is fastened by means of a cord running over
+a pulley, _P_, at the edge of the table. These weights are all to be
+supposed equally heavy and each of them pulls upon its piece of iron
+with a force just sufficient to balance the attraction of the magnet for
+the middle piece, No. _2_. It is clear that under this arrangement No.
+_2_ will move neither to the right nor to the left, since the forces
+exerted upon it by the magnet and the weight just balance each other.
+Upon No. _1_, however, the magnet pulls harder than upon No. _2_,
+because it is nearer and its pull therefore more than balances the force
+exerted by the weight, so that No. _1_ will be pulled away from No. _2_
+and will stretch the elastic cords, which are represented by the lines
+joining _1_ and _2_, until their tension, together with the force
+exerted by the weight, just balances the attraction of the magnet. For
+No. _3_, the force exerted by the magnet is less than that of the
+weight, and it will also be pulled away from No. _2_ until its elastic
+cords are stretched to the proper tension. The net result is that the
+three blocks which, without the magnet's influence, would be held close
+together by the elastic cords, are pulled apart by this outside force as
+far as the resistance of the cords will permit.
+
+[Illustration: FIG. 23.--Tide-raising forces.]
+
+An entirely analogous set of forces produces a similar effect upon the
+shape of the moon. The elastic cords of Fig. 23 stand for the attraction
+of gravitation by which all the parts of the moon are bound together.
+The magnet represents the earth pulling with unequal force upon
+different parts of the moon. The weights are the inertia of the moon in
+its orbital motion which, as we have seen in a previous section, upon
+the whole just balances the earth's attraction and keeps the moon from
+falling into it. The effect of these forces is to stretch out the
+moon along a line pointing toward the earth, just as the blocks were
+stretched out along the line of the magnet, and to make this diameter
+of the moon slightly but permanently longer than the others.
+
+[Illustration: FIG. 24.--The tides.]
+
+THE TIDES.--Similarly the moon and the sun attract opposite sides of the
+earth with different forces and feebly tend to pull it out of shape. But
+here a new element comes into play: the earth turns so rapidly upon its
+axis that its solid parts have no time in which to yield sensibly to the
+strains, which shift rapidly from one diameter to another as different
+parts of the earth are turned toward the moon, and it is chiefly the
+waters of the sea which respond to the distorting effect of the sun's
+and moon's attraction. These are heaped up on opposite sides of the
+earth so as to produce a slight elongation of its diameter, and Fig. 24
+shows how by the earth's rotation this swelling of the waters is swept
+out from under the moon and is pulled back by the moon until it finally
+takes up some such position as that shown in the figure where the effect
+of the earth's rotation in carrying it one way is just balanced by the
+moon's attraction urging it back on line with the moon. This heaping up
+of the waters is called a _tide_. If _I_ in the figure represents a
+little island in the sea the waters which surround it will of course
+accompany it in its diurnal rotation about the earth's axis, but
+whenever the island comes back to the position _I_, the waters will
+swell up as a part of the tidal wave and will encroach upon the land in
+what is called high tide or flood tide. So too when they reach _IĀ“Ā“_,
+half a day later, they will again rise in flood tide, and midway between
+these points, at _IĀ“_, the waters must subside, giving low or ebb tide.
+
+The height of the tide raised by the moon in the open sea is only a very
+few feet, and the tide raised by the sun is even less, but along the
+coast of a continent, in bays and angles of the shore, it often happens
+that a broad but low tidal wave is forced into a narrow corner, and then
+the rise of the water may be many feet, especially when the solar tide
+and the lunar tide come in together, as they do twice in every month, at
+new and full moon. Why do they come together at these times instead of
+some other?
+
+Small as are these tidal effects, it is worth noting that they may in
+certain cases be very much greater--e. g., if the moon were as massive
+as is the sun its tidal effect would be some millions of times greater
+than it now is and would suffice to grind the earth into fragments.
+Although the earth escapes this fate, some other bodies are not so
+fortunate, and we shall see in later chapters some evidence of their
+disintegration.
+
+43. THE SCOPE OF THE LAW OF GRAVITATION.--In all the domain of physical
+science there is no other law so famous as the Newtonian law of
+gravitation; none other that has been so dwelt upon, studied, and
+elaborated by astronomers and mathematicians, and perhaps none that can
+be considered so indisputably proved. Over and over again mathematical
+analysis, based upon this law, has pointed out conclusions which, though
+hitherto unsuspected, have afterward been found true, as when Newton
+himself derived as a corollary from this law that the earth ought to be
+flattened at the poles--a thing not known at that time, and not proved
+by actual measurement until long afterward. It is, in fact, this
+capacity for predicting the unknown and for explaining in minutest
+detail the complicated phenomena of the heavens and the earth that
+constitutes the real proof of the law of gravitation, and it is
+therefore worth while to note that at the present time there are a very
+few points at which the law fails to furnish a satisfactory account of
+things observed. Chief among these is the case of the planet Mercury,
+the long diameter of whose orbit is slowly turning around in a way for
+which the law of gravitation as yet furnishes no explanation. Whether
+this is because the law itself is inaccurate or incomplete, or whether
+it only marks a case in which astronomers have not yet properly applied
+the law and traced out its consequences, we do not know; but whether it
+be the one or the other, this and other similar cases show that even
+here, in its most perfect chapter, astronomy still remains an incomplete
+science.
+
+
+
+
+CHAPTER V
+
+THE EARTH AS A PLANET
+
+
+44. THE SIZE OF THE EARTH.--The student is presumed to have learned, in
+his study of geography, that the earth is a globe about 8,000 miles in
+diameter and, without dwelling upon the "proofs" which are commonly
+given for these statements, we proceed to consider the principles upon
+which the measurement of the earth's size and shape are based.
+
+[Illustration: FIG. 25.--Measuring the size of the earth.]
+
+In Fig. 25 the circle represents a meridian section of the earth; _P PĀ“_
+is the axis about which it rotates, and the dotted lines represent a
+beam of light coming from a star in the plane of the meridian, and so
+distant that the dotted lines are all practically parallel to each
+other. The several radii drawn through the points _1_, _2_, _3_,
+represent the direction of the vertical at these points, and the angles
+which these radii produced, make with the rays of starlight are each
+equal to the angular distance of the star from the zenith of the place
+at the moment the star crosses the meridian. We have already seen, in
+Chapter II, how these angles may be measured, and it is apparent from
+the figure that the difference between any two of these angles--e. g.,
+the angles at _1_ and _2_--is equal to the angle at the center, _O_,
+between the points _1_ and _2_. By measuring these angular distances of
+the star from the zenith, the astronomer finds the angles at the center
+of the earth between the stations _1_, _2_, _3_, etc., at which his
+observations are made. If the meridian were a perfect circle the change
+of zenith distance of the star, as one traveled along a meridian from
+the equator to the pole, would be perfectly uniform--the same number of
+degrees for each hundred miles traveled--and observations made in many
+parts of the earth show that this is very nearly true, but that, on the
+whole, as we approach the pole it is necessary to travel a little
+greater distance than is required for a given change in the angle at the
+equator. The earth is, in fact, flattened at the poles to the amount of
+about 27 miles in the length of its diameter, and by this amount, as
+well as by smaller variations due to mountains and valleys, the shape of
+the earth differs from a perfect sphere. These astronomical measurements
+of the curvature of the earth's surface furnish by far the most
+satisfactory proof that it is very approximately a sphere, and furnish
+as its equatorial diameter 7,926 miles.
+
+Neglecting the _compression_, as it is called, i. e., the 27 miles by
+which the equatorial diameter exceeds the polar, the size of the earth
+may easily be found by measuring the distance _1_--_2_ along the
+surface and by combining with this the angle _1 O 2_ obtained through
+measuring the meridian altitudes of any star as seen from _1_ and _2_.
+Draw on paper an angle equal to the measured difference of altitude and
+find how far you must go from its vertex in order to have the distance
+between the sides, measured along an arc of a circle, equal to the
+measured distance between _1_ and _2_. This distance from the vertex
+will be the earth's radius.
+
+EXERCISE 19.--Measure the diameter of the earth by the method given
+above. In order that this may be done satisfactorily, the two stations
+at which observations are made must be separated by a considerable
+distance--i. e., 200 miles. They need not be on the same meridian, but
+if they are on different meridians in place of the actual distance
+between them, there must be used the projection of that distance upon
+the meridian--i. e., the north and south part of the distance.
+
+By co-operation between schools in the Northern and Southern States,
+using a good map to obtain the required distances, the diameter of the
+earth may be measured with the plumb-line apparatus described in Chapter
+II and determined within a small percentage of its true value.
+
+45. THE MASS OF THE EARTH.--We have seen in Chapter IV the possibility
+of determining the masses of the planets as fractional parts of the
+sun's mass, but nothing was there shown, or could be shown, about
+measuring these masses after the common fashion in kilogrammes or tons.
+To do this we must first get the mass of the earth in tons or
+kilogrammes, and while the principles involved in this determination are
+simple enough, their actual application is delicate and difficult.
+
+[Illustration: FIG. 26.--Illustrating the principles involved in
+weighing the earth.]
+
+In Fig. 26 we suppose a long plumb line to be suspended above the
+surface of the earth and to be attracted toward the center of the earth,
+_C_, by a force whose intensity is (Chapter IV)
+
+    F = k mE/R^{2},
+
+where _E_ denotes the mass of the earth, which is to be determined by
+experiment, and _R_ is the radius of the earth, 3,963 miles. If there is
+no disturbing influence present, the plumb line will point directly
+downward, but if a massive ball of lead or other heavy substance is
+placed at one side, _1_, it will attract the plumb line with a force
+equal to
+
+    f = k mB/r^{2},
+
+where _r_ is the distance of its center from the plumb bob and _B_ is
+its mass which we may suppose, for illustration, to be a ton. In
+consequence of this attraction the plumb line will be pulled a little to
+one side, as shown by the dotted line, and if we represent by _l_ the
+length of the plumb line and by _d_ the distance between the original
+and the disturbed positions of the plumb bob we may write the proportion
+
+    F : f :: l : d;
+
+and introducing the values of _F_ and _f_ given above, and solving for
+_E_ the proportion thus transformed, we find
+
+    E = B Ɨ l/d Ɨ (R/r)^{2}.
+
+In this equation the mass of the ball, _B_, the length of the plumb
+line, _l_, the distance between the center of the ball and the center of
+the plumb bob, _r_, and the radius of the earth, _R_, can all be
+measured directly, and _d_, the amount by which the plumb bob is pulled
+to one side by the ball, is readily found by shifting the ball over to
+the other side, at _2_, and measuring with a microscope how far the
+plumb bob moves. This distance will, of course, be equal to _2 d_.
+
+By methods involving these principles, but applied in a manner more
+complicated as well as more precise, the mass of the earth is found to
+be, in tons, 6,642 Ɨ 10^{18}--i. e., 6,642 followed by 18 ciphers, or in
+kilogrammes 60,258 Ɨ 10^{20}. The earth's atmosphere makes up about a
+millionth part of this mass.
+
+If the length of the plumb line were 100 feet, the weight of the ball a
+ton, and the distance between the two positions of the ball, _1_ and
+_2_, six feet, how many inches, _d_, would the plumb bob be pulled out
+of place?
+
+Find from the mass of the earth and the data of Ā§ 40 the mass of the sun
+in tons. Find also the mass of Mars. The computation can be very greatly
+abridged by the use of logarithms.
+
+46. PRECESSION.--That the earth is isolated in space and has no support
+upon which to rest, is sufficiently shown by the fact that the stars are
+visible upon every side of it, and no support can be seen stretching out
+toward them. We must then consider the earth to be a globe traveling
+freely about the sun in a circuit which it completes once every year,
+and rotating once in every twenty-four hours about an axis which remains
+at all seasons directed very nearly toward the star Polaris. The student
+should be able to show from his own observations of the sun that, with
+reference to the stars, the direction of the sun from the earth changes
+about a degree a day. Does this prove that the earth revolves about the
+sun?
+
+But it is only in appearance that the pole maintains its fixed position
+among the stars. If photographs are taken year after year, after the
+manner of Exercise 7, it will be found that slowly the pole is moving
+(nearly) toward Polaris, and making this star describe a smaller and
+smaller circle in its diurnal path, while stars on the other side of the
+pole (in right ascension 12h.) become more distant from it and describe
+larger circles in their diurnal motion; but the process takes place so
+slowly that the space of a lifetime is required for the motion of the
+pole to equal the angular diameter of the full moon.
+
+Spin a top and note how its rapid whirl about its axis corresponds to
+the earth's diurnal rotation. When the axis about which the top spins is
+truly vertical the top "sleeps"; but if the axis is tipped ever so
+little away from the vertical it begins to wobble, so that if we imagine
+the axis prolonged out to the sky and provided with a pencil point as a
+marker, this would trace a circle around the zenith, along which the
+pole of the top would move, and a little observation will show that the
+more the top is tipped from the vertical the larger does this circle
+become and the more rapidly does the wobbling take place. Were it not
+for the spinning of the top about its axis, it would promptly fall over
+when tipped from the vertical position, but the spin combines with the
+force which pulls the top over and produces the wobbling motion. Spin
+the top in opposite directions, with the hands of a watch and contrary
+to the hands of a watch, and note the effect which is produced upon the
+wobbling.
+
+The earth presents many points of resemblance to the top. Its diurnal
+rotation is the spin about the axis. This axis is tipped 23.5Ā° away from
+the perpendicular to its orbit (obliquity of the ecliptic) just as the
+axis of the top is tipped away from the vertical line. In consequence of
+its rapid spin, the body of the earth bulges out at the equator (27
+miles), and the sun and moon, by virtue of their attraction (see Chapter
+IV), lay hold of this protuberance and pull it down toward the plane of
+the earth's orbit, so that if it were not for the spin this force would
+straighten the axis up and set it perpendicular to the orbit plane. But
+here, as in the case of the top, the spin and the tipping force combine
+to produce a wobble which is called precession, and whose effect we
+recognize in the shifting position of the pole among the stars. The
+motion of precession is very much slower than the wobbling of the top,
+since the tipping force for the earth is relatively very small, and a
+period of nearly 26,000 years is required for a complete circuit of the
+pole about its center of motion. Friction ultimately stops both the spin
+and the wobble of the top, but this influence seems wholly absent in the
+case of the earth, and both rotation and precession go on unchanged from
+century to century, save for certain minor forces which for a time
+change the direction or rate of the precessional motion, first in one
+way and then in another, without in the long run producing any results
+of consequence.
+
+The center of motion, about which the pole travels in a small circle
+having an angular radius of 23.5Ā°, is at that point of the heavens
+toward which a perpendicular to the plane of the earth's orbit points,
+and may be found on the star map in right ascension 18h. 0m. and
+declination 66.5Ā°.
+
+EXERCISE 20.--Find this point on the map, and draw as well as you can
+the path of the pole about it. The motion of the pole along its path is
+toward the constellation Cepheus. Mark the position of the pole along
+this path at intervals of 1,000 years, and refer to these positions in
+dealing with some of the following questions:
+
+Does the wobbling of the top occur in the same direction as the motion
+of precession? Do the tipping forces applied to the earth and top act in
+the same direction? What will be the polar star 12,000 years hence? The
+Great Pyramid of Egypt is thought to have been used as an observatory
+when Alpha Draconis was the bright star nearest the pole. How long ago
+was that?
+
+The motion of the pole of course carries the equator and the equinoxes
+with it, and thus slowly changes the right ascensions and declinations
+of all the stars. On this account it is frequently called the precession
+of the equinoxes, and this motion of the equinox, slow though it is, is
+a matter of some consequence in connection with chronology and the
+length of the year.
+
+Will the precession ever bring back the right ascensions and
+declinations to be again what they now are?
+
+In what direction is the pole moving with respect to the Big Dipper?
+Will its motion ever bring it exactly to Polaris? How far away from
+Polaris will the precession carry the pole? What other bright stars will
+be brought near the pole by the precession?
+
+47. THE WARMING OF THE EARTH.--Winter and summer alike the day is on the
+average warmer than the night, and it is easy to see that this surplus
+of heat comes from the sun by day and is lost by night through radiation
+into the void which surrounds the earth; just as the heat contained in a
+mass of molten iron is radiated away and the iron cooled when it is
+taken out from the furnace and placed amid colder surroundings. The
+earth's loss of heat by radiation goes on ceaselessly day and night,
+and were it not for the influx of solar heat this radiation would
+steadily diminish the temperature toward what is called the "absolute
+zero"--i. e., a state in which all heat has been taken away and beyond
+which there can be no greater degree of cold. This must not be
+confounded with the zero temperatures shown by our thermometers,
+since it lies nearly 500Ā° below the zero of the Fahrenheit scale (-273Ā°
+Centigrade), a temperature which by comparison makes the coldest winter
+weather seem warm, although the ordinary thermometer may register
+many degrees below its zero. The heat radiated by the sun into the
+surrounding space on every side of it is another example of the same
+cooling process, a hot body giving up its heat to the colder space about
+it, and it is the minute fraction of this heat poured out by the sun,
+and in small part intercepted by the earth, which warms the latter and
+produces what we call weather, climate, the seasons, etc.
+
+Observe the fluctuations, the ebb and flow, which are inherent in this
+process. From sunset to sunrise there is nothing to compensate the
+steady outflow of heat, and air and ground grow steadily colder, but
+with the sunrise there comes an influx of solar heat, feeble at first
+because it strikes the earth's surface very obliquely, but becoming more
+and more efficient as the sun rises higher in the sky. But as the air
+and the ground grow warm during the morning hours they part more and
+more readily and rapidly with their store of heat, just as a steam pipe
+or a cup of coffee radiates heat more rapidly when very hot. The warmest
+hour of the day is reached when these opposing tendencies of income and
+expenditure of heat are just balanced; and barring such disturbing
+factors as wind and clouds, the gain in temperature usually extends to
+the time--an hour or two beyond noon--at which the diminishing altitude
+of the sun renders his rays less efficient, when radiation gains the
+upper hand and the temperature becomes for a short time stationary, and
+then commences to fall steadily until the next sunrise.
+
+We have here an example of what is called a periodic change--i. e., one
+which, within a definite and uniform period (24 hours), oscillates from
+a minimum up to a maximum temperature and then back again to a minimum,
+repeating substantially the same variation day after day. But it must be
+understood that minor causes not taken into account above, such as
+winds, water, etc., produce other fluctuations from day to day which
+sometimes obscure or even obliterate the diurnal variation of
+temperature caused by the sun.
+
+Expose the back of your hand to the sun, holding the hand in such a
+position that the sunlight strikes perpendicularly upon it; then turn
+the hand so that the light falls quite obliquely upon it and note how
+much more vigorous is the warming effect of the sun in the first
+position than in the second. It is chiefly this difference of angle that
+makes the sun's warmth more effective when he is high up in the sky than
+when he is near the horizon, and more effective in summer than in
+winter.
+
+We have seen in Chapter III that the sun's motion among the stars takes
+place along a path which carries it alternately north and south of the
+equator to a distance of 23.5Ā°, and the stars show by their earlier
+risings and later settings, as we pass from the equator toward the north
+pole of the heavens, that as the sun moves northward from the equator,
+each day in the northern hemisphere will become a little longer, each
+night a little shorter, and every day the sun will rise higher toward
+the zenith until this process culminates toward the end of June, when
+the sun begins to move southward, bringing shorter days and smaller
+altitudes until the Christmas season, when again it is reversed and the
+sun moves northward. We have here another periodic variation, which runs
+its complete course in a period of a year, and it is easy to see that
+this variation must have a marked effect on the warming of the earth,
+the long days and great altitudes of summer producing the greater warmth
+of that season, while the shorter days and lower altitudes of December,
+by diminishing the daily supply of solar heat, bring on the winter's
+cold. The succession of the seasons, winter following summer and summer
+winter, is caused by the varying altitude of the sun, and this in turn
+is due to the obliquity of the ecliptic, or, what is the same thing, the
+amount by which the axis of the earth is tipped from being perpendicular
+to the plane of its orbit, and the seasons are simply a periodic change
+in the warming of the earth, quite comparable with the diurnal change
+but of longer period.
+
+It is evident that the period within which the succession of winter and
+summer is completed, the year, as we commonly call it, must equal the
+time required by the sun to go from the vernal equinox around to the
+vernal equinox again, since this furnishes a complete cycle of the sun's
+motions north and south from the equator. On account of the westward
+motion of the equinox (precession) this is not quite the same as the
+time required for a complete revolution of the earth in its orbit, but
+is a little shorter (20m. 23s.), since the equinox moves back to meet
+the sun.
+
+48. RELATION OF THE SUN TO CLIMATE.--It is clear that both the northern
+and southern hemispheres of the earth must have substantially the same
+kind of seasons, since the motion of the sun north and south affects
+both alike; but when the sun is north of the equator and warming our
+hemisphere most effectively, his light falls more obliquely upon the
+other hemisphere, the days there are short and winter reigns at the
+time we are enjoying summer, while six months later the conditions are
+reversed.
+
+In those parts of the earth near the equator--the torrid zone--there is
+no such marked change from cold to warm as we experience, because, as
+the sun never gets more than 23.5Ā° away from the celestial equator, on
+every day of the year he mounts high in the tropic skies, always coming
+within 23.5Ā° of the zenith, and usually closer than this, so that there
+is no such periodic change in the heat supply as is experienced in
+higher latitudes, and within the tropics the temperature is therefore
+both higher and more uniform than in our latitude.
+
+In the frigid zones, on the contrary, the sun never rises high in the
+sky; at the poles his greatest altitude is only 23.5Ā°, and during the
+winter season he does not rise at all, so that the temperature is here
+low the whole year round, and during the winter season, when for weeks
+or months at a time the supply of solar light is entirely cut off, the
+temperature falls to a degree unknown in more favored climes.
+
+If the obliquity of the ecliptic were made 10Ā° greater, what would be
+the effect upon the seasons in the temperate zones? What if it were made
+10Ā° less?
+
+Does the precession of the equinoxes have any effect upon the seasons or
+upon the climate of different parts of the earth?
+
+If the axis of the earth pointed toward Arcturus instead of Polaris,
+would the seasons be any different from what they are now?
+
+49. THE ATMOSPHERE.--Although we live upon its surface, we are not
+outside the earth, but at the bottom of a sea of air which forms the
+earth's outermost layer and extends above our heads to a height of many
+miles. The study of most of the phenomena of the atmosphere belongs to
+that branch of physics called meteorology, but there are a few matters
+which fairly come within our consideration of the earth as a planet. We
+can not see the stars save as we look through this atmosphere, and the
+light which comes through it is bent and oftentimes distorted so as to
+present serious obstacles to any accurate telescopic study of the
+heavenly bodies. Frequently this disturbance is visible to the naked
+eye, and the stars are said to twinkle--i. e., to quiver and change
+color many times per second, solely in consequence of a disturbed
+condition of the air and not from anything which goes on in the star.
+This effect is more marked low down in the sky than near the zenith, and
+it is worth noting that the planets show very little of it because the
+light they send to the earth comes from a disk of sensible area, while a
+star, being much smaller and farther from the earth, has its disk
+reduced practically to a mere point whose light is more easily affected
+by local disturbances in the atmosphere than is the broader beam which
+comes from the planets' disk.
+
+50. REFRACTION.--At all times, whether the stars twinkle or not, their
+light is bent in its passage through the atmosphere, so that the stars
+appear to stand higher up in the sky than their true positions. This
+effect, which the astronomer calls refraction, must be allowed for in
+observations of the more precise class, although save at low altitudes
+its amount is a very small fraction of a degree, but near the horizon it
+is much exaggerated in amount and becomes easily visible to the naked
+eye by distorting the disks of the sun and moon from circles into ovals
+with their long diameters horizontal. The refraction lifts both upper
+and lower edge of the sun, but lifts the lower edge more than the upper,
+thus shortening the vertical diameter. See Fig. 27, which shows not only
+this effect, but also the reflection of the sun from the curved surface
+of the sea, still further flattening the image. If the surface of the
+water were flat, the reflected image would have the same shape as the
+sun's disk, and its altered appearance is sometimes cited as a proof
+that the earth's surface is curved.
+
+The total amount of the refraction at the horizon is a little more than
+half a degree, and since the diameters of the sun and moon subtend an
+angle of about half a degree, we have the remarkable result that in
+reality the whole disk of either sun or moon is below the horizon at the
+instant that the lower edge appears to touch the horizon and sunset or
+moonset begins. The same effect exists at sunrise, and as a consequence
+the duration of sunshine or of moonshine is on the average about six
+minutes longer each day than it would be if there were no atmosphere and
+no refraction. A partial offset to this benefit is found in the fact
+that the atmosphere absorbs the light of the heavenly bodies, so that
+stars appear much less bright when near the horizon than when they are
+higher up in the sky, and by reason of this absorption the setting sun
+can be looked at with the naked eye without the discomfort which its
+dazzling luster causes at noon.
+
+[Illustration: FIG. 27.--Flattening of the sun's disk by refraction and
+by reflection from the surface of the sea.]
+
+51. THE TWILIGHT.--Another effect of the atmosphere, even more marked
+than the preceding, is the twilight. As at sunrise the mountain top
+catches the rays of the coming sun before they reach the lowland, and at
+sunset it keeps them after they have faded from the regions below, so
+the particles of dust and vapor, which always float in the atmosphere,
+catch the sunlight and reflect it to the surface of the earth while the
+sun is still below the horizon, giving at the beginning and end of day
+that vague and diffuse light which we call twilight.
+
+[Illustration: FIG. 28.--Twilight phenomena.]
+
+Fig. 28 shows a part of the earth surrounded by such a dust-laden
+atmosphere, which is illuminated on the left by the rays of the sun, but
+which, on the right of the figure, lies in the shadow cast by the earth.
+To an observer placed at _1_ the sun is just setting, and all the
+atmosphere above him is illumined with its rays, which furnish a bright
+twilight. When, by the earth's rotation, this observer has been carried
+to _2_, all the region to the east of his zenith lies in the shadow,
+while to the west there is a part of the atmosphere from which there
+still comes a twilight, but now comparatively faint, because the lower
+part of the atmosphere about our observer lies in the shadow, and it is
+mainly its upper regions from which the light comes, and here the dust
+and moisture are much less abundant than in the lower strata. Still
+later, when the observer has been carried by the earth's rotation to the
+point _3_, every vestige of twilight will have vanished from his sky,
+because all of the illuminated part of the atmosphere is now below his
+horizon, which is represented by the line _3 L_. In the figure the sun
+is represented to be 78Ā° below this horizon line at the end of twilight,
+but this is a gross exaggeration, made for the sake of clearness in the
+drawing--in fact, twilight is usually said to end when the sun is 18Ā°
+below the horizon.
+
+Let the student redraw Fig. 28 on a large scale, so that the points _1_
+and _3_ shall be only 18Ā° apart, as seen from the earth's center. He
+will find that the point _L_ is brought down much closer to the surface
+of the earth, and measuring the length of the line _2 L_, he should find
+for the "height of the atmosphere" about one-eightieth part of the
+radius of the earth--i. e., a little less than 50 miles. This, however,
+is not the true height of the atmosphere. The air extends far beyond
+this, but the particles of dust and vapor which are capable of sending
+sunlight down to the earth seem all to lie below this limit.
+
+The student should not fail to watch the eastern sky after sunset, and
+see the shadow of the earth rise up and fill it while the twilight arch
+retreats steadily toward the west.
+
+[Illustration: FIG. 29.--The cause of long and short twilights.]
+
+_Duration of twilight._--Since twilight ends when the sun is 18Ā° below
+the horizon, any circumstance which makes the sun go down rapidly will
+shorten the duration of twilight, and anything which retards the
+downward motion of the sun will correspondingly prolong it. Chief among
+influences of this kind is the angle which the sun's course makes with
+the horizon. If it goes straight down, as at _a_, Fig. 29, a much
+shorter time will suffice to carry it to a depression of 18Ā° than is
+needed in the case shown at _b_ in the same figure, where the motion is
+very oblique to the horizon. If we consider different latitudes and
+different seasons of the year, we shall find every possible variety of
+circumstance from _a_ to _b_, and corresponding to these, the duration
+of twilight varies from an all-night duration in the summers of Scotland
+and more northern lands to an hour or less in the mountains of Peru. For
+the sake of graphical effect, the shortness of tropical twilight is
+somewhat exaggerated by Coleridge in the lines,
+
+    "The sun's rim dips; the stars rush out:
+     At one stride comes the dark."
+                            _The Ancient Mariner._
+
+In the United States the longest twilights come at the end of June, and
+last for a little more than two hours, while the shortest ones are in
+March and September, amounting to a little more than an hour and a half;
+but at all times the last half hour of twilight is hardly to be
+distinguished from night, so small is the quantity of reflecting matter
+in the upper regions of the atmosphere. For practical convenience it is
+customary to assume in the courts of law that twilight ends an hour
+after sunset.
+
+How long does twilight last at the north pole?
+
+_The Aurora._--One other phenomenon of the atmosphere may be mentioned,
+only to point out that it is not of an astronomical character. The
+Aurora, or northern lights, is as purely an affair of the earth as is a
+thunderstorm, and its explanation belongs to the subject of terrestrial
+magnetism.
+
+
+
+
+CHAPTER VI
+
+THE MEASUREMENT OF TIME
+
+
+52. SOLAR TIME.--To measure any quantity we need a unit in terms of
+which it must be expressed. Angles are measured in degrees, and the
+degree is the unit for angular measurement. For most scientific purposes
+the centimeter is adopted as the unit with which to measure distances,
+and similarly a day is the fundamental unit for the measurement of time.
+Hours, minutes, and seconds are aliquot parts of this unit convenient
+for use in dealing with shorter periods than a day, and the week, month,
+and year which we use in our calendars are multiples of the day.
+
+Strictly speaking, a day is not the time required by the earth to make
+one revolution upon its axis, but it is best defined as the amount of
+time required for a particular part of the sky to make the complete
+circuit from the meridian of a particular place through west and east
+back to the meridian again. The day begins at the moment when this
+specified part of the sky is on the meridian, and "the time" at any
+moment is the hour angle of this particular part of the sky--i. e., the
+number of hours, minutes, etc., that have elapsed since it was on the
+meridian.
+
+The student has already become familiar with the kind of day which is
+based upon the motion of the vernal equinox, and which furnishes
+sidereal time, and he has seen that sidereal time, while very convenient
+in dealing with the motions of the stars, is decidedly inconvenient for
+the ordinary affairs of life since in the reckoning of the hours it
+takes no account of daylight and darkness. One can not tell off-hand
+whether 10 hours, sidereal time, falls in the day or in the night. We
+must in some way obtain a day and a system of time reckoning based upon
+the apparent diurnal motion of the sun, and we may, if we choose, take
+the sun itself as the point in the heavens whose transit over the
+meridian shall mark the beginning and the end of the day. In this system
+"the time" is the number of hours, minutes, etc., which have elapsed
+since the sun was on the meridian, and this is the kind of time which is
+shown by a sun dial, and which was in general use, years ago, before
+clocks and watches became common. Since the sun moves among the stars
+about a degree per day, it is easily seen that the rotating earth will
+have to turn farther in order to carry any particular meridian from the
+sun around to the sun again, than to carry it from a star around to the
+same star, or from the vernal equinox around to the vernal equinox
+again; just as the minute hand of a clock turns farther in going from
+the hour hand round to the hour hand again than it turns in going from
+XII to XII. These solar days and hours and minutes are therefore a
+little longer than the corresponding sidereal ones, and this furnishes
+the explanation why the stars come to the meridian a little earlier, by
+solar time, every night than on the night before, and why sidereal time
+gains steadily upon solar time, this gain amounting to approximately
+3m. 56.5s. per day, or exactly one day per year, since the sun makes the
+complete circuit of the constellations once in a year.
+
+With the general introduction of clocks and watches into use about a
+century ago this kind of solar time went out of common use, since no
+well-regulated clock could keep the time correctly. The earth in its
+orbital motion around the sun goes faster in some parts of its orbit
+than in others, and in consequence the sun appears to move more rapidly
+among the stars in winter than in summer; moreover, on account of the
+convergence of hour circles as we go away from the equator, the same
+amount of motion along the ecliptic produces more effect in winter and
+summer when the sun is north or south, than it does in the spring and
+autumn when the sun is near the equator, and as a combined result of
+these causes and other minor ones true solar time, as it is called, is
+itself not uniform, but falls behind the uniform lapse of sidereal time
+at a variable rate, sometimes quicker, sometimes slower. A true solar
+day, from noon to noon, is 51 seconds shorter in September than in
+December.
+
+[Illustration: FIG. 30.--The equation of time.]
+
+53. MEAN SOLAR TIME.--To remedy these inconveniences there has been
+invented and brought into common use what is called _mean solar time_,
+which is perfectly uniform in its lapse and which, by comparison with
+sidereal time, loses exactly one day per year. "The time" in this system
+never differs much from true solar time, and the difference between the
+two for any particular day may be found in any good almanac, or may be
+read from the curve in Fig. 30, in which the part of the curve above the
+line marked _0m_ shows how many minutes mean solar time is faster than
+true solar time. The correct name for this difference between the two
+kinds of solar time is the _equation of time_, but in the almanacs it is
+frequently marked "sun fast" or "sun slow." In sidereal time and true
+solar time the distinction between A. M. hours (_ante meridiem_ =
+before the sun reaches the meridian) and P. M. hours (_post meridiem_ =
+after the sun has passed the meridian) is not observed, "the time" being
+counted from 0 hours to 24 hours, commencing when the sun or vernal
+equinox is on the meridian. Occasionally the attempt is made to
+introduce into common use this mode of reckoning the hours, beginning
+the day (date) at midnight and counting the hours consecutively up to
+24, when the next date is reached and a new start made. Such a system
+would simplify railway time tables and similar publications; but the
+American public is slow to adopt it, although the system has come into
+practical use in Canada and Spain.
+
+54. TO FIND (APPROXIMATELY) THE SIDEREAL TIME AT ANY MOMENT.--RULE I.
+When the mean solar time is known. Let _W_ represent the time shown by
+an ordinary watch, and represent by _S_ the corresponding sidereal time
+and by _D_ the number of days that have elapsed from March 23d to the
+date in question. Then
+
+    S = W + 69/70 Ɨ D Ɨ 4.
+
+The last term is expressed in minutes, and should be reduced to hours
+and minutes. Thus at 4 P. M. on July 4th--
+
+                _D_ = 103 days.
+    69/70 Ɨ _D_ Ɨ 4 = 406m.
+                    = 6h. 46m.
+                _W_ = 4h. 0m.
+                _S_ = 10h. 46m.
+
+The daily gain of sidereal upon mean solar time is 69/70 of 4 minutes,
+and March 23d is the date on which sidereal and mean solar time are
+together, taking the average of one year with another, but it varies a
+little from year to year on account of the extra day introduced in leap
+years.
+
+RULE II. When the stars in the northern sky can be seen. Find Ī²
+CassiopeiƦ, and imagine a line drawn from it to Polaris, and another
+line from Polaris to the zenith. The sidereal time is equal to the angle
+between these lines, provided that that angle must be measured from the
+zenith toward the west. Turn the angle from degrees into hours by
+dividing by 15.
+
+55. THE EARTH'S ROTATION.--We are familiar with the fact that a watch
+may run faster at one time than at another, and it is worth while to
+inquire if the same is not true of our chief timepiece--the earth. It is
+assumed in the sections upon the measurement of time that the earth
+turns about its axis with absolute uniformity, so that mean solar time
+never gains or loses even the smallest fraction of a second. Whether
+this be absolutely true or not, no one has ever succeeded in finding
+convincing proof of a variation large enough to be measured, although it
+has recently been shown that the axis about which it rotates is not
+perfectly fixed within the body of the earth. The solid body of the
+earth wriggles about this axis like a fish upon a hook, so that the
+position of the north pole upon the earth's surface changes within a
+year to the extent of 40 or 50 feet (15 meters) without ever getting
+more than this distance away from its average position. This is probably
+caused by the periodical shifting of masses of air and water from one
+part of the earth to another as the seasons change, and it seems
+probable that these changes will produce some small effect upon the
+rotation of the earth. But in spite of these, for any such moderate
+interval of time as a year or a century, so far as present knowledge
+goes, we may regard the earth's rotation as uniform and undisturbed. For
+longer intervals--e. g., 1,000,000 or 10,000,000 years--the question is
+a very different one, and we shall have to meet it again in another
+connection.
+
+56. LONGITUDE AND TIME.--In what precedes there has been constant
+reference to the meridian. The day begins when the sun is on the
+meridian. Solar time is the angular distance of the sun past the
+meridian. Sidereal time was determined by observing transits of stars
+over a meridian line actually laid out upon the ground, etc. But every
+place upon the earth has its own meridian from which "the time" may be
+reckoned, and in Fig. 31, where the rays of sunlight are represented as
+falling upon a part of the earth's equator through which the meridians
+of New York, Chicago, and San Francisco pass, it is evident that these
+rays make different angles with the meridians, and that the sun is
+farther from the meridian of New York than from that of San Francisco by
+an amount just equal to the angle at _O_ between these meridians. This
+angle is called by geographers the difference of longitude between the
+two places, and the student should note that the word longitude is here
+used in a different sense from that on page 36. From Fig. 31 we obtain
+the
+
+_Theorem._--The difference between "the times" at any two meridians is
+equal to their difference of longitude, and the time at the eastern
+meridian is greater than at the western meridian. Astronomers usually
+express differences of longitude in hours instead of degrees. 1h. = 15Ā°.
+
+The name given to any kind of time should distinguish all the elements
+which enter into it--e. g., New York sidereal time means the hour angle
+of the vernal equinox measured from the meridian of New York, Chicago
+true solar time is the hour angle of the sun reckoned from the meridian
+of Chicago, etc.
+
+[Illustration: FIG. 31.--Longitude and time]
+
+[Illustration: FIG. 32.--Standard time.]
+
+57. STANDARD TIME.--The requirements of railroad traffic have led to the
+use throughout the United States and Canada of four "standard times,"
+each of which is a mean solar time some integral number of hours slower
+than the time of the meridian passing through the Royal Observatory at
+Greenwich, England.
+
+    Eastern time is 5 hours slower than that of Greenwich.
+    Central  "      6  "      "     "    "         "
+    Mountain "      7  "      "     "    "         "
+    Pacific  "      8  "      "     "    "         "
+
+In Fig. 32 the broken lines indicate roughly the parts of the United
+States and Canada in which these several kinds of time are used, and
+illustrate how irregular are the boundaries of these parts.
+
+Standard time is sent daily into all of the more important telegraph
+offices of the United States, and serves to regulate watches and clocks,
+to the almost complete exclusion of local time.
+
+58. TO DETERMINE THE LONGITUDE.--With an ordinary watch observe the time
+of the sun's transit over your local meridian, and correct the observed
+time for the equation of time by means of the curve in Fig. 30. The
+difference between the corrected time and 12 o'clock will be the
+correction of your watch referred to local mean solar time. Compare your
+watch with the time signals in the nearest telegraph office and find its
+correction referred to standard time. The difference between the two
+corrections is the difference between your longitude and that of the
+standard meridian.
+
+N. B.--Don't tamper with the watch by trying to "set it right." No harm
+will be done if it is wrong, provided you take due account of the
+correction as indicated above.
+
+If the correction of the watch changed between your observation and the
+comparison in the telegraph office, what effect would it have upon the
+longitude determination? How can you avoid this effect?
+
+59. CHRONOLOGY.--The Century Dictionary defines chronology as "the
+science of time"--that is, "the method of measuring or computing time
+by regular divisions or periods according to the revolutions of the sun
+or moon."
+
+We have already seen that for the measurement of short intervals of time
+the day and its subdivisions--hours, minutes, seconds--furnish a very
+complete and convenient system. But for longer periods, extending to
+hundreds and thousands of days, a larger unit of time is required, and
+for the most part these longer units have in all ages and among all
+peoples been based upon astronomical considerations. But to this there
+is one marked exception. The week is a simple multiple of the day, as
+the dime is a multiple of the cent, and while it may have had its origin
+in the changing phases of the moon this is at best doubtful, since it
+does not follow these with any considerable accuracy. If the still
+longer units of time--the month and the year--had equally been made to
+consist of an integral number of days much confusion and
+misunderstanding might have been avoided, and the annals of ancient
+times would have presented fewer pitfalls to the historian than is now
+the case. The month is plainly connected with the motion of the moon
+among the stars. The year is, of course, based upon the motion of the
+sun through the heavens and the change of seasons which is thus
+produced; although, as commonly employed, it is not quite the same as
+the time required by the earth to make one complete revolution in its
+orbit. This time of one revolution is called a sidereal year, while, as
+we have already seen in Chapter V, the year which measures the course of
+the seasons is shorter than this on account of the precession of the
+equinoxes. It is called a tropical year with reference to the circuit
+which the sun makes from one tropic to the other and back again.
+
+We can readily understand why primitive peoples should adopt as units of
+time these natural periods, but in so doing they incurred much the same
+kind of difficulty that we should experience in trying to use both
+English and American money in the ordinary transactions of life. How
+many dollars make a pound sterling? How shall we make change with
+English shillings and American dimes, etc.? How much is one unit worth
+in terms of the other?
+
+One of the Greek poets[2] has left us a quaint account of the confusion
+which existed in his time with regard to the place of months and moons
+in the calendar:
+
+    "The moon by us to you her greeting sends,
+    But bids us say that she's an ill-used moon
+    And takes it much amiss that you will still
+    Shuffle her days and turn them topsy-turvy,
+    So that when gods, who know their feast days well,
+    By your false count are sent home supperless,
+    They scold and storm at her for your neglect."
+
+  [2] Aristophanes, The Clouds, Whewell's translation.
+
+60. DAY, MONTH, AND YEAR.--If the day, the month, and the year are to be
+used concurrently, it is necessary to determine how many days are
+contained in the month and year, and when this has been done by the
+astronomer the numbers are found to be very awkward and inconvenient for
+daily use; and much of the history of chronology consists in an account
+of the various devices by which ingenious men have sought to use
+integral numbers to replace the cumbrous decimal fractions which follow.
+
+According to Professor Harkness, for the epoch 1900 A. D.--
+
+    One tropical year = 365.242197 mean solar days.
+     "     "      "   = 365d. 5h. 48m. 45.8s.
+    One lunation      = 29.530588 mean solar days.
+     "     "          = 29d. 12h. 44m. 2.8s.
+
+The word _lunation_ means the average interval from one new moon to the
+next one--i. e., the time required by the moon to go from conjunction
+with the sun round to conjunction again.
+
+A very ancient device was to call a year equal to 365 days, and to have
+months alternately of 29 and 30 days in length, but this was
+unsatisfactory in more than one way. At the end of four years this
+artificial calendar would be about one day ahead of the true one, at the
+end of forty years ten days in error, and within a single lifetime the
+seasons would have appreciably changed their position in the year, April
+weather being due in March, according to the calendar. So, too, the year
+under this arrangement did not consist of any integral number of months,
+12 months of the average length of 29.5 days being 354 days, and 13
+months 383.5 days, thus making any particular month change its position
+from the beginning to the middle and the end of the year within a
+comparatively short time. Some peoples gave up the astronomical year as
+an independent unit and adopted a conventional year of 12 lunar months,
+354 days, which is now in use in certain Mohammedan countries, where it
+is known as the wandering year, with reference to the changing positions
+of the seasons in such a year. Others held to the astronomical year and
+adopted a system of conventional months, such that twelve of them would
+just make up a year, as is done to this day in our own calendar, whose
+months of arbitrary length we are compelled to remember by some such
+jingle as the following:
+
+    "Thirty days hath September,
+    April, June, and November;
+    All the rest have thirty-one
+    Save February,
+    Which alone hath twenty-eight,
+    Till leap year gives it twenty-nine."
+
+
+61. THE CALENDAR.--The foundations of our calendar may fairly be
+ascribed to Julius CƦsar, who, under the advice of the Egyptian
+astronomer Sosigines, adopted the old Egyptian device of a leap year,
+whereby every fourth year was to consist of 366 days, while ordinary
+years were only 365 days long. He also placed the beginning of the year
+at the first of January, instead of in March, where it had formerly
+been, and gave his own name, Julius, to the month which we now call
+July. August was afterward named in honor of his successor, Augustus.
+The names of the earlier months of the year are drawn from Roman
+mythology; those of the later months, September, October, etc., meaning
+seventh month, eighth month, represent the places of these months in the
+year, before CƦsar's reformation, and also their places in some of the
+subsequent calendars, for the widest diversity of practice existed
+during mediƦval times with regard to the day on which the new year
+should begin, Christmas, Easter, March 25th, and others having been
+employed at different times and places.
+
+The system of leap years introduced by CƦsar makes the average length of
+a year 365.25 days, which differs by about eleven minutes from the true
+length of the tropical year, a difference so small that for ordinary
+purposes no better approximation to the true length of the year need be
+desired. But _any_ deviation from the true length, however small, must
+in the course of time shift the seasons, the vernal and autumnal
+equinox, to another part of the year, and the ecclesiastical authorities
+of mediƦval Europe found here ground for objection to CƦsar's calendar,
+since the great Church festival of Easter has its date determined with
+reference to the vernal equinox, and with the lapse of centuries Easter
+became more and more displaced in the calendar, until Pope Gregory XIII,
+late in the sixteenth century, decreed another reformation, whereby ten
+days were dropped from the calendar, the day after March 11th being
+called March 21st, to bring back the vernal equinox to the date on which
+it fell in A. D. 325, the time of the Council of NicƦa, which Gregory
+adopted as the fundamental epoch of his calendar.
+
+The calendar having thus been brought back into agreement with that of
+old time, Gregory purposed to keep it in such agreement for the future
+by modifying CƦsar's leap-year rule so that it should run: Every year
+whose number is divisible by 4 shall be a leap year except those years
+whose numbers are divisible by 100 but not divisible by 400. These
+latter years--e. g., 1900--are counted as common years. The calendar
+thus altered is called Gregorian to distinguish it from the older,
+Julian calendar, and it found speedy acceptance in those civilized
+countries whose Church adhered to Rome; but the Protestant powers were
+slow to adopt it, and it was introduced into England and her American
+colonies by act of Parliament in the year 1752, nearly two centuries
+after Gregory's time. In Russia the Julian calendar has remained in
+common use to our own day, but in commercial affairs it is there
+customary to write the date according to both calendars--e. g., July
+4/16, and at the present time strenuous exertions are making in that
+country for the adoption of the Gregorian calendar to the complete
+exclusion of the Julian one.
+
+The Julian and Gregorian calendars are frequently represented by the
+abbreviations O. S. and N. S., old style, new style, and as the older
+historical dates are usually expressed in O. S., it is sometimes
+convenient to transform a date from the one calendar to the other. This
+is readily done by the formula
+
+    G = J + (N - 2) - N/4,
+
+where _G_ and _J_ are the respective dates, _N_ is the number of the
+century, and the remainder is to be neglected in the division by 4. For
+September 3, 1752, O. S., we have
+
+        J = Sept. 3
+    N - 2 = + 15
+    - N/4 = -  4
+    ------------------
+        G = Sept. 14
+
+and September 14 is the date fixed by act of Parliament to correspond to
+September 3, 1752, O. S. Columbus discovered America on October 12,
+1492, O. S. What is the corresponding date in the Gregorian calendar?
+
+62. THE DAY OF THE WEEK.--A problem similar to the above but more
+complicated consists in finding the day of the week on which any given
+date of the Gregorian calendar falls--e. g., October 21, 1492.
+
+The formula for this case is
+
+    7q + r = Y + D + (Y - 1)/4 - (Y - 1)/100 + (Y - 1)/400
+
+where _Y_ denotes the given year, _D_ the number of the day (date) in
+that year, and _q_ and _r_ are respectively the quotient and the
+remainder obtained by dividing the second member of the equation by 7.
+If _r_ = 1 the date falls on Sunday, etc., and if _r_ = 0 the day is
+Saturday. For the example suggested above we have
+
+      Jan.  31
+      Feb.  29
+      Mch.  31
+      April 30
+      May   31
+      June  30
+      July  31
+      Aug.  31
+      Sept. 30
+      Oct.  21
+           ---
+       D = 295
+
+                  Y =  1492
+                + D = + 295
+    + (Y - 1) Ć·   4 = + 372
+    - (Y - 1) Ć· 100 = -  14
+    + (Y - 1) Ć· 400 = +   3
+                     -------
+                    7) 2148
+
+                  _q_ =   306
+                  _r_ =     6 = Friday.
+
+Find from some history the day of the week on which Columbus first saw
+America, and compare this with the above.
+
+On what day of the week did last Christmas fall? On what day of the week
+were you born? In the formula for the day of the week why does _q_ have
+the coefficient 7? What principles in the calendar give rise to the
+divisors 4, 100, 400?
+
+For much curious and interesting information about methods of reckoning
+the lapse of time the student may consult the articles Calendar and
+Chronology in any good encyclopƦdia.
+
+[Illustration: THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.]
+
+
+
+
+CHAPTER VII
+
+ECLIPSES
+
+
+63. THE NATURE OF ECLIPSES.--Every planet has a shadow which travels
+with the planet along its orbit, always pointing directly away from the
+sun, and cutting off from a certain region of space the sunlight which
+otherwise would fill it. For the most part these shadows are invisible,
+but occasionally one of them falls upon a planet or some other body
+which shines by reflected sunlight, and, cutting off its supply of
+light, produces the striking phenomenon which we call an eclipse. The
+satellites of Jupiter, Saturn, and Mars are eclipsed whenever they
+plunge into the shadows cast by their respective planets, and Jupiter
+himself is partially eclipsed when one of his own satellites passes
+between him and the sun, and casts upon his broad surface a shadow too
+small to cover more than a fraction of it.
+
+But the eclipses of most interest to us are those of the sun and moon,
+called respectively solar and lunar eclipses. In Fig. 33 the full moon,
+_MĀ“_, is shown immersed in the shadow cast by the earth, and therefore
+eclipsed, and in the same figure the new moon, _M_, is shown as casting
+its shadow upon the earth and producing an eclipse of the sun. From a
+mere inspection of the figure we may learn that an eclipse of the sun
+can occur only at new moon--i. e., when the moon is on line between the
+earth and sun--and an eclipse of the moon can occur only at full moon.
+Why? Also, the eclipsed moon, _MĀ“_, will present substantially the same
+appearance from every part of the earth where it is at all visible--the
+same from North America as from South America--but the eclipsed sun
+will present very different aspects from different parts of the earth.
+Thus, at _L_, within the moon's shadow, the sunlight will be entirely
+cut off, producing what is called a total eclipse. At points of the
+earth's surface near _J_ and _K_ there will be no interference whatever
+with the sunlight, and no eclipse, since the moon is quite off the line
+joining these regions to any part of the sun. At places between _J_ and
+_L_ or _K_ and _L_ the moon will cut off a part of the sun's light, but
+not all of it, and will produce what is called a partial eclipse, which,
+as seen from the northern parts of the earth, will be an eclipse of the
+lower (southern) part of the sun, and as seen from the southern
+hemisphere will be an eclipse of the northern part of the sun.
+
+[Illustration: FIG. 33.--Different kinds of eclipse.]
+
+The moon revolves around the earth in a plane, which, in the figure, we
+suppose to be perpendicular to the surface of the paper, and to pass
+through the sun along the line _MĀ“ M_ produced. But it frequently
+happens that this plane is turned to one side of the sun, along some
+such line as _P Q_, and in this case the full moon would cut through the
+edge of the earth's shadow without being at any time wholly immersed in
+it, giving a partial eclipse of the moon, as is shown in the figure.
+
+In what parts of the earth would this eclipse be visible? What kinds of
+solar eclipse would be produced by the new moon at _Q_? In what parts of
+the earth would they be visible?
+
+64. THE SHADOW CONE.--The shape and position of the earth's shadow are
+indicated in Fig. 33 by the lines drawn tangent to the circles which
+represent the sun and earth, since it is only between these lines that
+the earth interferes with the free radiation of sunlight, and since both
+sun and earth are spheres, and the earth is much the smaller of the two,
+it is evident that the earth's shadow must be, in geometrical language,
+a cone whose base is at the earth, and whose vertex lies far to the
+right of the figure--in other words, the earth's shadow, although very
+long, tapers off finally to a point and ends. So, too, the shadow of the
+moon is a cone, having its base at the moon and its vertex turned away
+from the sun, and, as shown in the figure, just about long enough to
+reach the earth.
+
+It is easily shown, by the theorem of similar triangles in connection
+with the known size of the earth and sun, that the distance from the
+center of the earth to the vertex of its shadow is always equal to the
+distance of the earth from the sun divided by 108, and, similarly, that
+the length of the moon's shadow is equal to the distance of the moon
+from the sun divided by 400, the moon's shadow being the smaller and
+shorter of the two, because the moon is smaller than the earth. The
+radius of the moon's orbit is just about 1/400th part of the radius of
+the earth's orbit--i. e., the distance of the moon from the earth is
+1/400th part of the distance of the earth from the sun, and it is this
+"chance" agreement between the length of the moon's shadow and the
+distance of the moon from the earth which makes the tip of the moon's
+shadow fall very near the earth at the time of solar eclipses. Indeed,
+the elliptical shape of the moon's orbit produces considerable
+variations in the distance of the moon from the earth, and in
+consequence of these variations the vertex of the shadow sometimes falls
+short of reaching the earth, and sometimes even projects considerably
+beyond its farther side. When the moon's distance is too great for the
+shadow to bridge the space between earth and moon there can be no total
+eclipse of the sun, for there is no shadow which can fall upon the
+earth, even though the moon does come directly between earth and sun.
+But there is then produced a peculiar kind of partial eclipse called
+_annular_, or ring-shaped, because the moon, although eclipsing the
+central parts of the sun, is not large enough to cover the whole of it,
+but leaves the sun's edge visible as a ring of light, which completely
+surrounds the moon. Although, strictly speaking, this is only a partial
+eclipse, it is customary to put total and annular eclipses together in
+one class, which is called central eclipses, since in these eclipses the
+line of centers of sun and moon strikes the earth, while in ordinary
+partial eclipses it passes to one side of the earth without striking it.
+In this latter case we have to consider another cone called the
+_penumbra_--i. e., partial shadow--which is shown in Fig. 33 by the
+broken lines tangent to the sun and moon, and crossing at the point _V_,
+which is the vertex of this cone. This penumbral cone includes within
+its surface all that region of space within which the moon cuts off any
+of the sunlight, and of course it includes the shadow cone which
+produces total eclipses. Wherever the penumbra falls there will be a
+solar eclipse of some kind, and the nearer the place is to the axis of
+the penumbra, the more nearly total will be the eclipse. Since the moon
+stands about midway between the earth and the vertex of the penumbra,
+the diameter of the penumbra where it strikes the earth will be about
+twice as great as the diameter of the moon, and the student should be
+able to show from this that the region of the earth's surface within
+which a partial solar eclipse is visible extends in a straight line
+about 2,100 miles on either side of the region where the eclipse is
+total. Measured along the curved surface of the earth, this distance is
+frequently much greater.
+
+Is it true that if at any time the axis of the shadow cone comes within
+2,100 miles of the earth's surface a partial eclipse will be visible in
+those parts of the earth nearest the axis of the shadow?
+
+65. DIFFERENT CHARACTERISTICS OF LUNAR AND SOLAR ECLIPSES.--One marked
+difference between lunar and solar eclipses which has been already
+suggested, may be learned from Fig. 33. The full moon, _MĀ“_, will be
+seen eclipsed from every part of the earth where it is visible at all at
+the time of the eclipse--that is, from the whole night side of the
+earth; while the eclipsed sun will be seen eclipsed only from those
+parts of the day side of the earth upon which the moon's shadow or
+penumbra falls. Since the point of the shadow at best but little more
+than reaches to the earth, the amount of space upon the earth which it
+can cover at any one moment is very small, seldom more than 100 to 200
+miles in length, and it is only within the space thus actually covered
+by the shadow that the sun is at any given moment totally eclipsed, but
+within this region the sun disappears, absolutely, behind the solid body
+of the moon, leaving to view only such outlying parts and appendages as
+are too large for the moon to cover. At a lunar eclipse, on the other
+hand, the earth coming between sun and moon cuts off the light from the
+latter, but, curiously enough, does not cut it off so completely that
+the moon disappears altogether from sight even in mid-eclipse. The
+explanation of this continued visibility is furnished by the broken
+lines extending, in Fig. 33, from the earth through the moon. These
+represent sunlight, which, entering the earth's atmosphere near the edge
+of the earth (edge as seen from sun and moon), passes through it and
+emerges in a changed direction, refracted, into the shadow cone and
+feebly illumines the moon's surface with a ruddy light like that often
+shown in our red sunsets. Eclipse and sunset alike show that when the
+sun's light shines through dense layers of air it is the red rays which
+come through most freely, and the attentive observer may often see at a
+clear sunset something which corresponds exactly to the bending of the
+sunlight into the shadow cone; just before the sun reaches the horizon
+its disk is distorted from a circle into an oval whose horizontal
+diameter is longer than the vertical one (see Ā§ 50).
+
+QUERY.--At a total lunar eclipse what would be the effect upon the
+appearance of the moon if the atmosphere around the edge of the earth
+were heavily laden with clouds?
+
+66. THE TRACK OF THE SHADOW.--We may regard the moon's shadow cone as a
+huge pencil attached to the moon, moving with it along its orbit in the
+direction of the arrowhead (Fig. 34), and as it moves drawing a black
+line across the face of the earth at the time of total eclipse. This
+black line is the path of the shadow and marks out those regions within
+which the eclipse will be total at some stage of its progress. If the
+point of the shadow just reaches the earth its trace will have no
+sensible width, while, if the moon is nearer, the point of the cone will
+be broken off, and, like a blunt pencil, it will draw a broad streak
+across the earth, and this under the most favorable circumstances may
+have a breadth of a little more than 160 miles and a length of 10,000 or
+12,000 miles. The student should be able to show from the known distance
+of the moon (240,000 miles) and the known interval between consecutive
+new moons (29.5 days) that on the average the moon's shadow sweeps past
+the earth at the rate of 2,100 miles per hour, and that in a general way
+this motion is from west to east, since that is the direction of the
+moon's motion in its orbit. The actual velocity with which the moon's
+shadow moves past a given station may, however, be considerably greater
+or less than this, since on the one hand when the shadow falls very
+obliquely, as when the eclipse occurs near sunrise or sunset, the
+shifting of the shadow will be very much greater than the actual motion
+of the moon which produces it, and on the other hand the earth in
+revolving upon its axis carries the spectator and the ground upon which
+he stands along the same direction in which the shadow is moving. At the
+equator, with the sun and moon overhead, this motion of the earth
+subtracts about 1,000 miles per hour from the velocity with which the
+shadow passes by. It is chiefly on this account, the diminished velocity
+with which the shadow passes by, that total solar eclipses last longer
+in the tropics than in higher latitudes, but even under the most
+favorable circumstances the duration of totality does not reach eight
+minutes at any one place, although it may take the shadow several hours
+to sweep the entire length of its path across the earth.
+
+According to Whitmell the greatest possible duration of a total solar
+eclipse is 7m. 40s., and it can attain this limit only when the eclipse
+occurs near the beginning of July and is visible at a place 5Ā° north of
+the equator.
+
+The duration of a lunar eclipse depends mainly upon the position of the
+moon with respect to the earth's shadow. If it strikes the shadow
+centrally, as at _MĀ“_, Fig. 33, a total eclipse may last for about two
+hours, with an additional hour at the beginning and end, during which
+the moon is entering and leaving the earth's shadow. If the moon meets
+the shadow at one side of the axis, as at _P_, the total phase of the
+eclipse may fail altogether, and between these extremes the duration of
+totality may be anything from two hours downward.
+
+[Illustration: FIG. 34.--Relation of the lunar nodes to eclipses.]
+
+67. RELATION OF THE LUNAR NODES TO ECLIPSES.--To show why the moon
+sometimes encounters the earth's shadow centrally and more frequently at
+full moon passes by without touching it at all, we resort to Fig. 34,
+which represents a part of the orbit of the earth about the sun, with
+dates showing the time in each year at which the earth passes the part
+of its orbit thus marked. The orbit of the moon about the earth, _M MĀ“_,
+is also shown, with the new moon, _M_, casting its shadow toward the
+earth and the full moon, _MĀ“_, apparently immersed in the earth's
+shadow. But here appearances are deceptive, and the student who has
+made the observations set forth in Chapter III has learned for himself
+a fact of which careful account must now be taken. The apparent paths of
+the moon and sun among the stars are great circles which lie near each
+other, but are not exactly the same; and since these great circles are
+only the intersections of the sky with the planes of the earth's orbit
+and the moon's orbit, we see that these planes are slightly inclined to
+each other and must therefore intersect along some line passing through
+the center of the earth. This line, _NĀ“ NĀ“Ā“_, is shown in the figure,
+and if we suppose the surface of the paper to represent the plane of the
+earth's orbit, we shall have to suppose the moon's orbit to be tipped
+around this line, so that the left side of the orbit lies above and the
+right side below the surface of the paper. But since the earth's shadow
+lies in the plane of its orbit--i. e., in the surface of the paper--the
+full moon of March, _MĀ“_, must have passed below the shadow, and the new
+moon, _M_, must have cast its shadow above the earth, so that neither a
+lunar nor a solar eclipse could occur in that month. But toward the end
+of May the earth and moon have reached a position where the line
+_NĀ“ NĀ“Ā“_ points almost directly toward the sun, in line with the shadow
+cones which hide it. Note that the line _NĀ“ NĀ“Ā“_ remains very nearly
+parallel to its original position, while the earth is moving along its
+orbit. The full moon will now be very near this line and therefore very
+close to the plane of the earth's orbit, if not actually in it, and must
+pass through the shadow of the earth and be eclipsed. So also the new
+moon will cast its shadow in the plane of the ecliptic, and this shadow,
+falling upon the earth, produced the total solar eclipse of May 28,
+1900.
+
+_NĀ“ NĀ“Ā“_ is called the line of nodes of the moon's orbit (Ā§ 39), and the
+two positions of the earth in its orbit, diametrically opposite each
+other, at which _NĀ“ NĀ“Ā“_ points exactly toward the sun, we shall call
+the _nodes_ of the lunar orbit. Strictly speaking, the nodes are those
+points of the sky against which the moon's center is projected at the
+moment when in its orbital motion it cuts through the plane of the
+earth's orbit. Bearing in mind these definitions, we may condense much
+of what precedes into the proposition: Eclipses of either sun or moon
+can occur only when the earth is at or near one of the nodes of the
+moon's orbit. Corresponding to these positions of the earth there are in
+each year two seasons, about six months apart, at which times, and at
+these only, eclipses can occur. Thus in the year 1900 the earth passed
+these two points on June 2d and November 24th respectively, and the
+following list of eclipses which occurred in that year shows that all of
+them were within a few days of one or the other of these dates:
+
+        _Eclipses of the Year 1900_
+
+    Total solar eclipse          May 28th.
+    Partial lunar eclipse        June 12th.
+    Annular (solar) eclipse      November 21st.
+
+68. ECLIPSE LIMITS.--If the earth is exactly at the node at the time of
+new moon, the moon's shadow will fall centrally upon it and will produce
+an eclipse visible within the torrid zone, since this is that part of
+the earth's surface nearest the plane of its orbit. If the earth is near
+but not at the node, the new moon will stand a little north or south of
+the plane of the earth's orbit, and its shadow will strike the earth
+farther north or south than before, producing an eclipse in the
+temperate or frigid zones; or the shadow may even pass entirely above or
+below the earth, producing no eclipse whatever, or at most a partial
+eclipse visible near the north or south pole. Just how many days' motion
+the earth may be away from the node and still permit an eclipse is shown
+in the following brief table of eclipse limits, as they are called:
+
+                  _Solar Eclipse Limits_
+
+  If at any new moon the earth is
+
+  Less than 10 days away from a node, a central eclipse is certain.
+  Between 10 and 16 days   "  "  "    some kind of eclipse is certain.
+  Between 16 and 19 days   "  "  "    a partial eclipse is possible.
+  More than 19 days        "  "  "    no eclipse is possible.
+
+                _Lunar Eclipse Limits_
+
+  If at any full moon the earth is
+
+  Less than 4 days away from a node, a total eclipse is certain.
+  Between 4 and 10 days   "  "  "    some kind of eclipse is certain.
+  Between 10 and 14 days  "  "  "    a partial eclipse is possible.
+  More than 14 days       "  "  "    no eclipse is possible.
+
+From this table of eclipse limits we may draw some interesting
+conclusions about the frequency with which eclipses occur.
+
+69. NUMBER OF ECLIPSES IN A YEAR.--Whenever the earth passes a node of
+the moon's orbit a new moon must occur at some time during the 2 Ɨ 16
+days that the earth remains inside the limits where some kind of eclipse
+is certain, and there must therefore be an eclipse of the sun every time
+the earth passes a node of the moon's orbit. But, since there are two
+nodes past which the earth moves at least once in each year, there must
+be at least two solar eclipses every year. Can there be more than two?
+On the average, will central or partial eclipses be the more numerous?
+
+A similar line of reasoning will not hold true for eclipses of the moon,
+since it is quite possible that no full moon should occur during the 20
+days required by the earth to move past the node from the western to the
+eastern limit. This omission of a full moon while the earth is within
+the eclipse limits sometimes happens at both nodes in the same year, and
+then we have a year with no eclipse of the moon. The student may note in
+the list of eclipses for 1900 that the partial lunar eclipse of June
+12th occurred 10 days after the earth passed the node, and was therefore
+within the doubtful zone where eclipses may occur and may fail, and
+corresponding to this position the eclipse was a very small one, only a
+thousandth part of the moon's diameter dipping into the shadow of the
+earth. By so much the year 1900 escaped being an illustration of a year
+in which no lunar eclipse occurred.
+
+A partial eclipse of the moon will usually occur about a fortnight
+before or after a total eclipse of the sun, since the full moon will
+then be within the eclipse limit at the opposite node. A partial eclipse
+of the sun will always occur about a fortnight before or after a total
+eclipse of the moon.
+
+[Illustration: FIG. 35.--The eclipse of May 28, 1900.]
+
+70. ECLIPSE MAPS.--It is the custom of astronomers to prepare, in
+advance of the more important eclipses, maps showing the trace of the
+moon's shadow across the earth, and indicating the times of beginning
+and ending of the eclipses, as is shown in Fig. 35. While the actual
+construction of such a map requires much technical knowledge, the
+principles involved are simple enough: the straight line passed through
+the center of sun and moon is the axis of the shadow cone, and the map
+contains little more than a graphical representation of when and where
+this cone meets the surface of the earth. Thus in the map, the "Path of
+Total Eclipse" is the trace of the shadow cone across the face of the
+earth, and the width of this path shows that the earth encountered the
+shadow considerably inside the vertex of the cone. The general direction
+of the path is from west to east, and the slight sinuousities which it
+presents are for the most part due to unavoidable distortion of the
+map caused by the attempt to represent the curved surface of the earth
+upon the flat surface of the paper. On either side of the Path of Total
+Eclipse is the region within which the eclipse was only partial, and the
+broken lines marked Begins at 3h., Ends at 3h., show the intersection of
+the penumbral cone with the surface of the earth at 3 P. M., Greenwich
+time. These two lines inclose every part of the earth's surface from
+which at that time any eclipse whatever could be seen, and at this
+moment the partial eclipse was just beginning at every point on the
+eastern edge of the penumbra and just ending at every point on the
+western edge, while at the center of the penumbra, on the Path of Total
+Eclipse, lay the shadow of the moon, an oval patch whose greatest
+diameter was but little more than 60 miles in length, and within which
+lay every part of the earth where the eclipse was total at that moment.
+
+The position of the penumbra at other hours is also shown on the map,
+although with more distortion, because it then meets the surface of the
+earth more obliquely, and from these lines it is easy to obtain the time
+of beginning and end of the eclipse at any desired place, and to
+estimate by the distance of the place from the Path of Total Eclipse how
+much of the sun's face was obscured.
+
+Let the student make these "predictions" for Washington, Chicago,
+London, and Algiers.
+
+The points in the map marked First Contact, Last Contact, show the
+places at which the penumbral cone first touched the earth and finally
+left it. According to computations made as a basis for the construction
+of the map the Greenwich time of First Contact was 0h. 12.5m. and of
+Last Contact 5h. 35.6m., and the difference between these two times
+gives the total duration of the eclipse upon the earth--i. e., 5 hours
+23.1 minutes.
+
+[Illustration: FIG. 36.--Central eclipses for the first two decades of
+the twentieth century. OPPOLZER.]
+
+71. FUTURE ECLIPSES.--An eclipse map of a different kind is shown in
+Fig. 36, which represents the shadow paths of all the central eclipses
+of the sun, visible during the period 1900-1918 A. D., in those parts of
+the earth north of the south temperate zone. Each continuous black line
+shows the path of the shadow in a total eclipse, from its beginning, at
+sunrise, at the western end of the line to its end, sunset, at the
+eastern end, the little circle near the middle of the line showing the
+place at which the eclipse was total at noon. The broken lines represent
+similar data for the annular eclipses. This map is one of a series
+prepared by the Austrian astronomer, Oppolzer, showing the path of every
+such eclipse from the year 1200 B. C. to 2160 A. D., a period of more
+than three thousand years.
+
+If we examine the dates of the eclipses shown in this map we shall find
+that they are not limited to the particular seasons, May and November,
+in which those of the year 1900 occurred, but are scattered through all
+the months of the year, from January to December. This shows at once
+that the line of nodes, _NĀ“ NĀ“Ā“_, of Fig. 34, does not remain in a fixed
+position, but turns round in the plane of the earth's orbit so that in
+different years the earth reaches the node in different months. The
+precession has already furnished us an illustration of a similar change,
+the slow rotation of the earth's axis, producing a corresponding
+shifting of the line in which the planes of the equator and ecliptic
+intersect; and in much the same way, through the disturbing influence of
+the sun's attraction, the line _NĀ“ NĀ“Ā“_ is made to revolve westward,
+opposite to the arrowheads in Fig. 34, at the rate of nearly 20Ā° per
+year, so that the earth comes to each node about 19 days earlier in each
+year than in the year preceding, and the eclipse season in each year
+comes on the average about 19 days earlier than in the year before,
+although there is a good deal of irregularity in the amount of change in
+particular years.
+
+72. RECURRENCE OF ECLIPSES.--Before the beginning of the Christian era
+astronomers had found out a rough-and-ready method of predicting
+eclipses, which is still of interest and value. The substance of the
+method is that if we start with any eclipse whatever--e. g., the eclipse
+of May 28, 1900--and reckon forward or backward from that date a period
+of 18 years and 10 or 11 days, we shall find another eclipse quite
+similar in its general characteristics to the one with which we started.
+Thus, from the map of eclipses (Fig. 36), we find that a total solar
+eclipse will occur on June 8, 1918, 18 years and 11 days after the one
+illustrated in Fig. 35. This period of 18 years and 11 days is called
+_saros_, an ancient word which means cycle or repetition, and since
+every eclipse is repeated after the lapse of a saros, we may find the
+dates of all the eclipses of 1918 by adding 11 days to the dates given
+in the table of eclipses for 1900 (Ā§ 67), and it is to be especially
+noted that each eclipse of 1918 will be like its predecessor of 1900 in
+character--lunar, solar, partial, total, etc. The eclipses of any year
+may be predicted by a similar reference to those which occurred eighteen
+years earlier. Consult a file of old almanacs.
+
+The exact length of a saros is 223 lunar months, each of which is a
+little more than 29.5 days long, and if we multiply the exact value of
+this last number (see Ā§ 60) by 223, we shall find for the product
+6,585.32 days, which is equal to 18 years 11.32 days when there are four
+leap years included in the 18, or 18 years 10.32 days when the number of
+leap years is five; and in applying the saros to the prediction of
+eclipses, due heed must be paid to the number of intervening leap years.
+To explain why eclipses are repeated at the end of the saros, we note
+that the occurrence of an eclipse depends solely upon the relative
+positions of the earth, moon, and node of the moon's orbit, and the
+eclipse will be repeated as often as these three come back to the
+position which first produced it. This happens at the end of every
+saros, since the saros is, approximately, the least common multiple of
+the length of the year, the length of the lunar month, and the length of
+time required by the line of nodes to make a complete revolution around
+the ecliptic. If the saros were exactly a multiple of these three
+periods, every eclipse would be repeated over and over again for
+thousands of years; but such is not the case, the saros is not an exact
+multiple of a year, nor is it an exact multiple of the time required for
+a revolution of the line of nodes, and in consequence the restitution
+which comes at the end of the saros is not a perfect one. The earth at
+the 223d new moon is in fact about half a day's motion farther west,
+relative to the node, than it was at the beginning, and the resulting
+eclipse, while very similar, is not precisely the same as before. After
+another 18 years, at the second repetition, the earth is a day farther
+from the node than at first, and the eclipse differs still more in
+character, etc. This is shown in Fig. 37, which represents the apparent
+positions of the disks of the sun and moon as seen from the center of
+the earth at the end of each sixth saros, 108 years, where the upper row
+of figures represents the number of repetitions of the eclipse from the
+beginning, marked _0_, to the end, _72_. The solar eclipse limits, 10,
+16, 19 days, are also shown, and all those eclipses which fall between
+the 10-day limits will be central as seen from some part of the earth,
+those between 16 and 19 partial wherever seen, while between 10 and 16
+they may be either total or partial. Compare the figure with the
+following description given by Professor Newcomb: "A series of such
+eclipses commences with a very small eclipse near one pole of the earth.
+Gradually increasing for about eleven recurrences, it will become
+central near the same pole. Forty or more central eclipses will then
+recur, the central line moving slowly toward the other pole. The series
+will then become partial, and finally cease. The entire duration of the
+series will be more than a thousand years. A new series commences, on
+the average, at intervals of thirty years."
+
+[Illustration: FIG. 37.--Graphical illustration of the saros.]
+
+A similar figure may be constructed to represent the recurrence of lunar
+eclipses; but here, in consequence of the smaller eclipse limits, we
+shall find that a series is of shorter duration, a little over eight
+centuries as compared with twelve centuries, which is the average
+duration of a series of solar eclipses.
+
+One further matter connected with the saros deserves attention. During
+the period of 6,585.32 days the earth has 6,585 times turned toward the
+sun the same face upon which the moon's shadow fell at the beginning of
+the saros, but at the end of the saros the odd 0.32 of a day gives the
+earth time to make about a third of a revolution more before the eclipse
+is repeated, and in consequence the eclipse is seen in a different
+region of the earth, on the average about 116Ā° farther west in
+longitude. Compare in Fig. 36 the regions in which the eclipses of 1900
+and 1918 are visible.
+
+Is this change in the region where the repeated eclipse is visible, true
+of lunar eclipses as well as solar?
+
+73. USE OF ECLIPSES.--At all times and among all peoples eclipses, and
+particularly total eclipses of the sun, have been reckoned among the
+most impressive phenomena of Nature. In early times and among
+uncultivated people they were usually regarded with apprehension, often
+amounting to a terror and frenzy, which civilized travelers have not
+scrupled to use for their own purposes with the aid of the eclipse
+predictions contained in their almanacs, threatening at the proper time
+to destroy the sun or moon, and pointing to the advancing eclipse as
+proof that their threats were not vain. In our own day and our own land
+these feelings of awe have not quite disappeared, but for the most part
+eclipses are now awaited with an interest and pleasure which, contrasted
+with the former feelings of mankind, furnish one of the most striking
+illustrations of the effect of scientific knowledge in transforming
+human fear and misery into a sense of security and enjoyment.
+
+But to the astronomer an eclipse is more than a beautiful illustration
+of the working of natural laws; it is in varying degree an opportunity
+of adding to his store of knowledge respecting the heavenly bodies. The
+region immediately surrounding the sun is at most times closed to
+research by the blinding glare of the sun's own light, so that a planet
+as large as the moon might exist here unseen were it not for the
+occasional opportunity presented by a total eclipse which shuts off the
+excessive light and permits not only a search for unknown planets but
+for anything and everything which may exist around the sun. More than
+one astronomer has reported the discovery of such planets, and at least
+one of these has found a name and a description in some of the books,
+but at the present time most astronomers are very skeptical about the
+existence of any such object of considerable size, although there is
+some reason to believe that an enormous number of little bodies, ranging
+in size from grains of sand upward, do move in this region, as yet
+unseen and offering to the future problems for investigation.
+
+But in other directions the study of this region at the times of total
+eclipse has yielded far larger returns, and in the chapter on the sun we
+shall have to consider the marvelous appearances presented by the solar
+prominences and by the corona, an appendage of the sun which reaches out
+from his surface for millions of miles but is never seen save at an
+eclipse. Photographs of the corona are taken by astronomers at every
+opportunity, and reproductions of some of these may be found in Chapter
+X.
+
+Annular eclipses and lunar eclipses are of comparatively little
+consequence, but any recorded eclipse may become of value in connection
+with chronology. We date our letters in a particular year of the
+twentieth century, and commonly suppose that the years are reckoned from
+the birth of Christ; but this is an error, for the eclipses which were
+observed of old and by the chroniclers have been associated with events
+of his life, when examined by the astronomers are found quite
+inconsistent with astronomic theory. They are, however, reconciled with
+it if we assume that our system of dates has its origin four years after
+the birth of Christ, or, in other words, that Christ was born in the
+year 4 B. C. A mistake was doubtless made at the time the Christian era
+was introduced into chronology. At many other points the chance record
+of an eclipse in the early annals of civilization furnishes a similar
+means of controlling and correcting the dates assigned by the historian
+to events long past.
+
+
+
+
+CHAPTER VIII
+
+INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE
+
+
+74. TWO FAMILIAR INSTRUMENTS.--In previous chapters we have seen that a
+clock and a divided circle (protractor) are needed for the observations
+which an astronomer makes, and it is worth while to note here that the
+geography of the sky and the science of celestial motions depend
+fundamentally upon these two instruments. The protractor is a simple
+instrument, a humble member of the family of divided circles, but untold
+labor and ingenuity have been expended on this family to make possible
+the construction of a circle so accurately divided that with it angles
+may be measured to the tenth of a second instead of to the tenth of a
+degree--i. e., 3,600 times as accurate as the protractor furnishes.
+
+The building of a good clock is equally important and has cost a like
+amount of labor and pains, so that it is a far cry from Galileo and his
+discovery that a pendulum "keeps time" to the modern clock with its
+accurate construction and elaborate provision against disturbing
+influences of every kind. Every such timepiece, whether it be of the
+nutmeg variety which sells for a dollar, or whether it be the standard
+clock of a great national observatory, is made up of the same essential
+parts that fall naturally into four classes, which we may compare with
+the departments of a well-ordered factory: I. A timekeeping department,
+the pendulum or balance spring, whose oscillations must all be of equal
+duration. II. A power department, the weights or mainspring, which,
+when wound, store up the power applied from outside and give it out
+piecemeal as required to keep the first department running. III. A
+publication department, the dial and hands, which give out the time
+furnished by Department I. IV. A transportation department, the wheels,
+which connect the other three and serve as a means of transmitting power
+and time from one to the other. The case of either clock or watch is
+merely the roof which shelters it and forms no department of its
+industry. Of these departments the first is by far the most important,
+and its good or bad performance makes or mars the credit of the clock.
+Beware of meddling with the balance wheel of your watch.
+
+75. RADIANT ENERGY.--But we have now to consider other instruments which
+in practice supplement or displace the simple apparatus hitherto
+employed. Among the most important of these modern instruments are the
+telescope, the spectroscope, and the photographic camera; and since all
+these instruments deal with the light which comes from the stars to the
+earth, we must for their proper understanding take account of the nature
+of that light, or, more strictly speaking, we must take account of the
+radiant energy emitted by the sun and stars, which energy, coming from
+the sun, is translated by our nerves into the two different sensations
+of light and heat. The radiant energy which comes from the stars is not
+fundamentally different from that of the sun, but the amount of energy
+furnished by any star is so small that it is unable to produce through
+our nerves any sensible perception of heat, and for the same reason the
+vast majority of stars are invisible to the unaided eye; they do not
+furnish a sufficient amount of energy to affect the optic nerves. A hot
+brick taken into the hand reveals its presence by the two different
+sensations of heat and pressure (weight); but as there is only one brick
+to produce the two sensations, so there is only one energy to produce
+through its action upon different nerves the two sensations of light
+and heat, and this energy is called _radiant_ because it appears to
+stream forth radially from everything which has the capacity of emitting
+it. For the detailed study of radiant energy the student is referred to
+that branch of science called physics; but some of its elementary
+principles may be learned through the following simple experiment, which
+the student should not fail to perform for himself:
+
+Drop a bullet or other similar object into a bucket of water and observe
+the circular waves which spread from the place where it enters the
+water. These waves are a form of radiant energy, but differing from
+light or heat in that they are visibly confined to a single plane, the
+surface of the water, instead of filling the entire surrounding space.
+By varying the size of the bucket, the depth of the water, the weight of
+the bullet, etc., different kinds of waves, big and little, may be
+produced; but every such set of waves may be described and defined in
+all its principal characteristics by means of three numbers--viz., the
+vertical height of the waves from hollow to crest; the distance of one
+wave from the next; and the velocity with which the waves travel across
+the water. The last of these quantities is called the velocity of
+propagation; the second is called the wave length; one half of the first
+is called the amplitude; and all these terms find important applications
+in the theory of light and heat.
+
+The energy of the falling bullet, the disturbance which it produced on
+entering the water, was carried by the waves from the center to the edge
+of the bucket but not beyond, for the wave can go only so far as the
+water extends. The transfer of energy in this way requires a perfectly
+continuous medium through which the waves may travel, and the whole
+visible universe is supposed to be filled with something called _ether_,
+which serves everywhere as a medium for the transmission of radiant
+energy just as the water in the experiment served as a medium for
+transmitting in waves the energy furnished to it by the falling bullet.
+The student may think of this energy as being transmitted in spherical
+waves through the ether, every glowing body, such as a star, a candle
+flame, an arc lamp, a hot coal, etc., being the origin and center of
+such systems of waves, and determining by its own physical and chemical
+properties the wave length and amplitude of the wave systems given off.
+
+The intensity of any light depends upon the amplitude of the
+corresponding vibration, and its color depends upon the wave length. By
+ingenious devices which need not be here described it has been found
+possible to measure the wave length corresponding to different
+colors--e. g., all of the colors of the rainbow, and some of these wave
+lengths expressed in tenth meters are as follows: A tenth meter is the
+length obtained by dividing a meter into 10^{10} equal parts. 10^{10} =
+10,000,000,000.
+
+                 Color.               Wave length.
+
+    Extreme limit of visible violet      3,900
+    Middle of the violet                 4,060
+      "      "    blue                   4,730
+      "      "    green                  5,270
+      "      "    yellow                 5,810
+      "      "    orange                 5,970
+      "      "    red                    7,000
+    Extreme limit of visible red         7,600
+
+[Illustration: PLATE I. THE NORTHERN CONSTELLATIONS]
+
+The phrase "extreme limit of visible violet" or red used above must be
+understood to mean that in general the eye is not able to detect radiant
+energy having a wave length less than 3,900 or greater than 7,600 tenth
+meters. Radiant energy, however, exists in waves of both greater and
+shorter length than the above, and may be readily detected by apparatus
+not subject to the limitations of the human eye--e. g., a common
+thermometer will show a rise of temperature when its bulb is exposed to
+radiant energy of wave length much greater than 7,600 tenth meters,
+and a photographic plate will be strongly affected by energy of
+shorter wave length than 3,900 tenth meters.
+
+76. REFLECTION AND CONDENSATION OF WAVES.--When the waves produced by
+dropping a bullet into a bucket of water meet the sides of the bucket,
+they appear to rebound and are reflected back toward the center, and if
+the bullet is dropped very near the center of the bucket the reflected
+waves will meet simultaneously at this point and produce there by their
+combined action a wave higher than that which was reflected at the walls
+of the bucket. There has been a condensation of energy produced by the
+reflection, and this increased energy is shown by the greater amplitude
+of the wave. The student should not fail to notice that each portion of
+the wave has traveled out and back over the radius of the bucket, and
+that they meet simultaneously at the center because of this equality of
+the paths over which they travel, and the resulting equality of time
+required to go out and back. If the bullet were dropped at one side of
+the center, would the reflected waves produce _at any point_ a
+condensation of energy?
+
+If the bucket were of elliptical instead of circular cross section and
+the bullet were dropped at one focus of the ellipse there would be
+produced a condensation of reflected energy at the other focus, since
+the sum of the paths traversed by each portion of the wave before and
+after reflection is equal to the sum of the paths traversed by every
+other portion, and all parts of the wave reach the second focus at the
+same time. Upon what geometrical principle does this depend?
+
+The condensation of wave energy in the circular and elliptical buckets
+are special cases under the general principle that such a condensation
+will be produced at any point which is so placed that different parts of
+the wave front reach it simultaneously, whether by reflection or by some
+other means, as shown below.
+
+The student will note that for the sake of greater precision we here
+say _wave front_ instead of wave. If in any wave we imagine a line drawn
+along the crest, so as to touch every drop which at that moment is
+exactly at the crest, we shall have what is called a wave front, and
+similarly a line drawn through the trough between two waves, or through
+any set of drops similarly placed on a wave, constitutes a wave front.
+
+77. MIRRORS AND LENSES.--That form of radiant energy which we recognize
+as light and heat may be reflected and condensed precisely as are the
+waves of water in the exercise considered above, but owing to the
+extreme shortness of the wave length in this case the reflecting surface
+should be very smooth and highly polished. A piece of glass hollowed out
+in the center by grinding, and with a light film of silver chemically
+deposited upon the hollow surface and carefully polished, is often used
+by astronomers for this purpose, and is called a concave mirror.
+
+The radiant energy coming from a star or other distant object and
+falling upon the silvered face of such a mirror is reflected and
+condensed at a point a little in front of the mirror, and there forms an
+image of the star, which may be seen with the unaided eye, if it is held
+in the right place, or may be examined through a magnifying glass.
+Similarly, an image of the sun, a planet, or a distant terrestrial
+object is formed by the mirror, which condenses at its appropriate place
+the radiant energy proceeding from each and every point in the surface
+of the object, and this, in common phrase, produces an image of the
+object.
+
+Another device more frequently used by astronomers for the production of
+images (condensation of energy) is a lens which in its simplest form is
+a round piece of glass, thick in the center and thin at the edge, with a
+cross section, such as is shown at _A B_ in Fig. 38. If we suppose _E G
+D_ to represent a small part of a wave front coming from a very distant
+source of radiant energy, such as a star, this wave front will be
+practically a plane surface represented by the straight line _E D_, but
+in passing through the lens this surface will become warped, since light
+travels slower in glass than in air, and the central part of the beam,
+_G_, in its onward motion will be retarded by the thick center of the
+lens, more than _E_ or _D_ will be retarded by the comparatively thin
+outer edges of _A B_. On the right of the lens the wave front therefore
+will be transformed into a curved surface whose exact character depends
+upon the shape of the lens and the kind of glass of which it is made. By
+properly choosing these the new wave front may be made a part of a
+sphere having its center at the point _F_ and the whole energy of the
+wave front, _E G D_, will then be condensed at _F_, because this point
+is equally distant from all parts of the warped wave front, and
+therefore is in a position to receive them simultaneously. The distance
+of _F_ from _A B_ is called the focal length of the lens, and _F_ itself
+is called the focus. The significance of this last word (Latin, _focus_
+= fireplace) will become painfully apparent to the student if he will
+hold a common reading glass between his hand and the sun in such a way
+that the focus falls upon his hand.
+
+[Illustration: FIG. 38.--Illustrating the theory of lenses.]
+
+All the energy transmitted by the lens in the direction _G F_ is
+concentrated upon a very small area at _F_, and an image of the
+object--e. g., a star, from which the light came--is formed here. Other
+stars situated near the one in question will also send beams of light
+along slightly different directions to the lens, and these will be
+concentrated, each in its appropriate place, in the _focal plane_,
+_F H_, passed through the focus, _F_, perpendicular to the line, _F G_,
+and we shall find in this plane a picture of all the stars or other
+objects within the range of the lens.
+
+[Illustration: FIG. 39.--Essential parts of a reflecting telescope.]
+
+78. TELESCOPES.--The simplest kind of telescope consists of a concave
+mirror to produce images, and a magnifying glass, called an _eyepiece_,
+through which to examine them; but for convenience' sake, so that the
+observer may not stand in his own light, a small mirror is frequently
+added to this combination, as at _H_ in Fig. 39, where the lines
+represent the directions along which the energy is propagated. By
+reflection from this mirror the focal plane and the images are shifted
+to _F_, where they may be examined from one side through the magnifying
+glass _E_.
+
+[Illustration: FIG. 40.--A simple form of refracting telescope.]
+
+Such a combination of parts is called a _reflecting_ telescope, while
+one in which the images are produced by a lens or combination of lenses
+is called a _refracting_ telescope, the adjective having reference to
+the bending, refraction, produced by the glass upon the direction in
+which the energy is propagated. The customary arrangement of parts in
+such a telescope is shown in Fig. 40, where the part marked _O_ is
+called the objective and _V E_ (the magnifying glass) is the eyepiece,
+or ocular, as it is sometimes called.
+
+Most objects with which we have to deal in using a telescope send to it
+not light of one color only, but a mixture of light of many colors,
+many different wave lengths, some of which are refracted more than
+others by the glass of which the lens is composed, and in consequence of
+these different amounts of refraction a single lens does not furnish a
+single image of a star, but gives a confused jumble of red and yellow
+and blue images much inferior in sharpness of outline (definition) to
+the images made by a good concave mirror. To remedy this defect it is
+customary to make the objective of two or more pieces of glass of
+different densities and ground to different shapes as is shown at _O_ in
+Fig. 40. The two pieces of glass thus mounted in one frame constitute a
+compound lens having its own focal plane, shown at _F_ in the figure,
+and similarly the lenses composing the eyepiece have a focal plane
+between the eyepiece and the objective which must also fall at _F_, and
+in the use of a telescope the eyepiece must be pushed out or in until
+its focal plane coincides with that of the objective. This process,
+which is called focusing, is what is accomplished in the ordinary opera
+glass by turning a screw placed between the two tubes, and it must be
+carefully done with every telescope in order to obtain distinct vision.
+
+79. MAGNIFYING POWER.--The amount by which a given telescope magnifies
+depends upon the focal length of the objective (or mirror) and the focal
+length of the eyepiece, and is equal to the ratio of these two
+quantities. Thus in Fig. 40 the distance of the objective from the focal
+plane _F_ is about 16 times as great as the distance of the eyepiece
+from the same plane, and the magnifying power of this telescope is
+therefore 16 diameters. A magnifying power of 16 diameters means that
+the diameter of any object seen in the telescope looks 16 times as large
+as it appears without the telescope, and is nearly equivalent to saying
+that the object appears only one sixteenth as far off. Sometimes the
+magnifying power is assumed to be the number of times that the _area_ of
+an object seems increased; and since areas are proportional to the
+squares of lines, the magnifying power of 16 diameters might be called
+a power of 256. Every large telescope is provided with several eyepieces
+of different focal lengths, ranging from a quarter of an inch to two and
+a half inches, which are used to furnish different magnifying powers as
+may be required for the different kinds of work undertaken with the
+instrument. Higher powers can be used with large telescopes than with
+small ones, but it is seldom advantageous to use with any telescope an
+eyepiece giving a higher power than 60 diameters for each inch of
+diameter of the objective.
+
+The part played by the eyepiece in determining magnifying power will be
+readily understood from the following experiment:
+
+Make a pin hole in a piece of cardboard. Bring a printed page so close
+to one eye that you can no longer see the letters distinctly, and then
+place the pin hole between the eye and the page. The letters which were
+before blurred may now be seen plainly through the pin hole, even when
+the page is brought nearer to the eye than before. As it is brought
+nearer, notice how the letters seem to become larger, solely because
+they are nearer. A pin hole is the simplest kind of a magnifier, and the
+eyepiece in a telescope plays the same part as does the pin hole in the
+experiment; it enables the eye to be brought nearer to the image, and
+the shorter the focal length of the eyepiece the nearer is the eye
+brought to the image and the higher is the magnifying power.
+
+80. THE EQUATORIAL MOUNTING.--Telescopes are of all sizes, from the
+modest opera glass which may be carried in the pocket and which requires
+no other support than the hand, to the giant which must have a special
+roof to shelter it and elaborate machinery to support and direct it
+toward the sky. But for even the largest telescopes this machinery
+consists of the following parts, which are illustrated, with exception
+of the last one, in the small equatorial telescope shown in Fig. 41. It
+is not customary to place a driving clock on so small a telescope as
+this:
+
+(_a_) A supporting pier or tripod.
+
+(_b_) An axis placed parallel to the axis of the earth.
+
+(_c_) Another axis at right angles to _b_ and capable of revolving upon
+_b_ as an axle.
+
+(_d_) The telescope tube attached to _c_ and capable of revolving about
+_c_.
+
+(_e_) Graduated circles attached to _c_ and _b_ to measure the amount by
+which the telescope is turned on these axes.
+
+(_f_) A driving clock so connected with _b_ as to make _c_ (and _d_)
+revolve about _b_ with an angular velocity equal and opposite to that
+with which the earth turns upon its axis.
+
+[Illustration: FIG. 41.--A simple equatorial mounting.]
+
+[Illustration: FIG. 42.--Equatorial mounting of the great telescope of
+the Yerkes Observatory.]
+
+Such a support is called an equatorial mounting, and the student should
+note from the figure that the circles, _e_, measure the hour angle and
+declination of any star toward which the telescope is directed, and
+conversely if the telescope be so set that these circles indicate the
+hour angle and declination of any given star, the telescope will then
+point toward that star. In this way it is easy to find with the
+telescope any moderately bright star, even in broad daylight, although
+it is then absolutely invisible to the naked eye. The rotation of the
+earth about its axis will speedily carry the telescope away from the
+star, but if the driving clock be started, its effect is to turn the
+telescope toward the west just as fast as the earth's rotation carries
+it toward the east, and by these compensating motions to keep it
+directed toward the star. In Fig. 42, which represents the largest and
+one of the most perfect refracting telescopes ever built, let the
+student pick out and identify the several parts of the mounting above
+described. A part of the driving clock may be seen within the head of
+the pier. In Fig. 43 trace out the corresponding parts in the mounting
+of a reflecting telescope.
+
+[Illustration: FIG. 43.--The reflecting telescope of the Paris
+Observatory.]
+
+A telescope is often only a subordinate part of some instrument or
+apparatus, and then its style of mounting is determined by the
+requirements of the special case; but when the telescope is the chief
+thing, and the remainder of the apparatus is subordinate to it, the
+equatorial mounting is almost always adopted, although sometimes the
+arrangement of the parts is very different in appearance from any of
+those shown above. Beware of the popular error that an object held close
+in front of a telescope can be seen by an observer at the eyepiece. The
+numerous stories of astronomers who saw spiders crawling over the
+objective of their telescope, and imagined they were beholding strange
+objects in the sky, are all fictitious, since nothing on or near the
+objective could possibly be seen through the telescope.
+
+81. PHOTOGRAPHY.--A photographic camera consists of a lens and a device
+for holding at its focus a specially prepared plate or film. This plate
+carries a chemical deposit which is very sensitive to the action of
+light, and which may be made to preserve the imprint of any picture
+which the lens forms upon it. If such a sensitive plate is placed at the
+focus of a reflecting telescope, the combination becomes a camera
+available for astronomical photography, and at the present time the
+tendency is strong in nearly every branch of astronomical research to
+substitute the sensitive plate in place of the observer at a telescope.
+A refracting telescope may also be used for astronomical photography,
+and is very much used, but some complications occur here on account of
+the resolution of the light into its constituent colors in passing
+through the objective. Fig. 44 shows such a telescope, or rather two
+telescopes, one photographic, the other visual, supported side by side
+upon the same equatorial mounting.
+
+[Illustration: FIG. 44.--Photographic telescope of the Paris
+Observatory.]
+
+One of the great advantages of photography is found in connection with
+what is called--
+
+82. PERSONAL EQUATION.--It is a remarkable fact, first investigated by
+the German astronomer Bessel, three quarters of a century ago, that
+where extreme accuracy is required the human senses can not be
+implicitly relied upon. The most skillful observers will not agree
+exactly in their measurement of an angle or in estimating the exact
+instant at which a star crossed the meridian; the most skillful artists
+can not draw identical pictures of the same object, etc.
+
+These minor deceptions of the senses are included in the term _personal
+equation_, which is a famous phrase in astronomy, denoting that the
+observations of any given person require to be corrected by means of
+some equation involving his personality.
+
+General health, digestion, nerves, fatigue, all influence the personal
+equation, and it was in reference to such matters that one of the most
+eminent of living astronomers has given this description of his habits
+of observing:
+
+"In order to avoid every physiological disturbance, I have adopted the
+rule to abstain for one or two hours before commencing observations from
+every laborious occupation; never to go to the telescope with stomach
+loaded with food; to abstain from everything which could affect the
+nervous system, from narcotics and alcohol, and especially from the
+abuse of coffee, which I have found to be exceedingly prejudicial to the
+accuracy of observation."[3] A regimen suggestive of preparation for an
+athletic contest rather than for the more quiet labors of an astronomer.
+
+  [3] Schiaparelli, Osservazioni sulle Stelle Doppie.
+
+83. VISUAL AND PHOTOGRAPHIC WORK.--The photographic plate has no stomach
+and no nerves, and is thus free from many of the sources of error which
+inhere in visual observations, and in special classes of work it
+possesses other marked advantages, such as rapidity when many stars are
+to be dealt with simultaneously, permanence of record, and owing to the
+cumulative effect of long exposure of the plate it is possible to
+photograph with a given telescope stars far too faint to be seen through
+it. On the other hand, the eye has the advantage in some respects, such
+as studying the minute details of a fairly bright object--e. g., the
+surface of a planet, or the sun's corona and, for the present at least,
+neither method of observing can exclude the other. For a remarkable case
+of discordance between the results of photographic and visual
+observations compare the pictures of the great nebula in the
+constellation Andromeda, which are given in Chapter XIV. A partial
+explanation of these discordances and other similar ones is that the eye
+is most strongly affected by greenish-yellow light, while the
+photographic plate responds most strongly to violet light; the
+photograph, therefore, represents things which the eye has little
+capacity for seeing, and _vice versa_.
+
+84. THE SPECTROSCOPE.--In some respects the spectroscope is the exact
+counterpart of the telescope. The latter condenses radiant energy and
+the former disperses it. As a measuring instrument the telescope is
+mainly concerned with the direction from which light comes, and the
+different colors of which that light is composed affect it only as an
+obstacle to be overcome in its construction. On the other hand, with the
+spectroscope the direction from which the radiant energy comes is of
+minor consequence, and the all-important consideration is the intrinsic
+character of that radiation. What colors are present in the light and in
+what proportions? What can these colors be made to tell about the nature
+and condition of the body from which they come, be it sun, or star, or
+some terrestrial source of light, such as an arc lamp, a candle flame,
+or a furnace in blast? These are some of the characteristic questions of
+the spectrum analysis, and, as the name implies, they are solved by
+analyzing the radiant energy into its component parts, setting down the
+blue light in one place, the yellow in another, the red in still
+another, etc., and interpreting this array of colors by means of
+principles which we shall have to consider. Something of this process of
+color analysis may be seen in the brilliant hues shown by a soap bubble,
+or reflected from a piece of mother-of-pearl, and still more strikingly
+exhibited in the rainbow, produced by raindrops which break up the
+sunlight into its component colors and arrange them each in its
+appropriate place. Any of these natural methods of decomposing light
+might be employed in the construction of a spectroscope, but in
+spectroscopes which are used for analyzing the light from feeble
+sources, such as a star, or a candle flame, a glass prism of triangular
+cross section is usually employed to resolve the light into its
+component colors, which it does by refracting it as shown at the edges
+of the lens in Fig. 38.
+
+[Illustration: FIG. 45.--Resolution of light into its component colors.]
+
+The course of a beam of light in passing through such a prism is shown
+in Fig. 45. Note that the bending of the light from its original course
+into a new one, which is here shown as produced by the prism, is quite
+similar to the bending shown at the edges of a lens and comes from the
+same cause, the slower velocity of light in glass than in air. It takes
+the light-waves as long to move over the path _A B_ in glass as over the
+longer path _1_, _2_, _3_, _4_, of which only the middle section lies in
+the glass.
+
+Not only does the prism bend the beam of light transmitted by it, but it
+bends in different degree light of different colors, as is shown in the
+figure, where the beam at the left of the prism is supposed to be made
+up of a mixture of blue and red light, while at the right of the prism
+the greater deviation imparted to the blue quite separates the colors,
+so that they fall at different places on the screen, _S S_. The compound
+light has been analyzed into its constituents, and in the same way every
+other color would be put down at its appropriate place on the screen,
+and a beam of white light falling upon the prism would be resolved by it
+into a sequence of colors, falling upon the screen in the order red,
+orange, yellow, green, blue, indigo, violet. The initial letters of
+these names make the word _Roygbiv_, and by means of it their order is
+easily remembered.
+
+[Illustration: FIG. 46.--Principal parts of a spectroscope.]
+
+If the light which is to be examined comes from a star the analysis made
+by the prism is complete, and when viewed through a telescope the image
+of the star is seen to be drawn out into a band of light, which is
+called a _spectrum_, and is red at one end and violet or blue at the
+other, with all the colors of the rainbow intervening in proper order
+between these extremes. Such a prism placed in front of the objective of
+a telescope is called an objective prism, and has been used for stellar
+work with marked success at the Harvard College Observatory. But if the
+light to be analyzed comes from an object having an appreciable extent
+of surface, such as the sun or a planet, the objective prism can not be
+successfully employed, since each point of the surface will produce its
+own spectrum, and these will appear in the _view telescope_ superposed
+and confused one with another in a very objectionable manner. To avoid
+this difficulty there is placed between the prism and the source of
+light an opaque screen, _S_, with a very narrow slit cut in it, through
+which all the light to be analyzed must pass and must also go through a
+lens, _A_, placed between the slit and the prism, as shown in Fig. 46.
+The slit and lens, together with the tube in which they are usually
+supported, are called a _collimator_. By this device a very limited
+amount of light is permitted to pass from the object through the slit
+and lens to the prism and is there resolved into a spectrum, which is in
+effect a series of images of the slit in light of different colors,
+placed side by side so close as to make practically a continuous ribbon
+of light whose width is the length of each individual picture of the
+slit. The length of the ribbon (dispersion) depends mainly upon the
+shape of the prism and the kind of glass of which it is made, and it may
+be very greatly increased and the efficiency of the spectroscope
+enhanced by putting two, three, or more prisms in place of the single
+one above described. When the amount of light is very great, as in the
+case of the sun or an electric arc lamp, it is advantageous to alter
+slightly the arrangement of the spectroscope and to substitute in place
+of the prism a grating--i. e., a metallic mirror with a great number of
+fine parallel lines ruled upon its surface at equal intervals, one from
+another. It is by virtue of such a system of fine parallel grooves that
+mother-of-pearl displays its beautiful color effects, and a brilliant
+spectrum of great purity and high dispersion is furnished by a grating
+ruled with from 10,000 to 20,000 lines to the inch. Fig. 47 represents,
+rather crudely, a part of the spectrum of an arc light furnished by such
+a grating, or rather it shows three different spectra arranged side by
+side, and looking something like a rude ladder. The sides of the ladder
+are the spectra furnished by the incandescent carbons of the lamp, and
+the cross pieces are the spectrum of the electric arc filling the space
+between the carbons. Fig. 48 shows a continuation of the same spectra
+into a region where the radiant energy is invisible to the eye, but is
+capable of being photographed.
+
+[Illustration: FIG. 47.--Green and blue part of the spectrum of an
+electric arc light.]
+
+It is only when a lens is placed between the lamp and the slit of the
+spectroscope that the three spectra are shown distinct from each other
+as in the figure. The purpose of the lens is to make a picture of the
+lamp upon the slit, so that all the radiant energy from any one point of
+the arc may be brought to one part of the slit, and thus appear in the
+resulting spectrum separated from the energy which comes from every
+other part of the arc. Such an instrument is called an _analyzing
+spectroscope_ while one without the lens is called an _integrating
+spectroscope_, since it furnishes to each point of the slit a sample of
+the radiant energy coming from every part of the source of light, and
+thus produces only an average spectrum of that source without
+distinction of its parts. When a spectroscope is attached to a
+telescope, as is often done (see Fig. 49), the eyepiece is removed to
+make way for it, and the telescope objective takes the part of the
+analyzing lens. A camera is frequently combined with such an apparatus
+to photograph the spectra it furnishes, and the whole instrument is then
+called a _spectrograph_.
+
+[Illustration: FIG. 48.--Violet and ultraviolet parts of spectrum of
+an arc lamp.]
+
+[Illustration: FIG. 49.--A spectroscope attached to the Yerkes
+telescope.]
+
+85. SPECTRUM ANALYSIS.--Having seen the mechanism of the spectroscope by
+which the light incident upon it is resolved into its constituent parts
+and drawn out into a series of colors arranged in the order of their
+wave lengths, we have now to consider the interpretation which is to be
+placed upon the various kinds of spectra which may be seen, and here we
+rely upon the experience of physicists and chemists, from whom we learn
+as follows:
+
+The radiant energy which is analyzed by the spectroscope has its source
+in the atoms and molecules which make up the luminous body from which
+the energy is radiated, and these atoms and molecules are able to
+impress upon the ether their own peculiarities in the shape of waves of
+different length and amplitude. We have seen that by varying the
+conditions of the experiment different kinds of waves may be produced in
+a bucket of water; and as a study of these waves might furnish an index
+to the conditions which produced them, so the study of the waves
+peculiar to the light which comes from any source may be made to give
+information about the molecules which make up that source. Thus the
+molecules of iron produce a system of waves peculiar to themselves and
+which can be duplicated by nothing else, and every other substance gives
+off its own peculiar type of energy, presenting a limited and definite
+number of wave lengths dependent upon the nature and condition of its
+molecules. If these molecules are free to behave in their own
+characteristic fashion without disturbance or crowding, they emit light
+of these wave lengths only, and we find in the spectrum a series of
+bright lines, pictures of the slit produced by light of these particular
+wave lengths, while between these bright lines lie dark spaces showing
+the absence from the radiant energy of light of intermediate wave
+lengths. Such a spectrum is shown in the central portion of Fig. 47,
+which, as we have already seen, is produced by the space between the
+carbons of the arc lamp. On the other hand, if the molecules are closely
+packed together under pressure they so interfere with each other as to
+give off a jumble of energy of all wave lengths, and this is translated
+by the spectroscope into a continuous ribbon of light with no dark
+spaces intervening, as in the upper and lower parts of Figs. 47 and 48,
+produced by the incandescent solid carbons of the lamp. These two types
+are known as the continuous and discontinuous spectrum, and we may lay
+down the following principle regarding them:
+
+A discontinuous spectrum, or bright-line spectrum as it is familiarly
+called, indicates that the molecules of the source of light are not
+crowded together, and therefore the light must come from an incandescent
+gas. A continuous spectrum shows only that the molecules are crowded
+together, or are so numerous that the body to which they belong is not
+transparent and gives no further information. The body may be solid,
+liquid, or gaseous, but in the latter case the gas must be under
+considerable pressure or of great extent.
+
+A second principle is: The lines which appear in a spectrum are
+characteristic of the source from which the light came--e. g., the
+double line in the yellow part of the spectrum at the extreme left in
+Fig. 47 is produced by sodium vapor in and around the electric arc and
+is never produced by anything but sodium. When by laboratory experiments
+we have learned the particular set of lines corresponding to iron, we
+may treat the presence of these lines in another spectrum as proof that
+iron is present in the source from which the light came, whether that
+source be a white-hot poker in the next room or a star immeasurably
+distant. The evidence that iron is present lies in the nature of the
+light, and there is no reason to suppose that nature to be altered on
+the way from star to earth. It may, however, be altered by something
+happening to the source from which it comes--e. g., changing temperature
+or pressure may affect, and does affect, the spectrum which such a
+substance as iron emits, and we must be prepared to find the same
+substance presenting different spectra under different conditions, only
+these conditions must be greatly altered in order to produce radical
+changes in the spectrum.
+
+[Illustration: FIG. 50.--The chief lines in the spectrum of
+sunlight.--HERSCHEL.]
+
+86. WAVE LENGTHS.--To identify a line as belonging to and produced by
+iron or any other substance, its position in the spectrum--i. e., its
+wave length--must be very accurately determined, and for the
+identification of a substance by means of its spectrum it is often
+necessary to determine accurately the wave lengths of many lines. A
+complicated spectrum may consist of hundreds or thousands of lines, due
+to the presence of many different substances in the source of light, and
+unless great care is taken in assigning the exact position of these
+lines in the spectrum, confusion and wrong identifications are sure to
+result. For the measurement of the required wave length a tenth meter
+(Ā§ 75) is the unit employed, and a scale of wave lengths expressed in
+this unit is presented in Fig. 50. The accuracy with which some of these
+wave lengths are determined is truly astounding; a ten-billionth of an
+inch! These numerical wave lengths save all necessity for referring to
+the color of any part of the spectrum, and pictures of spectra for
+scientific use are not usually printed in colors.
+
+87. ABSORPTION SPECTRA.--There is another kind of spectrum, of greater
+importance than either of those above considered, which is well
+illustrated by the spectrum of sunlight (Fig. 50). This is a nearly
+continuous spectrum crossed by numerous _dark_ lines due to absorption
+of radiant energy in a comparatively cool gas through which it passes on
+its way to the spectroscope. Fraunhofer, who made the first careful
+study of spectra, designated some of the more conspicuous of these lines
+by letters of the alphabet which are shown in the plate, and which are
+still in common use as names for the lines, not only in the spectrum of
+sunlight but wherever they occur in other spectra. Thus the double line
+marked _D_, wave length 5893, falls at precisely the same place in the
+spectrum as does the double (sodium) line which we have already seen in
+the yellow part of the arc-light spectrum, which line is also called _D_
+and bears a very intimate relation to the dark _D_ line of the solar
+spectrum.
+
+The student who has access to colored crayons should color one edge of
+Fig. 50 in accordance with the lettering there given and, so far as
+possible, he should make the transition from one color to the next a
+gradual one, as it is in the rainbow.
+
+Fig. 50 is far from being a complete representation of the spectrum of
+sunlight. Not only does this spectrum extend both to the right and to
+the left into regions invisible to the human eye, but within the limits
+of the figure, instead of the seventy-five lines there shown, there are
+literally thousands upon thousands of lines, of which only the most
+conspicuous can be shown in such a cut as this.
+
+The dark lines which appear in the spectrum of sunlight can, under
+proper conditions, be made to appear in the spectrum of an arc light,
+and Fig. 51 shows a magnified representation of a small part of such a
+spectrum adjacent to the _D_ (sodium) lines. Down the middle of each of
+these lines runs a black streak whose position (wave length) is
+precisely that of the _D_ lines in the spectrum of sunlight, and whose
+presence is explained as follows:
+
+The very hot sodium vapor at the center of the arc gives off its
+characteristic light, which, shining through the outer and cooler layers
+of sodium vapor, is partially absorbed by these, resulting in a fine
+dark line corresponding exactly in position and wave length to the
+bright lines, and seen against these as a background, since the higher
+temperature at the center of the arc tends to broaden the bright lines
+and make them diffuse. Similarly the dark lines in the spectrum of the
+sun (Fig. 50) point to the existence of a surrounding envelope of
+relatively cool gases, which absorb from the sunlight precisely those
+kinds of radiant energy which they would themselves emit if
+incandescent. The resulting dark lines in the spectrum are to be
+interpreted by the same set of principles which we have above applied to
+the bright lines of a discontinuous spectrum, and they may be used to
+determine the chemical composition of the sun, just as the bright lines
+serve to determine the chemical elements present in the electric arc.
+With reference to the mode of their formation, bright-line and dark-line
+spectra are sometimes called respectively _emission_ and _absorption_
+spectra.
+
+[Illustration: FIG. 51.--The lines reversed.]
+
+88. TYPES OF SPECTRUM.--The sun presents by far the most complex
+spectrum known, and Fig. 50 shows only a small number of the more
+conspicuous lines which appear in it. Spectra of stars, _per contra_,
+appear relatively simple, since their feeble light is insufficient to
+bring out faint details. In Chapters XIII and XIV there are shown types
+of the different kinds of spectra given by starlight, and these are to
+be interpreted by the principles above established. Thus the spectrum of
+the bright star Ī² AurigƦ shows a continuous spectrum crossed by a few
+heavy absorption lines which are known from laboratory experiments to be
+produced only by hydrogen. There must therefore be an atmosphere of
+relatively cool hydrogen surrounding this star. The spectrum of Pollux
+is quite similar to that of the sun and is to be interpreted as showing
+a physical condition similar to that of the sun, while the spectrum of Ī±
+Herculis is quite different from either of the others. In subsequent
+chapters we shall have occasion to consider more fully these different
+types of spectrum.
+
+89. THE DOPPLER PRINCIPLE.--This important principle of the spectrum
+analysis is most readily appreciated through the following experiment:
+
+Listen to the whistle of a locomotive rapidly approaching, and observe
+how the pitch changes and the note becomes more grave as the locomotive
+passes by and commences to recede. During the approach of the whistle
+each successive sound wave has a shorter distance to travel in coming to
+the ear of the listener than had its predecessor, and in consequence the
+waves appear to come in quicker succession, producing a higher note with
+a correspondingly shorter wave length than would be heard if the same
+whistle were blown with the locomotive at rest. On the other hand, the
+wave length is increased and the pitch of the note lowered by the
+receding motion of the whistle. A similar effect is produced upon the
+wave length of light by a rapid change of distance between the source
+from which it comes and the instrument which receives it, so that a
+diminishing distance diminishes very slightly the wave length of every
+line in the spectrum produced by the light, and an increasing distance
+increases these wave lengths, and this holds true whether the change of
+distance is produced by motion of the source of light or by motion of
+the instrument which receives it.
+
+This change of wave length is sometimes described by saying that when a
+body is rapidly approaching, the lines of its spectrum are all displaced
+toward the violet end of the spectrum, and are correspondingly displaced
+toward the red end by a receding motion. The amount of this shifting,
+when it can be measured, measures the velocity of the body along the
+line of sight, but the observations are exceedingly delicate, and it is
+only in recent years that it has been found possible to make them with
+precision. For this purpose there is made to pass through the
+spectroscope light from an artificial source which contains one or more
+chemical elements known to be present in the star which is to be
+observed, and the corresponding lines in the spectrum of this light and
+in the spectrum of the star are examined to determine whether they
+exactly match in position, or show, as they sometimes do, a slight
+displacement, as if one spectrum had been slipped past the other. The
+difficulty of the observations lies in the extremely small amount of
+this slipping, which rarely if ever in the case of a moving star amounts
+to one sixth part of the interval between the close parallel lines
+marked _D_ in Fig. 50. The spectral lines furnished by the headlight of
+a locomotive running at the rate of a hundred miles per hour would be
+displaced by this motion less than one six-thousandth part of the space
+between the _D_ lines, an amount absolutely imperceptible in the most
+powerful spectroscope yet constructed. But many of the celestial bodies
+have velocities so much greater than a hundred miles per hour that these
+may be detected and measured by means of the Doppler principle.
+
+90. OTHER INSTRUMENTS.--Other instruments of importance to the
+astronomer, but of which only casual mention can here be made, are the
+meridian-circle; the transit, one form of which is shown in Fig. 52, and
+the zenith telescope, which furnish refined methods for making
+observations similar in kind to those which the student has already
+learned to make with plumb line and protractor; the sextant, which is
+pre-eminently the sailor's instrument for finding the latitude and
+longitude at sea, by measuring the altitudes of sun and stars above the
+sea horizon; the heliometer, which serves for the very accurate
+measurement of small angles, such as the angular distance between two
+stars not more than one or two degrees apart; and the photometer, which
+is used for measuring the amount of light received from the celestial
+bodies.
+
+[Illustration: FIG. 52.--A combined transit instrument and zenith
+telescope.]
+
+
+
+
+CHAPTER IX
+
+THE MOON
+
+
+91. RESULTS OF OBSERVATION WITH THE UNAIDED EYE.--The student who has
+made the observations of the moon which are indicated in Chapter III has
+in hand data from which much may be learned about the earth's satellite.
+Perhaps the most striking feature brought out by them is the motion of
+the moon among the stars, always from west toward east, accompanied by
+that endless series of changes in shape and brightness--new moon, first
+quarter, full moon, etc.--whose successive stages we represent by the
+words, the phase of the moon. From his own observation the student
+should be able to verify, at least approximately, the following
+statements, although the degree of numerical precision contained in some
+of them can be reached only by more elaborate apparatus and longer study
+than he has given to the subject:
+
+A. The phase of the moon depends upon the distance apart of sun and moon
+in the sky, new moon coming when they are together, and full moon when
+they are as far apart as possible.
+
+[Illustration: THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph
+made at the Paris Observatory.]
+
+B. The moon is essentially a round, dark body, giving off no light of
+its own, but shining solely by reflected sunlight. The proof of this is
+that whenever we see a part of the moon which is turned away from the
+sun it looks dark--e. g., at new moon, sun and moon are in nearly the
+same direction from us and we see little or nothing of the moon, since
+the side upon which the sun shines is turned away from us. At full moon
+the earth is in line between sun and moon, and we see, round and
+bright, the face upon which the sun shines. At other phases, such as the
+quarters, the moon turns toward the earth a part of its night hemisphere
+and a part of its day hemisphere, but in general only that part which
+belongs to the day side of the moon is visible and the peculiar curved
+line which forms the boundary--the "ragged edge," or _terminator_, as it
+is called, is the dividing line between day and night upon the moon.
+
+A partial exception to what precedes is found for a few days after new
+moon when the moon and sun are not very far apart in the sky, for then
+the whole round disk of the moon may often be seen, a small part of it
+brightly illuminated by the sun and the larger part feebly illuminated
+by sunlight which fell first upon the earth and was by it reflected back
+to the moon, giving the pleasing effect which is sometimes called the
+old moon in the new moon's arms. The new moon--i. e., the part illumined
+by the sun--usually appears to belong to a sphere of larger radius than
+the old moon, but this is purely a trick played by the eyes of the
+observer, and the effect disappears altogether in a telescope. Is there
+any similar effect in the few days before new moon?
+
+C. The moon makes the circuit of the sky from a given star around to the
+same star again in a little more than 27 days (27.32166), but the
+interval between successive new moons--i. e., from the sun around to the
+sun again--is more than 29 days (29.53059). This last interval, which is
+called a lunar month or _synodical_ month, indicates what we have
+learned before--that the sun has changed its place among the stars
+during the month, so that it takes the moon an extra two days to
+overtake him after having made the circuit of the sky, just as it takes
+the minute hand of a clock an extra 5 minutes to catch up with the hour
+hand after having made a complete circuit of the dial.
+
+D. Wherever the moon may be in the sky, it turns always the same face
+toward the earth, as is shown by the fact that the dark markings which
+appear on its surface stand always upon (nearly) the same part of its
+disk. It does not always turn the same face toward the sun, for the
+boundary line between the illumined and unillumined parts of the moon
+shifts from one side to the other as the phase changes, dividing at each
+moment day from night upon the moon and illustrating by its slow
+progress that upon the moon the day and the month are of equal length
+(29.5 terrestrial days), instead of being time units of different
+lengths as with us.
+
+[Illustration: FIG. 53.--Motion of moon and earth relative to the sun.]
+
+92. THE MOON'S MOTION.--The student should compare the results of his
+own observations, as well as the preceding section, with Fig. 53, in
+which the lines with dates printed on them are all supposed to radiate
+from the sun and to represent the direction from the sun of earth and
+moon upon the given dates which are arbitrarily assumed for the sake of
+illustration, any other set would do equally well. The black dots, small
+and large, represent the moon revolving about the earth, but having the
+circular path shown in Fig. 34 (ellipse) transformed by the earth's
+forward motion into the peculiar sinuous line here shown. With respect
+to both earth and sun, the moon's orbit deviates but little from a
+circle, since the sinuous curve of Fig. 53 follows very closely the
+earth's orbit around the sun and is almost identical with it. For
+clearness of representation the distance between earth and moon in the
+figure has been made ten times too great, and to get a proper idea of
+the moon's orbit with reference to the sun, we must suppose the moon
+moved up toward the earth until its distance from the line of the
+earth's orbit is only a tenth part of what it is in the figure. When
+this is done, the moon's path becomes almost indistinguishable from that
+of the earth, as may be seen in the figure, where the attempt has been
+made to show both lines, and it is to be especially noted that this
+real orbit of the moon is everywhere concave toward the sun.
+
+The phase presented by the moon at different parts of its path is
+indicated by the row of circles at the right, and the student should
+show why a new moon is associated with June 30th and a full moon with
+July 15th, etc. What was the date of first quarter? Third quarter?
+
+We may find in Fig. 53 another effect of the same kind as that noted
+above in C. Between noon, June 30th, and noon, July 3d, the earth makes
+upon its axis three complete revolutions with respect to the sun, but
+the meridian which points toward the moon at noon on June 30th will not
+point toward it at noon on July 3d, since the moon has moved into a new
+position and is now 37Ā° away from the meridian. Verify this statement by
+measuring, in Fig. 53, with the protractor, the moon's angular distance
+from the meridian at noon on July 3d. When will the meridian overtake
+the moon?
+
+93. HARVEST MOON.--The interval between two successive transits of the
+meridian past the moon is called a lunar day, and the student should
+show from the figure that on the average a lunar day is 51 minutes
+longer than a solar day--i. e., upon the average each day the moon comes
+to the meridian 51 minutes of solar time later than on the day before.
+It is also true that on the average the moon rises and sets 51 minutes
+later each day than on the day before. But there is a good deal of
+irregularity in the retardation of the time of moonrise and moonset,
+since the time of rising depends largely upon the particular point of
+the horizon at which the moon appears, and between two days this point
+may change so much on account of the moon's orbital motion as to make
+the retardation considerably greater or less than its average value. In
+northern latitudes this effect is particularly marked in the month of
+September, when the eastern horizon is nearly parallel with the moon's
+apparent path in the sky, and near the time of full moon in that month
+the moon rises on several successive nights at nearly the same hour, and
+in less degree the same is true for October. This highly convenient
+arrangement of moonlight has caused the full moons of these two months
+to be christened respectively the Harvest Moon and the Hunter's Moon.
+
+94. SIZE AND MASS OF THE MOON.--It has been shown in Chapter I how the
+distance of the moon from the earth may be measured and its diameter
+determined by means of angles, and without enlarging upon the details of
+these observations, we note as their result that the moon is a globe
+2,163 miles in diameter, and distant from the earth on the average about
+240,000 miles. But, as we have seen in Chapter VII, this distance
+changes to the extent of a few thousand miles, sometimes less, sometimes
+greater, mainly on account of the elliptic shape of the moon's orbit
+about the earth, but also in part from the disturbing influence of other
+bodies, such as the sun, which pull the moon to and fro, backward and
+forward, to quite an appreciable extent.
+
+From the known diameter of the moon it is a matter of elementary
+geometry to derive in miles the area of its surface and its volume or
+solid contents. Leaving this as an exercise for the student, we adopt
+the earth as the standard of comparison and find that the diameter of
+the moon is rather more than a quarter, 4/15, that of the earth, the
+area of its surface is a trifle more than 1/14 that of the earth, and
+its volume a little more than 1/49 of the earth's. So much is pure
+geometry, but we may combine with it some mechanical principles which
+enable us to go a step farther and to "weigh" the moon--i. e., determine
+its mass and the average density of the material of which it is made.
+
+We have seen that the moon moves around the sun in a path differing but
+little from the smooth curve shown in Fig. 53, with arrows indicating
+the direction of motion, and it would follow absolutely such a smooth
+path were it not for the attraction of the earth, and in less degree of
+some of the other planets, which swing it about first to one side then
+to the other. But action and reaction are equal; the moon pulls as
+strongly upon the earth as does the earth upon the moon, and if earth
+and moon were of equal mass, the deviation of the earth from the smooth
+curve in the figure would be just as large as that of the moon. It is
+shown in the figure that the moon does displace the earth from this
+curve, and we have only to measure the amount of this displacement of
+the earth and compare it with the displacement suffered by the moon to
+find how much the mass of the one exceeds that of the other. It may be
+seen from the figure that at first quarter, about July 7th, the earth is
+thrust ahead in the direction of its orbital motion, while at the third
+quarter, July 22d, it is pulled back by the action of the moon, and at
+all times it is more or less displaced by this action, so that, in order
+to be strictly correct, we must amend our former statement about the
+moon moving around the earth and make it read, Both earth and moon
+revolve around a point on line between their centers. This point is
+called their _center of gravity_, and the earth and the moon both move
+in ellipses having this center of gravity at their common focus. Compare
+this with Kepler's First Law. These ellipses are similarly shaped, but
+of very different size, corresponding to Newton's third law of motion
+(Chapter IV), so that the action of the earth in causing the small moon
+to move around a large orbit is just equal to the reaction of the moon
+in causing the larger earth to move in the smaller orbit. This is
+equivalent to saying that the dimensions of the two orbits are inversely
+proportional to the masses of the earth and the moon.
+
+By observing throughout the month the direction from the earth to the
+sun or to a near planet, such as Mars or Venus, astronomers have
+determined that the diameter of the ellipse in which the earth moves is
+about 5,850 miles, so that the distance of the earth from the center of
+gravity is 2,925 miles, and the distance of the moon from it is
+240,000-2,925 = 237,075. We may now write in the form of a proportion--
+
+    Mass of earth : Mass of moon :: 237,075 : 2,925,
+
+and find from it that the mass of the earth is 81 times as great as the
+mass of the moon--i. e., leaving kind and quality out of account, there
+is enough material in the earth to make 81 moons. We may note in this
+connection that the diameter of the earth, 7,926 miles, is greater than
+the diameter of the monthly orbit in which the moon causes it to move,
+and therefore the center of gravity of earth and moon always lies inside
+the body of the earth, about 1,000 miles below the surface.
+
+95. DENSITY OF THE MOON.--It is believed that in a general way the moon
+is made of much the same kind of material which goes to make up the
+earth--metals, minerals, rocks, etc.--and a part of the evidence upon
+which this belief is based lies in the density of the moon. By density
+of a substance we mean the amount of it which is contained in a given
+volume--i. e., the weight of a bushel or a cubic centimeter of the
+stuff. The density of chalk is twice as great as the density of water,
+because a cubic centimeter of chalk weighs twice as much as an equal
+volume of water, and similarly in other cases the density is found by
+dividing the mass or weight of the body by the mass or weight of an
+equal volume of water.
+
+We know the mass of the earth (Ā§ 45), and knowing the mass of a cubic
+foot of water, it is easy, although a trifle tedious, to compute what
+would be the mass of a volume of water equal in size to the earth. The
+quotient obtained by dividing one of these masses by the other (mass of
+earth Ć· mass of water) is the average density of the material composing
+the earth, and we find numerically that this is 5.6--i. e., it would
+take 5.6 water earths to attract as strongly as does the real one. From
+direct experiment we know that the average density of the principal
+rocks which make up the crust of the earth is only about half of this,
+showing that the deep-lying central parts of the earth are denser than
+the surface parts, as we should expect them to be, because they have to
+bear the weight of all that lies above them and are compressed by it.
+
+Turning now to the moon, we find in the same way as for the earth that
+its average density is 3.4 as great as that of water.
+
+96. FORCE OF GRAVITY UPON THE MOON.--This number, 3.4, compared with the
+5.6 which we found for the earth, shows that on the whole the moon is
+made of lighter stuff than is the body of the earth, and this again is
+much what we should expect to find, for weight, the force which tends to
+compress the substance of the moon, is less there than here. The weight
+of a cubic yard of rock at the surface of either earth or moon is the
+force with which the earth or moon attracts it, and this by the law of
+gravitation is for the earth--
+
+    W = k Ɨ (m mĀ“) / (3963)^{2};
+
+and for the moon--
+
+    w = k Ɨ {m (mĀ“/81)} / (1081)^{2};
+
+from which we find by division--
+
+    w = (W / 81) (3963 / 1081)^{2} = (W / 6) (approximately).
+
+The cubic yard of rock, which upon the earth weighs two tons, would, if
+transported to the moon, weigh only one third of a ton, and would have
+only one sixth as much influence in compressing the rocks below it as it
+had upon the earth. Note that this rock when transported to the moon
+would be still attracted by the earth and would have weight toward the
+earth, but it is not this of which we are speaking; by its weight in
+the moon we mean the force with which the moon attracts it. Making due
+allowance for the difference in compression produced by weight, we may
+say that in general, so far as density goes, the moon is very like a
+piece of the earth of equal mass set off by itself alone.
+
+97. ALBEDO.--In another respect the lunar stuff is like that of which
+the earth is made: it reflects the sunlight in much the same way and to
+the same amount. The contrast of light and dark areas on the moon's
+surface shows, as we shall see in another section, the presence of
+different substances upon the moon which reflect the sunlight in
+different degrees. This capacity for reflecting a greater or less
+percentage of the incident sunlight is called _albedo_ (Latin,
+whiteness), and the brilliancy of the full moon might lead one to
+suppose that its albedo is very great, like that of snow or those masses
+of summer cloud which we call thunderheads. But this is only an effect
+of contrast with the dark background of the sky. The same moon by day
+looks pale, and its albedo is, in fact, not very different from that of
+our common rocks--weather-beaten sandstone according to Sir John
+Herschel--so that it would be possible to build an artificial moon of
+rock or brick which would shine in the sunlight much as does the real
+moon.
+
+The effect produced by the differences of albedo upon the moon's face is
+commonly called the "man in the moon," but, like the images presented by
+glowing coals, the face in the moon is anything which we choose to make
+it. Among the Chinese it is said to be a monkey pounding rice; in India,
+a rabbit; in Persia, the earth reflected as in a mirror, etc.
+
+98. LIBRATIONS.--We have already learned that the moon turns always the
+same face toward the earth, and we have now to modify this statement and
+to find that here, as in so many other cases, the thing we learn first
+is only approximately true and needs to be limited or added to or
+modified in some way. In general, Nature is too complex to be completely
+understood at first sight or to be perfectly represented by a simple
+statement. In Fig. 55 we have two photographs of the moon, taken nearly
+three years apart, the right-hand one a little after first quarter and
+the left-hand one a little before third quarter. They therefore
+represent different parts of the moon's surface, but along the ragged
+edge the same region is shown on both photographs, and features common
+to both pictures may readily be found--e. g., the three rings which form
+a right-angled triangle about one third of the way down from the top of
+the cut, and the curved mountain chain just below these. If the moon
+turned exactly the same face toward us in the two pictures, the distance
+of any one of these markings from any part of the moon's edge must be
+the same in both pictures; but careful measurement will show that this
+is not the case, and that in the left-hand picture the upper edge of the
+moon is tipped toward us and the lower edge away from us, as if the
+whole moon had been rotated slightly about a horizontal line and must be
+turned back a little (about 7Ā°) in order to match perfectly the other
+part of the picture.
+
+This turning is called a _libration_, and it should be borne in mind
+that the moon librates not only in the direction above measured, north
+and south, but also at right angles to this, east and west, so that we
+are able to see a little farther around every part of the moon's edge
+than would be possible if it turned toward us at all times exactly the
+same face. But in spite of the librations there remains on the farther
+side of the moon an area of 6,000,000 square miles which is forever
+hidden from us, and of whose character we have no direct knowledge,
+although there is no reason to suppose it very different from that which
+is visible, despite the fact that some of the books contain quaint
+speculations to the contrary. The continent of South America is just
+about equal in extent to this unknown region, while North America is a
+fair equivalent for all the rest of the moon's surface, both those
+central parts which are constantly visible, and the zone around the edge
+whose parts sometimes come into sight and are sometimes hidden.
+
+An interesting consequence of the peculiar rotation of the moon is that
+from our side of it the earth is always visible. Sun, stars, and planets
+rise and set there as well as here, but to an observer on the moon the
+earth swings always overhead, shifting its position a few degrees one
+way or the other on account of the libration but running through its
+succession of phases, new earth, first quarter, etc., without ever going
+below the horizon, provided the observer is anywhere near the center of
+the moon's disk.
+
+[Illustration: FIG. 54.--Illustrating the moon's rotation.]
+
+99. CAUSE OF LIBRATIONS.--That the moon should librate is by no means so
+remarkable a fact as that it should at all times turn very nearly the
+same face toward the earth. This latter fact can have but one meaning:
+the moon revolves about an axis as does the earth, but the time required
+for this revolution is just equal to the time required to make a
+revolution in its orbit. Place two coins upon a table with their heads
+turned toward the north, as in Fig. 54, and move the smaller one around
+the larger in such a way that its face shall always look away from the
+larger one. In making one revolution in its orbit the head on this small
+coin will be successively directed toward every point of the compass,
+and when it returns to its initial position the small coin will have
+made just one revolution about an axis perpendicular to the plane of its
+orbit. In no other way can it be made to face always away from the
+figure at the center of its orbit while moving around it.
+
+We are now in a position to understand the moon's librations, for, if
+the small coin at any time moves faster or slower in its orbit than it
+turns about its axis, a new side will be turned toward the center, and
+the same may happen if the central coin itself shifts into a new
+position. This is what happens to the moon, for its orbital motion, like
+that of Mercury (Fig. 17), is alternately fast and slow, and in addition
+to this there are present other minor influences, such as the fact that
+its rotation axis is not exactly perpendicular to the plane of its
+orbit; in addition to this the observer upon the earth is daily carried
+by its rotation from one point of view to another, etc., so that it is
+only in a general way that the rotation upon the axis and motion in the
+orbit keep pace with each other. In a general way a cable keeps a ship
+anchored in the same place, although wind and waves may cause it to
+"librate" about the anchor.
+
+How the moon came to have this exact equality between its times of
+revolution and rotation constitutes a chapter of its history upon which
+we shall not now enter; but the equality having once been established,
+the mechanism by which it is preserved is simple enough.
+
+The attraction of the earth for the moon has very slightly pulled the
+latter out of shape (Ā§ 42), so that the particular diameter, which
+points toward the earth, is a little longer than any other, and thus
+serves as a handle which the earth lays hold of and pulls down into its
+lowest possible position--i. e., the position in which it points toward
+the center of the earth. Just how long this handle is, remains unknown,
+but it may be shown from the law of gravitation that less than a hundred
+yards of elongation would suffice for the work it has to do.
+
+100. THE MOON AS A WORLD.--Thus far we have considered the moon as a
+satellite of the earth, dependent upon the earth, and interesting
+chiefly because of its relation to it. But the moon is something more
+than this; it is a world in itself, very different from the earth,
+although not wholly unlike it. The most characteristic feature of the
+earth's surface is its division into land and water, and nothing of this
+kind can be found upon the moon. It is true that the first generation of
+astronomers who studied the moon with telescopes fancied that the large
+dark patches shown in Fig. 55 were bodies of water, and named them
+oceans, seas, lakes, and ponds, and to the present day we keep those
+names, although it is long since recognized that these parts of the
+moon's surface are as dry as any other. Their dark appearance indicates
+a different kind of material from that composing the lighter parts of
+the moon, material with a different albedo, just as upon the earth we
+have light-colored and dark-colored rocks, marble and slate, which seen
+from the moon must present similar contrasts of brightness. Although
+these dark patches are almost the only features distinguishable with the
+unaided eye, it is far otherwise in the telescope or the photograph,
+especially along the ragged edge where great numbers of rings can be
+seen, which are apparently depressions in the moon and are called
+craters. These we find in great number all over the moon, but, as the
+figure shows, they are seen to the best advantage near the
+_terminator_--i. e., the dividing line between day and night, since the
+long shadows cast here by the rising or setting sun bring out the
+details of the surface better than elsewhere. Carefully examine Fig. 55
+with reference to these features.
+
+[Illustration: FIG. 55.--The moon at first and last quarter. Lick
+Observatory photographs.]
+
+Another feature which exists upon both earth and moon, although far less
+common there than here, is illustrated in the chain of mountains visible
+near the terminator, a little above the center of the moon in both parts
+of Fig. 55. This particular range of mountains, which is called the
+Lunar Apennines, is by far the most prominent one upon the moon,
+although others, the Alps and Caucasus, exist. But for the most part the
+lunar mountains stand alone, each by itself, instead of being grouped
+into ranges, as on the earth. Note in the figure that some of the lunar
+mountains stretch out into the night side of the moon, their peaks
+projecting up into the sunlight, and thus becoming visible, while the
+lowlands are buried in the shadow.
+
+A subordinate feature of the moon's surface is the system of _rays_
+which seem to radiate like spokes from some of the larger craters,
+extending over hill and valley sometimes for hundreds of miles. A
+suggestion of these rays may be seen in Fig. 55, extending from the
+great crater Copernicus a little southwest of the end of the Apennines,
+but their most perfect development is to be seen at the time of full
+moon around the crater Tycho, which lies near the south pole of the
+moon. Look for them with an opera glass.
+
+Another and even less conspicuous feature is furnished by the rills,
+which, under favorable conditions of illumination, appear like long
+cracks on the moon's surface, perhaps analogous to the caƱons of our
+Western country.
+
+101. THE MAP OF THE MOON.--Fig. 55 furnishes a fairly good map of a
+limited portion of the moon near the terminator, but at the edges little
+or no detail can be seen. This is always true; the whole of the moon can
+not be seen to advantage at any one time, and to remedy this we need to
+construct from many photographs or drawings a map which shall represent
+the several parts of the moon as they appear at their best. Fig. 56
+shows such a map photographed from a relief model of the moon, and
+representing the principal features of the lunar surface in a way they
+can never be seen simultaneously. Perhaps its most striking feature is
+the shape of the craters, which are shown round in the central parts of
+the map and oval at the edges, with their long diameters parallel to the
+moon's edge. This is, of course, an effect of the curvature of the
+moon's surface, for we look very obliquely at the edge portions, and
+thus see their formations much foreshortened in the direction of the
+moon's radius.
+
+[Illustration: FIG. 56.--Relief map of the moon's surface.--After
+NASMYTH and CARPENTER.]
+
+The north and south poles of the moon are at the top and bottom of the
+map respectively, and a mere inspection of the regions around them will
+show how much more rugged is the southern hemisphere of the moon than
+the northern. It furnishes, too, some indication of how numerous are the
+lunar craters, and how in crowded regions they overlap one another.
+
+The student should pick out upon the map those features which he has
+learned to know in the photograph (Fig. 55)--the Apennines, Copernicus,
+and the continuation of the Apennines, extending into the dark part of
+the moon.
+
+[Illustration: FIG. 57.--Mare Imbrium. Photographed by G. W. RITCHEY.]
+
+102. SIZE OF THE LUNAR FEATURES.--We may measure distances here in the
+same way as upon a terrestrial map, remembering that near the edges the
+scale of the map is very much distorted parallel to the moon's diameter,
+and measurements must not be taken in this direction, but may be taken
+parallel to the edge. Measuring with a millimeter scale, we find on the
+map for the diameter of the crater Copernicus, 2.1 millimeters. To turn
+this into the diameter of the real Copernicus in miles, we measure upon
+the same map the diameter of the moon, 79.7 millimeters, and then have
+the proportion--
+
+    Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,
+
+which when solved gives 57 miles. The real diameter of Copernicus is a
+trifle over 56 miles. At the eastern edge of the moon, opposite the
+Apennines, is a large oval spot called the Mare Crisium (Latin, _ma-re_
+= sea). Measure its length. The large crater to the northwest of the
+Apennines is called Archimedes. Measure its diameter both in the map and
+in the photograph (Fig. 55), and see how the two results agree. The true
+diameter of this crater, east and west, is very approximately 50 miles.
+The great smooth surface to the west of Archimedes is the Mare Imbrium.
+Is it larger or smaller than Lake Superior? Fig. 57 is from a photograph
+of the Mare Imbrium, and the amount of detail here shown at the bottom
+of the sea is a sufficient indication that, in this case at least, the
+water has been drawn off, if indeed any was ever present.
+
+[Illustration: FIG. 58.--Mare Crisium. Lick Observatory photographs.]
+
+Fig. 58 is a representation of the Mare Crisium at a time when night was
+beginning to encroach upon its eastern border, and it serves well to
+show the rugged character of the ring-shaped wall which incloses this
+area.
+
+With these pictures of the smoother parts of the moon's surface we may
+compare Fig. 59, which shows a region near the north pole of the moon,
+and Fig. 60, giving an early morning view of Archimedes and the
+Apennines. Note how long and sharp are the shadows.
+
+[Illustration: FIG. 59.--Illustrating the rugged character of the moon's
+surface.--NASMYTH and CARPENTER.]
+
+103. THE MOON'S ATMOSPHERE.--Upon the earth the sun casts no shadows so
+sharp and black as those of Fig. 60, because his rays are here scattered
+and reflected in all directions by the dust and vapors of the
+atmosphere (Ā§ 51), so that the place from which direct sunlight is cut
+off is at least partially illumined by this reflected light. The shadows
+of Fig. 60 show that upon the moon it must be otherwise, and suggest
+that if the moon has any atmosphere whatever, its density must be
+utterly insignificant in comparison with that of the earth. In its
+motion around the earth the moon frequently eclipses stars (_occults_ is
+the technical word), and if the moon had an atmosphere such as is shown
+in Fig. 61, the light from the star _A_ must shine through this
+atmosphere just before the moon's advancing body cuts it off, and it
+must be refracted by the atmosphere so that the star would appear in a
+slightly different direction (nearer to _B_) than before. The earth's
+atmosphere refracts the starlight under such circumstances by more than
+a degree, but no one has been able to find in the case of the moon any
+effect of this kind amounting to even a fraction of a second of arc.
+While this hardly justifies the statement sometimes made that the moon
+has no atmosphere, we shall be entirely safe in saying that if it has
+one at all its density is less than a thousandth part of that of the
+earth's atmosphere. Quite in keeping with this absence of an atmosphere
+is the fact that clouds never float over the surface of the moon. Its
+features always stand out hard and clear, without any of that haze and
+softness of outline which our atmosphere introduces into all terrestrial
+landscapes.
+
+[Illustration: FIG. 60.--Archimedes and Apennines. NASMYTH and
+CARPENTER.]
+
+104. HEIGHT OF THE LUNAR MOUNTAINS.--Attention has already been called
+to the detached mountain peaks, which in Fig. 55 prolong the range of
+Apennines into the lunar night. These are the beginnings of the Caucasus
+mountains, and from the photograph we may measure as follows the height
+to which they rise above the surrounding level of the moon: Fig. 62
+represents a part of the lunar surface along the boundary line between
+night and day, the horizontal line at the top of the figure representing
+a level ray of sunlight which just touches the moon at _T_ and barely
+illuminates the top of the mountain, _M_, whose height, _h_, is to be
+determined. If we let _R_ stand for the radius of the moon and _s_ for
+the distance, _T M_, we shall have in the right-angled triangle _M T C_,
+
+    R^{2} + s^{2} = (R + h)^{2},
+
+and we need only to measure _s_--that is, the distance from the
+terminator to the detached mountain peak--to make this equation
+determine _h_, since _R_ is already known, being half the diameter of
+the moon--1,081 miles. Practically it is more convenient to use instead
+of this equation another form, which the student who is expert in
+algebra may show to be very nearly equivalent to it:
+
+        _h_ (miles) = s^{2} / 2163,
+    or  _h_ (feet) = 2.44 s^{2}.
+
+The distance _s_ must be expressed in miles in all of these equations.
+In Fig. 55 the distance from the terminator to the first detached peak
+of the Caucasus mountains is 1.7 millimeters = 52 miles, from which we
+find the height of the mountain to be 1.25 miles, or 6,600 feet.
+
+[Illustration: FIG. 61.--Occultations and the moon's atmosphere.]
+
+[Illustration: FIG. 62.--Determining the height of a lunar mountain.]
+
+Two things, however, need to be borne in mind in this connection. On the
+earth we measure the heights of mountains _above sea level_, while on
+the moon there is no sea, and our 6,600 feet is simply the height of the
+mountain top above the level of that particular point in the terminator,
+from which we measure its distance. So too it is evident from the
+appearance of things, that the sunlight, instead of just touching the
+top of the particular mountain whose height we have measured, really
+extends some little distance down from its summit, and the 6,600 feet is
+therefore the elevation of the lowest point on the mountains to which
+the sunlight reaches. The peak itself may be several hundred feet
+higher, and our photograph must be taken at the exact moment when this
+peak appears in the lunar morning or disappears in the evening if we are
+to measure the altitude of the mountain's summit. Measure the height of
+the most northern visible mountain of the Caucasus range. This is one of
+the outlying spurs of the great mountain Calippus, whose principal peak,
+19,000 feet high, is shown in Fig. 55 as the brightest part of the
+Caucasus range.
+
+The highest peak of the lunar Apennines, Huyghens, has an altitude of
+18,000 feet, and the Leibnitz and Doerfel Mountains, near the south pole
+of the moon, reach an altitude 50 per cent greater than this, and are
+probably the highest peaks on the moon. This falls very little short of
+the highest mountain on the earth, although the moon is much smaller
+than the earth, and these mountains are considerably higher than
+anything on the western continent of the earth.
+
+The vagueness of outline of the terminator makes it difficult to measure
+from it with precision, and somewhat more accurate determinations of the
+heights of lunar mountains can be obtained by measuring the length of
+the shadows which they cast, and the depths of craters may also be
+measured by means of the shadows which fall into them.
+
+105. CRATERS.--Fig. 63 shows a typical lunar crater, and conveys a good
+idea of the ruggedness of the lunar landscape. Compare the appearance of
+this crater with the following generalizations, which are based upon the
+accurate measurement of many such:
+
+A. A crater is a real depression in the surface of the moon, surrounded
+usually by an elevated ring which rises above the general level of the
+region outside, while the bottom of the crater is about an equal
+distance below that level.
+
+B. Craters are shallow, their diameters ranging from five times to more
+than fifty times their depth. Archimedes, whose diameter we found to be
+50 miles, has an average depth of about 4,000 feet below the crest of
+its surrounding wall, and is relatively a shallow crater.
+
+[Illustration: FIG. 63.--A typical lunar crater.--NASMYTH and
+CARPENTER.]
+
+C. Craters frequently have one or more hills rising within them which,
+however, rarely, if ever, reach up to the level of the surrounding wall.
+
+D. Whatever may have been the mode of their formation, the craters can
+not have been produced by scooping out material from the center and
+piling it up to make the wall, for in three cases out of four the volume
+of the excavation is greater than the volume of material contained in
+the wall.
+
+106. MOON AND EARTH.--We have gone far enough now to appreciate both the
+likeness and the unlikeness of the moon and earth. They may fairly
+enough be likened to offspring of the same parent who have followed very
+different careers, and in the fullness of time find themselves in very
+different circumstances. The most serious point of difference in these
+circumstances is the atmosphere, which gives to the earth a wealth of
+phenomena altogether lacking in the moon. Clouds, wind, rain, snow,
+dew, frost, and hail are all dependent upon the atmosphere and can not
+be found where it is not. There can be nothing upon the moon at all like
+that great group of changes which we call weather, and the unruffled
+aspect of the moon's face contrasts sharply with the succession of cloud
+and sunshine which the earth would present if seen from the moon.
+
+The atmosphere is the chief agent in the propagation of sound, and
+without it the moon must be wrapped in silence more absolute than can be
+found upon the surface of the earth. So, too, the absence of an
+atmosphere shows that there can be no water or other liquid upon the
+moon, for if so it would immediately evaporate and produce a gaseous
+envelope which we have seen does not exist. With air and water absent
+there can be of course no vegetation or life of any kind upon the moon,
+and we are compelled to regard it as an arid desert, utterly waste.
+
+107. TEMPERATURE OF THE MOON.--A characteristic feature of terrestrial
+deserts, which is possessed in exaggerated degree by the moon, is the
+great extremes of temperature to which they and it are subject. Owing to
+its slow rotation about its axis, a point on the moon receives the solar
+radiation uninterruptedly for more than a fortnight, and that too
+unmitigated by any cloud or vaporous covering. Then for a like period it
+is turned away from the sun and allowed to cool off, radiating into
+interplanetary space without hindrance its accumulated store of heat. It
+is easy to see that the range of temperature between day and night must
+be much greater under these circumstances than it is with us where
+shorter days and clouded skies render day and night more nearly alike,
+to say nothing of the ocean whose waters serve as a great balance wheel
+for equalizing temperatures. Just how hot or how cold the moon becomes
+is hard to determine, and very different estimates are to be found in
+the books. Perhaps the most reliable of these are furnished by the
+recent researches of Professor Very, whose experiments lead him to
+conclude that "its rocky surface at midday, in latitudes where the sun
+is high, is probably hotter than boiling water and only the most
+terrible of earth's deserts, where the burning sands blister the skin,
+and men, beasts, and birds drop dead, can approach a noontide on the
+cloudless surface of our satellite. Only the extreme polar latitudes of
+the moon can have an endurable temperature by day, to say nothing of the
+night, when we should have to become troglodytes to preserve ourselves
+from such intense cold."
+
+While the night temperature of the moon, even very soon after sunset,
+sinks to something like 200Ā° below zero on the centigrade scale, or 320Ā°
+below zero on the Fahrenheit scale, the lowest known temperature upon
+the earth, according to General Greely, is 90Ā° Fahr. below zero,
+recorded in Siberia in January, 1885.
+
+Winter and summer are not markedly different upon the moon, since its
+rotation axis is nearly perpendicular to the plane of the earth's orbit
+about the sun, and the sun never goes far north or south of the moon's
+equator. The month is the one cycle within which all seasonal changes in
+its physical condition appear to run their complete course.
+
+108. CHANGES IN THE MOON.--It is evidently idle to look for any such
+changes in the condition of the moon's surface as with us mark the
+progress of the seasons or the spread of civilization over the
+wilderness. But minor changes there may be, and it would seem that the
+violent oscillations of temperature from day to night ought to have some
+effect in breaking down and crumbling the sharp peaks and crags which
+are there so common and so pronounced. For a century past astronomers
+have searched carefully for changes of this kind--the filling up of some
+crater or the fall of a mountain peak; but while some things of this
+kind have been reported from time to time, the evidence in their behalf
+has not been altogether conclusive. At the present time it is an open
+question whether changes of this sort large enough to be seen from the
+earth are in progress. A crater much less than a mile wide can be seen
+in the telescope, but it is not easy to tell whether so minute an object
+has changed in size or shape during a year or a decade, and even if
+changes are seen they may be apparent rather than real. Fig. 64 contains
+two views of the crater Archimedes, taken under a morning and an
+afternoon sun respectively, and shows a very pronounced difference
+between the two which proceeds solely from a difference of illumination.
+In the presence of such large fictitious changes astronomers are slow to
+accept smaller ones as real.
+
+[Illustration: FIG. 64.--Archimedes in the lunar morning and
+afternoon.--WEINEK.]
+
+It is this absence of change that is responsible for the rugged and
+sharp-cut features of the moon which continue substantially as they were
+made, while upon the earth rain and frost are continually wearing down
+the mountains and spreading their substance upon the lowland in an
+unending process of smoothing off the roughnesses of its surface. Upon
+the moon this process is almost if not wholly wanting, and the moon
+abides to-day much more like its primitive condition than is the earth.
+
+109. THE MOON'S INFLUENCE UPON THE EARTH.--There is a widespread popular
+belief that in many ways the moon exercises a considerable influence
+upon terrestrial affairs: that it affects the weather for good or ill,
+that crops must be planted and harvested, pigs must be killed, and
+timber cut at the right time of the moon, etc. Our common word lunatic
+means moonstruck--i. e., one upon whom the moon has shone while
+sleeping. There is not the slightest scientific basis for any of these
+beliefs, and astronomers everywhere class them with tales of witchcraft,
+magic, and popular delusion. For the most part the moon's influence upon
+the earth is limited to the light which it sends and the effect of its
+gravitation, chiefly exhibited in the ocean tides. We receive from the
+moon a very small amount of second-hand solar heat and there is also a
+trifling magnetic influence, but neither of these last effects comes
+within the range of ordinary observation, and we shall not go far wrong
+in saying that, save the moonlight and the tides, every supposed lunar
+influence upon the earth is either fictitious or too small to be readily
+detected.
+
+
+
+
+CHAPTER X
+
+THE SUN
+
+
+110. DEPENDENCE OF THE EARTH UPON THE SUN.--There is no better
+introduction to the study of the sun than Byron's Ode to Darkness,
+beginning with the lines--
+
+    "I dreamed a dream
+    That was not all a dream.
+    The bright sun was extinguished,"
+
+and proceeding to depict in vivid words the consequences of this
+extinction. The most matter-of-fact language of science agrees with the
+words of the poet in declaring the earth's dependence upon the sun for
+all those varied forms of energy which make it a fit abode for living
+beings. The winds blow and the rivers run; the crops grow, are gathered
+and consumed, by virtue of the solar energy. Factory, locomotive, beast,
+bird, and the human body furnish types of machines run by energy derived
+from the sun; and the student will find it an instructive exercise to
+search for kinds of terrestrial energy which are not derived either
+directly or indirectly from the sun. There are a few such, but they are
+neither numerous nor important.
+
+111. THE SUN'S DISTANCE FROM THE EARTH.--To the astronomer the sun
+presents problems of the highest consequence and apparently of very
+diverse character, but all tending toward the same goal: the framing of
+a mechanical explanation of the sun considered as a machine; what it is,
+and how it does its work. In the forefront of these problems stand those
+numerical determinations of distance, size, mass, density, etc., which
+we have already encountered in connection with the moon, but which must
+here be dealt with in a different manner, because the immensely greater
+distance of the sun makes impossible the resort to any such simple
+method as the triangle used for determining the moon's distance. It
+would be like determining the distance of a steeple a mile away by
+observing its direction first from one eye, then from the other; too
+short a base for the triangle. In one respect, however, we stand upon a
+better footing than in the case of the moon, for the mass of the earth
+has already been found (Chapter IV) as a fractional part of the sun's
+mass, and we have only to invert the fraction in order to find that the
+sun's mass is 329,000 times that of the earth and moon combined, or
+333,000 times that of the earth alone.
+
+If we could rely implicitly upon this number we might make it determine
+for us the distance of the sun through the law of gravitation as
+follows: It was suggested in Ā§ 38 that Newton proved Kepler's three laws
+to be imperfect corollaries from the law of gravitation, requiring a
+little amendment to make them strictly correct, and below we give in the
+form of an equation Kepler's statement of the Third Law together with
+Newton's amendment of it. In these equations--
+
+_T_ = Periodic time of any planet;
+
+_a_ = One half the major axis of its orbit;
+
+_m_ = Its mass;
+
+_M_ = The mass of the sun;
+
+_k_ = The gravitation constant corresponding to the particular set of
+units in which _T_, _a_, _m_, and _M_ are expressed.
+
+  (Kepler) a^{3}/T^{2} = h;
+  (Newton) a^{3}/T^{2} = k (M + m).
+
+Kepler's idea was: For every planet which moves around the sun, _a^{3}_
+divided by _T^{2}_ always gives the same quotient, _h_; and he did not
+concern himself with the significance of this quotient further than to
+note that if the particular _a_ and _T_ which belong to any
+planet--e. g., the earth--be taken as the units of length and time, then
+the quotient will be 1. Newton, on the other hand, attached a meaning to
+the quotient, and showed that it is equal to the product obtained by
+multiplying the sum of the two masses, planet and sun, by a number which
+is always the same when we are dealing with the action of gravitation,
+whether it be between the sun and planet, or between moon and earth, or
+between the earth and a roast of beef in the butcher's scales, provided
+only that we use always the same units with which to measure times,
+distances, and masses.
+
+Numerically, Newton's correction to Kepler's Third Law does not amount
+to much in the motion of the planets. Jupiter, which shows the greatest
+effect, makes the circuit of his orbit in 4,333 days instead of 4,335,
+which it would require if Kepler's law were strictly true. But in
+another respect the change is of the utmost importance, since it enables
+us to extend Kepler's law, which relates solely to the sun and its
+planets, to other attracting bodies, such as the earth, moon, and stars.
+Thus for the moon's motion around the earth we write--
+
+    (240,000^{3})/(27.32^{2}) = k (1 + 1/81),
+
+from which we may find that, with the units here employed, the earth's
+mass as the unit of mass, the mean solar day as the unit of time, and
+the mile as the unit of distance--
+
+    k = 1830 Ɨ 10^{10}.
+
+If we introduce this value of _k_ into the corresponding equation, which
+represents the motion of the earth around the sun, we shall have--
+
+    a^{3}/(365.25)^{2} = 1830 Ɨ 10^{10} (333,000 + 1),
+
+where the large number in the parenthesis represents the number of times
+the mass of the sun is greater than the mass of the earth. We shall find
+by solving this equation that _a_, the mean distance of the sun from the
+earth, is very approximately 93,000,000 miles.
+
+113. ANOTHER METHOD OF DETERMINING THE SUN'S DISTANCE.--This will be
+best appreciated by a reference to Fig. 17. It appears here that the
+earth makes its nearest approach to the orbit of Mars in the month of
+August, and if in any August Mars happens to be in opposition, its
+distance from the earth will be very much less than the distance of the
+sun from the earth, and may be measured by methods not unlike those
+which served for the moon. If now the orbits of Mars and the earth were
+circles having their centers at the sun this distance between them,
+which we may represent by _D_, would be the difference of the radii of
+these orbits--
+
+    D = aĀ“Ā“ - aĀ“,
+
+where the accents Ā“Ā“, Ā“ represent Mars and the earth respectively.
+Kepler's Third Law furnishes the relation--
+
+    (aĀ“Ā“)^{3}/(TĀ“Ā“)^{2} = (aĀ“)^{3}/(TĀ“)^{2};
+
+and since the periodic times of the earth and Mars, _TĀ“_, _TĀ“Ā“_, are
+known to a high degree of accuracy, these two equations are sufficient
+to determine the two unknown quantities, _aĀ“_, _aĀ“Ā“_--i. e., the
+distance of the sun from Mars as well as from the earth. The first of
+these equations is, of course, not strictly true, on account of the
+elliptical shape of the orbits, but this can be allowed for easily
+enough.
+
+In practice it is found better to apply this method of determining the
+sun's distance through observations of an asteroid rather than
+observations of Mars, and great interest has been aroused among
+astronomers by the discovery, in 1898, of an asteroid, or planet, Eros,
+which at times comes much closer to the earth than does Mars or any
+other heavenly body except the moon, and which will at future
+oppositions furnish a more accurate determination of the sun's distance
+than any hitherto available. Observations for this purpose are being
+made at the present time (October, 1900).
+
+Many other methods of measuring the sun's distance have been devised by
+astronomers, some of them extremely ingenious and interesting, but every
+one of them has its weak point--e. g., the determination of the mass of
+the earth in the first method given above and the measurement of _D_ in
+the second method, so that even the best results at present are
+uncertain to the extent of 200,000 miles or more, and astronomers,
+instead of relying upon any one method, must use all of them, and take
+an average of their results. According to Professor Harkness, this
+average value is 92,796,950 miles, and it seems certain that a line of
+this length drawn from the earth toward the sun would end somewhere
+within the body of the sun, but whether on the nearer or the farther
+side of the center, or exactly at it, no man knows.
+
+114. PARALLAX AND DISTANCE.--It is quite customary among astronomers to
+speak of the sun's parallax, instead of its distance from the earth,
+meaning by parallax its difference of direction as seen from the center
+and surface of the earth--i. e., the angle subtended at the sun by a
+radius of the earth placed at right angles to the line of sight. The
+greater the sun's distance the smaller will this angle be, and it
+therefore makes a substitute for the distance which has the advantage of
+being represented by a small number, 8".8, instead of a large one.
+
+The books abound with illustrations intended to help the reader
+comprehend how great is a distance of 93,000,000 miles, but a single one
+of these must suffice here. To ride 100 miles a day 365 days in the year
+would be counted a good bicycling record, but the rider who started at
+the beginning of the Christian era and rode at that rate toward the sun
+from the year 1 A. D. down to the present moment would not yet have
+reached his destination, although his journey would be about three
+quarters done. He would have crossed the orbit of Venus about the time
+of Charlemagne, and that of Mercury soon after the discovery of America.
+
+115. SIZE AND DENSITY OF THE SUN.--Knowing the distance of the sun, it
+is easy to find from the angle subtended by its diameter (32 minutes of
+arc) that the length of that diameter is 865,000 miles. We recall in
+this connection that the diameter of the moon's _orbit_ is only 480,000
+miles, but little more than half the diameter of the sun, thus affording
+abundant room inside the sun, and to spare, for the moon to perform the
+monthly revolution about its orbit, as shown in Fig. 65.
+
+[Illustration: FIG. 65.--The sun's size.--YOUNG.]
+
+In the same manner in which the density of the moon was found from its
+mass and diameter, the student may find from the mass and diameter of
+the sun given above that its mean density is 1.4 times that of water.
+This is about the same as the density of gravel or soft coal, and is
+just about one quarter of the average density of the earth.
+
+We recall that the small density of the moon was accounted for by the
+diminished weight of objects upon it, but this explanation can not hold
+in the case of the sun, for not only is the density less but the force
+of gravity (weight) is there 28 times as great as upon the earth. The
+athlete who here weighs 175 pounds, if transported to the surface of the
+sun would weigh more than an elephant does here, and would find his
+bones break under his own weight if his muscles were strong enough to
+hold him upright. The tremendous pressure exerted by gravity at the
+surface of the sun must be surpassed below the surface, and as it does
+not pack the material together and make it dense, we are driven to one
+of two conclusions: Either the stuff of which the sun is made is
+altogether unlike that of the earth, not so readily compressed by
+pressure, or there is some opposing influence at work which more than
+balances the effect of gravity and makes the solar stuff much lighter
+than the terrestrial.
+
+116. MATERIAL OF WHICH THE SUN IS MADE.--As to the first of these
+alternatives, the spectroscope comes to our aid and shows in the sun's
+spectrum (Fig. 50) the characteristic line marked _D_, which we know
+always indicates the presence of sodium and identifies at least one
+terrestrial substance as present in the sun in considerable quantity.
+The lines marked _C_ and _F_ are produced by hydrogen, which is one of
+the constituents of water, _E_ shows calcium to be present in the sun,
+_b_ magnesium, etc. In this way it has been shown that about one half of
+our terrestrial elements, mainly the metallic ones, are present as gases
+on or near the sun's surface, but it must not be inferred that elements
+not found in this way are absent from the sun. They may be there,
+probably are there, but the spectroscopic proof of their presence is
+more difficult to obtain. Professor Rowland, who has been prominent in
+the study of the solar spectrum, says: "Were the whole earth heated to
+the temperature of the sun, its spectrum would probably resemble that of
+the sun very closely."
+
+Some of the common terrestrial elements found in the sun are:
+
+      Aluminium.
+      Calcium.
+      Carbon.
+      Copper.
+      Hydrogen.
+      Iron.
+      Lead.
+      Nickel.
+      Potassium.
+      Silicon.
+      Silver.
+      Sodium.
+      Tin.
+      Zinc.
+      Oxygen (?)
+
+Whatever differences of chemical structure may exist between the sun and
+the earth, it seems that we must regard these bodies as more like than
+unlike to each other in substance, and we are brought back to the second
+of our alternatives: there must be some influence opposing the force of
+gravity and making the substance of the sun light instead of heavy, and
+we need not seek far to find it in--
+
+117. THE HEAT OF THE SUN.--That the sun is hot is too evident to require
+proof, and it is a familiar fact that heat expands most substances and
+makes them less dense. The sun's heat falling upon the earth expands it
+and diminishes its density in some small degree, and we have only to
+imagine this process of expansion continued until the earth's diameter
+becomes 58 per cent larger than it now is, to find the earth's density
+reduced to a level with that of the sun. Just how much the temperature
+of the earth must be raised to produce this amount of expansion we do
+not know, neither do we know accurately the temperature of the sun, but
+there can be no doubt that heat is the cause of the sun's low density
+and that the corresponding temperature is very high.
+
+Before we inquire more closely into the sun's temperature, it will be
+well to draw a sharp distinction between the two terms heat and
+temperature, which are often used as if they meant the same thing. Heat
+is a form of energy which may be found in varying degree in every
+substance, whether warm or cold--a block of ice contains a considerable
+amount of heat--while temperature corresponds to our sensations of warm
+and cold, and measures the extent to which heat is concentrated in the
+body. It is the amount of heat per molecule of the body. A barrel of
+warm water contains more heat than the flame of a match, but its
+temperature is not so high. Bearing in mind this distinction, we seek to
+determine not the amount of heat contained in the sun but the sun's
+temperature, and this involves the same difficulty as does the question,
+What is the temperature of a locomotive? It is one thing in the fire box
+and another thing in the driving wheels, and still another at the
+headlight; and so with the sun, its temperature is certainly different
+in different parts--one thing at the center and another at the surface.
+Even those parts which we see are covered by a veil of gases which
+produce by absorption the dark lines of the solar spectrum, and
+seriously interfere both with the emission of energy from the sun and
+with our attempts at measuring the temperature of those parts of the
+surface from which that energy streams.
+
+In view of these and other difficulties we need not be surprised that
+the wildest discordance has been found in estimates of the solar
+temperature made by different investigators, who have assigned to it
+values ranging from 1,400Ā° C. to more than 5,000,000Ā° C. Quite recently,
+however, improved methods and a better understanding of the problem have
+brought about a better agreement of results, and it now seems probable
+that the temperature of the visible surface of the sun lies somewhere
+between 5,000Ā° and 10,000Ā° C., say 15,000Ā° of the Fahrenheit scale.
+
+118. DETERMINING THE SUN'S TEMPERATURE.--One ingenious method which has
+been used for determining this temperature is based upon the principle
+stated above, that every object, whether warm or cold, contains heat and
+gives it off in the form of radiant energy. The radiation from a body
+whose temperature is lower than 500Ā° C. is made up exclusively of energy
+whose wave length is greater than 7,600 tenth meters, and is therefore
+invisible to the eye, although a thermometer or even the human hand can
+often detect it as radiant heat. A brick wall in the summer sunshine
+gives off energy which can be felt as heat but can not be seen. When
+such a body is further heated it continues to send off the same kinds
+(wave lengths) of energy as before, but new and shorter waves are added
+to its radiation, and when it begins to emit energy of wave length 7,500
+or 7,600 tenth meters, it also begins to shine with a dull-red light,
+which presently becomes brighter and less ruddy and changes to white as
+the temperature rises, and waves of still shorter length are thereby
+added to the radiation. We say, in common speech, the body becomes first
+red hot and then white hot, and we thus recognize in a general way that
+the kind or color of the radiation which a body gives off is an index to
+its temperature. The greater the proportion of energy of short wave
+lengths the higher is the temperature of the radiating body. In sunlight
+the maximum of brilliancy to the eye lies at or near the wave length,
+5,600 tenth meters, but the greatest intensity of radiation of all kinds
+(light included) is estimated to fall somewhere between green and blue
+in the spectrum at or near the wave length 5,000 tenth meters, and if we
+can apply to this wave length Paschen's law--temperature reckoned in
+degrees centigrade from the absolute zero is always equal to the
+quotient obtained by dividing the number 27,000,000 by the wave length
+corresponding to maximum radiation--we shall find at once for the
+absolute temperature of the sun's surface 5,400Ā° C.
+
+Paschen's law has been shown to hold true, at least approximately, for
+lower temperatures and longer wave lengths than are here involved, but
+as it is not yet certain that it is strictly true and holds for all
+temperatures, too great reliance must not be attached to the numerical
+result furnished by it.
+
+[Illustration: FIG. 66.--The sun, August 11, 1894. Photographed at the
+Goodsell Observatory.]
+
+[Illustration: FIG. 67.--The sun, August 14, 1894. Photographed at the
+Goodsell Observatory.]
+
+119. THE SUN'S SURFACE.--A marked contrast exists between the faces of
+sun and moon in respect of the amount of detail to be seen upon them,
+the sun showing nothing whatever to correspond with the mountains,
+craters, and seas of the moon. The unaided eye in general finds in the
+sun only a blank bright circle as smooth and unmarked as the surface of
+still water, and even the telescope at first sight seems to show but
+little more. There may usually be found upon the sun's face a certain
+number of black patches called _sun spots_, such as are shown in Figs.
+66 to 69, and occasionally these are large enough to be seen through a
+smoked glass without the aid of a telescope. When seen near the edge of
+the sun they are quite frequently accompanied, as in Fig. 69, by vague
+patches called _faculƦ_ (Latin, _facula_ = a little torch), which look a
+little brighter than the surrounding parts of the sun. So, too, a good
+photograph of the sun usually shows that the central parts of the disk
+are rather brighter than the edge, as indeed we should expect them to
+be, since the absorption lines in the sun's spectrum have already taught
+us that the visible surface of the sun is enveloped by invisible vapors
+which in some measure absorb the emitted light and render it feebler at
+the edge where it passes through a greater thickness of this envelope
+than at the center. See Fig. 70, where it is shown that the energy
+coming from the edge of the sun to the earth has to traverse a much
+longer path inside the vapors than does that coming from the center.
+
+[Illustration: FIG. 68.--The sun, August 18, 1894. Photographed at the
+Goodsell Observatory.]
+
+Examine the sun spots in the four photographs, Figs. 66 to 69, and note
+that the two spots which appear at the extreme left of the first
+photograph, very much distorted and foreshortened by the curvature of
+the sun's surface, are seen in a different part of the second picture,
+and are not only more conspicuous but show better their true shape.
+
+[Illustration: PLATE II. THE EQUATORIAL CONSTELLATIONS]
+
+120. THE SUN'S ROTATION.--The changed position of these spots shows that
+the sun rotates about an axis at right angles to the direction of the
+spot's motion, and the position of this axis is shown in the figure by a
+faint line ruled obliquely across the face of the sun nearly north and
+south in each of the four photographs. This rotation in the space of
+three days has carried the spots from the edge halfway to the center of
+the disk, and the student should note the progress of the spots in the
+two later photographs, that of August 21st showing them just ready to
+disappear around the farther edge of the sun.
+
+[Illustration: FIG. 69.--The sun, August 21, 1894. Photographed at the
+Goodsell Observatory.]
+
+Plot accurately in one of these figures the positions of the spots as
+shown in the other three, and observe whether the path of the spots
+across the sun's face is a straight line. Is there any reason why it
+should not be straight?
+
+These four pictures may be made to illustrate many things about the sun.
+Thus the sun's axis is not parallel to that of the earth, for the
+letters _N S_ mark the direction of a north and south line across the
+face of the sun, and this line, of course, is parallel to the earth's
+axis, while it is evidently not parallel to the sun's axis. The group of
+spots took more than ten days to move across the sun's face, and as at
+least an equal time must be required to move around the opposite side of
+the sun, it is evident that the period of the sun's rotation is
+something more than 20 days. It is, in fact, rather more than 25 days,
+for this same group of spots reappeared again on the left-hand edge of
+the sun on September 5th.
+
+[Illustration: FIG. 70.--Absorption at the sun's edge.]
+
+121. SUN SPOTS.--Another significant fact comes out plainly from the
+photographs. The spots are not permanent features of the sun's face,
+since they changed their size and shape very appreciably in the few days
+covered by the pictures. Compare particularly the photographs of August
+14th and August 18th, where the spots are least distorted by the
+curvature of the sun's surface. By September 16th this group of spots
+had disappeared absolutely from the sun's face, although when at its
+largest the group extended more than 80,000 miles in length, and several
+of the individual spots were large enough to contain the earth if it had
+been dropped upon them. From Fig. 67 determine in miles the length of
+the group on August 14th. Fig. 71 shows an enlarged view of these spots
+as they appeared on August 17th, and in this we find some details not so
+well shown in the preceding pictures. The larger spots consist of a
+black part called the _nucleus_ or _umbra_ (Latin, shadow), which is
+surrounded by an irregular border called the _penumbra_ (partial
+shadow), which is intermediate in brightness between the nucleus and
+the surrounding parts of the sun. It should not be inferred from the
+picture that the nucleus is really black or even dark. It shines, in
+fact, with a brilliancy greater than that of an electric lamp, but the
+background furnished by the sun's surface is so much brighter that by
+contrast with it the nucleus and penumbra appear relatively dark.
+
+[Illustration: FIG. 71.--Sun spots, August 17, 1894. Goodsell
+Observatory.]
+
+[Illustration: FIG. 72.--Sun spot of March 5, 1873.--From LANGLEY, The
+New Astronomy. By permission of the publishers.]
+
+The bright shining surface of the sun, the background for the spots, is
+called the _photosphere_ (Greek, light sphere), and, as Fig. 71 shows,
+it assumes under a suitable magnifying power a mottled aspect quite
+different from the featureless expanse shown in the earlier pictures.
+The photosphere is, in fact, a layer of little clouds with darker
+spaces between them, and the fine detail of these clouds, their
+complicated structure, and the way in which, when projected against the
+background of a sun spot, they produce its penumbra, are all brought out
+in Fig. 72. Note that the little patch in one corner of this picture
+represents North and South America drawn to the same scale as the sun
+spots.
+
+[Illustration: FIG. 73.--Spectroheliograph, showing distribution of
+faculƦ upon the sun.--HALE.]
+
+[Illustration: FIG. 74.--Eclipse of July 20, 1878.--TROUVELOT.]
+
+122. FACULƆ.--We have seen in Fig. 69 a few of the bright spots called
+faculƦ. At the telescope or in the ordinary photograph these can be seen
+only at the edge of the sun, because elsewhere the background furnished
+by the photosphere is so bright that they are lost in it. It is
+possible, however, by an ingenious application of the spectroscope to
+break up the sunlight into a spectrum in such a way as to diminish the
+brightness of this background, much more than the brightness of the
+faculƦ is diminished, and in this way to obtain a photograph of the
+sun's surface which shall show them wherever they occur, and such a
+photograph, showing faintly the spectral lines, is reproduced in Fig.
+73. The faculƦ are the bright patches which stretch inconspicuously
+across the face of the sun, in two rather irregular belts with a
+comparatively empty lane between them. This lane lies along the sun's
+equator, and it is upon either side of it between latitudes 5Ā° and 40Ā°
+that faculƦ seem to be produced. It is significant of their connection
+with sun spots that the spots occur in these particular zones and are
+rarely found outside them.
+
+[Illustration: FIG. 75.--Eclipse of April 16, 1893.--SCHAEBERLE.]
+
+123. INVISIBLE PARTS OF THE SUN. THE CORONA.--Thus far we have been
+dealing with parts of the sun that may be seen and photographed under
+all ordinary conditions. But outside of and surrounding these parts is
+an envelope, or rather several envelopes, of much greater extent than
+the visible sun. These envelopes are for the most part invisible save at
+those times when the brighter central portions of the sun are hidden in
+a total eclipse.
+
+[Illustration: FIG. 76.--Eclipse of January 21, 1898.--CAMPBELL.]
+
+Fig. 74 is from a drawing, and Figs. 75 and 76 are from eclipse
+photographs showing this region, in which the most conspicuous object
+is the halo of soft light called the _corona_, that completely surrounds
+the sun but is seen to be of differing shapes and differing extent at
+the several eclipses here shown, although a large part of these apparent
+differences is due to technical difficulties in photographing, and
+reproducing an object with outlines so vague as those of the corona. The
+outline of the corona is so indefinite and its outer portions so faint
+that it is impossible to assign to it precise dimensions, but at its
+greatest extent it reaches out for several millions of miles and fills a
+space more than twenty times as large as the visible part of the sun.
+Despite its huge bulk, it is of most unsubstantial character, an airy
+nothing through which comets have been known to force their way around
+the sun from one side to the other, literally for millions of miles,
+without having their course influenced or their velocity checked to any
+appreciable extent. This would hardly be possible if the density even at
+the bottom of the corona were greater than that of the best vacuum which
+we are able to produce in laboratory experiments. It seems odd that a
+vacuum should give off so bright a light as the coronal pictures show,
+and the exact character of that light and the nature of the corona are
+still subjects of dispute among astronomers, although it is generally
+agreed that, in part at least, its light is ordinary sunlight faintly
+reflected from the widely scattered molecules composing the substance of
+the corona. It is also probable that in part the light has its origin in
+the corona itself. A curious and at present unconfirmed result announced
+by one of the observers of the eclipse of May 28, 1900, is that _the
+corona is not hot_, its effective temperature being lower than that of
+the instrument used for the observation.
+
+[Illustration: FIG. 77.--Solar prominence of March 25, 1895.--HALE.]
+
+124. THE CHROMOSPHERE.--Between the corona and the photosphere there is
+a thin separating layer called the _chromosphere_ (Greek, color sphere),
+because when seen at an eclipse it shines with a brilliant red light
+quite unlike anything else upon the sun save the _prominences_ which are
+themselves only parts of the chromosphere temporarily thrown above its
+surface, as in a fountain a jet of water is thrown up from the basin and
+remains for a few moments suspended in mid-air. Not infrequently in such
+a fountain foreign matter is swept up by the rush of the water--dirt,
+twigs, small fish, etc.--and in like manner the prominences often carry
+along with them parts of the underlying layers of the sun, photosphere,
+faculƦ, etc., which reveal their presence in the prominence by adding
+their characteristic lines to the spectrum, like that of the
+chromosphere, which the prominence presents when they are absent. None
+of the eclipse photographs (Figs. 74 to 76) show the chromosphere,
+because the color effect is lacking in them, but a great curving
+prominence may be seen near the bottom of Fig. 75, and smaller ones at
+other parts of the sun's edge.
+
+[Illustration: FIG. 78.--A solar prominence.--HALE.]
+
+125. PROMINENCES.--Fig. 77 shows upon a larger scale one of these
+prominences rising to a height of 160,000 miles above the photosphere;
+and another photograph, taken 18 minutes later, but not reproduced here,
+showed the same prominence grown in this brief interval to a stature of
+280,000 miles. These pictures were not taken during an eclipse, but in
+full sunlight, using the same spectroscopic apparatus which was employed
+in connection with the faculƦ to diminish the brightness of the
+background without much enfeebling the brilliancy of the prominence
+itself. The dark base from which the prominence seems to spring is not
+the sun's edge, but a part of the apparatus used to cut off the direct
+sunlight.
+
+Fig. 78 contains a series of photographs of another prominence taken
+within an interval of 1 hour 47 minutes and showing changes in size and
+shape which are much more nearly typical of the ordinary prominence than
+was the very unusual change in the case of Fig. 77.
+
+[Illustration: FIG. 79.--Contrasted forms of solar
+prominences.--ZOELLNER.]
+
+The preceding pictures are from photographs, and with them the student
+may compare Fig. 79, which is constructed from drawings made at the
+spectroscope by the German astronomer Zoellner. The changes here shown
+are most marked in the prominence at the left, which is shaped like a
+broken tree trunk, and which appears to be vibrating from one side to
+the other like a reed shaken in the wind. Such a prominence is
+frequently called an _eruptive_ one, a name suggested by its appearance
+of having been blown out from the sun by something like an explosion,
+while the prominence at the right in this series of drawings, which
+appears much less agitated, is called by contrast with the other a
+_quiescent_ prominence. These quiescent prominences are, as a rule, much
+longer-lived than the eruptive ones. One more picture of prominences
+(Fig. 80) is introduced to show the continuous stretch of chromosphere
+out of which they spring.
+
+[Illustration: FIG. 80.--Prominences and chromosphere.--HALE.]
+
+Prominences are seen only at the edge of the sun, because it is there
+alone that the necessary background can be obtained, but they must occur
+at the center of the sun and elsewhere quite as well as at the edge, and
+it is probable that quiescent prominences are distributed over all parts
+of the sun's surface, but eruptive prominences show a strong tendency
+toward the regions of sun spots and faculƦ as if all three were
+intimately related phenomena.
+
+126. THE SUN AS A MACHINE.--Thus far we have considered the anatomy of
+the sun, dissecting it into its several parts, and our next step should
+be a consideration of its physiology, the relation of the parts to each
+other, and their function in carrying on the work of the solar organism,
+but this step, unfortunately, must be a lame one. The science of
+astronomy to-day possesses no comprehensive and well-established theory
+of this kind, but looks to the future for the solution of this the
+greatest pending problem of solar physics. Progress has been made
+toward its solution, and among the steps of this progress that we shall
+have to consider, the first and most important is the conception of the
+sun as a kind of heat engine.
+
+In a steam engine coal is burned under the boiler, and its chemical
+energy, transformed into heat, is taken up by the water and delivered,
+through steam as a medium, to the engine, which again transforms and
+gives it out as mechanical work in the turning of shafts, the driving of
+machinery, etc. Now, the function of the sun is exactly opposite to that
+of the engine and boiler: it gives out, instead of receiving, radiant
+energy; but, like the engine, it must be fed from some source; it can
+not be run upon nothing at all any more than the engine can run day
+after day without fresh supplies of fuel under its boiler. We know that
+for some thousands of years the sun has been furnishing light and heat
+to the earth in practically unvarying amount, and not to the earth
+alone, but it has been pouring forth these forms of energy in every
+direction, without apparent regard to either use or economy. Of all the
+radiant energy given off by the sun, only two parts out of every
+thousand million fall upon any planet of the solar system, and of this
+small fraction the earth takes about one tenth for the maintenance of
+its varied forms of life and action. Astronomers and physicists have
+sought on every hand for an explanation of the means by which this
+tremendous output of energy is maintained century after century without
+sensible diminution, and have come with almost one mind to the
+conclusion that the gravitative forces which reside in the sun's own
+mass furnish the only adequate explanation for it, although they may be
+in some small measure re-enforced by minor influences, such as the fall
+of meteoric dust and stones into the sun.
+
+Every boy who has inflated a bicycle tire with a hand pump knows that
+the pump grows warm during the operation, on account of the compression
+of the air within the cylinder. A part of the muscular force (energy)
+expended in working the pump reappears in the heat which warms both air
+and pump, and a similar process is forever going on in the sun, only in
+place of muscular force we must there substitute the tremendous
+attraction of gravitation, 28 times as great as upon the earth. "The
+matter in the interior of the sun must be as a shuttlecock between the
+stupendous pressure and the enormously high temperature," the one
+tending to compress and the other to expand it, but with this important
+difference between them: the temperature steadily tends to fall as the
+heat energy is wasted away, while the gravitative force suffers no
+corresponding diminution, and in the long run must gain the upper hand,
+causing the sun to shrink and become more dense. It is this progressive
+shrinking and compression of its molecules into a smaller space which
+supplies the energy contained in the sun's output of light and heat.
+According to Lord Kelvin, each centimeter of shrinkage in the sun's
+diameter furnishes the energy required to keep up its radiation for
+something more than an hour, and, on account of the sun's great
+distance, the shrinkage might go on at this rate for many centuries
+without producing any measurable effect in the sun's appearance.
+
+127. GASEOUS CONSTITUTION OF THE SUN.--But Helmholtz's dynamical theory
+of the maintenance of the sun's heat, which we are here considering,
+includes one essential feature that is not sufficiently stated above. In
+order that the explanation may hold true, it is necessary that the sun
+should be in the main a gaseous body, composed from center to
+circumference of gases instead of solid or liquid parts. Pumping air
+warms the bicycle pump in a way that pumping water or oil will not.
+
+The high temperature of the sun itself furnishes sufficient reason for
+supposing the solar material to be in the gaseous state, but the gas
+composing those parts of the sun below the photosphere must be very
+different in some of its characteristics from the air or other gases
+with which we are familiar at the earth, since its average density is
+1,000 times as great as that of air, and its consistence and mechanical
+behavior must be more like that of honey or tar than that of any gas
+with which we are familiar. It is worth noting, however, that if a hole
+were dug into the crust of the earth to a depth of 15 or 20 miles the
+air at the bottom of the hole would be compressed by that above it to a
+density comparable with that of the solar gases.
+
+128. THE SUN'S CIRCULATION.--It is plain that under the conditions which
+exist in the sun the outer portions, which can radiate their heat freely
+into space, must be cooler than the inner central parts, and this
+difference of temperature must set up currents of hot matter drifting
+upward and outward from within the sun and counter currents of cooler
+matter settling down to take its place. So, too, there must be some
+level at which the free radiation into outer space chills the hot matter
+sufficiently to condense its less refractory gases into clouds made up
+of liquid drops, just as on a cloudy day there is a level in our own
+atmosphere at which the vapor of water condenses into liquid drops which
+form the thin shell of clouds that hovers above the earth's surface,
+while above and below is the gaseous atmosphere. In the case of the sun
+this cloud layer is always present and is that part which we have
+learned to call the photosphere. Above the photosphere lies the
+chromosphere, composed of gases less easily liquefied, hydrogen is the
+chief one, while between photosphere and chromosphere is a thin layer of
+metallic vapors, perhaps indistinguishable from the top crust of the
+photosphere itself, which by absorbing the light given off from the
+liquid photosphere produces the greater part of the Fraunhofer lines in
+the solar spectrum.
+
+From time to time the hot matter struggling up from below breaks through
+the photosphere and, carrying with it a certain amount of the metallic
+vapors, is launched into the upper and cooler regions of the sun,
+where, parting with its heat, it falls back again upon the photosphere
+and is absorbed into it. It is altogether probable that the corona is
+chiefly composed of fine particles ejected from the sun with velocities
+sufficient to carry them to a height of millions of miles, or even
+sufficient to carry them off never to return. The matter of the corona
+must certainly be in a state of the most lively agitation, its particles
+being alternately hurled up from the photosphere and falling back again
+like fireworks, the particles which make up the corona of to-day being
+quite a different set from those of yesterday or last week. It seems
+beyond question that the prominences and faculƦ too are produced in some
+way by this up-and-down circulation of the sun's matter, and that any
+mechanical explanation of the sun must be worked out along these lines;
+but the problem is an exceedingly difficult one, and must include and
+explain many other features of the sun's activity of which only a few
+can be considered here.
+
+129. THE SUN-SPOT PERIOD.--Sun spots come and go, and at best any
+particular spot is but short-lived, rarely lasting more than a month or
+two, and more often its duration is a matter of only a few days. They
+are not equally numerous at all times, but, like swarms of locusts, they
+seem to come and abound for a season and then almost to disappear, as if
+the forces which produced them were of a periodic character alternately
+active and quiet. The effect of this periodic activity since 1870 is
+shown in Fig. 81, where the horizontal line is a scale of times, and the
+distance of the curve above this line for any year shows the relative
+number of spots which appeared upon the sun in that year. This indicates
+very plainly that 1870, 1883, and 1893 were years of great sun-spot
+activity, while 1879 and 1889 were years in which few spots appeared.
+The older records, covering a period of two centuries, show the same
+fluctuations in the frequency of sun spots and from these records
+curves (which may be found in Young's, The Sun) have been plotted,
+showing a succession of waves extending back for many years.
+
+[Illustration: FIG. 81.--The curve of sun-spot frequency.]
+
+The sun-spot period is the interval of time from the crest or hollow of
+one wave to the corresponding part of the next one, and on the average
+this appears to be a little more than eleven years, but is subject to
+considerable variation. In accordance with this period there is drawn in
+broken lines at the right of Fig. 81 a predicted continuation of the
+sun-spot curve for the first decade of the twentieth century. The
+irregularity shown by the three preceding waves is such that we must not
+expect the actual course of future sun spots to correspond very closely
+to the prediction here made; but in a general way 1901 and 1911 will
+probably be years of few sun spots, while they will be numerous in 1905,
+but whether more or less numerous than at preceding epochs of greatest
+frequency can not be foretold with any approach to certainty so long as
+we remain in our present ignorance of the causes which make the sun-spot
+period.
+
+Determine from Fig. 81 as accurately as possible the length of the
+sun-spot period. It is hard to tell the exact position of a crest or
+hollow of the curve. Would it do to draw a horizontal line midway
+between top and bottom of the curve and determine the length of the
+period from its intersections with the curve--e. g., in 1874 and 1885?
+
+[Illustration: FIG. 82.--Illustrating change of the sun-spot zones.]
+
+130. THE SUN-SPOT ZONES.--It has been already noted that sun spots are
+found only in certain zones of latitude upon the sun, and that faculƦ
+and eruptive prominences abound in these zones more than elsewhere,
+although not strictly confined to them. We have now to note a
+peculiarity of these zones which ought to furnish a clew to the sun's
+mechanism, although up to the present time it has not been successfully
+traced out. Just before a sun-spot minimum the few spots which appear
+are for the most part clustered near the sun's equator. As these spots
+die out two new groups appear, one north the other south of the sun's
+equator and about 25Ā° or 30Ā° distant from it, and as the period advances
+toward a maximum these groups shift their positions more and more toward
+the equator, thus approaching each other but leaving between them a
+vacant lane, which becomes steadily narrower until at the close of the
+period, when the next minimum is at hand, it reaches its narrowest
+dimensions, but does not altogether close up even then. In Fig. 82 these
+relations are shown for the period falling between 1879 and 1890, by
+means of the horizontal lines; for each year one line in the northern
+and one in the southern hemisphere of the sun, their lengths being
+proportional to the number of spots which appeared in the corresponding
+hemisphere during the year, and their positions on the sun's disk
+showing the average latitude of the spots in question. It is very
+apparent from the figure that during this decade the sun's southern
+hemisphere was much more active than the northern one in the production
+of spots, and this appears to be generally the case, although the
+difference is not usually as great as in this particular decade.
+
+131. INFLUENCE OF THE SUN-SPOT PERIOD.--Sun spots are certainly less hot
+than the surrounding parts of the sun's surface, and, in view of the
+intimate dependence of the earth upon the solar radiation, it would be
+in no way surprising if their presence or absence from the sun's face
+should make itself felt in some degree upon the earth, raising and
+lowering its temperature and quite possibly affecting it in other ways.
+Ingenious men have suggested many such kinds of influence, which,
+according to their investigations, appear to run in cycles of eleven
+years. Abundant and scanty harvests, cyclones, tornadoes, epidemics,
+rainfall, etc., are among these alleged effects, and it is possible that
+there may be a real connection between any or all of them and the
+sun-spot period, but for the most part astronomers are inclined to hold
+that there is only one case in which the evidence is strong enough to
+really establish a connection of this kind. The magnetic condition of
+the earth and its disturbances, which are called magnetic storms, do
+certainly follow in a very marked manner the course of sun-spot
+activity, and perhaps there should be added to this the statement that
+auroras (northern lights) stand in close relation to these magnetic
+disturbances and are most frequent at the times of sun-spot maxima.
+
+Upon the sun, however, the influence of the spot period is not limited
+to things in and near the photosphere, but extends to the outermost
+limits of the corona. Determine from Fig. 81 the particular part of the
+sun-spot period corresponding to the date of each picture of the corona
+and note how the pictures which were taken near times of sun-spot minima
+present a general agreement in the shape and extent of the corona, while
+the pictures taken at a time of maximum activity of the sun spots show a
+very differently shaped and much smaller corona.
+
+132. THE LAW OF THE SUN'S ROTATION.--We have seen in a previous part of
+the chapter how the time required by the sun to make a complete rotation
+upon its axis may be determined from photographs showing the progress of
+a spot or group of spots across its disk, and we have now to add that
+when this is done systematically by means of many spots situated in
+different solar latitudes it leads to a very peculiar and extraordinary
+result. Each particular parallel of latitude has its own period of
+rotation different from that of its neighbors on either side, so that
+there can be no such thing as a fixed geography of the sun's surface.
+Every part of it is constantly taking up a new position with respect to
+every other part, much as if the Gulf of Mexico should be south of the
+United States this year, southeast of it next year, and at the end of a
+decade should have shifted around to the opposite side of the earth from
+us. A meridian of longitude drawn down the Mississippi Valley remains
+always a straight line, or, rather, great circle, upon the surface of
+the earth, while Fig. 83 shows what would become of such a meridian
+drawn through the equatorial parts of the sun's disk. In the first
+diagram it appears as a straight line running down the middle of the
+sun's disk. Twenty-five days later, when the same face of the sun comes
+back into view again, after making a complete revolution about the axis,
+the equatorial parts will have moved so much faster and farther than
+those in higher latitudes that the meridian will be warped as in the
+second diagram, and still more warped after another and another
+revolution, as shown in the figure.
+
+[Illustration: FIG. 83.--Effect of the sun's peculiar rotation in
+warping a meridian, originally straight.]
+
+At least such is the case if the spots truly represent the way in which
+the sun turns round. There is, however, a possibility that the spots
+themselves drift with varying speeds across the face of the sun, and
+that the differences which we find in their rates of motion belong to
+them rather than to the photosphere. Just what happens in the regions
+near the poles is hard to say, for the sun spots only extend about
+halfway from the equator to the poles, and the spectroscope, which may
+be made to furnish a certain amount of information bearing upon the
+case, is not as yet altogether conclusive, nor are the faculƦ which have
+also been observed for this purpose.
+
+The simple theory that the solar phenomena are caused by an interchange
+of hotter and cooler matter between the photosphere and the lower strata
+of the sun furnishes in its present shape little or no explanation of
+such features as the sun-spot period, the variations in the corona, the
+peculiar character of the sun's rotation, etc., and we have still
+unsolved in the mechanical theory of the sun one of the noblest problems
+of astronomy, and one upon which both observers and theoretical
+astronomers are assiduously working at the present time. A close watch
+is kept upon sun spots and prominences, the corona is observed at every
+total eclipse, and numerous are the ingenious methods which are being
+suggested and tried for observing it without an eclipse in ordinary
+daylight. Attempts, more or less plausible, have been made and are now
+pending to explain photosphere, spots and the reversing layer by means
+of the refraction of light within the sun's outer envelope of gases, and
+it seems altogether probable, in view of these combined activities, that
+a considerable addition to our store of knowledge concerning the sun may
+be expected in the not distant future.
+
+
+
+
+CHAPTER XI
+
+THE PLANETS
+
+
+133. PLANETS.--Circling about the sun, under the influence of his
+attraction, is a family of planets each member of which is, like the
+moon, a dark body shining by reflected sunlight, and therefore
+presenting phases; although only two of them, Mercury and Venus, run
+through the complete series--new, first quarter, full, last
+quarter--which the moon presents. The way in which their orbits are
+grouped about the sun has been considered in Chapter III, and Figs. 16
+and 17 of that chapter may be completed so as to represent all of the
+planets by drawing in Fig. 16 two circles with radii of 7.9 and 12.4
+centimeters respectively, to represent the orbits of the planets Uranus
+and Neptune, which are more remote from the sun than Saturn, and by
+introducing a little inside the orbit of Jupiter about 500 ellipses of
+different sizes, shapes, and positions to represent a group of minor
+planets or asteroids as they are often called. It is convenient to
+regard these asteroids as composing by themselves a class of very small
+planets, while the remaining 8 larger planets fall naturally into two
+other classes, a group of medium-sized ones--Mercury, Venus, Earth, and
+Mars--called inner planets by reason of their nearness to the sun; and
+the outer planets--Jupiter, Saturn, Uranus, Neptune--each of which is
+much larger and more massive than any planet of the inner group. Compare
+in Figs. 84 and 85 their relative sizes. The earth, _E_, is introduced
+into Fig. 85 as a connecting link between the two figures.
+
+Some of these planets, like the earth, are attended by one or more
+moons, technically called satellites, which also shine by reflected
+sunlight and which move about their respective planets in accordance
+with the law of gravitation, much as the moon moves around the earth.
+
+[Illustration: FIG. 84.--The inner planets and the moon.]
+
+[Illustration: FIG. 85.--The outer planets.]
+
+134. DISTANCES OF THE PLANETS FROM THE SUN.--It is a comparatively
+simple matter to observe these planets year after year as they move
+among the stars, and to find from these observations how long each one
+of them requires to make its circuit around the sun--that is, its
+periodic time, _T_, which figures in Kepler's Third Law, and when these
+periodic times have been ascertained, to use them in connection with
+that law to determine the mean distance of each planet from the sun.
+Thus, Jupiter requires 4,333 days to move completely around its orbit;
+and comparing this with the periodic time and mean distance of the earth
+we find--
+
+    a^{3} / (4333^{2}) = (93,000,000^{3}) / (365.25^{2}),
+
+which when solved gives as the mean distance of Jupiter from the sun,
+483,730,000 miles, or 5.20 times as distant as the earth. If we make a
+similar computation for each planet, we shall find that their distances
+from the sun show a remarkable agreement with an artificial series of
+numbers called Bode's law. We write down the numbers contained in the
+first line of figures below, each of which, after the second, is
+obtained by doubling the preceding one, add 4 to each number and point
+off one place of decimals; the resulting number is (approximately) the
+distance of the corresponding planet from the sun.
+
+ Mercury.  Venus.  Earth.  Mars.    Jupiter.  Saturn.  Uranus.  Neptune.
+    0        3       6      12   24   48        96       192      384
+    4        4       4       4    4    4         4         4        4
+ -----------------------------------------------------------------------
+   0.4      0.7     1.0    1.6  2.8  5.2      10.0      19.6     38.8
+   0.4      0.7     1.0    1.5  2.8  5.2       9.5      19.2     30.1
+
+The last line of figures shows the real distance of the planet as
+determined from Kepler's law, the earth's mean distance from the sun
+being taken as the unit for this purpose. With exception of Neptune, the
+agreement between Bode's law and the true distances is very striking,
+but most remarkable is the presence in the series of a number, 2.8, with
+no planet corresponding to it. This led astronomers at the time Bode
+published the law, something more than a century ago, to give new heed
+to a suggestion made long before by Kepler, that there might be an
+unknown planet moving between the orbits of Mars and Jupiter, and a
+number of them agreed to search for such a planet, each in a part of the
+sky assigned him for that purpose. But they were anticipated by Piazzi,
+an Italian, who found the new planet, by accident, on the first day of
+the nineteenth century, moving at a distance from the sun represented by
+the number 2.77.
+
+This planet was the first of the asteroids, and in the century that has
+elapsed hundreds of them have been discovered, while at the present time
+no year passes by without several more being added to the number. While
+some of these are nearer to the sun than is the first one discovered,
+and others are farther from it, their average distance is fairly
+represented by the number 2.8.
+
+Why Bode's law should hold true, or even so nearly true as it does, is
+an unexplained riddle, and many astronomers are inclined to call it no
+law at all, but only a chance coincidence--an illustration of the
+"inherent capacity of figures to be juggled with"; but if so, it is
+passing strange that it should represent the distance of the asteroids
+and of Uranus, which was also an undiscovered planet at the time the law
+was published.
+
+135. THE PLANETS COMPARED WITH EACH OTHER.--When we pass from general
+considerations to a study of the individual peculiarities of the
+planets, we find great differences in the extent of knowledge concerning
+them, and the reason for this is not far to seek. Neptune and Uranus, at
+the outskirts of the solar system, are so remote from us and so feebly
+illumined by the sun that any detailed study of them can go but little
+beyond determining the numbers which represent their size, mass,
+density, the character of their orbits, etc. The asteroids are so small
+that in the telescope they look like mere points of light, absolutely
+indistinguishable in appearance from the fainter stars. Mercury,
+although closer at hand and presenting a disk of considerable size,
+always stands so near the sun that its observation is difficult on this
+account. Something of the same kind is true for Venus, although in much
+less degree; while Mars, Jupiter, and Saturn are comparatively easy
+objects for telescopic study, and our knowledge of them, while far from
+complete, is considerably greater than for the other planets.
+
+Figs. 84 and 85 show the relative sizes of the planets composing the
+inner and outer groups respectively, and furnish the numerical data
+concerning their diameters, masses, densities, etc., which are of most
+importance in judging of their physical condition. Each planet, save
+Saturn, is represented by two circles, of which the outer is drawn
+proportional to the size of the planet, and the inner shows the amount
+of material that must be subtracted from the interior in order that the
+remaining shell shall just float in water. Note the great difference in
+thickness of shell between the two groups. Saturn, having a mean density
+less than that of water, must have something loaded upon it, instead of
+removed, in order that it should float just submerged.
+
+
+JUPITER
+
+136. APPEARANCE.--Commencing our consideration of the individual planets
+with Jupiter, which is by far the largest of them, exceeding both in
+bulk and mass all the others combined, we have in Fig. 86 four
+representations of Jupiter and his family of satellites as they may be
+seen in a very small telescope--e. g., an opera glass--save that the
+little dots which here represent the satellites are numbered _1_, _2_,
+_3_, _4_, in order to preserve their identity in the successive
+pictures.
+
+The chief interest of these pictures lies in the satellites, but,
+reserving them for future consideration, we note that the planet itself
+resembles in shape the full moon, although in respect of brightness it
+sends to us less than 1/6000 part as much light as the moon. From a
+consideration of the motion of Jupiter and the earth in Fig. 16, show
+that Jupiter can not present any such phases as does the moon, but that
+its disk must be at all times nearly full. As seen from Saturn, what
+kind of phases would Jupiter present?
+
+137. THE BELTS.--Even upon the small scale of Fig. 86 we detect the most
+characteristic feature of Jupiter's appearance in the telescope, the two
+bands extending across his face parallel to the line of the satellites,
+and in Fig. 87 these same dark bands may be recognized amid the
+abundance of detail which is here brought out by a large telescope.
+Photography does not succeed as a means of reproducing this detail, and
+for it we have to rely upon the skill of the artist astronomer. The
+lettering shows the Pacific Standard time at which the sketches were
+made, and also the longitude of the meridian of Jupiter passing down the
+center of the planet's disk.
+
+[Illustration: FIG. 86.--Jupiter and his satellites.]
+
+[Illustration: FIG. 87.--Drawings of Jupiter made at the 36-inch
+telescope of the Lick Observatory.--KEELER.]
+
+The dark bands are called technically the belts of Jupiter; and a
+comparison of these belts in the second and third pictures of the group,
+in which nearly the same face of the planet is turned toward us, will
+show that they are subject to considerable changes of form and position
+even within the space of a few days. So, too, by a comparison of such
+markings as the round white spots in the upper parts of the disks, and
+the indentations in the edges of the belts, we may recognize that the
+planet is in the act of turning round, and must therefore have an axis
+about which it turns, and poles, an equator, etc. The belts are in fact
+parallel to the planet's equator; and generalizing from what appears in
+the pictures, we may say that there is always a strongly marked belt on
+each side of the equator with a lighter colored streak between them,
+and that farther from the equator are other belts variable in number,
+less conspicuous, and less permanent than the two first seen. Compare
+the position of the principal belts with the position of the zones of
+sun-spot activity in the sun. A feature of the planet's surface, which
+can not be here reproduced, is the rich color effect to be found upon
+it. The principal belts are a brick-red or salmon color, the intervening
+spaces in general white but richly mottled, and streaked with purples,
+browns, and greens.
+
+The drawings show the planet as it appeared in the telescope, inverted,
+and they must be turned upside down if we wish the points of the compass
+to appear as upon a terrestrial map. Bearing this in mind, note in the
+last picture the great oval spot in the southern hemisphere of Jupiter.
+This is a famous marking, known from its color as the _great red spot_,
+which appeared first in 1878 and has persisted to the present day
+(1900), sometimes the most conspicuous marking on the planet, at others
+reduced to a mere ghost of itself, almost invisible save for the
+indentation which it makes in the southern edge of the belt near it.
+
+138. ROTATION AND FLATTENING AT THE POLES.--One further significant fact
+with respect to Jupiter may be obtained from a careful measurement of
+the drawings; the planet is flattened at the poles, so that its polar
+diameter is about one sixteenth part shorter than the equatorial
+diameter. The flattening of the earth amounts to only one
+three-hundredth part, and the marked difference between these two
+numbers finds its explanation in the greater swiftness of Jupiter's
+rotation about its axis, since in both cases it is this rotation which
+makes the flattening.
+
+It is not easy to determine the precise dimensions of the planet, since
+this involves a knowledge both of its distance from us and of the angle
+subtended by its diameter, but the most recent determinations of this
+kind assign as the equatorial diameter 90,200 miles, and for the polar
+diameter 84,400 miles. Determine from either of these numbers the size
+of the great red spot.
+
+The earth turns on its axis once in 24 hours but no such definite time
+can be assigned to Jupiter, which, like the sun, seems to have different
+rotation periods in different latitudes--9h. 50m. in the equatorial belt
+and 9h. 56m. in the dark belts and higher latitudes. There is some
+indication that the larger part of the visible surface rotates in 9h.
+55.6m., while a broad stream along the equator flows eastward some 270
+miles per hour, and thus comes back to the center of the planet, as seen
+from the earth, five or six minutes earlier than the parts which do not
+share in this motion. Judged by terrestrial standards, 270 miles per
+hour is a great velocity, but Jupiter is constructed on a colossal
+scale, and, too, we have to compare this movement, not to a current
+flowing in the ocean, but to a wind blowing in the upper regions of the
+earth's atmosphere. The visible surface of Jupiter is only the top of a
+cloud formation, and contains nothing solid or permanent, if indeed
+there is anything solid even at the core of the planet. The great red
+spot during the first dozen years of its existence, instead of remaining
+fixed relative to the surrounding formations, drifted two thirds of the
+way around the planet, and having come to a standstill about 1891, it is
+now slowly retracing its path.
+
+139. PHYSICAL CONDITION.--For a better understanding of the physical
+condition of Jupiter, we have now to consider some independent lines of
+evidence which agree in pointing to the conclusion that Jupiter,
+although classed with the earth as a planet, is in its essential
+character much more like the sun.
+
+_Appearance._--The formations which we see in Fig. 87 look like clouds.
+They gather and disappear, and the only element of permanence about them
+is their tendency to group themselves along zones of latitude. If we
+measure the light reflected from the planet we find that its albedo is
+very high, like that of snow or our own cumulus clouds, and it is of
+course greater from the light parts of the disk than from the darker
+bands. The spectroscope shows that the sunlight reflected from these
+darker belts is like that reflected from the lighter parts, save that a
+larger portion of the blue and violet rays has been absorbed out of it,
+thus producing the ruddy tint of the belts, as sunset colors are
+produced on the earth, and showing that here the light has penetrated
+farther into the planet's atmosphere before being thrown back by
+reflection from lower-lying cloud surfaces. The dark bands are therefore
+to be regarded as rifts in the clouds, reaching down to some
+considerable distance and indicating an atmosphere of great depth. The
+great red spot, 28,000 miles long, and obviously thrusting back the
+white clouds on every side of it, year after year, can hardly be a mere
+patch on the face of the planet, but indicates some considerable depth
+of atmosphere.
+
+_Density._--So, too, the small mean density of the planet, only 1.3
+times that of water and actually less than the density of the sun,
+suggests that the larger part of the planet's bulk may be made of gases
+and clouds, with very little solid matter even at the center; but here
+we get into a difficulty from which there seems but one escape. The
+force of gravity at the visible surface of Jupiter may be found from its
+mass and dimensions to be 2.6 times as great as at the surface of the
+earth, and the pressure exerted upon its atmosphere by this force ought
+to compress the lower strata into something more dense than we find in
+the planet. Some idea of this compression may be obtained from Fig. 88,
+where the line marked _E_ shows approximately how the density of the air
+increases as we move from its upper strata down toward the surface of
+the earth through a distance of 16 miles, the density at any level being
+proportional to the distance of the curved line from the straight one
+near it. The line marked _J_ in the same figure shows how the density
+would increase if the force of gravity were as great here as it is in
+Jupiter, and indicates a much greater rate of increase. Starting from
+the upper surface of the cloud in Jupiter's atmosphere, if we descend,
+not 16 miles, but 1,600 or 16,000, what must the density of the
+atmosphere become and how is this to be reconciled with what we know to
+be the very small mean density of the planet?
+
+We are here in a dilemma between density on the one hand and the effects
+of gravity on the other, and the only escape from it lies in the
+assumption that the interior of Jupiter is tremendously hot, and that
+this heat expands the substance of the planet in spite of the pressure
+to which it is subject, making a large planet with a low density,
+possibly gaseous at the very center, but in its outer part surrounded by
+a shell of clouds condensed from the gases by radiating their heat into
+the cold of outer space.
+
+[Illustration: FIG. 88.--Increase of density in the atmospheres of
+Jupiter and the earth.]
+
+This is essentially the same physical condition that we found for the
+sun, and we may add, as further points of resemblance between it and
+Jupiter, that there seems to be a circulation of matter from the hot
+interior of the planet to its cooler surface that is more pronounced in
+the southern hemisphere than in the northern, and that has its periods
+of maximum and minimum activity, which, curiously enough, seem to
+coincide with periods of maximum and minimum sun-spot development. Of
+this, however, we can not be entirely sure, since it is only in recent
+years that it has been studied with sufficient care, and further
+observations are required to show whether the agreement is something
+more than an accidental and short-lived coincidence.
+
+_Temperature._--The temperature of Jupiter must, of course, be much
+lower than that of the sun, since the surface which we see is not
+luminous like the sun's; but below the clouds it is not improbable that
+Jupiter may be incandescent, white hot, and it is surmised with some
+show of probability that a little of its light escapes through the
+clouds from time to time, and helps to produce the striking brilliancy
+with which this planet shines.
+
+140. THE SATELLITES OF JUPITER.--The satellites bear much the same
+relation to Jupiter that the moon bears to the earth, revolving about
+the planet in accordance with the law of gravitation, and conforming to
+Kepler's three laws, as do the planets in their courses about the sun.
+Observe in Fig. 86 the position of satellite No. _1_ on the four dates,
+and note how it oscillates back and forth from left to right of Jupiter,
+apparently making a complete revolution in about two days, while No. _4_
+moves steadily from left to right during the entire period, and has
+evidently made only a fraction of a revolution in the time covered by
+the pictures. This quicker motion, of course, means that No. _1_ is
+nearer to Jupiter than No. _4_, and the numbers given to the satellites
+show the order of their distances from the planet. The peculiar way in
+which the satellites are grouped, always standing nearly in a straight
+line, shows that their orbits must lie nearly in the same plane, and
+that this plane, which is also the plane of the planets' equator, is
+turned edgewise toward the earth.
+
+These satellites enjoy the distinction of being the first objects ever
+discovered with the telescope, having been found by Galileo almost
+immediately after its invention, A. D. 1610. It is quite possible that
+before this time they may have been seen with the naked eye, for in more
+recent years reports are current that they have been seen under
+favorable circumstances by sharp-eyed persons, and very little
+telescopic aid is required to show them. Look for them with an opera or
+field glass. They bear the names Io, Europa, Ganymede, Callisto, which,
+however, are rarely used, and, following the custom of astronomers, we
+shall designate them by the Roman numerals I, II, III, IV.
+
+[Illustration: FIG. 89.--Orbits of Jupiter's satellites.]
+
+For nearly three centuries (1610 to 1892) astronomers spoke of the four
+satellites of Jupiter; but in September, 1892, a fifth one was added to
+the number by Professor Barnard, who, observing with the largest
+telescope then extant, found very close to Jupiter a tiny object only
+1/600 part as bright as the other satellites, but, like them, revolving
+around Jupiter, a permanent member of his system. This is called the
+fifth satellite, and Fig. 89 shows the orbits of these satellites around
+Jupiter, which is here represented on the same scale as the orbits
+themselves. The broken line just inside the orbit of I represents the
+size of the moon's orbit. The cut shows also the periodic times of the
+satellites expressed in days, and furnishes in this respect a striking
+illustration of the great mass of Jupiter. Satellite I is a little
+farther from Jupiter than is the moon from the earth, but under the
+influence of a greater attraction it makes the circuit of its orbit in
+1.77 days, instead of taking 29.53 days, as does the moon. Determine
+from the figure by the method employed in Ā§ 111 how much more massive is
+Jupiter than the earth.
+
+Small as these satellites seem in Fig. 86, they are really bodies of
+considerable size, as appears from Fig. 90, where their dimensions are
+compared with those of the earth and moon, save that the fifth satellite
+is not included. This one is so small as to escape all attempts at
+measuring its diameter, but, judging from the amount of light it
+reflects, the period printed with the legend of the figure represents a
+gross exaggeration of this satellite's size.
+
+[Illustration: FIG. 90.--Jupiter's satellites compared with the earth
+and moon.]
+
+Like the moon, each of these satellites may fairly be considered a world
+in itself, and as such a fitting object of detailed study, but,
+unfortunately, their great distance from us makes it impossible, even
+with the most powerful telescope, to see more upon their surfaces than
+occasional vague markings, which hardly suffice to show the rotations of
+the satellites upon their axes.
+
+One striking feature, however, comes out from a study of their influence
+in disturbing each other's motion about Jupiter. Their masses and the
+resulting densities of the satellites are smaller than we should have
+expected to find, the density being less than that of the moon, and
+averaging only a little greater than the density of Jupiter itself. At
+the surface of the third satellite the force of gravity is but little
+less than on the moon, although the moon's density is nearly twice as
+great as that of III, and there can be no question here of accounting
+for the low density through expansion by great heat, as in the case of
+the sun and Jupiter. It has been surmised that these satellites are not
+solid bodies, like the earth and moon, but only shoals of rock and
+stone, loosely piled together and kept from packing into a solid mass by
+the action of Jupiter in raising tides within them. But the explanation
+can hardly be regarded as an accepted article of astronomical belief,
+although it is supported by some observations which tend to show that
+the apparent shapes of the satellites change under the influence of the
+tidal forces impressed upon them.
+
+141. ECLIPSES OF THE SATELLITES.--It may be seen from Fig. 89 that in
+their motion around the planet Jupiter's satellites must from time to
+time pass through his shadow and be eclipsed, and that the shadows of
+the satellites will occasionally fall upon the planet, producing to an
+observer upon Jupiter an eclipse of the sun, but to an observer on the
+earth presenting only the appearance of a round black spot moving slowly
+across the face of the planet. Occasionally also a satellite will pass
+exactly between the earth and Jupiter, and may be seen projected against
+the planet as a background. All of these phenomena are duly predicted
+and observed by astronomers, but the eclipses are the only ones we need
+consider here. The importance of these eclipses was early recognized,
+and astronomers endeavored to construct a theory of their recurrence
+which would permit accurate predictions of them to be made. But in this
+they met with no great success, for while it was easy enough to foretell
+on what night an eclipse of a given satellite would occur, and even to
+assign the hour of the night, it was not possible to make the predicted
+minute agree with the actual time of eclipse until after Roemer, a
+Danish astronomer of the seventeenth century, found where lay the
+trouble. His discovery was, that whenever the earth was on the side of
+its orbit toward Jupiter the eclipses really occurred before the
+predicted time, and when the earth was on the far side of its orbit they
+came a few minutes later than the predicted time. He correctly inferred
+that this was to be explained, not by any influence which the earth
+exerted upon Jupiter and his satellites, but through the fact that the
+light by which we see the satellite and its eclipse requires an
+appreciable time to cross the intervening space, and a longer time when
+the earth is far from Jupiter than when it is near.
+
+For half a century Roemer's views found little credence, but we know now
+that he was right, and that on the average the eclipses come 8m. 18s.
+early when the earth is nearest to Jupiter, and 8m. 18s. late when it is
+on the opposite side of its orbit. This is equivalent to saying that
+light takes 8m. 18s. to cover the distance from the sun to the earth, so
+that at any moment we see the sun not as it then is, but as it was 8
+minutes earlier. It has been found possible in recent years to measure
+by direct experiment the velocity with which light travels--186,337
+miles per second--and multiplying this number by the 498s. (= 8m. 18s.)
+we obtain a new determination of the sun's distance from the earth. The
+product of the two numbers is 92,795,826, in very fair agreement with
+the 93,000,000 miles found in Chapter X; but, as noted there, this
+method, like every other, has its weak side, and the result may be a
+good many thousands of miles in error.
+
+It is worthy of note in this connection that both methods of obtaining
+the sun's distance which were given in Chapter X involve Kepler's Third
+Law, while the result obtained from Jupiter's satellites is entirely
+independent of this law, and the agreement of the several results is
+therefore good evidence both for the truth of Kepler's laws and for the
+soundness of Roemer's explanation of the eclipses. This mode of proof,
+by comparing the numerical results furnished by two or more different
+principles, and showing that they agree or disagree, is of wide
+application and great importance in physical science.
+
+
+SATURN
+
+142. THE RING OF SATURN.--In respect of size and mass Saturn stands next
+to Jupiter, and although far inferior to him in these respects, it
+contains more material than all the remaining planets combined. But the
+unique feature of Saturn which distinguishes it from every other known
+body in the heavens is its ring, which was long a puzzle to the
+astronomers who first studied the planet with a telescope (one of them
+called Saturn a planet with ears), but, was after nearly half a century
+correctly understood and described by Huyghens, whose Latin text we
+translate into--"It is surrounded by a ring, thin, flat, nowhere
+touching it, and making quite an angle with the ecliptic."
+
+[Illustration: FIG. 91.--Aspects of Saturn's rings.]
+
+Compare with this description Fig. 91, which shows some of the
+appearances presented by the ring at different positions of Saturn in
+its orbit. It was their varying aspects that led Huyghens to insert the
+last words of his description, for, if the plane of the ring coincided
+with the plane of the earth's orbit, then at all times the ring must be
+turned edgewise toward the earth, as shown in the middle picture of the
+group. Fig. 92 shows the sun and the orbit of the earth placed near the
+center of Saturn's orbit, across whose circumference are ruled some
+oblique lines representing the plane of the ring, the right end always
+tilted up, no matter where the planet is in its orbit. It is evident
+that an observer upon the earth will see the _N_ side of the ring when
+the planet is at _N_ and the _S_ side when it is at _S_, as is shown in
+the first and third pictures of Fig. 91, while midway between these
+positions the edge of the ring will be presented to the earth.
+
+[Illustration: FIG. 92.--Aspects of the ring in their relation to
+Saturn's orbital motion.]
+
+The last occasion of this kind was in October, 1891, and with the large
+telescope of the Washburn Observatory the writer at that time saw
+Saturn without a trace of a ring surrounding it. The ring is so thin
+that it disappears altogether when turned edgewise. The names of the
+zodiacal constellations are inserted in Fig. 92 in their proper
+direction from the sun, and from these we learn that the ring will
+disappear, or be exceedingly narrow, whenever Saturn is in the
+constellation Pisces or near the boundary line between Leo and Virgo. It
+will be broad and show its northern side when Saturn is in Scorpius or
+Sagittarius, and its southern face when the planet is in Gemini. What
+will be its appearance in 1907 at the date marked in the figure?
+
+143. NATURE OF THE RING.--It is apparent from Figs. 91 and 93 that
+Saturn's ring is really made up of two or more rings lying one inside of
+the other and completely separated by a dark space which, though narrow,
+is as clean and sharp as if cut with a knife. Also, the inner edge of
+the ring fades off into an obscure border called the _dusky ring_ or
+_crape ring_. This requires a pretty good telescope to show it, as may
+be inferred from the fact that it escaped notice for more than two
+centuries during which the planet was assiduously studied with
+telescopes, and was discovered at the Harvard College Observatory as
+recently as 1850.
+
+Although the rings appear oval in all of the pictures, this is mainly an
+effect of perspective, and they are in fact nearly circular with the
+planet at their center. The extreme diameter of the ring is 172,000
+miles, and from this number, by methods already explained (Chapter IX),
+the student should obtain the width of the rings, their distance from
+the ball of the planet, and the diameter of the ball. As to thickness,
+it is evident, from the disappearance of the ring when its edge is
+turned toward the earth, that it is very thin in comparison with its
+diameter, probably not more than 100 miles thick, although no exact
+measurement of this can be made.
+
+[Illustration: FIG. 93.--Saturn.]
+
+From theoretical reasons based upon the law of gravitation astronomers
+have held that the rings of Saturn could not possibly be solid or
+liquid bodies. The strains impressed upon them by the planet's
+attraction would tear into fragments steel rings made after their size
+and shape. Quite recently Professor Keeler has shown, by applying the
+spectroscope (Doppler's principle) to determine the velocity of the
+ring's rotation about Saturn, that the inner parts of the ring move, as
+Kepler's Third Law requires, more rapidly than do the outer parts, thus
+furnishing a direct proof that they are not solid, and leaving no doubt
+that they are made up of separate fragments, each moving about the
+planet in its own orbit, like an independent satellite, but standing so
+close to its neighbors that the whole space reflects the sunlight as
+completely as if it were solid. With this understanding of the rings it
+is easy to see why they are so thin. Like Jupiter, Saturn is greatly
+flattened at the poles, and this flattening, or rather the protuberant
+mass about the equator, lays hold of every satellite near the planet and
+exerts upon it a direct force tending to thrust it down into the plane
+of the planet's equator and hold it there. The ring lies in the plane of
+Saturn's equator because each particle is constrained to move there.
+
+The division of the ring into two parts, an outer and an inner ring, is
+usually explained as follows: Saturn is surrounded by a numerous brood
+of satellites, which by their attractions produce perturbations in the
+material composing the rings, and the dividing line between the outer
+and inner rings falls at the place where by the law of gravitation the
+perturbations would have their greatest effect. The dividing line
+between the rings is therefore a narrow lane, 2,400 miles wide, from
+which the fragments have been swept clean away by the perturbing action
+of the satellites. Less conspicuous divisions are seen from time to time
+in other parts of the ring, where the perturbations, though less, are
+still appreciable. But it is open to some question whether this
+explanation is sufficient.
+
+The curious darkness of the inner or crape ring is easily explained.
+The particles composing it are not packed together so closely as in the
+outer ring, and therefore reflect less sunlight. Indeed, so sparsely
+strewn are the particles in this ring that it is in great measure
+transparent to the sunlight, as is shown by a recorded observation of
+one of the satellites which was distinctly although faintly seen while
+moving through the shadow of the dark ring, but disappeared in total
+eclipse when it entered the shadow cast by the bright ring.
+
+144. THE BALL OF SATURN.--The ball of the planet is in most respects a
+smaller copy of Jupiter. With an equatorial diameter of 76,000 miles, a
+polar diameter of 69,000 miles, and a mass 95 times that of the earth,
+its density is found to be the least of any planet in the solar system,
+only 0.70 of the density of water, and about one half as great as is the
+density of Jupiter. The force of gravity at its surface is only a little
+greater (1.18) than on the earth; and this, in connection with the low
+density, leads, as in the case of Jupiter, to the conclusion that the
+planet must be mainly composed of gases and vapors, very hot within, but
+inclosed by a shell of clouds which cuts off their glow from our eyes.
+
+Like Jupiter in another respect, the planet turns very swiftly upon its
+axis, making a revolution in 10 hours 14 minutes, but up to the present
+it remains unknown whether different parts of the surface have different
+rotation times.
+
+145. THE SATELLITES.--Saturn is attended by a family of nine satellites,
+a larger number than belongs to any other planet, but with one exception
+they are exceedingly small and difficult to observe save with a very
+large telescope. Indeed, the latest one is said to have been discovered
+in 1898 by means of the image which it impressed upon a photographic
+plate, and it has never been _seen_.
+
+Titan, the largest of them, is distant 771,000 miles from the planet and
+bears much the same relation to Saturn that Satellite III bears to
+Jupiter, the similarity in distance, size and mass being rather
+striking, although, of course, the smaller mass of Saturn as compared
+with Jupiter makes the periodic time of Titan--15 days 23 hours--much
+greater than that of III. Can you apply Kepler's Third Law to the motion
+of Titan so as to determine from the data given above, the time required
+for a particle at the outer or inner edge of the ring to revolve once
+around Saturn?
+
+Japetus, the second satellite in point of size, whose distance from
+Saturn is about ten times as great as the moon's distance from the
+earth, presents the remarkable peculiarity of being always brighter in
+one part of its orbit than in another, three or four times as bright
+when west of Saturn as when east of it. This probably indicates that,
+like our own moon, the satellite turns always the same face toward its
+planet, and further, that one side of the satellite reflects the
+sunlight much better than the other side--i. e., has a higher albedo.
+With these two assumptions it is easily seen that the satellite will
+always turn toward the earth one face when west, and the other face when
+east of Saturn, and thus give the observed difference of brightness.
+
+
+URANUS AND NEPTUNE
+
+146. CHIEF CHARACTERISTICS.--The two remaining large planets are
+interesting chiefly as modern additions to the known members of the
+sun's family. The circumstances leading to the discovery of Neptune have
+been touched upon in Chapter IV, and for Uranus we need only note that
+it was found by accident in the year 1781 by William Herschel, who for
+some time after the discovery considered it to be only a comet. It was
+the first planet ever discovered, all of its predecessors having been
+known from prehistoric times.
+
+[Illustration: WILLIAM HERSCHEL (1738-1822).]
+
+Uranus has four satellites, all of them very faint, which present only
+one feature of special importance. Instead of moving in orbits which are
+approximately parallel to the plane of the ecliptic, as do the
+satellites of the inner planets, their orbit planes are tipped up nearly
+perpendicular to the planes of the orbits of both Uranus and the earth.
+The one satellite which Neptune possesses has the same peculiarity in
+even greater degree, for its motion around the planet takes place in the
+direction opposite to that in which all the planets move around the sun,
+much as if the orbit of the satellite had been tipped over through an
+angle of 150Ā°. Turn a watch face down and note how the hands go round in
+the direction opposite to that in which they moved before the face was
+turned through 180Ā°.
+
+Both Uranus and Neptune are too distant to allow much detail to be seen
+upon their surfaces, but the presence of broad absorption bands in their
+spectra shows that they must possess dense atmospheres quite different
+in constitution from the atmosphere of the earth. In respect of density
+and the force of gravity at their surfaces, they are not very unlike
+Saturn, although their density is greater and gravity less than his,
+leading to the supposition that they are for the most part gaseous
+bodies, but cooler and probably more nearly solid than either Jupiter or
+Saturn.
+
+Under favorable circumstances Uranus may be seen with the naked eye by
+one who knows just where to look for it. Neptune is never visible save
+in a telescope.
+
+147. THE INNER PLANETS.--In sharp contrast with the giant planets which
+we have been considering stands the group of four inner planets, or five
+if we count the moon as an independent body, which resemble each other
+in being all small, dense, and solid bodies, which by comparison with
+the great distances separating the outer planets may fairly be described
+as huddled together close to the sun. Their relative sizes are shown in
+Fig. 84, together with the numerical data concerning size, mass,
+density, etc., which we have already found important for the
+understanding of a planet's physical condition.
+
+
+VENUS
+
+[Illustration: FIG. 94.--The phases of Venus.--ANTONIADI.]
+
+148. APPEARANCE.--Omitting the earth, Venus is by far the most
+conspicuous member of this group, and when at its brightest is, with
+exception of the sun and moon, the most brilliant object in the sky, and
+may be seen with the naked eye in broad daylight if the observer knows
+just where to look for it. But its brilliancy is subject to considerable
+variations on account of its changing distance from the earth, and the
+apparent size of its disk varies for the same reason, as may be seen
+from Fig. 94. These drawings bring out well the phases of the planet,
+and the student should determine from Fig. 17 what are the relative
+positions in their orbits of the earth and Venus at which the planet
+would present each of these phases. As a guide to this, observe that the
+dark part of Venus's earthward side is always proportional in area to
+the angle at Venus between the earth and sun. In the first picture of
+Fig. 94 about two thirds of the surface corresponding to the full
+hemisphere of the planet is dark, and the angle at Venus between earth
+and sun is therefore two thirds of 180Ā°--i. e., 120Ā°. In Fig. 17 find a
+place on the orbit of Venus from which if lines be drawn to the sun and
+earth, as there shown, the angle between them will be 120Ā°. Make a
+similar construction for the fourth picture in Fig. 94. Which of these
+two positions is farther from the earth? How do the distances compare
+with the apparent size of Venus in the two pictures? What is the phase
+of Venus to-day?
+
+The irregularities in the shading of the illuminated parts of the disk
+are too conspicuous in Fig. 94, on account of difficulties of
+reproduction; these shadings are at the best hard to see in the
+telescope, and distinct permanent markings upon the planet are wholly
+lacking. This absence of markings makes almost impossible a
+determination of the planet's time of rotation about its axis, and
+astronomers are divided in this respect into two parties, one of which
+maintains that Venus, like the earth, turns upon its axis in some period
+not very different from 24 hours, while the other contends that, like
+the moon, it turns always the same face toward the center of its orbit,
+making a rotation upon its axis in the same period in which it makes a
+revolution about the sun. The reason why no permanent markings are to be
+seen on this planet is easily found. Like Jupiter and Saturn, its
+atmosphere is at all times heavily cloud-laden, so that we seldom, if
+ever, see down to the level of its solid parts. There is, however, no
+reason here to suppose the interior parts hot and gaseous. It is much
+more probable that Venus, like the earth, possesses a solid crust whose
+temperature we should expect to be considerably higher than that of the
+earth, because Venus is nearer the sun. But the cloud layer in its
+atmosphere must modify the temperature in some degree, and we have
+practically no knowledge of the real temperature conditions at the
+surface of the planet.
+
+It is the clouds of Venus which in great measure are responsible for its
+marked brilliancy, since they are an excellent medium for reflecting the
+sunlight, and give to its surface an albedo greater than that of any
+other planet, although Saturn is nearly equal to it.
+
+Of course, the presence of such cloud formations indicates that Venus is
+surrounded by a dense atmosphere, and we have independent evidence of
+this in the shape of its disk when the planet is very nearly between the
+earth and sun. The illuminated part, from tip to tip of the horns, then
+stretches more than halfway around the planet's circumference, and shows
+that a certain amount of light must have been refracted through its
+atmosphere, thus making the horns of the crescent appear unduly
+prolonged. This atmosphere is shown by the spectroscope to be not unlike
+that of the earth, although, possibly, more dense.
+
+
+MERCURY
+
+149. CHIEF CHARACTERISTICS.--Mercury, on account of its nearness to the
+sun, is at all times a difficult object to observe, and Copernicus, who
+spent most of his life in Poland, is said, despite all his efforts, to
+have gone to his grave without ever seeing it. In our more southern
+latitude it can usually be seen for about a fortnight at the time of
+each elongation--i. e., when at its greatest angular distance from the
+sun--and the student should find from Fig. 16 the time at which the next
+elongation occurs and look for the planet, shining like a star of the
+first magnitude, low down in the sky just after sunset or before
+sunrise, according as the elongation is to the east or west of the sun.
+When seen in the morning sky the planet grows brighter day after day
+until it disappears in the sun's rays, while in the evening sky its
+brilliancy as steadily diminishes until the planet is lost. It should
+therefore be looked for in the evening as soon as possible after it
+emerges from the sun's rays.
+
+Mercury, as the smallest of the planets, is best compared with the
+moon, which it does not greatly surpass in size and which it strongly
+resembles in other respects. Careful comparisons of the amount of light
+reflected by the planet in different parts of its orbit show not only
+that its albedo agrees very closely with that of the moon, but also that
+its light changes with the varying phase of the planet in almost exactly
+the same way as the amount of moonlight changes. We may therefore infer
+that its surface is like that of the moon, a rough and solid one, with
+few or no clouds hanging over it, and most probably covered with very
+little or no atmosphere. Like Venus, its rotation period is uncertain,
+with the balance of probability favoring the view that it rotates upon
+its axis once in 88 days, and therefore always turns the same face
+toward the sun.
+
+If such is the case, its climate must be very peculiar: one side roasted
+in a perpetual day, where the direct heating power of the sun's rays,
+when the planet is at perihelion, is ten times as great as on the moon,
+and which six weeks later, when the planet is at its farthest from the
+sun, has fallen off to less than half of this. On the opposite side of
+the planet there must reign perpetual night and perpetual cold,
+mitigated by some slight access of warmth from the day side, and perhaps
+feebly imitating the rapid change of season which takes place on the day
+side of the planet. This view, however, takes no account of a possible
+deviation of the planet's axis from being perpendicular to the plane of
+its orbit, or of the librations which must be produced by the great
+eccentricity of the orbit, either of which would complicate without
+entirely destroying the ideal conditions outlined above.
+
+
+MARS
+
+150. APPEARANCE.--The one remaining member of the inner group, Mars, has
+in recent years received more attention than any other planet, and the
+newspapers and magazines have announced marvelous things concerning it:
+that it is inhabited by a race of beings superior in intelligence to
+men; that the work of their hands may be seen upon the face of the
+planet; that we should endeavor to communicate with them, if indeed they
+are not already sending messages to us, etc.--all of which is certainly
+important, if true, but it rests upon a very slender foundation of
+evidence, a part of which we shall have to consider.
+
+Beginning with facts of which there is no doubt, this ruddy-colored
+planet, which usually shines about as brightly as a star of the first
+magnitude, sometimes displays more than tenfold this brilliancy,
+surpassing every other planet save Venus and presenting at these times
+especially favorable opportunities for the study of its surface. The
+explanation of this increase of brilliancy is, of course, that the
+planet approaches unusually near to the earth, and we have already seen
+from a consideration of Fig. 17 that this can only happen in the months
+of August and September. The last favorable epoch of this kind was in
+1894. From Fig. 17 the student should determine when the next one will
+come.
+
+[Illustration: FIG. 95.--Mars.--SCHAEBERLE.]
+
+Fig. 95 presents nine drawings of the planet made at one of the epochs
+of close approach to the earth, and shows that its face bears certain
+faint markings which, though inconspicuous, are fixed and permanent
+features of the planet. The dark triangular projection in the lower
+half of the second drawing was seen and sketched by Huyghens, 1659
+A. D. In Fig. 96 some of these markings are shown much more plainly, but
+Fig. 95 gives a better idea of their usual appearance in the telescope.
+
+[Illustration: FIG. 96.--Four views of Mars differing 90Ā° in
+longitude.--BARNARD.]
+
+151. ROTATION.--It may be seen readily enough, from a comparison of the
+first two sketches of Fig. 95, that the planet rotates about an axis,
+and from a more extensive study it is found to be very like the earth in
+this respect, turning once in 24h. 37m. around an axis tipped from being
+perpendicular to the plane of its orbit about a degree and a half more
+than is the earth's axis. Since it is this inclination of the axis which
+is the cause of changing seasons upon the earth, there must be similar
+changes, winter and summer, as well as day and night, upon Mars, only
+each season is longer there than here in the same proportion that its
+year is longer than ours--i. e., nearly two to one. It is summer in the
+northern hemisphere of Mars whenever the sun, as seen from Mars, stands
+in that constellation which is nearest the point of the sky toward which
+the planet's axis points. But this axis points toward the constellation
+Cygnus, and Alpha Cygni is the bright star nearest the north pole of
+Mars. As Pisces is the zodiacal constellation nearest to Cygnus, it must
+be summer in the northern hemisphere of Mars when the sun is in Pisces,
+or, turning the proposition about, it must be summer in the _southern_
+hemisphere of Mars when the planet, as seen from the sun, lies in the
+direction of Pisces.
+
+152. THE POLAR CAPS.--One effect of the changing seasons upon Mars is
+shown in Fig. 97, where we have a series of drawings of the region about
+its south pole made in 1894, on dates between May 21st and December
+10th. Show from Fig. 17 that during this time it was summer in the
+region here shown. Mars crossed the prime radius in 1894 on September
+5th. The striking thing in these pictures is the white spot surrounding
+the pole, which shrinks in size from the beginning to near the end of
+the series, and then disappears altogether. The spot came back again a
+year later, and like a similar spot at the north pole of the planet it
+waxes in the winter and wanes during the summer of Mars in endless
+succession.
+
+[Illustration: FIG. 97.--The south polar cap of Mars in 1894.--BARNARD.]
+
+Sir W. Herschel, who studied these appearances a century ago, compared
+them with the snow fields which every winter spread out from the region
+around the terrestrial pole, and in the summer melt and shrink, although
+with us they do not entirely disappear. This explanation of the polar
+caps of Mars has been generally accepted among astronomers, and from it
+we may draw one interesting conclusion: the temperature upon Mars
+between summer and winter oscillates above and below the freezing point
+of water, as it does in the temperate zones of the earth. But this
+conclusion plunges us into a serious difficulty. The temperature of the
+earth is made by the sun, and at the distance of Mars from the sun the
+heating effect of the latter is reduced to less than half what it is at
+the earth, so that, if Mars is to be kept at the same temperature as the
+earth, there must be some peculiar means for storing the solar heat and
+using it more economically than is done here. Possibly there is some
+such mechanism, although no one has yet found it, and some astronomers
+are very confident that it does not exist, and assert that the
+comparison of the polar caps with snow fields is misleading, and that
+the temperature upon Mars must be at least 100Ā°, and perhaps 200Ā° or
+more, below zero.
+
+153. ATMOSPHERE AND CLIMATE.--In this connection one feature of Mars is
+of importance. The markings upon its surface are always visible when
+turned toward the earth, thus showing that the atmosphere contains no
+such amount of cloud as does our own, but on the whole is decidedly
+clear and sunny, and presumably much less dense than ours. We have seen
+in comparing the earth and the moon how important is the service which
+the earth's atmosphere renders in storing the sun's heat and checking
+those great vicissitudes of temperature to which the moon is subject;
+and with this in mind we must regard the smaller density and cloudless
+character of the atmosphere of Mars as unfavorable to the maintenance
+there of a temperature like that of the earth. Indeed, this
+cloudlessness must mean one of two things: either the temperature is so
+low that vapors can not exist in any considerable quantity, or the
+surface of Mars is so dry that there is little water or other liquid to
+be evaporated. The latter alternative is adopted by those astronomers
+who look upon the polar caps as true snow fields, which serve as the
+chief reservoir of the planet's water supply, and who find in Fig. 98
+evidence that as the snow melts and the water flows away over the flat,
+dry surface of the planet, vegetation springs up, as shown by the dark
+markings on the disk, and gradually dies out with the advancing season.
+Note that in the first of these pictures the season upon Mars
+corresponds to the end of May with us, and in the last picture to the
+beginning of August, a period during which in much of our western
+country the luxuriant vegetation of spring is burned out by the
+scorching sun. From this point of view the permanent dark spots are the
+low-lying parts of the planet's surface, in which at all times there is
+a sufficient accumulation of water to support vegetable life.
+
+[Illustration: FIG. 98.--The same face of Mars at three different
+seasons.--LOWELL.]
+
+154. THE CANALS.--In Fig. 98 the lower part of the disk of Mars shows
+certain faint dark lines which are generally called canals, and in Plate
+III there is given a map of Mars showing many of these canals running in
+narrow, dusky streaks across the face of the planet according to a
+pattern almost as geometrical as that of a spider's web. This must not
+be taken for a picture of the planet's appearance in a telescope. No man
+ever saw Mars look like this, but the map is useful as a plain
+representation of things dimly seen. Some of the regions of this map are
+marked Mare (sea), in accordance with the older view which regarded the
+darker parts of the planet--and of the moon--as bodies of water, but
+this is now known to be an error in both cases. The curved surface of a
+planet can not be accurately reproduced upon the flat surface of paper,
+but is always more or less distorted by the various methods of
+"projecting" it which are in use. Compare the map of Mars in Plate III
+with Fig. 99, in which the projection represents very well the
+equatorial parts of the planet, but enormously exaggerates the region
+around the poles.
+
+It is a remarkable feature of the canals that they all begin and end in
+one of these dark parts of the planet's surface; they show no loose ends
+lying on the bright parts of the planet. Another even more remarkable
+feature is that while the larger canals are permanent features of the
+planet's surface, they at times appear "doubled"--i. e., in place of one
+canal two parallel ones side by side, lasting for a time and then giving
+place again to a single canal.
+
+It is exceedingly difficult to frame any reasonable explanation of these
+canals and the varied appearances which they present. The source of the
+wild speculations about Mars, to which reference is made above, is to be
+found in the suggestion frequently made, half in jest and half in
+earnest, that the canals are artificial water courses constructed upon a
+scale vastly exceeding any public works upon the earth, and testifying
+to the presence in Mars of an advanced civilization. The distinguished
+Italian astronomer, Schiaparelli, who has studied these formations
+longer than any one else, seems inclined to regard them as water courses
+lined on either side by vegetation, which flourishes as far back from
+the central channel as water can be supplied from it--a plausible enough
+explanation if the fundamental difficulty about temperature can be
+overcome.
+
+[Illustration: FIG. 99.--A chart of Mars, 1898-'99.--CERULLI.]
+
+[Illustration: PLATE III. MAP OF MARS (AFTER SCHIAPARELLI)]
+
+155. SATELLITES.--In 1877, one of the times of near approach, Professor
+Hall, of Washington, discovered two tiny satellites revolving about Mars
+in orbits so small that the nearer one, Phobos, presents the remarkable
+anomaly of completing the circuit of its orbit in less time than the
+planet takes for a rotation about its axis. This satellite, in fact,
+makes three revolutions in its orbit while the planet turns once upon
+its axis, and it therefore rises in the west and sets in the east, as
+seen from Mars, going from one horizon to the other in a little less
+than 6 hours. The other satellite, Deimos, takes a few hours more than a
+day to make the circuit of its orbit, but the difference is so small
+that it remains continuously above the horizon of any given place upon
+Mars for more than 60 hours at a time, and during this period runs twice
+through its complete set of phases--new, first quarter, full, etc. In
+ordinary telescopes these satellites can be seen only under especially
+favorable circumstances, and are far too small to permit of any direct
+measurement of their size. The amount of light which they reflect has
+been compared with that of Mars and found to be as much inferior to it
+as is Polaris to two full moons, and, judging from this comparison,
+their diameters can not much exceed a half dozen miles, unless their
+albedo is far less than that of Mars, which does not seem probable.
+
+
+THE ASTEROIDS
+
+156. MINOR PLANETS.--These may be dismissed with few words. There are
+about 500 of them known, all discovered since the beginning of the
+nineteenth century, and new ones are still found every year. No one
+pretends to remember the names which have been assigned them, and they
+are commonly represented by a number inclosed in a circle, showing the
+order in which they were discovered--e. g., [circle 1] = Ceres,
+[circle 433] = Eros, etc. For the most part they are little more than
+chips, world fragments, adrift in space, and naturally it was the larger
+and brighter of them that were first discovered. The size of the first
+four of them--Ceres, Pallas, Juno, and Vesta--compared with the size of
+the moon, according to Professor Barnard, is shown in Fig. 100. The
+great majority of them must be much smaller than the smallest of these,
+perhaps not more than a score of miles in diameter.
+
+A few of the asteroids present problems of special interest, such as
+Eros, on account of its close approach to the earth; Polyhymnia, whose
+very eccentric orbit makes it a valuable means for determining the mass
+of Jupiter, etc.; but these are special cases and the average asteroid
+now receives scant attention, although half a century ago, when only a
+few of them were known, they were regarded with much interest, and the
+discovery of a new one was an event of some consequence.
+
+It was then a favorite speculation that they were in fact fragments of
+an ill-fated planet which once filled the gap between the orbits of Mars
+and Jupiter, but which, by some mischance, had been blown into pieces.
+This is now known to be well-nigh impossible, for every fragment which
+after the explosion moved in an elliptical orbit, as all the asteroids
+do move, would be brought back once in every revolution to the place of
+the explosion, and all the asteroid orbits must therefore intersect at
+this place. But there is no such common point of intersection.
+
+[Illustration: FIG. 100.--The size of the first four
+asteroids.--BARNARD.]
+
+157. LIFE ON THE PLANETS.--There is a belief firmly grounded in the
+popular mind, and not without its advocates among professional
+astronomers, that the planets are inhabited by living and intelligent
+beings, and it seems proper at the close of this chapter to inquire
+briefly how far the facts and principles here developed are consistent
+with this belief, and what support, if any, they lend to it.
+
+At the outset we must observe that the word life is an elastic term,
+hard to define in any satisfactory way, and yet standing for something
+which we know here upon the earth. It is this idea, our familiar though
+crude knowledge of life, which lies at the root of the matter. Life, if
+it exists in another planet, must be in its essential character like
+life upon the earth, and must at least possess those features which are
+common to all forms of terrestrial life. It is an abuse of language to
+say that life in Mars may be utterly unlike life in the earth; if it is
+absolutely unlike, it is not life, whatever else it may be. Now, every
+form of life found upon the earth has for its physical basis a certain
+chemical compound, called protoplasm, which can exist and perpetuate
+itself only within a narrow range of temperature, roughly speaking,
+between 0Ā° and 100Ā° centigrade, although these limits can be
+considerably overstepped for short periods of time. Moreover, this
+protoplasm can be active only in the presence of water, or water vapor,
+and we may therefore establish as the necessary conditions for the
+continued existence and reproduction of life in any place that its
+temperature must not be permanently above 100Ā° or below 0Ā°, C., and
+water must be present in that place in some form.
+
+With these conditions before us it is plain that life can not exist in
+the sun on account of its high temperature. It is conceivable that
+active and intelligent beings, salamanders, might exist there, but they
+could not properly be said to live. In Jupiter and Saturn the same
+condition of high temperature prevails, and probably also in Uranus and
+Neptune, so that it seems highly improbable that any of these planets
+should be the home of life.
+
+Of the inner planets, Mercury and the moon seem destitute of any
+considerable atmospheres, and are therefore lacking in the supply of
+water necessary for life, and the same is almost certainly true of all
+the asteroids. There remain Venus, Mars, and the satellites of the outer
+planets, which latter, however, we must drop from consideration as being
+too little known. On Venus there is an atmosphere probably containing
+vapor of water, and it is well within the range of possibility that
+liquid water should exist upon the surface of this planet and that its
+temperature should fall within the prescribed limits. It would, however,
+be straining our actual knowledge to affirm that such is the case, or to
+insist that if such were the case, life would necessarily exist upon the
+planet.
+
+On Mars we encounter the fundamental difficulty of temperature already
+noted in Ā§ 152. If in some unknown way the temperature is maintained
+sufficiently high for the polar caps to be real snow, thawing and
+forming again with the progress of the seasons, the necessary conditions
+of life would seem to be fulfilled here and life if once introduced upon
+the planet might abide and flourish. But of positive proof that such is
+the case we have none.
+
+On the whole, our survey lends little encouragement to the belief in
+planetary life, for aside from the earth, of all the hundreds of bodies
+in the solar system, not one is found in which the necessary conditions
+of life are certainly fulfilled, and only two exist in which there is a
+reasonable probability that these conditions may be satisfied.
+
+
+
+
+CHAPTER XII
+
+COMETS AND METEORS
+
+
+158. VISITORS IN THE SOLAR SYSTEM.--All of the objects--sun, moon,
+planets, stars--which we have thus far had to consider, are permanent
+citizens of the sky, and we have no reason to suppose that their present
+appearance differs appreciably from what it was 1,000 years or 10,000
+years ago. But there is another class of objects--comets, meteors--which
+appear unexpectedly, are visible for a time, and then vanish and are
+seen no more. On account of this temporary character the astronomers of
+ancient and mediƦval times for the most part refused to regard them as
+celestial bodies but classed them along with clouds, fogs,
+Jack-o'-lanterns, and fireflies, as exhalations from the swamps or the
+volcano; admitting them to be indeed important as harbingers of evil to
+mankind, but having no especial significance for the astronomer.
+
+The comet of 1618 A. D. inspired the lines--
+
+    "Eight things there be a Comet brings,
+      When it on high doth horrid range:
+    Wind, Famine, Plague, and Death to Kings,
+      War, Earthquakes, Floods, and Direful Change,"
+
+which, according to White (History of the Doctrine of Comets), were to
+be taught in all seriousness to peasants and school children.
+
+It was by slow degrees, and only after direct measurements of parallax
+had shown some of them to be more distant than the moon, that the tide
+of old opinion was turned and comets were transferred from the sublunary
+to the celestial sphere, and in more recent times meteors also have
+been recognized as coming to us from outside the earth. A meteor, or
+shooting star as it is often called, is one of the commonest of
+phenomena, and one can hardly watch the sky for an hour on any clear and
+moonless night without seeing several of those quick flashes of light
+which look as if some star had suddenly left its place, dashed swiftly
+across a portion of the sky and then vanished. It is this misleading
+appearance that probably is responsible for the name shooting star.
+
+[Illustration: FIG. 101.--Donati's comet.--BOND.]
+
+159. COMETS.--Comets are less common and much longer-lived than meteors,
+lasting usually for several weeks, and may be visible night after night
+for many months, but never for many years, at a time. During the last
+decade there is no year in which less than three comets have appeared,
+and 1898 is distinguished by the discovery of ten of these bodies, the
+largest number ever found in one year. On the average, we may expect a
+new comet to be found about once in every ten weeks, but for the most
+part they are small affairs, visible only in the telescope, and a fine
+large one, like Donati's comet of 1858 (Fig. 101), or the Great Comet of
+September, 1882, which was visible in broad daylight close beside the
+sun, is a rare spectacle, and as striking and impressive as it is rare.
+
+[Illustration: FIG. 102.--Some famous comets.]
+
+Note in Fig. 102 the great variety of aspect presented by some of the
+more famous comets, which are here represented upon a very small scale.
+
+Fig. 103 is from a photograph of one of the faint comets of the year
+1893, which appears here as a rather feeble streak of light amid the
+stars which are scattered over the background of the picture. An
+apparently detached portion of this comet is shown at the extreme left
+of the picture, looking almost like another independent comet. The
+clean, straight line running diagonally across the picture is the flash
+of a bright meteor that chanced to pass within the range of the camera
+while the comet was being photographed.
+
+A more striking representation of a moderately bright telescopic comet
+is contained in Figs. 104 and 105, which present two different views of
+the same comet, showing a considerable change in its appearance. A
+striking feature of Fig. 105 is the star images, which are here drawn
+out into short lines all parallel with each other. During the exposure
+of 2h. 20m. required to imprint this picture upon the photographic
+plate, the comet was continually changing its position among the stars
+on account of its orbital motion, and the plate was therefore moved
+from time to time, so as to follow the comet and make its image always
+fall at the same place. Hence the plate was continually shifted relative
+to the stars whose images, drawn out into lines, show the direction in
+which the plate was moved--i. e., the direction in which the comet was
+moving across the sky. The same effect is shown in the other
+photographs, but less conspicuously than here on account of their
+shorter exposure times.
+
+These pictures all show that one end of the comet is brighter and
+apparently more dense than the other, and it is customary to call this
+bright part the _head_ of the comet, while the brushlike appendage that
+streams away from it is called the comet's _tail_.
+
+[Illustration: FIG. 103.--Brooks's comet, November 13, 1893. BARNARD.]
+
+160. THE PARTS OF A COMET.--It is not every comet that has a tail,
+though all the large ones do, and in Fig. 103 the detached piece of
+cometary matter at the left of the picture represents very well the
+appearance of a tailless comet, a rather large but not very bright star
+of a fuzzy or hairy appearance. The word comet means long-haired or
+hairy star. Something of this vagueness of outline is found in all
+comets, whose exact boundaries are hard to define, instead of being
+sharp and clean-cut like those of a planet or satellite. Often,
+however, there is found in the head of a comet a much more solid
+appearing part, like the round white ball at the center of Fig. 106,
+which is called the nucleus of the comet, and appears to be in some sort
+the center from which its activities radiate. As shown in Figs. 106 and
+107, the nucleus is sometimes surrounded by what are called envelopes,
+which have the appearance of successive wrappings or halos placed about
+it, and odd, spurlike projections, called jets, are sometimes found in
+connection with the envelopes or in place of them. These figures also
+show what is quite a common characteristic of large comets, a dark
+streak running down the axis of the tail, showing that the tail is
+hollow, a mere shell surrounding empty space.
+
+[Illustration: FIG. 104.--Swift's comet, April 17, 1892.--BARNARD.]
+
+The amount of detail shown in Figs. 106 and 107 is, however, quite
+exceptional, and the ordinary comet is much more like Fig. 103 or 104.
+Even a great comet when it first appears is not unlike the detached
+fragment in Fig. 103, a faint and roundish patch of foggy light which
+grows through successive stages to its maximum estate, developing a
+tail, nucleus, envelopes, etc., only to lose them again as it shrinks
+and finally disappears.
+
+[Illustration: FIG. 105.--Swift's comet, April 24, 1892.--BARNARD.]
+
+161. THE ORBITS OF COMETS.--It will be remembered that Newton found, as
+a theoretical consequence of the law of gravitation, that a body moving
+under the influence of the sun's attraction might have as its orbit any
+one of the conic sections, ellipse, parabola, or hyperbola, and among
+the 400 and more comet orbits which have been determined every one of
+these orbit forms appears, but curiously enough there is not a hyperbola
+among them which, if drawn upon paper, could be distinguished by the
+unaided eye from a parabola, and the ellipses are all so long and
+narrow, not one of them being so nearly round as is the most eccentric
+planet orbit, that astronomers are accustomed to look upon the parabola
+as being the normal type of comet orbit, and to regard a comet whose
+motion differs much from a parabola as being abnormal and calling for
+some special explanation.
+
+The fact that comet orbits are parabolas, or differ but little from
+them, explains at once the temporary character and speedy disappearance
+of these bodies. They are visitors to the solar system and visible for
+only a short time, because the parabola in which they travel is not a
+closed curve, and the comet, having passed once along that portion of it
+near the earth and the sun, moves off along a path which ever thereafter
+takes it farther and farther away, beyond the limit of visibility. The
+development of the comet during the time it is visible, the growth and
+disappearance of tail, nucleus, etc., depend upon its changing distance
+from the sun, the highest development and most complex structure being
+presented when it is nearest to the sun.
+
+[Illustration: FIG. 106.--Head of Coggia's comet, July 13,
+1874.--TROUVELOT.]
+
+Fig. 108 shows the path of the Great Comet of 1882 during the period in
+which it was seen, from September 3, 1882, to May 26, 1883. These
+dates--IX, 3, and V, 26--are marked in the figure opposite the parts of
+the orbit in which the comet stood at those times. Similarly, the
+positions of the earth in its orbit at the beginning of September,
+October, November, etc., are marked by the Roman numerals IX, X, XI,
+etc. The line _S V_ shows the direction from the sun to the vernal
+equinox, and _S_ Ī© is the line along which the plane of the
+comet's orbit intersects the plane of the earth's orbit--i. e., it is
+the line of nodes of the comet orbit. Since the comet approached the sun
+from the south side of the ecliptic, all of its orbit, save the little
+segment which falls to the left of _S_ Ī©, lies below (south) of
+the plane of the earth's orbit, and the part which would be hidden if
+this plane were opaque is represented by a broken line.
+
+[Illustration: FIG. 107.--Head of Donati's comet, September 30, October
+2, 1858.--BOND.]
+
+162. ELEMENTS OF A COMET'S ORBIT.--There is a theorem of geometry to the
+effect that through any three points not in the same straight line one
+circle, and only one, can be drawn. Corresponding to this there is a
+theorem of celestial mechanics, that through any three positions of a
+comet one conic section, and only one, can be passed along which the
+comet can move in accordance with the law of gravitation. This conic
+section is, of course, its orbit, and at the discovery of a comet
+astronomers always hasten to observe its position in the sky on
+different nights in order to obtain the three positions (right
+ascensions and declinations) necessary for determining the particular
+orbit in which it moves. The circle, to which reference was made above,
+is completely ascertained and defined when we know its radius and the
+position of its center. A parabola is not so simply defined, and five
+numbers, called the _elements_ of its orbit, are required to fix
+accurately a comet's path around the sun. Two of these relate to the
+position of the line of nodes and the angle which the orbit plane makes
+with the plane of the ecliptic; a third fixes the direction of the axis
+of the orbit in its plane, and the remaining two, which are of more
+interest to us, are the date at which the comet makes its nearest
+approach to the sun (_perihelion passage_) and its distance from the sun
+at that date (_perihelion distance_). The date, September 17th, placed
+near the center of Fig. 108, is the former of these elements, while the
+latter, which is too small to be accurately measured here, may be found
+from Fig. 109 to be 0.82 of the sun's diameter, or, in terms of the
+earth's distance from the sun, 0.008.
+
+[Illustration: FIG. 108.--Orbits of the earth and the Great Comet of
+1882.]
+
+Fig. 109 shows on a large scale the shape of that part of the orbit near
+the sun and gives the successive positions of the comet, at intervals of
+2/10 of a day, on September 16th and 17th, showing that in less than 10
+hours--17.0 to 17.4--the comet swung around the sun through an angle of
+more than 240Ā°. When at its perihelion it was moving with a velocity of
+300 miles per second! This very unusual velocity was due to the comet's
+extraordinarily close approach to the sun. The earth's velocity in its
+orbit is only 19 miles per second, and the velocity of any comet at any
+distance from the sun, provided its orbit is a parabola, may be found
+by dividing this number by the square root of half the comet's
+distance--e. g., 300 miles per second equals 19 Ć· āˆš 0.004.
+
+[Illustration: FIG. 109.--Motion of the Great Comet of 1883 in passing
+around the sun.]
+
+Most of the visible comets have their perihelion distances included
+between 1/3 and 4/3 of the earth's distance from the sun, but
+occasionally one is found, like the second comet of 1885, whose nearest
+approach to the sun lies far outside the earth's orbit, in this case
+halfway out to the orbit of Jupiter; but such a comet must be a very
+large one in order to be seen at all from the earth. There is, however,
+some reason for believing that the number of comets which move around
+the sun without ever coming inside the orbit of Jupiter, or even that of
+Saturn, is much larger than the number of those which come close enough
+to be discovered from the earth. In any case we are reminded of Kepler's
+saying, that comets in the sky are as plentiful as fishes in the sea,
+which seems to be very little exaggerated when we consider that,
+according to Kleiber, out of all the comets which enter the solar system
+probably not more than 2 or 3 per cent are ever discovered.
+
+[Illustration: FIG. 110.--The Great Comet of 1843.]
+
+163. DIMENSIONS OF COMETS.--The comet whose orbit is shown in Figs. 108
+and 109 is the finest and largest that has appeared in recent years. Its
+tail, which at its maximum extent would have more than bridged the space
+between sun and earth (100,000,000 miles), is made very much too short
+in Fig. 109, but when at its best was probably not inferior to that of
+the Great Comet of 1843, shown in Fig. 110. As we shall see later,
+there is a peculiar and special relationship between these two comets.
+
+The head of the comet of 1882 was not especially large--about twice the
+diameter of the ball of Saturn--but its nucleus, according to an
+estimate made by Dr. Elkin when it was very near perihelion, was as
+large as the moon. The head of the comet shown in Fig. 107 was too large
+to be put in the space between the earth and the moon, and the Great
+Comet of 1811 had a head considerably larger than the sun itself. From
+these colossal sizes down to the smallest shred just visible in the
+telescope, comets of all dimensions may be found, but the smaller the
+comet the less the chance of its being discovered, and a comet as small
+as the earth would probably go unobserved unless it approached very
+close to us.
+
+164. THE MASS OF A COMET.--There is no known case in which the mass of a
+comet has ever been measured, yet nothing about them is more sure than
+that they are bodies with mass which is attracted by the sun and the
+planets, and which in its turn attracts both sun and planets and
+produces perturbations in their motion. These perturbations are,
+however, too small to be measured, although the corresponding
+perturbations in the comet's motion are sometimes enormous, and since
+these mutual perturbations are proportional to the masses of comet and
+planet, we are forced to say that, by comparison with even such small
+bodies as the moon or Mercury, the mass of a comet is utterly
+insignificant, certainly not as great as a ten-thousandth part of the
+mass of the earth. In the case of the Great Comet of 1882, if we leave
+its hundred million miles of tail out of account and suppose the entire
+mass condensed into its head, we find by a little computation that the
+average density of the head under these circumstances must have been
+less than 1/1500 of the density of air. In ordinary laboratory practice
+this would be called a pretty good vacuum. A striking observation made
+on September 17, 1882, goes to confirm the very small density of this
+comet. It is shown in Fig. 109 that early on that day the comet crossed
+the line joining earth and sun, and therefore passed in transit over the
+sun's disk. Two observers at the Cape of Good Hope saw the comet
+approach the sun, and followed it with their telescopes until the
+nucleus actually reached the edge of the sun and disappeared, behind it
+as they supposed, for no trace of the comet, not even its nucleus, could
+be seen against the sun, although it was carefully looked for. Now, the
+figure shows that the comet passed between the earth and sun, and its
+densest parts were therefore too attenuated to cut off any perceptible
+fraction of the sun's rays. In other cases stars have been seen through
+the head of a comet, shining apparently with undimmed luster, although
+in some cases they seem to have been slightly refracted out of their
+true positions.
+
+165. METEORS.--Before proceeding further with the study of comets it is
+well to turn aside and consider their humbler relatives, the shooting
+stars. On some clear evening, when the moon is absent from the sky,
+watch the heavens for an hour and count the meteors visible during that
+time. Note their paths, the part of the sky where they appear and where
+they disappear, their brightness, and whether they all move with equal
+swiftness. Out of such simple observations with the unaided eye there
+has grown a large and important branch of astronomical science, some
+parts of which we shall briefly summarize here.
+
+A particular meteor is a local phenomenon seen over only a small part of
+the earth's surface, although occasionally a very big and bright one may
+travel and be visible over a considerable territory. Such a one in
+December, 1876, swept over the United States from Kansas to
+Pennsylvania, and was seen from eleven different States. But the
+ordinary shooting star is much less conspicuous, and, as we know from
+simultaneous observations made at neighboring places, it makes its
+appearance at a height of some 75 miles above the earth's surface,
+occupies something like a second in moving over its path, and then
+disappears at a height of about 50 miles or more, although occasionally
+a big one comes down to the very surface of the earth with force
+sufficient to bury itself in the ground, from which it may be dug up,
+handled, weighed, and turned over to the chemist to be analyzed. The
+pieces thus found show that the big meteors, at least, are masses of
+stone or mineral; iron is quite commonly found in them, as are a
+considerable number of other terrestrial substances combined in rather
+peculiar ways. But no chemical element not found on the earth has ever
+been discovered in a meteor.
+
+166. NATURE OF METEORS.--The swiftness with which the meteors sweep down
+shows that they must come from outside the earth, for even half their
+velocity, if given to them by some terrestrial volcano or other
+explosive agent, would send them completely away from the earth never to
+return. We must therefore look upon them as so many projectiles,
+bullets, fired against the earth from some outside source and arrested
+in their motion by the earth's atmosphere, which serves as a cushion to
+protect the ground from the bombardment which would otherwise prove in
+the highest degree dangerous to both property and life. The speed of the
+meteor is checked by the resistance which the atmosphere offers to its
+motion, and the energy represented by that speed is transformed into
+heat, which in less than a second raises the meteor and the surrounding
+air to incandescence, melts the meteor either wholly or in part, and
+usually destroys its identity, leaving only an impalpable dust, which
+cools off as it settles slowly through the lower atmosphere to the
+ground. The heating effect of the air's resistance is proportional to
+the square of the meteor's velocity, and even at such a moderate speed
+as 1 mile per second the effect upon the meteor is the same as if it
+stood still in a bath of red-hot air. Now, the actual velocity of
+meteors through the air is often 30 or 40 times as great as this, and
+the corresponding effect of the air in raising its temperature is more
+than 1,000 times that of red heat. Small wonder that the meteor is
+brought to lively incandescence and consumed even in a fraction of a
+second.
+
+167. THE NUMBER OF METEORS.--A single observer may expect to see in the
+evening hours about one meteor every 10 minutes on the average,
+although, of course, in this respect much irregularity may occur. Later
+in the night they become more frequent, and after 2 A. M. there are
+about three times as many to be seen as in the evening hours. But no one
+person can keep a watch upon the whole sky, high and low, in front and
+behind, and experience shows that by increasing the number of observers
+and assigning to each a particular part of the sky, the total number of
+meteors counted may be increased about five-fold. So, too, the observers
+at any one place can keep an effective watch upon only those meteors
+which come into the earth's atmosphere within some moderate distance of
+their station, say 50 or 100 miles, and to watch every part of that
+atmosphere would require a large number of stations, estimated at
+something more than 10,000, scattered systematically over the whole face
+of the earth. If we piece together the several numbers above considered,
+taking 14 as a fair average of the hourly number of meteors to be seen
+by a single observer at all hours of the night, we shall find for
+the total number of meteors encountered by the earth in 24 hours,
+14 Ɨ 5 Ɨ 10,000 Ɨ 24 = 16,800,000. Without laying too much stress upon
+this particular number, we may fairly say that the meteors picked up by
+the earth every day are to be reckoned by millions, and since they come
+at all seasons of the year, we shall have to admit that the region
+through which the earth moves, instead of being empty space, is really a
+dust cloud, each individual particle of dust being a prospective meteor.
+
+On the average these individual particles are very small and very far
+apart; a cloud of silver dimes each about 250 miles from its nearest
+neighbor is perhaps a fair representation of their average mass and
+distance from each other, but, of course, great variations are to be
+expected both in the size and in the frequency of the particles. There
+must be great numbers of them that are too small to make shooting stars
+visible to the naked eye, and such are occasionally seen darting by
+chance across the field of view of a telescope.
+
+168. THE ZODIACAL LIGHT is an effect probably due to the reflection of
+sunlight from the myriads of these tiny meteors which occupy the space
+inside the earth's orbit. It is a faint and diffuse stream of light,
+something like the Milky Way, which may be seen in the early evening or
+morning stretching up from the sunrise or sunset point of the horizon
+along the ecliptic and following its course for many degrees, possibly
+around the entire circumference of the sky. It may be seen at any season
+of the year, although it shows to the best advantage in spring evenings
+and autumn mornings. Look for it.
+
+169. GREAT METEORS.--But there are other meteors, veritable fireballs in
+appearance, far more conspicuous and imposing than the ordinary shooting
+star. Such a one exploded over the city of Madrid, Spain, on the morning
+of February 10, 1896, giving in broad sunlight "a brilliant flash which
+was followed ninety seconds later by a succession of terrific noises
+like the discharge of a battery of artillery." Fig. 111 shows a large
+meteor which was seen in California in the early evening of July 27,
+1894, and which left behind it a luminous trail or cloud visible for
+more than half an hour.
+
+Not infrequently large meteors are found traveling together, two or
+three or more in company, making their appearance simultaneously as did
+the California meteor of October 22, 1896, which is described as triple,
+the trio following one another like a train of cars, and Arago cites an
+instance, from the year 1830, where within a short space of time some
+forty brilliant meteors crossed the sky, all moving in the same
+direction with a whistling noise and displaying in their flight all the
+colors of the rainbow.
+
+The mass of great meteors such as these must be measured in hundreds if
+not thousands of pounds, and stories are current, although not very well
+authenticated, of even larger ones, many tons in weight, having been
+found partially buried in the ground. Of meteors which have been
+actually seen to fall from the sky, the largest single fragment
+recovered weighs about 500 pounds, but it is only a fragment of the
+original meteor, which must have been much more massive before it was
+broken up by collision with the atmosphere.
+
+[Illustration: FIG. 111.--The California meteor of July 27, 1894.]
+
+170. THE VELOCITY OF METEORS.--Every meteor, big or little, is subject
+to the law of gravitation, and before it encounters the earth must be
+moving in some kind of orbit having the sun at its focus, the particular
+species of orbit--ellipse, parabola, hyperbola--depending upon the
+velocity and direction of its motion. Now, the direction in which a
+meteor is moving can be determined without serious difficulty from
+observations of its apparent path across the sky made by two or more
+observers, but the velocity can not be so readily found, since the
+meteors go too fast for any ordinary process of timing. But by
+photographing one of them two or three times on the same plate, with an
+interval of only a tenth of a second between exposures, Dr. Elkin has
+succeeded in showing, in a few cases, that their velocities varied from
+20 to 25 miles per second, and must have been considerably greater than
+this before the meteors encountered the earth's atmosphere. This is a
+greater velocity than that of the earth in its orbit, 19 miles per
+second, as might have been anticipated, since the mere fact that meteors
+can be seen at all in the evening hours shows that some of them at least
+must travel considerably faster than the earth, for, counting in the
+direction of the earth's motion, the region of sunset and evening is
+always on the rear side of the earth, and meteors in order to strike
+this region must overtake it by their swifter motion. We have here, in
+fact, the reason why meteors are especially abundant in the morning
+hours; at this time the observer is on the front side of the earth which
+catches swift and slow meteors alike, while the rear is pelted only by
+the swifter ones which follow it.
+
+A comparison of the relative number of morning and evening meteors makes
+it probable that the average meteor moves, relative to the sun, with a
+velocity of about 26 miles per second, which is very approximately the
+average velocity of comets when they are at the earth's distance from
+the sun. Astronomers, therefore, consider meteors as well as comets to
+have the parabola and the elongated ellipse as their characteristic
+orbits.
+
+171. METEOR SHOWERS--THE RADIANT.--There is evident among meteors a
+distinct tendency for individuals, to the number of hundreds or even
+hundreds of millions, to travel together in flocks or swarms, all going
+the same way in orbits almost exactly alike. This gregarious tendency is
+made manifest not only by the fact that from time to time there are
+unusually abundant meteoric displays, but also by a striking peculiarity
+of their behavior at such times. The meteors all seem to come from a
+particular part of the heavens, as if here were a hole in the sky
+through which they were introduced, and from which they flow away in
+every direction, even those which do not visibly start from this place
+having paths among the stars which, if prolonged backward, would pass
+through it. The cause of this appearance may be understood from Fig.
+112, which represents a group of meteors moving together along parallel
+paths toward an observer at _D_. Traveling unseen above the earth until
+they encounter the upper strata of its atmosphere, they here become
+incandescent and speed on in parallel paths, _1_, _2_, _3_, _4_, _5_,
+_6_, which, as seen by the observer, are projected back against the sky
+into luminous streaks that, as is shown by the arrowheads, _b_, _c_,
+_d_, all seem to radiate from the point _a_--i. e., from the point in
+the sky whose direction from the observer is parallel to the paths of
+the meteors.
+
+[Illustration: FIG. 112.--Explanation of the radiant of a meteoric
+shower.--DENNING.]
+
+Such a display is called a meteor shower, and the point _a_ is called
+its radiant. Note how those meteors which appear near the radiant all
+have short paths, while those remote from it in the sky have longer
+ones. Query: As the night wears on and the stars shift toward the west,
+will the radiant share in their motion or will it be left behind? Would
+the luminous part of the path of any of these meteors pass across the
+radiant from one side to the other? Is such a crossing of the radiant
+possible under any circumstances? Fig. 113 shows how the meteor paths
+are grouped around the radiant of a strongly marked shower. Select from
+it the meteors which do not belong to this shower.
+
+[Illustration: FIG. 113.--The radiant of a meteoric shower, showing
+also the paths of three meteors which do not belong to this
+shower.--DENNING.]
+
+Many hundreds of these radiants have been observed in the sky, each of
+which represents an orbit along which a group of meteors moves, and the
+relation of one of these orbits to that of the earth is shown in Fig.
+114. The orbit of the meteors is an ellipse extending out beyond the
+orbit of Uranus, but so eccentric that a part of it comes inside the
+orbit of the earth, and the figure shows only that part of it which lies
+nearest the sun. The Roman numerals which are placed along the earth's
+orbit show the position of the earth at the beginning of the tenth
+month, eleventh month, etc. The meteors flow along their orbit in a long
+procession, whose direction of motion is indicated by the arrow heads,
+and the earth, coming in the opposite direction, plunges into this
+stream and receives the meteor shower when it reaches the intersection
+of the two orbits. The long arrow at the left of the figure represents
+the direction of motion of another meteor shower which encounters the
+earth at this point.
+
+[Illustration: FIG. 114.--The orbits of the earth and the November
+meteors.]
+
+Can you determine from the figure answers to the following questions? On
+what day of the year will the earth meet each of these showers? Will the
+radiant points of the showers lie above or below the plane of the
+earth's orbit? Will these meteors strike the front or the rear of the
+earth? Can they be seen in the evening hours?
+
+From many of the radiants year after year, upon the same day or week in
+each year, there comes a swarm of shooting stars, showing that there
+must be a continuous procession of meteors moving along this orbit, so
+that some are always ready to strike the earth whenever it reaches the
+intersection of its orbit with theirs. Such is the explanation of the
+shower which appears each year in the first half of August, and whose
+meteors are sometimes called Perseids, because their radiant lies in the
+constellation Perseus, and a similar explanation holds for all the star
+showers which are repeated year after year.
+
+172. THE LEONIDS.--There is, however, a kind of star shower, of which
+the Leonids (radiant in Leo) is the most conspicuous type, in which the
+shower, although repeated from year to year, is much more striking in
+some years than in others. Thus, to quote from the historian: "In 1833
+the shower was well observed along the whole eastern coast of North
+America from the Gulf of Mexico to Halifax. The meteors were most
+numerous at about 5 A. M. on November 13th, and the rising sun could not
+blot out all traces of the phenomena, for large meteors were seen now
+and then in full daylight. Within the scope that the eye could contain,
+more than twenty could be seen at a time shooting in every direction.
+Not a cloud obscured the broad expanse, and millions of meteors sped
+their way across in every point of the compass. Their coruscations were
+bright, gleaming, and incessant, and they fell thick as the flakes in
+the early snows of December." But, so far as is known, none of them
+reached the ground. An illiterate man on the following day remarked:
+"The stars continued to fall until none were left. I am anxious to see
+how the heavens will appear this evening, for I believe we shall see no
+more stars."
+
+An eyewitness in the Southern States thus describes the effect of this
+shower upon the plantation negroes: "Upward of a hundred lay prostrate
+upon the ground, some speechless and some with the bitterest cries, but
+with their hands upraised, imploring God to save the world and them. The
+scene was truly awful, for never did rain fall much thicker than the
+meteors fell toward the earth--east, west, north, and south it was the
+same." In the preceding year a similar but feebler shower from the same
+radiant created much alarm in France, and through the old historic
+records its repetitions may be traced back at intervals of 33 or 34
+years, although with many interruptions, to October 12, 902, O. S., when
+"an immense number of falling stars were seen to spread themselves over
+the face of the sky like rain."
+
+Such a star shower differs from the one repeated every year chiefly in
+the fact that its meteors, instead of being drawn out into a long
+procession, are mainly clustered in a single flock which may be long
+enough to require two or three or four years to pass a given point of
+its orbit, but which is far from extending entirely around it, so that
+meteors from this source are abundant only in those years in which the
+flock is at or near the intersection of its orbit with that of the
+earth. The fact that the Leonid shower is repeated at intervals of 33 or
+34 years (it appeared in 1799, 1832-'33, 1866-'67) shows that this is
+the "periodic time" in its orbit, which latter must of course be an
+ellipse, and presumably a long and narrow one. It is this orbit which is
+shown in Fig. 114, and the student should note in this figure that if
+the meteor stream at the point where it cuts through the plane of the
+earth's orbit were either nearer to or farther from the sun than is the
+earth there could be no shower; the earth and the meteors would pass by
+without a collision. Now, the meteors in their motion are subject to
+perturbations, particularly by the large planets Jupiter, Saturn, and
+Uranus, which slightly change the meteor orbit, and it seems certain
+that the changes thus produced will sometimes thrust the swarm inside or
+outside the orbit of the earth, and thus cause a failure of the shower
+at times when it is expected. The meteors were due at the crossing of
+the orbits in November, 1899 and 1900, and, although a few were then
+seen, the shower was far from being a brilliant one, and its failure was
+doubtless caused by the outer planets, which switched the meteors aside
+from the path in which they had been moving for a century. Whether they
+will be again switched back so as to produce future showers is at the
+present time uncertain.
+
+173. CAPTURE OF THE LEONIDS.--But a far more striking effect of
+perturbations is to be found in Fig. 115, which shows the relation of
+the Leonid orbit to those of the principal planets, and illustrates a
+curious chapter in the history of the meteor swarm that has been worked
+out by mathematical analysis, and is probably a pretty good account of
+what actually befell them. Early in the second century of the Christian
+era this flock of meteors came down toward the sun from outer space,
+moving along a parabolic orbit which would have carried it just inside
+the orbit of Jupiter, and then have sent it off to return no more. But
+such was not to be its fate. As it approached the orbit of Uranus, in
+the year 126 A. D., that planet chanced to be very near at hand and
+perturbed the motion of the meteors to such an extent that the character
+of their orbit was completely changed into the ellipse shown in the
+figure, and in this new orbit they have moved from that time to this,
+permanent instead of transient members of the solar system. The
+perturbations, however, did not end with the year in which the meteors
+were captured and annexed to the solar system, but ever since that time
+Jupiter, Saturn, and Uranus have been pulling together upon the orbit,
+and have gradually turned it around into its present position as shown
+in the figure, and it is chiefly this shifting of the orbit's position
+in the thousand years that have elapsed since 902 A. D. that makes the
+meteor shower now come in November instead of in October as it did
+then.
+
+[Illustration: FIG. 115.--Supposed capture of the November meteors by
+Uranus.]
+
+174. BREAKING UP A METEOR SWARM.--How closely packed together these
+meteors were at the time of their annexation to the solar system is
+unknown, but it is certain that ever since that time the sun has been
+exerting upon them a tidal influence tending to break up the swarm and
+distribute its particles around the orbit, as the Perseids are
+distributed, and, given sufficient time, it will accomplish this, but up
+to the present the work is only partly done. A certain number of the
+meteors have gained so much over the slower moving ones as to have made
+an extra circuit of the orbit and overtaken the rear of the procession,
+so that there is a thin stream of them extending entirely around the
+orbit and furnishing in every November a Leonid shower; but by far the
+larger part of the meteors still cling together, although drawn out into
+a stream or ribbon, which, though very thin, is so long that it takes
+some three years to pass through the perihelion of its orbit. It is only
+when the earth plunges through this ribbon, as it should in 1899, 1900,
+1901, that brilliant Leonid showers can be expected.
+
+175. RELATION OF COMETS AND METEORS.--It appears from the foregoing that
+meteors and comets move in similar orbits, and we have now to push the
+analogy a little further and note that in some instances at least they
+move in identically the same orbit, or at least in orbits so like that
+an appreciable difference between them is hardly to be found. Thus a
+comet which was discovered and observed early in the year 1866, moves in
+the same orbit with the Leonid meteors, passing its perihelion about ten
+months ahead of the main body of the meteors. If it were set back in its
+orbit by ten months' motion, _it would be a part of the meteor swarm_.
+Similarly, the Perseid meteors have a comet moving in their orbit
+actually immersed in the stream of meteor particles, and several other
+of the more conspicuous star showers have comets attending them.
+
+Perhaps the most remarkable case of this character is that of a shower
+which comes in the latter part of November from the constellation
+Andromeda, and which from its association with the comet called Biela
+(after the name of its discoverer) is frequently referred to as the
+Bielid shower. This comet, an inconspicuous one moving in an unusually
+small elliptical orbit, had been observed at various times from 1772
+down to 1846 without presenting anything remarkable in its appearance;
+but about the beginning of the latter year, with very little warning, it
+broke in two, and for three months the pieces were watched by
+astronomers moving off, side by side, something more than half as far
+apart as are the earth and moon. It disappeared, made the circuit of its
+orbit, and six years later came back, with the fragments nearly ten
+times as far apart as before, and after a short stay near the earth once
+more disappeared in the distance, never to be seen again, although the
+fragments should have returned to perihelion at least half a dozen times
+since then. In one respect the orbit of the comet was remarkable: it
+passed through the place in which the earth stands on November 27th of
+each year, so that if the comet were at that particular part of its
+orbit on any November 27th, a collision between it and the earth would
+be inevitable. So far as is known, no such collision with the comet has
+ever occurred, but the Bielid meteors which are strung along its orbit
+do encounter the earth on that date, in greater or less abundance in
+different years, and are watched with much interest by the astronomers
+who look upon them as the final appearance of the _dƩbris_ of a worn-out
+comet.
+
+176. PERIODIC COMETS.--The Biela comet is a specimen of the type which
+astronomers call periodic comets--i. e., those which move in small
+ellipses and have correspondingly short periodic times, so that they
+return frequently and regularly to perihelion. The comets which
+accompany the other meteor swarms--Leonids, Perseids, etc.--also belong
+to this class as do some 30 or 40 others which have periodic times less
+than a century. As has been already indicated, these deviations from the
+normal parabolic orbit call for some special explanation, and the
+substance of that explanation is contained in the account of the Leonid
+meteors and their capture by Uranus. Any comet may be thus captured by
+the attraction of a planet near which it passes. It is only necessary
+that the perturbing action of the planet should result in a diminution
+of the comet's velocity, for we have already learned that it is this
+velocity which determines the character of the orbit, and anything less
+than the velocity appropriate to a parabola must produce an
+ellipse--i. e., a closed orbit around which the body will revolve time
+after time in endless succession. We note in Fig. 115 that when the
+Leonid swarm encountered Uranus it passed _in front of_ the planet and
+had its velocity diminished and its orbit changed into an ellipse
+thereby. It might have passed behind Uranus, it would have passed behind
+had it come a little later, and the effect would then have been just the
+opposite. Its velocity would have been increased, its orbit changed to a
+hyperbola, and it would have left the solar system more rapidly than it
+came into it, thrust out instead of held in by the disturbing planet. Of
+such cases we can expect no record to remain, but the captured comet is
+its own witness to what has happened, and bears imprinted upon its orbit
+the brand of the planet which slowed down its motion. Thus in Fig. 115
+the changed orbit of the meteors has its _aphelion_ (part remotest from
+the sun) quite close to the orbit of Uranus, and one of its nodes, ā„§,
+the point in which it cuts through the plane of the ecliptic from north
+to south side, is also very near to the same orbit. It is these two
+marks, aphelion and node, which by their position identify Uranus as the
+planet instrumental in capturing the meteor swarm, and the date of the
+capture is found by working back with their respective periodic times to
+an epoch at which planet and comet were simultaneously near this node.
+
+Jupiter, by reason of his great mass, is an especially efficient
+capturer of comets, and Fig. 116 shows his group of captives, his
+family of comets as they are sometimes called. The several orbits are
+marked with the names commonly given to the comets. Frequently this is
+the name of their discoverer, but often a different system is
+followed--e. g., the name 1886, IV, means the fourth comet to pass
+through perihelion in the year 1886. The other great planets--Saturn,
+Uranus, Neptune--have also their families of captured comets, and
+according to Schulhof, who does not entirely agree with the common
+opinion about captured comets, the earth has caught no less than nine of
+these bodies.
+
+[Illustration: FIG. 116.--Jupiter's family of comets.]
+
+177. COMET GROUPS.--But there is another kind of comet family, or comet
+group as it is called, which deserves some notice, and which is best
+exemplified by the Great Comet of 1882 and its relatives. No less than
+four other comets are known to be traveling in substantially the same
+orbit with this one, the group consisting of comets 1668, I; 1843, I;
+1880, I; 1882, II; 1887, I. The orbit itself is not quite a parabola,
+but a very elongated ellipse, whose major axis and corresponding
+periodic time can not be very accurately determined from the available
+data, but it certainly extends far beyond the orbit of Neptune, and
+requires not less than 500 years for the comet to complete a revolution
+in it. It was for a time supposed that some one of the recent comets of
+this group of five might be a return of the comet of 1668 brought back
+ahead of time by unknown perturbations. There is still a possibility of
+this, but it is quite out of the question to suppose that the last four
+members of the group are anything other than separate and distinct
+comets moving in practically the same orbit. This common orbit suggests
+a common origin for the comets, but leaves us to conjecture how they
+became separated.
+
+The observed orbits of these five comets present some slight
+discordances among themselves, but if we suppose each comet to move in
+the average of the observed paths it is a simple matter to fix their
+several positions at the present time. They have all receded from the
+sun nearly on line toward the bright star Sirius, and were all of them,
+at the beginning of the year 1900, standing nearly motionless inside of
+a space not bigger than the sun and distant from the sun about 150 radii
+of the earth's orbit. The great rapidity with which they swept through
+that part of their orbit near the sun (see Ā§ 162) is being compensated
+by the present extreme slowness of their motions, so that the comets of
+1668 and 1882, whose passages through the solar system were separated by
+an interval of more than two centuries, now stand together near the
+aphelion of their orbits, separated by a distance only 50 per cent
+greater than the diameter of the moon's orbit, and they will continue
+substantially in this position for some two or three centuries to come.
+
+The slowness with which these bodies move when far from the sun is
+strikingly illustrated by an equation of celestial mechanics which for
+parabolic orbits takes the place of Kepler's Third Law--viz.:
+
+    r^3 / T^2 = 178,
+
+where _T_ is the time, in years, required for the comet to move from its
+perihelion to any remote part of the orbit, whose distance from the sun
+is represented, in radii of the earth's orbit, by _r_. If the comet of
+1668 had moved in a parabola instead of the ellipse supposed above, how
+many years would have been required to reach its present distance from
+the sun?
+
+178. RELATION OF COMETS TO THE SOLAR SYSTEM.--The orbits of these comets
+illustrate a tendency which is becoming ever more strongly marked.
+Because comet orbits are nearly parabolas, it used to be assumed that
+they were exactly parabolic, and this carried with it the conclusion
+that comets have their origin outside the solar system. It may be so,
+and this view is in some degree supported by the fact that these nearly
+parabolic orbits of both comets and meteors are tipped at all possible
+angles to the plane of the ecliptic instead of lying near it as do the
+orbits of the planets; and by the further fact that, unlike the planets,
+the comets show no marked tendency to move around their orbits in the
+direction in which the sun rotates upon his axis. There is, in fact, the
+utmost confusion among them in this respect, some going one way and some
+another. The law of the solar system (gravitation) is impressed upon
+their movements, but its order is not.
+
+But as observations grow more numerous and more precise, and comet
+orbits are determined with increasing accuracy, there is a steady gain
+in the number of elliptic orbits at the expense of the parabolic ones,
+and if comets are of extraneous origin we must admit that a very
+considerable percentage of them have their velocities slowed down
+within the solar system, perhaps not so much by the attraction of the
+planets as by the resistance offered to their motion by meteor particles
+and swarms along their paths. A striking instance of what may befall a
+comet in this way is shown in Fig. 117, where the tail of a comet
+appears sadly distorted and broken by what is presumed to have been a
+collision with a meteor swarm. A more famous case of impeded motion is
+offered by the comet which bears the name of Encke. This has a periodic
+time less than that of any other known comet, and at intervals of forty
+months comes back to perihelion, each time moving in a little smaller
+orbit than before, unquestionably on account of some resistance which it
+has suffered.
+
+[Illustration: FIG. 117.--Brooks's comet, October 21, 1893.--BARNARD.]
+
+179. THE DEVELOPMENT OF A COMET.--We saw in Ā§ 174 that the sun's action
+upon a meteor swarm tends to break it up into a long stream, and the
+same tendency to break up is true of comets whose attenuated substance
+presents scant resistance to this force. According to the mathematical
+analysis of Roche, if the comet stood still the sun's tidal force would
+tend first to draw it out on line with the sun, just as the earth's
+tidal force pulled the moon out of shape (Ā§ 42), and then it would cause
+the lighter part of the comet's substance to flow away from both ends of
+this long diameter. This destructive action of the sun is not limited to
+comets and meteor streams, for it tends to tear the earth and moon to
+pieces as well; but the densities and the resulting mutual attractions
+of their parts are far too great to permit this to be accomplished.
+
+As a curiosity of mathematical analysis we may note that a spherical
+cloud of meteors, or dust particles weighing a gramme each, and placed
+at the earth's distance from the sun, will be broken up and dissipated
+by the sun's tidal action if the average distance between the particles
+exceeds two yards. Now, the earth is far more dense than such a cloud,
+whose extreme tenuity, however, suggests what we have already learned of
+the small density of comets, and prepares us in their case for an
+outflow of particles at both ends of the diameter directed toward the
+sun. Something of this kind actually occurs, for the tail of a comet
+streams out on the side opposite to the sun, and in general points away
+from the sun, as is shown in Fig. 109, and the envelopes and jets rise
+up toward the sun; but an inspection of Fig. 106 will show that the tail
+and the envelope are too unlike to be produced by one and the same set
+of forces.
+
+It was long ago suggested that the sun possibly exerts upon a comet's
+substance a repelling force in addition to the attracting force which we
+call gravity. We think naturally in this connection of the repelling
+force which a charge of electricity exerts upon a similar charge placed
+on a neighboring body, and we note that if both sun and comet carried a
+considerable store of electricity upon their surfaces this would furnish
+just such a repelling force as seems indicated by the phenomena of
+comets' tails; for the force of gravity would operate between the
+substance of sun and comet, and on the whole would be the controlling
+force, while the electric charges would produce a repulsion, relatively
+feeble for the big particles and strong for the little ones, since an
+electric charge lies wholly on the surface, while gravity permeates the
+whole mass of a body, and the ratio of volume (gravity) to surface
+(electric charge) increases rapidly with increasing size. The repelling
+force would thrust back toward the comet those particles which flowed
+out toward the sun, while it would urge forward those which flowed away
+from it, thus producing the difference in appearance between tail and
+envelopes, the latter being regarded from this standpoint as stunted
+tails strongly curved backward. In recent years the Russian astronomer
+Bredichin has made a careful study of the shape and positions of comets'
+tails and finds that they fit with mathematical precision to the
+theories of electric repulsion.
+
+180. COMET TAILS.--According to Bredichin, a comet's tail is formed by
+something like the following process: In the head of the comet itself a
+certain part of its matter is broken up into fine bits, single molecules
+perhaps, which, as they no longer cling together, may be described as in
+the condition of vapor. By the repellent action of both sun and comet
+these molecules are cast out from the head of the comet and stream away
+in the direction opposite to the sun with different velocities, the
+heavy ones slowly and the light ones faster, much as particles of smoke
+stream away from a smokestack, making for the comet a tail which like a
+trail of smoke is composed of constantly changing particles. The result
+of this process is shown in Fig. 118, where the positions of the comet
+in its orbit on successive days are marked by the Roman numerals, and
+the broken lines represent the paths of molecules _m^{I}_, _m^{II}_,
+_m^{III}_, etc., expelled from it on their several dates and traveling
+thereafter in orbits determined by the combined effect of the sun's
+attraction, the sun's repulsion, and the comet's repulsion. The comet's
+attraction (gravity) is too small to be taken into account. The line
+drawn upward from _VI_ represents the positions of these molecules on
+the sixth day, and shows that all of them are arranged in a tail
+pointing nearly away from the sun. A similar construction for the other
+dates gives the corresponding positions of the tail, always pointing
+away from the sun.
+
+[Illustration: FIG. 118.--Formation of a comet's tail.]
+
+Only the lightest kind of molecules--e. g., hydrogen--could drift away
+from the comet so rapidly as is here shown. The heavier ones, such as
+carbon and iron, would be repelled as strongly by the electric forces,
+but they would be more strongly pulled back by the gravitative forces,
+thus producing a much slower separation between them and the head of the
+comet. Construct a figure such as the above, in which the molecules
+shall recede from the comet only one eighth as fast as in Fig. 118, and
+note what a different position it gives to the comet's tail. Instead of
+pointing directly away from the sun, it will be bent strongly to one
+side, as is the large plume-shaped tail of the Donati comet shown in
+Fig. 101. But observe that this comet has also a nearly straight tail,
+like the theoretical one of Fig. 118. We have here two distinct types of
+comet tails, and according to Bredichin there is still another but
+unusual type, even more strongly bent to one side of the line joining
+comet and sun, and appearing quite short and stubby. The existence of
+these three types, and their peculiarities of shape and position, are
+all satisfactorily accounted for by the supposition that they are made
+of different materials. The relative molecular weights of hydrogen, some
+of the hydrocarbons, and iron, are such that tails composed of these
+molecules would behave just as do the actual tails observed and
+classified into these three types. The spectroscope shows that these
+materials--hydrogen, hydrocarbons, and iron--are present in comets, and
+leaves little room for doubt of the essential soundness of Bredichin's
+theory.
+
+181. DISINTEGRATION OF COMETS.--We must regard the tail as waste matter
+cast off from the comet's head, and although the amount of this matter
+is very small, it must in some measure diminish the comet's mass. This
+process is, of course, most active at the time of perihelion passage,
+and if the comet returns to perihelion time after time, as the periodic
+ones which move in elliptic orbits must do, this waste of material may
+become a serious matter, leading ultimately to the comet's destruction.
+It is significant in this connection that the periodic comets are all
+small and inconspicuous, not one of them showing a tail of any
+considerable dimensions, and it appears probable that they are far
+advanced along the road which, in the case of Biela's comet, led to its
+disintegration. Their fragments are in part strewn through the solar
+system, making some small fraction of its cloud of cosmic dust, and in
+part they have been carried away from the sun and scattered throughout
+the universe along hyperbolic orbits impressed upon them at the time
+they left the comet.
+
+But it is not through the tail only that the disintegrating process is
+worked out. While Biela's comet is perhaps the most striking instance in
+which the head has broken up, it is by no means the only one. The Great
+Comet of 1882 cast off a considerable number of fragments which moved
+away as independent though small comets and other more recent comets
+have been seen to do the same. An even more striking phenomenon was the
+gradual breaking up of the nucleus of the same comet, 1882, II, into a
+half dozen nuclei arranged in line like beads upon a string, and
+pointing along the axis of the tail. See Fig. 119, which shows the
+series of changes observed in the head of this comet.
+
+182. COMETS AND THE SPECTROSCOPE.--The spectrum presented by comets was
+long a puzzle, and still retains something of that character, although
+much progress has been made toward an understanding of it. In general it
+consists of two quite distinct parts--first, a faint background of
+continuous spectrum due to ordinary sunlight reflected from the comet;
+and, second, superposed upon this, three bright bands like the carbon
+band shown at the middle of Fig. 48, only not so sharply defined. These
+bands make a discontinuous spectrum quite similar to that given off by
+compounds of hydrogen and carbon, and of course indicate that a part of
+the comet's light originates in the body itself, which must therefore be
+incandescent, or at least must contain some incandescent portions.
+
+[Illustration: FIG. 119.--The head of the Great Comet of
+1882.--WINLOCK.]
+
+By heating hydrocarbons in our laboratories until they become
+incandescent, something like the comet spectrum may be artificially
+produced, but the best approximation to it is obtained by passing a
+disruptive electrical discharge through a tube in which fragments of
+meteors have been placed. A flash of lightning is a disruptive
+electrical discharge upon a grand scale. Now, meteors and electric
+phenomena have been independently brought to our notice in connection
+with comets, and with this suggestion it is easy to frame a general idea
+of the physical condition of these objects--for example, a cloud of
+meteors of different sizes so loosely clustered that the average density
+of the swarm is very low indeed; the several particles in motion
+relative to each other, as well as to the sun, and disturbed in that
+motion by the sun's tidal action. Each particle carries its own electric
+charge, which may be of higher or lower tension than that of its
+neighbor, and is ready to leap across the intervening gap whenever two
+particles approach each other. To these conditions add the inductive
+effect of the sun's electric charge, which tends to produce a particular
+and artificial distribution of electricity among the comet's particles,
+and we may expect to find an endless succession of sparks, tiny
+lightning flashes, springing from one particle to another, most frequent
+and most vivid when the comet is near the sun, but never strong enough
+to be separately visible. Their number is, however, great enough to make
+the comet in part self-luminous with three kinds of light--i. e., the
+three bright bands of its spectrum, whose wave lengths show in the comet
+the same elements and compounds of the elements--carbon, hydrogen, and
+oxygen--which chemical analysis finds in the fallen meteor. It is not to
+be supposed that these are the only chemical elements in the comet, as
+they certainly are not the only ones in the meteor. They are the easy
+ones to detect under ordinary circumstances, but in special cases, like
+that of the Great Comet of 1882, whose near approach to the sun rendered
+its whole substance incandescent, the spectrum glows with additional
+bright lines of sodium, iron, etc.
+
+183. COLLISIONS.--A question sometimes asked, What would be the effect
+of a collision between the earth and a comet? finds its answer in the
+results reached in the preceding sections. There would be a star
+shower, more or less brilliant according to the number and size of the
+pieces which made up the comet's head. If these were like the remains of
+the Biela comet, the shower might even be a very tame one; but a
+collision with a great comet would certainly produce a brilliant
+meteoric display if its head came in contact with the earth. If the
+comet were built of small pieces whose individual weights did not exceed
+a few ounces or pounds, the earth's atmosphere would prove a perfect
+shield against their attacks, reducing the pieces to harmless dust
+before they could reach the ground, and leaving the earth uninjured by
+the encounter, although the comet might suffer sadly from it. But big
+stones in the comet, meteors too massive to be consumed in their flight
+through the air, might work a very different effect, and by their
+bombardment play sad havoc with parts of the earth's surface, although
+any such result as the wrecking of the earth, or the destruction of all
+life upon it, does not seem probable. The 40 meteors of Ā§ 169 may stand
+for a collision with a small comet. Consult the Bible (Joshua x, 11) for
+an example of what might happen with a larger one.
+
+
+
+
+CHAPTER XIII
+
+THE FIXED STARS
+
+
+184. THE CONSTELLATIONS.--In the earlier chapters the student has
+learned to distinguish between wandering stars (planets) and those fixed
+luminaries which remain year after year in the same constellation,
+shining for the most part with unvarying brilliancy, and presenting the
+most perfect known image of immutability. Homer and Job and prehistoric
+man saw Orion and the Pleiades much as we see them to-day, although the
+precession, by changing their relation to the pole of the heavens, has
+altered their risings and settings, and it may be that their luster has
+changed in some degree as they grew old with the passing centuries.
+
+[Illustration: FIG. 120.--Illustrating the division of the sky into
+constellations.]
+
+The division of the sky into constellations dates back to the most
+primitive times, long before the Christian era, and the crooked and
+irregular boundaries of these constellations, shown by the dotted lines
+in Fig. 120, such as no modern astronomer would devise, are an
+inheritance from antiquity, confounded and made worse in its descent to
+our day. The boundaries assigned to constellations near the south pole
+are much more smooth and regular, since this part of the sky, invisible
+to the peoples from whom we inherit, was not studied and mapped until
+more modern times. The old traditions associated with each constellation
+a figure, often drawn from classical mythology, which was supposed to be
+suggested by the grouping of the stars: thus Ursa Major is a great bear,
+stalking across the sky, with the handle of the Dipper for his tail; Leo
+is a lion; Cassiopeia, a lady in a chair; Andromeda, a maiden chained
+to a rock, etc.; but for the most part the resemblances are far-fetched
+and quite too fanciful to be followed by the ordinary eye.
+
+185. THE NUMBER OF STARS.--"As numerous as the stars of heaven" is a
+familiar figure of speech for expressing the idea of countless number,
+but as applied to the visible stars of the sky the words convey quite a
+wrong impression, for, under ordinary circumstances, in a clear sky
+every star to be seen may be counted in the course of a few hours, since
+they do not exceed 3,000 or 4,000, the exact number depending upon
+atmospheric conditions and the keenness of the individual eye. Test your
+own vision by counting the stars of the Pleiades. Six are easily seen,
+and you may possibly find as many as ten or twelve; but however many are
+seen, there will be a vague impression of more just beyond the limit of
+visibility, and doubtless this impression is partly responsible for the
+popular exaggeration of the number of the stars. In fact, much more than
+half of what we call starlight comes from stars which are separately too
+small to be seen, but whose number is so great as to more than make up
+for their individual faintness.
+
+The Milky Way is just such a cloud of faint stars, and the student who
+can obtain access to a small telescope, or even an opera glass, should
+not fail to turn it toward the Milky Way and see for himself how that
+vague stream of light breaks up into shining points, each an independent
+star. These faint stars, which are found in every part of the sky as
+well as in the Milky Way, are usually called _telescopic_, in
+recognition of the fact that they can be seen only in the telescope,
+while the other brighter ones are known as _lucid stars_.
+
+186. MAGNITUDES.--The telescopic stars show among themselves an even
+greater range of brightness than do the lucid ones, and the system of
+magnitudes (Ā§ 9) has accordingly been extended to include them, the
+faintest star visible in the greatest telescope of the present time
+being of the sixteenth or seventeenth magnitude, while, as we have
+already learned, stars on the dividing line between the telescopic and
+the lucid ones are of the sixth magnitude. To compare the amount of
+light received from the stars with that from the planets, and
+particularly from the sun and moon, it has been found necessary to
+prolong the scale of magnitudes backward into the negative numbers, and
+we speak of the sun as having a stellar magnitude represented by the
+number -26.5. The full moon's stellar magnitude is -12, and the planets
+range from -3 (Venus) to +8 (Neptune). Even a very few of the stars are
+so bright that negative magnitudes must be used to represent their true
+relation to the fainter ones. Sirius, for example, the brightest of the
+fixed stars, is of the -1 magnitude, and such stars as Arcturus and Vega
+are of the 0 magnitude.
+
+The relation of these magnitudes to each other has been so chosen that a
+star of any one magnitude is very approximately 2.5 times as bright as
+one of the next fainter magnitude, and this ratio furnishes a convenient
+method of comparing the amount of light received from different stars.
+Thus the brightness of Venus is 2.5 Ɨ 2.5 times that of Sirius. The full
+moon is 2.5^{9} times as bright as Venus, etc.; only it should be
+observed that the number 2.5 is not exactly the value of the _light
+ratio_ between two consecutive magnitudes. Strictly this ratio is the
+100^{1/5} = 2.5119+, so that to be entirely accurate we must say that
+a difference of five magnitudes gives a hundredfold difference of
+brightness. In mathematical symbols, if _B_ represents the ratio of
+brightness (quantity of light) of two stars whose magnitudes are _m_ and
+_n_, then
+
+    B = (100)^{(m-n)/5}
+
+How much brighter is an ordinary first-magnitude star, such as Aldebaran
+or Spica, than a star just visible to the naked eye? How many of the
+faintest stars visible in a great telescope would be required to make
+one star just visible to the unaided eye? How many full moons must be
+put in the sky in order to give an illumination as bright as daylight?
+How large a part of the visible hemisphere would they occupy?
+
+187. CLASSIFICATION BY MAGNITUDES.--The brightness of all the lucid
+stars has been carefully measured with an instrument (photometer)
+designed for that special purpose, and the following table shows,
+according to the Harvard Photometry, the number of stars in the whole
+sky, from pole to pole, which are brighter than the several magnitudes
+named in the table:
+
+    The number of stars brighter than magnitude 1.0 is    11
+        "       "          "      "       "     2.0 "     39
+        "       "          "      "       "     3.0 "    142
+        "       "          "      "       "     4.0 "    463
+        "       "          "      "       "     5.0 "  1,483
+        "       "          "      "       "     6.0 "  4,326
+
+It must not be inferred from this table that there are in the whole sky
+only 4,326 stars visible to the naked eye. The actual number is probably
+50 or 60 per cent greater than this, and the normal human eye sees stars
+as faint as the magnitude 6.4 or 6.5, the discordance between this
+number and the previous statement, that the sixth magnitude is the limit
+of the naked-eye vision, having been introduced in the attempt to make
+precise and accurate a classification into magnitudes which was at first
+only rough and approximate. This same striving after accuracy leads to
+the introduction of fractional numbers to represent gradations of
+brightness intermediate between whole magnitudes. Thus of the 2,843
+stars included between the fifth and sixth magnitudes a certain
+proportion are said to be of the 5.1 magnitude, 5.2 magnitude, and so on
+to the 5.9 magnitude, even hundredths of a magnitude being sometimes
+employed.
+
+We have found the number of stars included between the fifth and sixth
+magnitudes by subtracting from the last number of the preceding table
+the number immediately preceding it, and similarly we may find the
+number included between each other pair of consecutive magnitudes, as
+follows:
+
+    Magnitude       0    1    2     3     4       5       6
+    Number of stars   11   28   103   321   1,020   2,843
+    4 Ɨ 3^{m}         12   36   108   324     972   2,916
+
+In the last line each number after the first is found by multiplying the
+preceding one by 3, and the approximate agreement of each such number
+with that printed above it shows that on the whole, as far as the table
+goes, the fainter stars are approximately three times as numerous as
+those a magnitude brighter.
+
+The magnitudes of the telescopic stars have not yet been measured
+completely, and their exact number is unknown; but if we apply our
+principle of a threefold increase for each successive magnitude, we
+shall find for the fainter stars--those of the tenth and twelfth
+magnitudes--prodigious numbers which run up into the millions, and even
+these are probably too small, since down to the ninth or tenth magnitude
+it is certain that the number of the telescopic stars increases from
+magnitude to magnitude in more than a threefold ratio. This is balanced
+in some degree by the less rapid increase which is known to exist in
+magnitudes still fainter; and applying our formula without regard to
+these variations in the rate of increase, we obtain as a rude
+approximation to the total number of stars down to the fifteenth
+magnitude, 86,000,000. The Herschels, father and son, actually counted
+the number of stars visible in nearly 8,000 sample regions of the sky,
+and, inferring the character of the whole sky from these samples, we
+find it to contain 58,500,000 stars; but the magnitude of the faintest
+star visible in their telescope, and included in their count, is rather
+uncertain.
+
+How many first-magnitude stars would be needed to give as much light as
+do the 2,843 stars of magnitude 5.0 to 6.0? How many tenth-magnitude
+stars are required to give the same amount of light?
+
+To the modern man it seems natural to ascribe the different brilliancies
+of the stars to their different distances from us; but such was not the
+case 2,000 years ago, when each fixed star was commonly thought to be
+fastened to a "crystal sphere," which carried them with it, all at the
+same distance from us, as it turned about the earth. In breaking away
+from this erroneous idea and learning to think of the sky itself as only
+an atmospheric illusion through which we look to stars at very different
+distances beyond, it was easy to fall into the opposite error and to
+think of the stars as being much alike one with another, and, like
+pebbles on the beach, scattered throughout space with some rough degree
+of uniformity, so that in every direction there should be found in equal
+measure stars near at hand and stars far off, each shining with a luster
+proportioned to its remoteness.
+
+188. DISTANCES OF THE STARS.--Now, in order to separate the true from
+the false in this last mode of thinking about the stars, we need some
+knowledge of their real distances from the earth, and in seeking it we
+encounter what is perhaps the most delicate and difficult problem in the
+whole range of observational astronomy. As shown in Fig. 121, the
+principles involved in determining these distances are not fundamentally
+different from those employed in determining the moon's distance from
+the earth. Thus, the ellipse at the left of the figure represents the
+earth's orbit and the position of the earth at different times of the
+year. The direction of the star _A_ at these several times is shown by
+lines drawn through _A_ and prolonged to the background apparently
+furnished by the sky. A similar construction is made for the star _B_,
+and it is readily seen that owing to the changing position of the
+observer as he moves around the earth's orbit, both _A_ and _B_ will
+appear to move upon the background in orbits shaped like that of the
+earth as seen from the star, but having their size dependent upon the
+star's distance, the apparent orbit of _A_ being larger than that of
+_B_, because _A_ is nearer the earth. By measuring the angular distance
+between _A_ and _B_ at opposite seasons of the year (e. g., the angles
+_A--Jan.--B_, and _A--July--B_) the astronomer determines from the
+change in this angle how much larger is the one path than the other, and
+thus concludes how much nearer is _A_ than _B_. Strictly, the difference
+between the January and July angles is equal to the difference between
+the angles subtended at _A_ and _B_ by the diameter of the earth's
+orbit, and if _B_ were so far away that the angle _Jan.--B--July_ were
+nothing at all we should get immediately from the observations the angle
+_Jan.--A--July_, which would suffice to determine the stars' distance.
+Supposing the diameter of the earth's orbit and the angle at _A_ to be
+known, can you make a graphical construction that will determine the
+distance of _A_ from the earth?
+
+[Illustration: FIG. 121.--Determining a star's parallax.]
+
+The angle subtended at _A_ by the radius of the earth's orbit--i. e.,
+1/2 (_Jan.--A--July_)--is called the star's parallax, and this is
+commonly used by astronomers as a measure of the star's distance instead
+of expressing it in linear units such as miles or radii of the earth's
+orbit. The distance of a star is equal to the radius of the earth's
+orbit divided by the parallax, in seconds of arc, and multiplied by the
+number 206265.
+
+A weak point of this method of measuring stellar distances is that it
+always gives what is called a relative parallax--i. e., the difference
+between the parallaxes of _A_ and _B_; and while it is customary to
+select for _B_ a star or stars supposed to be much farther off than _A_,
+it may happen, and sometimes does happen, that these comparison stars as
+they are called are as near or nearer than _A_, and give a negative
+parallax--i. e., the difference between the angles at _A_ and _B_ proves
+to be negative, as it must whenever the star _B_ is nearer than _A_.
+
+The first really successful determinations of stellar parallax were made
+by Struve and Bessel a little prior to 1840, and since that time the
+distances of perhaps 100 stars have been measured with some degree of
+reliability, although the parallaxes themselves are so small--never as
+great as 1''--that it is extremely difficult to avoid falling into
+error, since even for the nearest star the problem of its distance is
+equivalent to finding the distance of an object more than 5 miles away
+by looking at it first with one eye and then with the other. Too short a
+base line.
+
+189. THE SUN AND HIS NEIGHBORS.--The distances of the sun's nearer
+neighbors among the stars are shown in Fig. 122, where the two circles
+having the sun at their center represent distances from it equal
+respectively to 1,000,000 and 2,000,000 times the distance between earth
+and sun. In the figure the direction of each star from the sun
+corresponds to its right ascension, as shown by the Roman numerals about
+the outer circle; the true direction of the star from the sun can not,
+of course, be shown upon the flat surface of the paper, but it may be
+found by elevating or depressing the star from the surface of the paper
+through an angle, as seen from the sun, equal to its declination, as
+shown in the fifth column of the following table,
+
+                       _The Sun's Nearest Neighbors_
+
+  ---+------------------+----------+-------+-----+----------+---------
+  No.| STAR.            |Magnitude.| R. A. |Dec. | Parallax.|Distance.
+  ---+------------------+----------+-------+-----+----------+---------
+  1  | Ī± Centauri       |   0.7    | 14.5h.| -60Ā°|   0.75"  |  0.27
+     |                  |          |       |     |          |
+  2  | Ll. 21,185       |   6.8    | 11.0  | +37 |   0.45   |  0.46
+     |                  |          |       |     |          |
+  3  | 61 Cygni         |   5.0    | 21.0  | +38 |   0.40   |  0.51
+     |                  |          |       |     |          |
+  4  | Ī· Herculis       |   3.6    | 16.7  | +39 |   0.40   |  0.51
+     |                  |          |       |     |          |
+  5  | Sirius           |  -1.4    |  6.7  | -17 |   0.37   |  0.56
+     |                  |          |       |     |          |
+  6  | Ī£ 2,398          |   8.2    | 18.7  | +59 |   0.35   |  0.58
+     |                  |          |       |     |          |
+  7  | Procyon          |   0.5    |  7.6  | + 5 |   0.34   |  0.60
+     |                  |          |       |     |          |
+  8  | Ī³ Draconis       |   4.8    | 17.5  | +55 |   0.30   |  0.68
+     |                  |          |       |     |          |
+  9  | Gr. 34           |   7.9    |  0.2  | +43 |   0.29   |  0.71
+     |                  |          |       |     |          |
+  10 | Lac. 9,352       |   7.5    | 23.0  | -36 |   0.28   |  0.74
+     |                  |          |       |     |          |
+  11 | Ļƒ Draconis       |   4.8    | 19.5  | +69 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  12 | A. O. 17,415-6   |   9.0    | 17.6  | +68 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  13 | Ī· CassiopeiƦ     |   3.4    |  0.7  | +57 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  14 | Altair           |   1.0    | 19.8  | + 9 |   0.21   |  0.97
+     |                  |          |       |     |          |
+  15 | Īµ Indi           |   5.2    | 21.9  | -57 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  16 | Gr. 1,618        |   6.7    | 10.1  | +50 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  17 | 10 UrsƦ Majoris  |   4.2    |  8.9  | +42 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  18 | Castor           |   1.5    |  7.5  | +32 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  19 | Ll. 21,258       |   8.5    | 11.0  | +44 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  20 | Īæ^{2} Eridani    |   4.5    |  4.2  | - 8 |   0.19   |  1.08
+     |                  |          |       |     |          |
+  21 | A. O. 11,677     |   9.0    | 11.2  | +66 |   0.19   |  1.08
+     |                  |          |       |     |          |
+  22 | Ll. 18,115       |   8.0    |  9.1  | +53 |   0.18   |  1.14
+     |                  |          |       |     |          |
+  23 | B. D. 36Ā°, 3,883 |   7.1    | 20.0  | +36 |   0.18   |  1.14
+     |                  |          |       |     |          |
+  24 | Gr. 1,618        |   6.5    | 10.1  | +50 |   0.17   |  1.21
+     |                  |          |       |     |          |
+  25 | Ī² CassiopeiƦ     |   2.3    |  0.1  | +59 |   0.16   |  1.28
+     |                  |          |       |     |          |
+  26 | 70 Ophiuchi      |   4.4    | 18.0  | + 2 |   0.16   |  1.28
+     |                  |          |       |     |          |
+  27 | Ī£ 1,516          |   6.5    | 11.2  | +74 |   0.15   |  1.38
+     |                  |          |       |     |          |
+  28 | Gr. 1,830        |   6.6    | 11.8  | +39 |   0.15   |  1.38
+     |                  |          |       |     |          |
+  29 | Ī¼ CassiopeiƦ     |   5.4    |  1.0  | +54 |   0.14   |  1.47
+     |                  |          |       |     |          |
+  30 | Īµ Eridani        |   4.4    |  3.5  | -10 |   0.14   |  1.47
+     |                  |          |       |     |          |
+  31 | Ī¹ UrsƦ Majoris   |   3.2    |  8.9  | +48 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  32 | Ī² Hydri          |   2.9    |  0.3  | -78 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  33 | Fomalhaut        |   1.0    | 22.9  | -30 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  34 | Br. 3,077        |   6.0    | 23.1  | +57 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  35 | Īµ Cygni          |   2.5    | 20.8  | +33 |   0.12   |  1.71
+     |                  |          |       |     |          |
+  36 | Ī² ComƦ           |   4.5    | 13.1  | +28 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  37 | Ļˆ^{5} AurigƦ     |   8.8    |  6.6  | +44 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  38 | Ļ€ Herculis       |   3.3    | 17.2  | +37 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  39 | Aldebaran        |   1.1    |  4.5  | +16 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  40 | Capella          |   0.1    |  5.1  | +46 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  41 | B. D. 35Ā°, 4,003 |   9.2    | 20.1  | +35 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  42 | Gr. 1,646        |   6.3    | 10.3  | +49 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  43 | Ī³ Cygni          |   2.3    | 20.3  | +40 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  44 | Regulus          |   1.2    | 10.0  | +12 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  45 | Vega             |   0.2    | 18.6  | +39 |   0.10   |  2.06
+  ---+------------------+----------+-------+-----+----------+---------
+
+in which the numbers in the first column are those placed adjacent to
+the stars in the diagram to identify them.
+
+[Illustration: FIG. 122.--Stellar neighbors of the sun.]
+
+190. LIGHT YEARS.--The radius of the inner circle in Fig. 122, 1,000,000
+times the earth's distance from the sun, is a convenient unit in which
+to express the stellar distances, and in the preceding table the
+distances of the stars from the sun are expressed in terms of this
+unit. To express them in miles the numbers in the table must be
+multiplied by 93,000,000,000,000. The nearest star, Ī± Centauri, is
+25,000,000,000,000 miles away. But there is another unit in more common
+use--i. e., the distance traveled over by light in the period of one
+year. We have already found (Ā§ 141) that it requires light 8m. 18s. to
+come from the sun to the earth, and it is a simple matter to find from
+this datum that in a year light moves over a space equal to 63,368 radii
+of the earth's orbit. This distance is called a _light year_, and the
+distance of the same star, Ī± Centauri, expressed in terms of this
+unit, is 4.26 years--i. e., it takes light that long to come from the
+star to the earth.
+
+In Fig. 122 the stellar magnitudes of the stars are indicated by the
+size of the dots--the bigger the dot the brighter the star--and a mere
+inspection of the figure will serve to show that within a radius of 30
+light years from the sun bright stars and faint ones are mixed up
+together, and that, so far as distance is concerned, the sun is only a
+member of this swarm of stars, whose distances apart, each from its
+nearest neighbor, are of the same order of magnitude as those which
+separate the sun from the three or four stars nearest it.
+
+Fig. 122 is not to be supposed complete. Doubtless other stars will be
+found whose distance from the sun is less than 2,000,000 radii of the
+earth's orbit, but it is not probable that they will ever suffice to
+more than double or perhaps treble the number here shown. The vast
+majority of the stars lie far beyond the limits of the figure.
+
+191. PROPER MOTIONS.--It is evident that these stars are too far apart
+for their mutual attractions to have much influence one upon another,
+and that we have here a case in which, according to Ā§ 34, each star is
+free to keep unchanged its state of rest or motion with unvarying
+velocity along a straight line. Their very name, _fixed stars_, implies
+that they are at rest, and so astronomers long believed. Hipparchus (125
+B. C.) and Ptolemy (130 A. D.) observed and recorded many allineations
+among the stars, in order to give to future generations a means of
+settling this very question of a possible motion of the stars and a
+resulting change in their relative positions upon the sky. For example,
+they found at the beginning of the Christian era that the four stars,
+Capella, Īµ Persei, Ī± and Ī² Arietis, stood in a straight line--i. e.,
+upon a great circle of the sky. Verify this by direct reference to the
+sky, and see how nearly these stars have kept the same position for
+nearly twenty centuries. Three of them may be identified from the star
+maps, and the fourth, Īµ Persei, is a third-magnitude star between
+Capella and the other two.
+
+Other allineations given by Ptolemy are: Spica, Arcturus and Ī² Bootis;
+Spica, Ī“ Corvi and Ī³ Corvi; Ī± LibrƦ, Arcturus and Ī¶ UrsƦ Majoris.
+Arcturus does not now fit very well to these alignments, and nearly two
+centuries ago it, together with Aldebaran and Sirius, was on other
+grounds suspected to have changed its place in the sky since the days of
+Ptolemy. This discovery, long since fully confirmed, gave a great
+impetus to observing with all possible accuracy the right ascensions and
+declinations of the stars, with a view to finding other cases of what
+was called _proper motion_--i. e., a motion peculiar to the individual
+star as contrasted with the change of right ascension and declination
+produced for all stars by the precession.
+
+Since the middle of the eighteenth century there have been made many
+thousands of observations of this kind, whose results have gone into
+star charts and star catalogues, and which are now being supplemented by
+a photographic survey of the sky that is intended to record permanently
+upon photographic plates the position and magnitude of every star in the
+heavens down to the fourteenth magnitude, with a view to ultimately
+determining all their proper motions.
+
+The complete achievement of this result is, of course, a thing of the
+remote future, but sufficient progress in determining these motions has
+been made during the past century and a half to show that nearly every
+lucid star possesses some proper motion, although in most cases it is
+very small, there being less than 100 known stars in which it amounts
+to so much as 1" per annum--i. e., a rate of motion across the sky which
+would require nearly the whole Christian era to alter a star's direction
+from us by so much as the moon's angular diameter. The most rapid known
+proper motion is that of a telescopic star midway between the equator
+and the south pole, which changes its position at the rate of nearly 9"
+per annum, and the next greatest is that of another telescopic star, in
+the northern sky, No. 28 of Fig. 122. It is not until we reach the tenth
+place in a list of large proper motions that we find a bright lucid
+star, No. 1 of Fig. 122. It is a significant fact that for the most part
+the stars with large proper motions are precisely the ones shown in Fig.
+122, which is designed to show stars near the earth. This connection
+between nearness and rapidity of proper motions is indeed what we should
+expect to find, since a given amount of real motion of the star along
+its orbit will produce a larger angular displacement, proper motion, the
+nearer the star is to the earth, and this fact has guided astronomers in
+selecting the stars to be observed for parallax, the proper motion being
+determined first and the parallax afterward.
+
+192. THE PATHS OF THE STARS.--We have already seen reason for thinking
+that the orbit along which a star moves is practically a straight line,
+and from a study of proper motions, particularly their directions across
+the sky, it appears that these orbits point in all possible ways--north,
+south, east, and west--so that some of them are doubtless directed
+nearly toward or from the sun; others are square to the line joining sun
+and star; while the vast majority occupy some position intermediate
+between these two. Now, our relation to these real motions of the stars
+is well illustrated in Fig. 112, where the observer finds in some of the
+shooting stars a tremendous proper motion across the sky, but sees
+nothing of their rapid approach to him, while others appear to stand
+motionless, although, in fact, they are moving quite as rapidly as are
+their fellows. The fixed star resembles the shooting star in this
+respect, that its proper motion is only that part of its real motion
+which lies at right angles to the line of sight, and this needs to be
+supplemented by that other part of the motion which lies parallel to the
+line of sight, in order to give us any knowledge of the star's real
+orbit.
+
+[Illustration: FIG. 123.--Motion of Polaris in the line of sight as
+determined by the spectroscope. FROST.]
+
+193. MOTION IN THE LINE OF SIGHT.--It is only within the last 25 years
+that anything whatever has been accomplished in determining these
+stellar motions of approach or recession, but within that time much
+progress has been made by applying the Doppler principle (Ā§ 89) to the
+study of stellar spectra, and at the present time nearly every great
+telescope in the world is engaged upon work of this kind. The shifting
+of the lines of the spectrum toward the violet or toward the red end of
+the spectrum indicates with certainty the approach or recession of the
+star, but this shifting, which must be determined by comparing the
+star's spectrum with that of some artificial light showing corresponding
+lines, is so small in amount that its accurate measurement is a matter
+of extreme difficulty, as may be seen from Fig. 123. This cut shows
+along its central line a part of the spectrum of Polaris, between wave
+lengths 4,450 and 4,600 tenth meters, while above and below are the
+corresponding parts of the spectrum of an electric spark whose light
+passed through the same spectroscope and was photographed upon the same
+plate with that of Polaris. This comparison spectrum is, as it should
+be, a discontinuous or bright-line one, while the spectrum of the star
+is a continuous one, broken only by dark gaps or lines, many of which
+have no corresponding lines in the comparison spectrum. But a certain
+number of lines in the two spectra do correspond, save that the dark
+line is always pushed a very little toward the direction of shorter wave
+lengths, showing that this star is approaching the earth. This spectrum
+was photographed for the express purpose of determining the star's
+motion in the line of sight, and with it there should be compared Figs.
+124 and 125, which show in the upper part of each a photograph obtained
+without comparison spectra by allowing the star's light to pass through
+some prisms placed just in front of the telescope. The lower section of
+each figure shows an enlargement of the original photograph, bringing
+out its details in a way not visible to the unaided eye. In the enlarged
+spectrum of Ī² AurigƦ a rate of motion equal to that of the
+earth in its orbit would be represented by a shifting of 0.03 of a
+millimeter in the position of the broad, hazy lines.
+
+[Illustration: FIG. 124.--Spectrum of Ī² AurigƦ.--PICKERING.]
+
+Despite the difficulty of dealing with such small quantities as the
+above, very satisfactory results are now obtained, and from them it is
+known that the velocities of stars in the line of sight are of the same
+order of magnitude as the velocities of the planets in their orbits,
+ranging all the way from 0 to 60 miles per second--more than 200,000
+miles per hour--which latter velocity, according to Campbell, is the
+rate at which Ī¼ CassiopeiƦ is approaching the sun.
+
+The student should not fail to note one important difference between
+proper motions and the motions determined spectroscopically: the latter
+are given directly in miles per second, or per hour, while the former
+are expressed in angular measure, seconds of arc, and there can be no
+direct comparison between the two until by means of the known distances
+of the stars their proper motions are converted from angular into linear
+measure. We are brought thus to the very heart of the matter; parallax,
+proper motion, and motion in the line of sight are intimately related
+quantities, all of which are essential to a knowledge of the real
+motions of the stars.
+
+[Illustration: FIG. 125.--Spectrum of Pollux.--PICKERING.]
+
+194. STAR DRIFT.--An illustration of how they may be made to work
+together is furnished by some of the stars--which make up the Great
+Dipper--Ī², Ī³, Īµ, and Ī¶ UrsƦ Majoris, whose proper motions have
+long been known to point in nearly the same direction across the sky and
+to be nearly equal in amount. More recently it has been found that these
+stars are all moving toward the sun with approximately the same
+velocity--18 miles per second. One other star of the Dipper, Ī“ UrsƦ
+Majoris, shares in the common proper motion, but its velocity in the
+line of sight has not yet been determined with the spectroscope. These
+similar motions make it probable that the stars are really traveling
+together through space along parallel lines; and on the supposition
+that such is the case it is quite possible to write out a set of
+equations which shall involve their known proper motions and motions in
+the line of sight, together with their unknown distances and the unknown
+direction and velocity of their real motion along their orbits. Solving
+these equations for the values of the unknown quantities, it is found
+that the five stars probably lie in a plane which is turned nearly
+edgewise toward us, and that in this plane they are moving about twice
+as fast as the earth moves around the sun, and are at a distance from us
+represented by a parallax of less than 0.02"--i. e., six times as great
+as the outermost circle in Fig. 122. A most extraordinary system of
+stars which, although separated from each other by distances as great as
+the whole breadth of Fig. 122, yet move along in parallel paths which it
+is difficult to regard as the result of chance, and for which it is
+equally difficult to frame an explanation.
+
+[Illustration: FIG. 126.--The Great Dipper, past, present, and future.]
+
+The stars Ī± and Ī· of the Great Dipper do not share in this motion, and
+must ultimately part company with the other five, to the complete
+destruction of the Dipper's shape. Fig. 126 illustrates this change of
+shape, the upper part of the figure (_a_) showing these seven stars as
+they were grouped at a remote epoch in the past, while the lower
+section (_c_) shows their position for an equally remote epoch in the
+future. There is no resemblance to a dipper in either of these
+configurations, but it should be observed that in each of them the stars
+Ī± and Ī· keep their relative position unaltered, and the other five stars
+also keep together, the entire change of appearance being due to the
+changing positions of these two groups with respect to each other.
+
+This phenomenon of groups of stars moving together is called _star
+drift_, and quite a number of cases of it are found in different parts
+of the sky. The Pleiades are perhaps the most conspicuous one, for here
+some sixty or more stars are found traveling together along similar
+paths. Repeated careful measurements of the relative positions of stars
+in this cluster show that one of the lucid stars and four or five of the
+telescopic ones do not share in this motion, and therefore are not to be
+considered as members of the group, but rather as isolated stars which,
+for a time, chance to be nearly on line with the Pleiades, and probably
+farther off, since their proper motions are smaller.
+
+To rightly appreciate the extreme slowness with which proper motions
+alter the constellations, the student should bear in mind that the
+changes shown in passing from one section of Fig. 126 to the next
+represent the effect of the present proper motions of the stars
+accumulated for a period of 200,000 years. Will the stars continue to
+move in straight paths for so long a time?
+
+195. THE SUN'S WAY.--Another and even more interesting application of
+proper motions and motions in the line of sight is the determination
+from them of the sun's orbit among the stars. The principle involved is
+simple enough. If the sun moves with respect to the stars and carries
+the earth and the other planets year after year into new regions of
+space, our changing point of view must displace in some measure every
+star in the sky save those which happen to be exactly on the line of the
+sun's motion, and even these will show its effect by their apparent
+motion of approach or recession along the line of sight. So far as their
+own orbital motions are concerned, there is no reason to suppose that
+more stars move north than south, or that more go east than west; and
+when we find in their proper motions a distinct tendency to radiate from
+a point somewhere near the bright star Vega and to converge toward a
+point on the opposite side of the sky, we infer that this does not come
+from any general drift of the stars in that direction, but that it marks
+the course of the sun among them. That it is moving along a straight
+line pointing toward Vega, and that at least a part of the velocities
+which the spectroscope shows in the line of sight, comes from the motion
+of the sun and earth. Working along these lines, Kapteyn finds that the
+sun is moving through space with a velocity of 11 miles per second,
+which is decidedly below the average rate of stellar motion--19 miles
+per second.
+
+196. DISTANCE OF SIRIAN AND SOLAR STARS.--By combining this rate of
+motion of the sun with the average proper motions of the stars of
+different magnitudes, it is possible to obtain some idea of the average
+distance from us of a first-magnitude star or a sixth-magnitude star,
+which, while it gives no information about the actual distance of any
+particular star, does show that on the whole the fainter stars are more
+remote. But here a broad distinction must be drawn. By far the larger
+part of the stars belong to one of two well-marked classes, called
+respectively Sirian and solar stars, which are readily distinguished
+from each other by the kind of spectrum they furnish. Thus Ī²
+AurigƦ belongs to the Sirian class, as does every other star which has a
+spectrum like that of Fig. 124, while Pollux is a solar star presenting
+in Fig. 125 a spectrum like that of the sun, as do the other stars of
+this class.
+
+Two thirds of the sun's near neighbors, shown in Fig. 122, have spectra
+of the solar type, and in general stars of this class are nearer to us
+than are the stars with spectra unlike that of the sun. The average
+distance of a solar star of the first magnitude is very approximately
+represented by the outer circle in Fig. 122, 2,000,000 times the
+distance of the sun from the earth; while the corresponding distance for
+a Sirian star of the first magnitude is represented by the number
+4,600,000.
+
+A third-magnitude star is on the average twice as far away as one of the
+first magnitude, a fifth-magnitude star four times as far off, etc.,
+each additional two magnitudes doubling the average distance of the
+stars, at least down to the eighth magnitude and possibly farther,
+although beyond this limit we have no certain knowledge. Put in another
+way, the naked eye sees many Sirian stars which _may_ have "gone out"
+and ceased to shine centuries ago, for the light by which we now see
+them left those stars before the discovery of America by Columbus. For
+the student of mathematical tastes we note that the results of Kapteyn's
+investigation of the mean distances (_D_) of the stars of magnitude
+(_m_) may be put into two equations:
+
+    For Solar Stars, D = 23 Ɨ 2^{m/2}
+
+    For Sirian Stars, D = 52 Ɨ 2^{m/2}
+
+where the coefficients 23 and 52 are expressed in light years. How long
+a time is required for light to come from an average solar star of the
+sixth magnitude?
+
+197. CONSEQUENCES OF STELLAR DISTANCE.--The amount of light which comes
+to us from any luminous body varies inversely as the square of its
+distance, and since many of the stars are changing their distance from
+us quite rapidly, it must be that with the lapse of time they will grow
+brighter or fainter by reason of this altered distance. But the
+distances themselves are so great that the most rapid known motion in
+the line of sight would require more than 1,000 years (probably several
+thousand) to produce any perceptible change in brilliancy.
+
+The law in accordance with which this change of brilliancy takes place
+is that the distance must be increased or diminished tenfold in order to
+produce a change of five magnitudes in the brightness of the object, and
+we may apply this law to determine the sun's rank among the stars. If it
+were removed to the distance of an average first-, or second-, or
+third-magnitude star, how would its light compare with that of the
+stars? The average distance of a third-magnitude star of the solar type
+is, as we have seen above, 4,000,000 times the sun's distance from the
+earth, and since 4,000,000 = 10^{6.6}, we find that at this distance the
+sun's stellar magnitude would be altered by 6.6 Ɨ 5 magnitudes, and
+would therefore be -26.5 + 33.0 = 6.5--i. e., the sun if removed to the
+average distance of the third-magnitude stars of its type would be
+reduced to the very limit of naked-eye visibility. It must therefore be
+relatively small and feeble as compared with the brightness of the
+average star. It is only its close proximity to us that makes the sun
+look brighter than the stars.
+
+The fixed stars may have planets circling around them, but an
+application of the same principles will show how hopeless is the
+prospect of ever seeing them in a telescope. If the sun's nearest
+neighbor, Ī± Centauri, were attended by a planet like Jupiter, this
+planet would furnish to us no more light than does a star of the
+twenty-second magnitude--i. e., it would be absolutely invisible, and
+would remain invisible in the most powerful telescope yet built, even
+though its bulk were increased to equal that of the sun. Let the student
+make the computation leading to this result, assuming the stellar
+magnitude of Jupiter to be -1.7.
+
+198. DOUBLE STARS.--In the constellation Taurus, not far from Aldebaran,
+is the fourth-magnitude star Īø Tauri, which can readily be seen to
+consist of two stars close together. The star Ī± Capricorni is plainly
+double, and a sharp eye can detect that one of the faint stars which
+with Vega make a small equilateral triangle, is also a double star.
+Look for them in the sky.
+
+In the strict language of astronomy the term double star would not be
+applied to the first two of these objects, since it is usually
+restricted to those stars whose angular distance from each other is so
+small that in the telescope they appear much as do the stars named above
+to the naked eye--i. e., their angular separation is measured by a few
+seconds or fractions of a single second, instead of the six minutes
+which separate the component stars of Īø Tauri or Ī± Capricorni. There are
+found in the sky many thousands of these close double stars, of which
+some are only optically double--i. e., two stars nearly on line with the
+earth but at very different distances from it--while more of them are
+really what they seem, stars near each other, and in many cases near
+enough to influence each other's motion. These are called _binary_
+systems, and in cases of this kind the principles of celestial mechanics
+set forth in Chapter IV hold true, and we may expect to find each
+component of a double star moving in a conic section of some kind,
+having its focus at the common center of gravity of the two stars.
+We are thus presented with problems of orbital motion quite similar
+to those which occur in the solar system, and careful telescopic
+observations are required year after year to fix the relative positions
+of the two stars--i. e., their angular separation, which it is customary
+to call their _distance_, and their direction one from the other, which
+is called _position angle_.
+
+199. ORBITS OF DOUBLE STARS.--The sun's nearest neighbor, Ī± Centauri, is
+such a double star, whose position angle and distance have been measured
+by successive generations of astronomers for more than a century, and
+Fig. 127 shows the result of plotting their observations. Each black dot
+that lies on or near the circumference of the long ellipse stands for
+an observed direction and distance of the fainter of the two stars from
+the brighter one, which is represented by the small circle at the
+intersection of the lines inside the ellipse. It appears from the figure
+that during this time the one star has gone completely around the other,
+as a planet goes around the sun, and the true orbit must therefore be
+an ellipse having one of its foci at the center of gravity of the two
+stars. The other star moves in an ellipse of precisely similar shape,
+but probably smaller size, since the dimensions of the two orbits are
+inversely proportional to the masses of the two bodies, but it is
+customary to neglect this motion of the larger star and to give to the
+smaller one an orbit whose diameter is equal to the sum of the diameters
+of the two real orbits. This practice, which has been followed in Fig.
+127, gives correctly the relative positions of the two stars, and makes
+one orbit do the work of two.
+
+[Illustration: FIG. 127.--The orbit of Ī± Centauri.--SEE.]
+
+In Fig. 127 the bright star does not fall anywhere near the focus of the
+ellipse marked out by the smaller one, and from this we infer that the
+figure does not show the true shape of the orbit, which is certainly
+distorted, foreshortened, by the fact that we look obliquely down upon
+its plane. It is possible, however, by mathematical analysis, to find
+just how much and in what direction that plane should be turned in order
+to bring the focus of the ellipse up to the position of the principal
+star, and thus give the true shape and size of the orbit. See Fig. 128
+for a case in which the true orbit is turned exactly edgewise toward the
+earth, and the small star, which really moves in an ellipse like that
+shown in the figure, appears to oscillate to and fro along a straight
+line drawn through the principal star, as shown at the left of the
+figure.
+
+In the case of Ī± Centauri the true orbit proves to have a major
+axis 47 times, and a minor axis 40 times, as great as the distance of
+the earth from the sun. The orbit, in fact, is intermediate in size
+between the orbits of Uranus and Neptune, and the periodic time of the
+star in this orbit is 81 years, a little less than the period of Uranus.
+
+[Illustration: FIG. 128.--Apparent orbit and real orbit of the double
+star 42 ComƦ Berenicis.--SEE.]
+
+200. MASSES OF DOUBLE STARS.--If we apply to this orbit Kepler's Third
+Law in the form given it at page 179, we shall find--
+
+    a^3 / T^2 = (23.5)^3 / (81)^2 = k (M + m),
+
+where _M_ and _m_ represent the masses of the two stars. We have already
+seen that _k_, the gravitation constant, is equal to 1 when the masses
+are measured in terms of the sun's mass taken as unity, and when _T_ and
+_a_ are expressed in years and radii of the earth's orbit respectively,
+and with this value of _k_ we may readily find from the above equation,
+_M_ + _m_ = 2.5--i. e., the combined mass of the two components of
+Ī± Centauri is equal to rather more than twice the mass of the sun. It is
+not every double star to which this process of weighing can be applied.
+The major axis of the orbit, _a_, is found from the observations in
+angular measure, 35" in this case, and it is only when the parallax of
+the star is known that this can be converted into the required linear
+units, radii of the earth's orbit, by dividing the angular major axis by
+the parallax; 47 = 35" Ć· 0.75".
+
+Our list of distances (Ā§ 189) contains four double stars whose periodic
+times and major axes have been fairly well determined, and we find in
+the accompanying table the information which they give about the masses
+of double stars and the size of the orbits in which they move:
+
+  ---------------------+-------+-------+----------+-------
+  STAR.                | Major | Minor | Periodic | Mass.
+                       | axis. | axis. | time.    |
+  ---------------------+-------+-------+----------+-------
+  Ī± Centauri           |  47   |  40   |   81 y.  |   2
+  70 Ophiuchi          |  56   |  48   |   88     |   3
+  Procyon              |  34   |  31   |   40     |   3
+  Sirius               |  43   |  34   |   52     |   4
+  ---------------------+-------+-------+----------+-------
+
+The orbit of Uranus, diameter = 38, and Neptune, diameter = 60, are of
+much the same size as these double-star orbits; but the planetary orbits
+are nearly circular, while in every case the double stars show a
+substantial difference between the long and short diameters of their
+orbits. This is a characteristic feature of most double-star orbits, and
+seems to stand in some relation to their periodic times, for, on the
+average, the longer the time required by a star to make its orbital
+revolution the more eccentric is its orbit likely to prove.
+
+Another element of the orbits of double stars, which stands in even
+closer relation to the periodic time, is the major axis; the smaller the
+long diameter of the orbit the more rapid is the motion and the shorter
+the periodic time, so that astronomers in search of interesting
+double-star orbits devote themselves by preference to those stars whose
+distance apart is so small that they can barely be distinguished one
+from the other in the telescope.
+
+Although the half-dozen stars contained in the table all have orbits of
+much the same size and with much the same periodic time as those in
+which Uranus and Neptune move, this is by no means true of all the
+double stars, many of which have periods running up into the hundreds if
+not thousands of years, while a few complete their orbital revolutions
+in periods comparable with, or even shorter than, that of Jupiter.
+
+201. DARK STARS.--Procyon, the next to the last star of the preceding
+table, calls for some special mention, as the determination of its mass
+and orbit stands upon a rather different basis from that of the other
+stars. More than half a century ago it was discovered that its proper
+motion was not straight and uniform after the fashion of ordinary stars,
+but presented a series of loops like those marked out by a bright point
+on the rim of a swiftly running bicycle wheel. The hub may move straight
+forward with uniform velocity, but the point near the tire goes up and
+down, and, while sharing in the forward motion of the hub, runs
+sometimes ahead of it, sometimes behind, and such seemed to be the
+motion of Procyon and of Sirius as well. Bessel, who discovered it, did
+not hesitate to apply the laws of motion, and to affirm that this
+visible change of the star's motion pointed to the presence of an unseen
+companion, which produced upon the motions of Sirius and Procyon just
+such effects as the visible companions produce in the motions of double
+stars. A new kind of star, dark instead of bright, was added to the
+astronomer's domain, and its discoverer boldly suggested the possible
+existence of many more. "That countless stars are visible is clearly no
+argument against the existence of as many more invisible ones." "There
+is no reason to think radiance a necessary property of celestial
+bodies." But most astronomers were incredulous, and it was not until
+1862 that, in the testing of a new and powerful telescope just built, a
+dark star was brought to light and the companion of Sirius actually
+seen. The visual discovery of the dark companion of Procyon is of still
+more recent date (November, 1896), when it was detected with the great
+telescope of the Lick Observatory. This discovery is so recent that the
+orbit is still very uncertain, being based almost wholly upon the
+variations in the proper motion of the star, and while the periodic time
+must be very nearly correct, the mass of the stars and dimensions of the
+orbit may require considerable correction.
+
+The companion of Sirius is about ten magnitudes and that of Procyon
+about twelve magnitudes fainter than the star itself. How much more
+light does the bright star give than its faint companion? Despite the
+tremendous difference of brightness represented by the answer to this
+question, the mass of Sirius is only about twice as great as that of its
+companion, and for Procyon the ratio does not exceed five or six.
+
+The visual discovery of the companions to Sirius and Procyon removes
+them from the list of dark stars, but others still remain unseen,
+although their existence is indicated by variable proper motions or by
+variable orbital motion, as in the case of Ī¶ Cancri, where one
+of the components of a triple star moves around the other two in a
+series of loops whose presence indicates a disturbing body which has
+never yet been seen.
+
+202. MULTIPLE STARS.--Combinations of three, four, or more stars close
+to each other, like Ī¶ Cancri, are called multiple stars, and
+while they are far from being as common as are double stars, there is a
+considerable number of them in the sky, 100 or more as against the more
+than 10,000 double stars that are known. That their relative motions are
+subject to the law of gravitation admits of no serious doubt, but
+mathematical analysis breaks down in face of the difficulties here
+presented, and no astronomer has ever been able to determine what will
+be the general character of the motions in such a system.
+
+[Illustration: FIG. 129.--Illustrating the motion of a spectroscopic
+binary.]
+
+203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of
+the Harvard Observatory, announced the discovery of a new class of
+double stars, invisible as such in even the most powerful telescope,
+and producing no perturbations such as have been considered above, but
+showing in their spectrum that two or more bodies must be present in the
+source of light which to the eye is indistinguishable from a single
+star. In Fig. 129 we suppose _A_ and _B_ to be the two components of a
+double star, each moving in its own orbit about their common center of
+gravity, _C_, whose distance from the earth is several million times
+greater than the distance between the stars themselves. Under such
+circumstances no telescope could distinguish between the two stars,
+which would appear fused into one; but the smaller the orbit the more
+rapid would be their motion in it, and if this orbit were turned
+edgewise toward the earth, as is supposed in the figure, whenever the
+stars were in the relative position there shown, _A_ would be rapidly
+approaching the earth by reason of its orbital motion, while _B_ would
+move away from it, so that in accordance with the Doppler principle the
+lines composing their respective spectra would be shifted in opposite
+directions, thus producing a doubling of the lines, each single line
+breaking up into two, like the double-sodium line _D_, only not spaced
+so far apart. When the stars have moved a quarter way round their orbit
+to the points _AĀ“_, _BĀ“_, their velocities are turned at right angles to
+the line of sight and the spectrum returns to the normal type with
+single lines, only to break up again when after another quarter
+revolution their velocities are again parallel with the line of sight.
+The interval of time between consecutive doublings of the lines in the
+spectrum thus furnishes half the time of a revolution in the orbit. The
+distance between the components of a double line shows by means of the
+Doppler principle how fast the stars are traveling, and this in
+connection with the periodic times fixes the size of the orbit, provided
+we assume that it is turned exactly edgewise to the earth. This
+assumption may not be quite true, but even though the orbit should
+deviate considerably from this position, it will still present the
+phenomenon of the double lines whose displacement will now show
+something less than the true velocities of the stars in their orbits,
+since the spectroscope measures only that component of the whole
+velocity which is directed toward the earth, and it is important to note
+that the real orbits and masses of these _spectroscopic binaries_, as
+they are called, will usually be somewhat larger than those indicated by
+the spectroscope, since it is only in exceptional cases that the orbit
+will be turned exactly edgewise to us.
+
+The bright star Capella is an excellent illustration of these
+spectroscopic binaries. At intervals of a little less than a month the
+lines of its spectrum are alternately single and double, their maximum
+separation corresponding to a velocity in the line of sight amounting to
+37 miles per second. Each component of a doubled line appears to be
+shifted an equal amount from the position occupied by the line when it
+is single, thus indicating equal velocities and equal masses for the two
+component stars whose periodic time in their orbit is 104 days. From
+this periodic time, together with the velocity of the star's motion, let
+the student show that the diameter of the orbit--i. e., the distance of
+the stars from each other--is approximately 53,000,000 miles, and that
+their combined mass is a little less than that of Ī± Centauri, provided
+that their orbit plane is turned exactly edgewise toward the earth.
+
+There are at the present time (1901) 34 spectroscopic binaries known,
+including among them such stars as Polaris, Capella, Algol, Spica, Ī²
+AurigƦ, Ī¶ UrsƦ Majoris, etc., and their number is rapidly increasing,
+about one star out of every seven whose motion in the line of sight
+is determined proving to be a binary or, as in the case of Polaris,
+possibly triple. On account of smaller distance apart their periodic
+times are much shorter than those of the ordinary double stars, and
+range from a few days up to several months--more than two years in the
+case of Ī· Pegasi, which has the longest known period of any star of this
+class.
+
+Spectroscopic binaries agree with ordinary double stars in having masses
+rather greater than that of the sun, but there is as yet no assured case
+of a mass ten times as great as that of the sun.
+
+204. VARIABLE STARS.--Attention has already been drawn (Ā§ 23) to the
+fact that some stars shine with a changing brightness--e. g., Algol, the
+most famous of these _variable stars_, at its maximum of brightness
+furnishes three times as much light as when at its minimum, and other
+variable stars show an even greater range. The star Īæ Ceti has
+been named Mira (Latin, _the wonderful_), from its extraordinary range
+of brightness, more than six-hundred-fold. For the greater part of the
+time this star is invisible to the naked eye, but during some three
+months in every year it brightens up sufficiently to be seen, rising
+quite rapidly to its maximum brilliancy, which is sometimes that of a
+second-magnitude star, but more frequently only third or even fourth
+magnitude, and, after shining for a few weeks with nearly maximum
+brilliancy, falling off to become invisible for a time and then return
+to its maximum brightness after an interval of eleven months from the
+preceding maximum. In 1901 it should reach its greatest brilliancy about
+midsummer, and a month earlier than this for each succeeding year. Find
+it by means of the star map, and by comparing its brightness from night
+to night with neighboring stars of about the same magnitude see how it
+changes with respect to them.
+
+The interval of time from maximum to maximum of brightness--331.6 days
+for Mira--is called the star's period, and within its period a star
+regularly variable runs through all its changes of brilliancy, much as
+the weather runs through its cycle of changes in the period of a year.
+But, as there are wet years and dry ones, hot years and cold, so also
+with variable stars, many of them show differences more or less
+pronounced between different periods, and one such difference has
+already been noted in the case of Mira; its maximum brilliancy is
+different in different years. So, too, the length of the period
+fluctuates in many cases, as does every other circumstance connected
+with it, and predictions of what such a variable star will do are
+notoriously unreliable.
+
+205. THE ALGOL VARIABLES.--On the other hand, some variable stars
+present an almost perfect regularity, repeating their changes time after
+time with a precision like that of clockwork. Algol is one type of these
+regular variables, having a period of 68.8154 hours, during six sevenths
+of which time it shines with unchanging luster as a star of the 2.3
+magnitude, but during the remaining 9 hours of each period it runs down
+to the 3.5 magnitude, and comes back again, as is shown by a curve in
+Fig. 130. The horizontal scale here represents hours, reckoned from the
+time of the star's minimum brightness, and the vertical scale shows
+stellar magnitudes. Such a diagram is called the star's light curve, and
+we may read from it that at any time between 5h. and 32h. after the time
+of minimum the star's magnitude is 2.32; at 2h. after a minimum the
+magnitude is 2.88, etc. What is the magnitude an hour and a half before
+the time of minimum? What is the magnitude 43 days after a minimum?
+
+[Illustration: FIG. 130.--The light curve of Algol.]
+
+The arrows shown in Fig. 130 are a feature not usually found with light
+curves, but in this case each one represents a spectroscopic
+determination of the motion of Algol in the line of sight. These
+observations extended over a period of more than two years, but they are
+plotted in the figure with reference to the number of hours each one
+preceded or followed a minimum of the star's light, and each arrow shows
+not only the direction of the star's motion along the line of sight, the
+arrows pointing down denoting approach of the star toward the earth, but
+also its velocity, each square of the ruling corresponding to 10
+kilometers (6.2 miles per second). The differences of velocity shown by
+adjacent arrows come mainly from errors of observation and furnish some
+idea of how consistent among themselves such observations are, but there
+can be no doubt that before minimum the star is moving away from the
+earth, and after minimum is approaching it. It is evident from these
+observations that in Algol we have to do with a spectroscopic binary,
+one of whose components is a dark star which, once in each revolution,
+partially eclipses the bright star and produces thus the variations in
+its light. By combining the spectroscopic observations with the
+variations in the star's light, Vogel finds that the bright star, Algol,
+itself has a diameter somewhat greater than that of the sun, but is of
+low density, so that its mass is less than half that of the sun, while
+the dark star is a very little smaller than the sun and has about a
+quarter of its mass. The distance between the two stars, dark and
+bright, is 3,200,000 miles. Fig. 129, which is drawn to scale, shows the
+relative positions and sizes of these stars as well as the orbits in
+which they move.
+
+The mere fact already noted that close binary systems exist in
+considerable numbers is sufficient to make it probable that a certain
+proportion of these stars would have their orbit planes turned so nearly
+edgewise toward the earth as to produce eclipses, and corresponding to
+this probability there are already known no less than 15 stars of the
+Algol type of eclipse variables, and only a beginning has been made in
+the search for them.
+
+[Illustration: FIG. 131.--The light curve of Ī² LyrƦ.]
+
+206. VARIABLES OF THE Ī² LYRƆ TYPE.--In addition to these there
+is a certain further number of binary variables in which both components
+are bright and where the variation of brightness follows a very
+different course. Capella would be such a variable if its orbit plane
+were directed exactly toward the earth, and the fact that its light is
+not variable shows conclusively that such is not the position of the
+orbit. Fig. 131 represents the light curve of one of the best-known
+variable systems of this second type, that of Ī² LyrƦ, whose
+period is 12 days 21.8 hours, and the student should read from the curve
+the magnitude of the star for different times during this interval.
+According to Myers, this light curve and the spectroscopic observations
+of the star point to the existence of a binary star of very remarkable
+character, such as is shown, together with its orbit and a scale of
+miles, in Fig. 132. Note the tide which each of these stars raises in
+the other, thus changing their shapes from spheres into ellipsoids. The
+astonishing dimensions of these stars are in part compensated by their
+very low density, which is less than that of air, so that their masses
+are respectively only 10 times and 21 times that of the sun! But these
+dimensions and masses perhaps require confirmation, since they depend
+upon spectroscopic observations of doubtful interpretation. In Fig. 132
+what relative positions must the stars occupy in their orbit in order
+that their combined light should give Ī² LyrƦ its maximum
+brightness? What position will furnish a minimum brightness?
+
+[Illustration: FIG. 132.--The system of Ī² LyrƦ.--MYERS.]
+
+207. VARIABLES OF LONG AND SHORT PERIODS.--It must not be supposed that
+all variable stars are binaries which eclipse each other. By far the
+larger part of them, like Mira, are not to be accounted for in this way,
+and a distinction which is pretty well marked in the length of their
+periods is significant in this connection. There is a considerable
+number of variable stars with periods shorter than a month, and there
+are many having periods longer than 6 months, but there are very few
+having periods longer than 18 months, or intermediate between 1 month
+and 6 months, so that it is quite customary to divide variable stars
+into two classes--those of long period, 6 months or more, and those of
+short period less than 6 months, and that this distinction corresponds
+to some real difference in the stars themselves is further marked by the
+fact that the long-period variables are prevailingly red in color, while
+the short-period stars are almost without exception white or very pale
+yellow. In fact, the longer the period the redder the star, although it
+is not to be inferred that all red stars are variable; a considerable
+percentage of them shine with constant light. The eclipse explanation of
+variability holds good only for short-period variables, and possibly not
+for all of them, while for the long-period variables there is no
+explanation which commands the general assent of astronomers, although
+unverified hypotheses are plenty.
+
+The number of stars known to be variable is about 400, while a
+considerable number of others are "suspected," and it would not be
+surprising if a large fraction of all the stars should be found to
+fluctuate a little in brightness. The sun's spots may suffice to make it
+a variable star with a period of 11 years.
+
+The discovery of new variables is of frequent occurrence, and may be
+expected to become more frequent when the sky is systematically explored
+for them by the ingenious device suggested by Pickering and illustrated
+in Fig. 133. A given region of the sky--e. g., the Northern Crown--is
+photographed repeatedly upon the same plate, which is shifted a little
+at each new exposure, so that the stars shall fall at new places upon
+it. The finally developed plate shows a row of images corresponding to
+each star, and if the star's light is constant the images in any given
+row will all be of the same size, as are most of those in Fig. 133; but
+a variable star such as is shown by the arrowhead reveals its presence
+by the broken aspect of its row of dots, a minimum brilliancy being
+shown by smaller and a maximum by larger ones. In this particular case,
+at two exposures the star was too faint to print its image upon the
+plate.
+
+[Illustration: FIG. 133.--Discovery of a variable star by means of
+photography.--PICKERING.]
+
+208. NEW STARS.--Next to the variable stars of very long or very
+irregular period stand the so-called _new_ or _temporary stars_, which
+appear for the most part suddenly, and after a brief time either vanish
+altogether or sink to comparative insignificance. These were formerly
+thought to be very remarkable and unusual occurrences--"the birth of a
+new world"--and it is noteworthy that no new star is recorded to have
+been seen from 1670 to 1848 A. D., for since that time there have been
+no less than five of them visible to the naked eye and others
+telescopic. In so far as these new stars are not ordinary variables
+(Mira, first seen in 1596, was long counted as a new star), they are
+commonly supposed due to chance encounters between stars or other cosmic
+bodies moving with considerable velocities along orbits which approach
+very close to each other. The actual collision of two dark bodies moving
+with high velocities is clearly sufficient to produce a luminous
+star--e. g., meteors--and even the close approach of two cooled-off
+stars, might result in tidal actions which would rend open their crusts
+and pour out the glowing matter from within so as to produce temporarily
+a very great accession of brightness.
+
+The most famous of all new stars is that which, according to Tycho
+Brahe's report, appeared in the year 1572, and was so bright when at its
+best as to be seen with the naked eye in broad daylight. It continued
+visible, though with fading light, for about 16 months, and finally
+disappeared to the naked eye, although there is some reason to suppose
+that it can be identified with a ruddy star of the eleventh magnitude in
+the constellation Cassiopeia, whose light still shows traces of
+variability.
+
+No modern temporary star approaches that of Tycho in splendor, but in
+some respects the recent ones surpass it in interest, since it has been
+possible to apply the spectroscope to the analysis of their light and to
+find thereby a much more complex set of conditions in the star than
+would have been suspected from its light changes alone.
+
+One of the most extraordinary of new stars, and the most brilliant one
+since that of Tycho, appeared suddenly in the constellation Perseus in
+February, 1901, and for a short time equaled Capella in brightness. But
+its light rapidly waned, with periodic fluctuations of brightness like
+those of a variable star, and at the present time (September, 1902) it
+is lost to the naked eye, although in the telescope it still shines like
+a star of the ninth or tenth magnitude.
+
+By the aid of powerful photographic apparatus, during the period of its
+waning brilliancy a ring of faint nebulous matter was detected
+surrounding the star and drifting around and away from it much as if a
+series of nebulƦ had been thrown off by the star at the time of its
+sudden outburst of light. But the extraordinary velocity of this nebular
+motion, nearly a billion miles per hour, makes such an explanation
+almost incredible, and astronomers are more inclined to believe that the
+ring was merely a reflection of the star's own light from a cloud of
+meteoric matter, into which a rapidly moving dark star plunged and,
+after the fashion of terrestrial meteors, was raised to brilliant
+incandescence by the collision. If we assume this to be the true
+explanation of these extraordinary phenomena, it is possible to show
+from the known velocity with which light travels through space and from
+the rate at which the nebula spread, that the distance of Nova Persei,
+as the new star is called, corresponds to a parallax of about one
+one-hundredth of a second, a result that is, in substance, confirmed by
+direct telescopic measurements of its parallax.
+
+Another modern temporary star is Nova AurigƦ, which appeared suddenly in
+December, 1891, waned, and in the following April vanished, only to
+reappear three months later for another season of renewed brightness.
+The spectra of both these modern NovƦ contain both dark and bright lines
+displaced toward opposite ends of the spectrum, and suggesting the
+Doppler effect that would be produced by two or more glowing bodies
+having rapid and opposite motions in the line of sight. But the most
+recent investigations cast discredit on this explanation and leave the
+spectra of temporary stars still a subject of debate among astronomers,
+with respect both to the motion they indicate and the intrinsic nature
+of the stars themselves. The varying aspect of the spectra suggested at
+one time the sun's chromosphere, at another time the conditions that are
+present in nebulƦ, etc.
+
+
+
+
+CHAPTER XIV
+
+STARS AND NEBULƆ
+
+
+209. STELLAR COLORS.--We have already seen that one star differs from
+another in respect of color as well as brightness, and the diligent
+student of the sky will not fail to observe for himself how the luster
+of Sirius and Rigel is more nearly a pure white than is that of any
+other stars in the heavens, while at the other end of the scale
+Ī± Orionis and Aldebaran are strongly ruddy, and Antares presents an
+even deeper tone of red. Between these extremes the light of every star
+shows a mixture of the rainbow hues, in which a very pale yellow is the
+predominant color, shading off, as we have seen, to white at one end of
+the scale and red at the other. There are no green stars, or blue stars,
+or violet stars, save in one exceptional class of cases--viz., where the
+two components of a double star are of very different brightness, it is
+quite the usual thing for them to have different colors, and then,
+almost without exception, the color of the fainter star lies nearer to
+the violet end of the spectrum than does the color of the bright one,
+and sometimes shows a distinctly blue or green hue. A fine type of such
+double star is Ī² Cygni, in which the components are respectively
+yellow and blue, and the yellow star furnishes eight times as much light
+as the blue one.
+
+The exception which double stars thus make to the general rule of
+stellar colors, yellow and red, but no color of shorter wave length, has
+never been satisfactorily explained, but the rule itself presents no
+difficulties. Each star is an incandescent body, giving off radiant
+energy of every wave length within the limits of the visible spectrum,
+and, indeed, far beyond these limits. If this radiant energy could come
+unhindered to our eyes every star would appear white, but they are all
+surrounded by atmospheres--analogous to the chromosphere and reversing
+layer of the sun--which absorb a portion of their radiant energy and,
+like the earth's atmosphere, take a heavier toll from the violet than
+from the red end of the spectrum. The greater the absorption in the
+star's atmosphere, therefore, the feebler and the ruddier will be its
+light, and corresponding to this the red stars are as a class fainter
+than the white ones.
+
+210. CHEMISTRY OF THE STARS.--The spectroscope is pre-eminently the
+instrument to deal with this absorption of light in the stellar
+atmospheres, just as it deals with that absorption in the sun's
+atmosphere to which are due the dark lines of the solar spectrum,
+although the faintness of starlight, compared with that of the sun,
+presents a serious obstacle to its use. Despite this difficulty most of
+the lucid stars and many of the telescopic ones have been studied with
+the spectroscope and found to be similar to the sun and the earth as
+respects the material of which they are made. Such familiar chemical
+elements as hydrogen and iron, carbon, sodium, and calcium are scattered
+broadcast throughout the visible universe, and while it would be
+unwarranted by the present state of knowledge to say that the stars
+contain nothing not found in the earth and the sun, it is evident that
+in a broad way their substance is like rather than unlike that composing
+the solar system, and is subject to the same physical and chemical laws
+which obtain here. Galileo and Newton extended to the heavens the
+terrestrial sciences of mathematics and mechanics, but it remained to
+the nineteenth century to show that the physics and chemistry of the sky
+are like the physics and chemistry of the earth.
+
+211. STELLAR SPECTRA.--When the spectra of great numbers of stars are
+compared one with another, it is found that they bear some relation to
+the colors of the stars, as, indeed, we should expect, since spectrum
+and color are both produced by the stellar atmospheres, and it is found
+useful to classify these spectra into three types, as follows:
+
+_Type I. Sirian stars._--Speaking generally, the stars which are white
+or very faintly tinged with yellow, furnish spectra like that of Sirius,
+from which they take their name, or that of Ī² AurigƦ (Fig.
+124), which is a continuous spectrum, especially rich in energy of short
+wave length--i. e., violet and ultraviolet light, and is crossed by a
+relatively small number of heavy dark lines corresponding to the
+spectrum of hydrogen. Sometimes, however, these lines are much fainter
+than is here shown, and we find associated with them still other faint
+ones pointing to the presence of other metallic substances in the star's
+atmosphere. These metallic lines are not always present, and sometimes
+even the hydrogen lines themselves are lacking, but the spectrum is
+always rich in violet and ultraviolet light.
+
+Since with increasing temperature a body emits a continually increasing
+proportion of energy of short wave length (Ā§ 118), the richness of these
+spectra in such energy points to a very high temperature in these stars,
+probably surpassing in some considerable measure that of the sun. Stars
+with this type of spectrum are more numerous than all others combined,
+but next to them in point of numbers stands--
+
+_Type II. Solar stars._--To this type of spectrum belong the yellow
+stars, which show spectra like that of the sun, or of Pollux (Fig. 125).
+These are not so rich in violet light as are those of Type I, but in
+complexity of spectrum and in the number of their absorption lines they
+far surpass the Sirian stars. They are supposed to be at a lower
+temperature than the Sirian stars, and a much larger number of chemical
+elements seems present and active in the reversing layer of their
+atmospheres. The strong resemblance which these spectra bear to that of
+the sun, together with the fact that most of the sun's stellar neighbors
+have spectra of this type, justify us in ranking both them and it as
+members of one class, called _solar stars_.
+
+_Type III. Red stars._--A small number of stars show spectra comparable
+with that of Ī± Herculis (Fig. 134), in which the blue and the violet
+part of the spectrum is almost obliterated, and the remaining yellow and
+red parts show not only dark lines, but also numerous broad dark bands,
+sharp at one edge, and gradually fading out at the other. It is this
+_selective absorption_, extinguishing the blue and leaving the red end
+of the spectrum, which produces the ruddy color of these stars, while
+the bands in their spectra "are characteristic of chemical combinations,
+and their presence ... proves that at certain elevations in the
+atmospheres of these stars the temperature has sunk so low that chemical
+combinations can be formed and maintained" (Scheiner-Frost). One of the
+chemical compounds here indicated is a hydrocarbon similar to that found
+in comets. In the white and yellow stars the temperatures are so high
+that the same chemical elements, although present, can not unite one
+with another to form compound substances.
+
+[Illustration: FIG. 134.--The spectrum of Ī± Herculis.--ESPIN.]
+
+Most of the variable stars are red and have spectra of the third type;
+but this does not hold true for the eclipse variables like Algol, all of
+which are white stars with spectra of the first type. The ordinary
+variable star is therefore one with a dense atmosphere of relatively low
+temperature and complex structure, which produces the prevailing red
+color of these stars by absorbing the major part of their radiant
+energy of short wave length while allowing the longer, red waves to
+escape. Although their exact nature is not understood, there can be
+little doubt that the fluctuation in the light of these stars is due to
+processes taking place within the star itself, but whether above or
+below its photosphere is still uncertain.
+
+212. CLASSES OF STARS.--There is no hard-and-fast dividing line between
+these types of stellar spectra, but the change from one to another is by
+insensible gradations, like the transition from youth to manhood and
+from manhood to old age, and along the line of transition are to be
+found numberless peculiarities and varieties of spectra not enumerated
+above--e. g., a few stars show not only dark absorption lines in their
+spectra but bright lines as well, which, like those in Fig. 48, point to
+the presence of incandescent vapors, even in the outer parts of their
+atmospheres. Among the lucid stars about 75 per cent have spectra of the
+first type, 23 per cent are of the second type, 1 per cent of the third
+type, and the remaining 1 per cent are peculiar or of doubtful
+classification. Among the telescopic stars it is probable that much the
+same distribution holds, but in the present state of knowledge it is not
+prudent to speak with entire confidence upon this point.
+
+That the great number of stars whose spectra have been studied should
+admit of a classification so simple as the above, is an impressive fact
+which, when supplemented by the further fact of a gradual transition
+from one type of spectrum to the next, leaves little room for doubt that
+in the stars we have an innumerable throng of individuals belonging to
+the same species but in different stages of development, and that the
+sun is only one of these individuals, of something less than medium size
+and in a stage of development which is not at all peculiar, since it is
+shared by nearly a fourth of all the stars.
+
+213. STAR CLUSTERS.--In previous chapters we have noted the Pleiades and
+PrƦsepe as star clusters visible to the naked eye, and to them we may
+add the Hyades, near Aldebaran, and the little constellation Coma
+Berenices. But more impressive than any of these, although visible only
+in a telescope, is the splendid cluster in Hercules, whose appearance in
+a telescope of moderate size is shown in Fig. 135, while Fig. 136 is a
+photograph of the same cluster taken with a very large reflecting
+telescope. This is only a type of many telescopic clusters which are
+scattered over the sky, and which are made up of stars packed so closely
+together as to become indistinguishable, one from another, at the center
+of the cluster. Within an area which could be covered by a third of the
+full moon's face are crowded in this cluster more than five thousand
+stars which are unquestionably close neighbors, but whose apparent
+nearness to each other is doubtless due to their great distance from us.
+It is quite probable that even at the center of this cluster, where more
+than a thousand stars are included within a radius of 160", the actual
+distances separating adjoining stars are much greater than that
+separating earth and sun, but far less than that separating the sun from
+its nearest stellar neighbor.
+
+[Illustration: FIG 135.--Star cluster in Hercules.]
+
+An interesting discovery of recent date, made by Professor Bailey in
+photographing star clusters, is that some few of them, which are
+especially rich in stars, contain an extraordinary number of variable
+stars, mostly very faint and of short period. Two clusters, one in the
+northern and one in the southern hemisphere, contain each more than a
+hundred variables, and an even more extraordinary case is presented by
+a cluster, called Messier 5, not far from the star Ī± Serpentis,
+which contains no less than sixty-three variables, all about of the
+fourteenth magnitude, all having light periods which differ but little
+from half a day, all having light curves of about the same shape, and
+all having a range of brightness from maximum to minimum of about one
+magnitude. An extraordinary set of coincidences which "points
+unmistakably to a common origin and cause of variability."
+
+[Illustration: FIG. 136.--Star cluster in Hercules.--KEELER.]
+
+[Illustration: FIG. 137.--The Andromeda nebula as seen in a very small
+telescope.]
+
+[Illustration: FIG. 138.--The Andromeda nebula and Holmes's comet.
+Photographed by BARNARD.]
+
+[Illustration: FIG. 139.--A drawing of the Andromeda nebula.]
+
+[Illustration: FIG. 140.--A photograph of the Andromeda
+nebula.--ROBERTS.]
+
+214. NEBULƆ.--Returning to Fig. 136, we note that its background has a
+hazy appearance, and that at its center the stars can no longer be
+distinguished, but blend one with another so as to appear like a bright
+cloud. The outer part of the cluster is _resolved_ into stars, while in
+the picture the inner portion is not so resolved, although in the
+original photographic plate the individual stars can be distinguished to
+the very center of the cluster. In many cases, however, this is not
+possible, and we have an _irresolvable cluster_ which it is customary to
+call a _nebula_ (Latin, _little cloud_).
+
+The most conspicuous example of this in the northern heavens is the
+great nebula in Andromeda (R. A. 0^{h} 37^{m}, Dec. + 41Ā°), which may be
+seen with the naked eye as a faint patch of foggy light. Look for it.
+This appears in an opera glass or very small telescope not unlike Fig.
+137, which is reproduced from a sketch. Fig. 138 is from a photograph of
+the same object showing essentially the same shape as in the preceding
+figure, but bringing out more detail. Note the two small nebulƦ
+adjoining the large one, and at the bottom of the picture an object
+which might easily be taken for another nebula but which is in fact a
+tailless comet that chanced to be passing that part of the sky when the
+picture was taken. Fig. 139 is from another drawing of this nebula,
+although it is hardly to be recognized as a representation of the same
+thing; but its characteristic feature, the two dark streaks near the
+center of the picture, is justified in part by Fig. 140, which is from a
+photograph made with a large reflecting telescope.
+
+[Illustration: FIG. 141.--Types of nebulƦ.]
+
+A comparison of these several representations of the same thing will
+serve to illustrate the vagueness of its outlines, and how much the
+impressions to be derived from nebulƦ depend upon the telescopes
+employed and upon the observer's own prepossessions. The differences
+among the pictures can not be due to any change in the nebula itself,
+for half a century ago it was sketched much as shown in the latest of
+them (Fig. 140).
+
+[Illustration: FIG. 142.--The Trifid nebula.--KEELER.]
+
+215. TYPICAL NEBULƆ.--Some of the fantastic forms which nebulƦ present
+in the telescope are shown on a small scale in Fig. 141, but in recent
+years astronomers have learned to place little reliance upon drawings
+such as these, which are now almost entirely supplanted by photographs
+made with long exposures in powerful telescopes. One of the most
+exquisite of these modern photographs is that of the Trifid nebula in
+Sagittarius (Fig. 142). Note especially the dark lanes that give to this
+nebula its name, Trifid, and which run through its brightest parts,
+breaking it into seemingly independent sections. The area of the sky
+shown in this cut is about 15 per cent less than that covered by the
+full moon.
+
+[Illustration: FIG. 143.--A nebula in Cygnus.--KEELER.]
+
+Fig. 143 shows a very different type of nebula, found in the
+constellation Cygnus, which appears made up of filaments closely
+intertwined, and stretches across the sky for a distance considerably
+greater than the moon's diameter.
+
+[Illustration: FIG. 144.--Spiral nebula in Canes Venatici.--KEELER.]
+
+A much smaller but equally striking nebula is that in the constellation
+Canes Venatici (Fig. 144), which shows a most extraordinary spiral
+structure, as if the stars composing it were flowing in along curved
+lines toward a center of condensation. The diameter of the circular part
+of this nebula, omitting the projection toward the bottom of the
+picture, is about five minutes of arc, a sixth part of the diameter of
+the moon, and its thickness is probably very small compared with its
+breadth, perhaps not much exceeding the width of the spiral streams
+which compose it. Note how the bright stars that appear within the area
+of this nebula fall on the streams of nebulous matter as if they were
+part of them. This characteristic grouping of the stars, which is
+followed in many other nebulƦ, shows that they are really part and
+parcel of the nebula and not merely on line with it. Fig. 145 shows how
+a great nebula is associated with the star Ļ Ophiuchi.
+
+[Illustration: FIG. 145.--Great nebula about the star Ļ
+Ophiuchi.--BARNARD.]
+
+Probably the most impressive of all nebulƦ is the great one in Orion
+(Fig. 146), whose position is shown on the star map between Rigel and
+Ī¶ Orionis. Look for it with an opera glass or even with the
+unaided eye. This is sometimes called an _amorphous_--i. e.,
+shapeless--nebula, because it presents no definite form which the eye
+can grasp and little trace of structure or organization. It is "without
+form and void" at least in its central portions, although on its edges
+curved filaments may be traced streaming away from the brighter parts
+of the central region. This nebula, as shown in Fig. 146, covers an area
+about equal to that of the full moon, without counting as any part of
+this the companion nebula shown at one side, but photographs made with
+suitable exposures show that faint outlying parts of the nebula extend
+in curved lines over the larger part of the constellation Orion. Indeed,
+over a large part of the entire sky the background is faintly covered
+with nebulous light whose brighter portions, if each were counted as a
+separate nebula, would carry the total number of such objects well into
+the hundreds of thousands.
+
+[Illustration: FIG. 146.--The Orion nebula.]
+
+The Pleiades (Plate IV) present a case of a resolvable star cluster
+projected against such a nebulous background whose varying intensity
+should be noted in the figure. A part of this nebulous matter is shown
+in wisps extending from one star to the next, after the fashion of a
+bridge, and leaving little doubt that the nebula is actually a part of
+the cluster and not merely a background for it.
+
+[Illustration: THE PLEIADES (AFTER A PHOTOGRAPH)]
+
+Fig. 147 shows a series of so-called double nebulƦ perhaps comparable
+with double stars, although the most recent photographic work seems to
+indicate that they are really faint spiral nebulƦ in which only the
+brightest parts are shown by the telescope.
+
+According to Keeler, the spiral is the prevailing type of nebulƦ, and
+while Fig. 144 presents the most perfect example of such a nebula, the
+student should not fail to note that the Andromeda nebula (Fig. 140)
+shows distinct traces of a spiral structure, only here we do not see its
+true shape, the nebula being turned nearly edgewise toward us so that
+its presumably circular outline is foreshortened into a narrow ellipse.
+
+[Illustration: FIG. 147.--Double nebulƦ. HERSCHEL.]
+
+Another type of nebula of some consequence presents in the telescope
+round disks like those of Uranus or Neptune, and this appearance has
+given them the name _planetary nebulƦ_. The comet in Fig. 138, if
+smaller, would represent fairly well the nebulƦ of this type. Sometimes
+a planetary nebula has a star at its center, and sometimes it appears
+hollow, like a smoke ring, and is then called a ring nebula. The most
+famous of these is in the constellation Lyra, not far from Vega.
+
+216. SPECTRA OF NEBULƆ.--A star cluster, like the one in Hercules,
+shows, of course, stellar spectra, and even when irresolvable the
+spectrum is a continuous one, testifying to the presence of stars,
+although they stand too close together to be separately seen. But in a
+certain number of nebulƦ the spectrum is altogether different, a
+discontinuous one containing only a few bright lines, showing that here
+the nebular light comes from glowing gases which are subject to no
+considerable pressure. The planetary nebulƦ all have spectra of this
+kind and make up about half of all the known gaseous nebulƦ. It is
+worthy of note that a century ago Sir William Herschel had observed a
+green shimmer in the light of certain nebulƦ which led him to believe
+that they were "not of a starry nature," a conclusion which has been
+abundantly confirmed by the spectroscope. The green shimmer is, in fact,
+caused by a line in the green part of the spectrum that is always
+present and is always the brightest part of the spectrum of gaseous
+nebulƦ.
+
+In faint nebulƦ this line constitutes the whole of their visible
+spectrum, but in brighter ones two or three other and fainter lines are
+usually associated with it, and a very bright nebula, like that in
+Orion, may show a considerable number of extra lines, but for the most
+part they can not be identified in the spectrum of any terrestrial
+substances. An exception to this is found in the hydrogen lines, which
+are well marked in most spectra of gaseous nebulƦ, and there are
+indications of one or two other known substances.
+
+217. DENSITY OF NEBULƆ.--It is known from laboratory experiments that
+diminishing the pressure to which an incandescent gas is subject,
+diminishes the number of lines contained in its spectrum, and we may
+surmise from the very simple character and few lines of these nebular
+spectra that the gas which produces them has a very small density. But
+this is far from showing that the nebula itself is correspondingly
+attenuated, for we must not assume that this shining gas is all that
+exists in the nebula; so far as telescope or camera are concerned, there
+may be associated with it any amount of dark matter which can not be
+seen because it sends to us no light. It is easy to think in this
+connection of meteoric dust or the stuff of which comets are made, for
+these seem to be scattered broadcast on every side of the solar system
+and may, perchance, extend out to the region of the nebulƦ.
+
+But, whatever may be associated in the nebula with the glowing gas which
+we see, the total amount of matter, invisible as well as visible, must
+be very small, or rather its average density must be very small, for the
+space occupied by such a nebula as that of Orion is so great that if the
+average density of its matter were equal to that of air the resulting
+mass by its attraction would exert a sensible effect upon the motion of
+the sun through space. The brighter parts of this nebula as seen from
+the earth subtend an angle of about half a degree, and while we know
+nothing of its distance from us, it is easy to see that the farther it
+is away the greater must be its real dimensions, and that this increase
+of bulk and mass with increasing distance will just compensate the
+diminishing intensity of gravity at great distances, so that for a given
+angular diameter--e. g., half a degree--the force with which this nebula
+attracts the sun depends upon its density but not at all upon its
+distance. Now, the nebula must attract the sun in some degree, and must
+tend to move it and the planets in an orbit about the attracting center
+so that year after year we should see the nebula from slightly different
+points of view, and this changed point of view should produce a change
+in the apparent direction of the nebula from us--i. e., a proper motion,
+whose amount would depend upon the attracting force, and therefore upon
+the density of the attracting matter. Observations of the Orion nebula
+show that its proper motion is wholly inappreciable, certainly far less
+than half a second of arc per year, and corresponding to this amount of
+proper motion the mean density of the nebula must be some millions of
+times (10^{10} according to Ranyard) less than that of air at sea
+level--i. e., the average density throughout the nebula is comparable
+with that of those upper parts of the earth's atmosphere in which
+meteors first become visible.
+
+218. MOTION OF NEBULƆ.--The extreme minuteness of their proper motions
+is a characteristic feature of all nebulƦ. Indeed, there is hardly a
+known case of sensible proper motion of one of these bodies, although a
+dozen or more of them show velocities in the line of sight ranging in
+amount from +30 to -40 miles per second, the plus sign indicating an
+increasing distance. While a part of these velocities may be only
+apparent and due to the motion of earth and sun through space, a part at
+least is real motion of the nebulƦ themselves. These seem to move
+through the celestial spaces in much the same way and with the same
+velocities as do the stars, and their smaller proper motions across the
+line of sight (angular motions) are an index of their great distance
+from us. No one has ever succeeded in measuring the parallax of a nebula
+or star cluster.
+
+[Illustration: FIG. 148.--A part of the Milky Way.]
+
+The law of gravitation presumably holds sway within these bodies, and
+the fact that their several parts and the stars which are involved
+within them, although attracted by each other, have shown little or no
+change of position during the past century, is further evidence of
+their low density and feeble attraction. In a few cases, however, there
+seem to be in progress within a nebula changes of brightness, so that
+what was formerly a faint part has become a brighter one, or _vice
+versa_; but, on the whole, even these changes are very small.
+
+[Illustration: FIG. 149.--The Milky Way near Īø Ophiuchi.--BARNARD.]
+
+219. THE MILKY WAY.--Closely related to nebulƦ and star clusters is
+another feature of the sky, the _galaxy_ or _Milky Way_, with whose
+appearance to the unaided eye the student should become familiar by
+direct study of the thing itself. Figs. 148 and 149 are from photographs
+of two small parts of it, and serve to bring out the small stars of
+which it is composed. Every star shown in these pictures is invisible to
+the naked eye, although their combined light is easily seen. The general
+course of the galaxy across the heavens is shown in the star maps, but
+these contain no indication of the wealth of detail which even the naked
+eye may detect in it. Bright and faint parts, dark rifts which cut it
+into segments, here and there a hole as if the ribbon of light had been
+shot away--such are some of the features to be found by attentive
+examination.
+
+[Illustration: FIG. 150.--The Milky Way near Ī² Cygni.--BARNARD.]
+
+Speaking generally, the course of the Milky Way is a great circle
+completely girdling the sky and having its north pole in the
+constellation Coma Berenices. The width of this stream of light is very
+different in different parts of the heavens, amounting where it is
+widest, in Lyra and Cygnus, to something more than 30Ā°, although its
+boundaries are too vague and ill defined to permit much accuracy of
+measurement. Observe the very bright part between Ī² and Ī³ Cygni, nearly
+opposite Vega, and note how even an opera glass will partially resolve
+the nebulous light into a great number of stars, which are here rather
+brighter than in other parts of its course. But the resolution into
+stars is only partial, and there still remains a background of
+unresolved shimmer. Fig. 150 is a photograph of a small part of this
+region in which, although each fleck of light represents a separate
+star, the galaxy is not completely resolved. Compare with this region,
+rich in stars, the nearly empty space between the branches of the galaxy
+a little west of Altair. Another hole in the Milky Way may be found a
+little north and east of Ī± Cygni, and between the extremes of abundance
+and poverty here noted there may be found every gradation of nebulous
+light.
+
+The Milky Way is not so simple in its structure as might at first be
+thought, but a clear and moonless night is required to bring out its
+details. The nature of these details, the structure of the galaxy, its
+shape and extent, the arrangement of its parts, and their relation to
+stars and nebulƦ in general, have been subjects of much speculation by
+astronomers and others who have sought to trace out in this way what is
+called the _construction of the heavens_.
+
+220. DISTRIBUTION OF THE STARS.--How far out into space do the stars
+extend? Are they limited or infinite in number? Do they form a system of
+mutually related parts, or are they bunched promiscuously, each for
+itself, without reference to the others? Here is what has been well
+called "the most important problem of stellar astronomy, the acquisition
+of well-founded ideas about the distribution of the stars." While many
+of the ideas upon this subject which have been advanced by eminent
+astronomers and which are still current in the books are certainly
+wrong, and few of their speculations along this line are demonstrably
+true, the theme itself is of such grandeur and permanent interest as to
+demand at least a brief consideration. But before proceeding to its
+speculative side we need to collect facts upon which to build, and
+these, however inadequate, are in the main simple and not far to seek.
+
+Parallaxes, proper motions, motions in the line of sight, while
+pertinent to the problem of stellar distribution, are of small avail,
+since they are far too scanty in number and relate only to limited
+classes of stars, usually the very bright ones or those nearest to the
+sun. Almost the sole available data are contained in the brightness of
+the stars and the way in which they seem scattered in the sky. The most
+casual survey of the heavens is enough to show that the stars are not
+evenly sprinkled upon it. The lucid stars are abundant in some regions,
+few in others, and the laborious star gauges, actual counting of the
+stars in sample regions of the sky, which have been made by the
+Herschels, Celoria, and others, suffice to show that this lack of
+uniformity in distribution is even more markedly true of the telescopic
+stars.
+
+The rate of increase in the number of stars from one magnitude to the
+next, as shown in Ā§ 187, is proof of another kind of irregularity in
+their distribution. It is not difficult to show, mathematically, that if
+in distant regions of space the stars were on the average as numerous
+and as bright as they are in the regions nearer to the sun, then the
+stars of any particular magnitude ought to be four times as numerous as
+those of the next brighter magnitude--e. g., four times as many
+sixth-magnitude stars as there are fifth-magnitude ones. But, as we have
+already seen in Ā§ 187, by actual count there are only three times as
+many, and from the discrepancy between these numbers, an actual
+threefold increase instead of a fourfold one, we must conclude that on
+the whole the stars near the sun are either bigger or brighter or more
+numerous than in the remoter depths of space.
+
+221. THE STELLAR SYSTEM.--But the arrangement of the stars is not
+altogether lawless and chaotic; there are traces of order and system,
+and among these the Milky Way is the dominant feature. Telescope and
+photographic plate alike show that it is made up of stars which,
+although quite irregularly scattered along its course, are on the
+average some twenty times as numerous in the galaxy as at its poles,
+and which thin out as we recede from it on either side, at first rapidly
+and then more slowly. This tendency to cluster along the Milky Way is
+much more pronounced among the very faint telescopic stars than among
+the brighter ones, for the lucid stars and the telescopic ones down to
+the tenth or eleventh magnitude, while very plainly showing the
+clustering tendency, are not more than three times as numerous in the
+galaxy as in the constellations most remote from it. It is remarkable as
+showing the condensation of the brightest stars that one half of all the
+stars in the sky which are brighter than the second magnitude are
+included within a belt extending 12Ā° on either side of the center line
+of the galaxy.
+
+In addition to this general condensation of stars toward the Milky Way,
+there are peculiarities in the distribution of certain classes of stars
+which are worth attention. Planetary nebulƦ and new stars are seldom, if
+ever, found far from the Milky Way, and stars with bright lines in their
+spectra especially affect this region of the sky. Stars with spectra of
+the first type--Sirian stars--are much more strongly condensed toward
+the Milky Way than are stars of the solar type, and in consequence of
+this the Milky Way is peculiarly rich in light of short wave lengths.
+Resolvable star clusters are so much more numerous in the galaxy than
+elsewhere, that its course across the sky would be plainly indicated by
+their grouping upon a map showing nothing but clusters of this kind.
+
+On the other hand, nebulƦ as a class show a distinct aversion for the
+galaxy, and are found most abundantly in those parts of the sky farthest
+from it, much as if they represented raw material which was lacking
+along the Milky Way, because already worked up to make the stars which
+are there so numerous.
+
+222. RELATION OF THE SUN TO THE MILKY WAY.--The fact that the galaxy is
+a _great circle_ of the sky, but only of moderate width, shows that it
+is a widely extended and comparatively thin stratum of stars within
+which the solar system lies, a member of the galactic system, and
+probably not very far from its center. This position, however, is not to
+be looked upon as a permanent one, since the sun's motion, which lies
+nearly in the plane of the Milky Way, is ceaselessly altering its
+relation to the center of that system, and may ultimately carry us
+outside its limits.
+
+The Milky Way itself is commonly thought to be a ring, or series of
+rings, like the coils of the great spiral nebula in Andromeda, and
+separated from us by a space far greater than the thickness of the ring
+itself. Note in Figs. 149 and 150 how the background is made up of
+bright and dark parts curiously interlaced, and presenting much the
+appearance of a thin sheet of cloud through which we look to barren
+space beyond. While, mathematically, this appearance can not be
+considered as proof that the galaxy is in fact a distant ring, rather
+than a sheet of starry matter stretching continuously from the nearer
+stellar neighbors of the sun into the remotest depths of space,
+nevertheless, most students of the question hold it to be such a ring of
+stars, which are relatively close together while its center is
+comparatively vacant, although even here are some hundreds of thousands
+of stars which on the whole have a tendency to cluster near its plane
+and to crowd together a little more densely than elsewhere in the region
+where the sun is placed.
+
+223. DIMENSIONS OF THE GALAXY.--The dimensions of this stellar system
+are wholly unknown, but there can be no doubt that it extends farther in
+the plane of the Milky Way than at right angles to that plane, for stars
+of the fifteenth and sixteenth magnitudes are common in the galaxy, and
+testify by their feeble light to their great distance from the earth,
+while near the poles of the Milky Way there seem to be few stars fainter
+than the twelfth magnitude. Herschel, with his telescope of 18 inches
+aperture, could count in the Milky Way more than a dozen times as many
+stars per square degree as could Celoria with a telescope of 4 inches
+aperture; but around the poles of the galaxy the two telescopes showed
+practically the same number of stars, indicating that here even the
+smaller telescope reached to the limits of the stellar system. Very
+recently, indeed, the telescope with which Fig. 140 was photographed
+seems to have reached the farthest limit of the Milky Way, for on a
+photographic plate of one of its richest regions Roberts finds it
+completely resolved into stars which stand out upon a black background
+with no trace of nebulous light between them.
+
+224. BEYOND THE MILKY WAY.--Each additional step into the depths of
+space brings us into a region of which less is known, and what lies
+beyond the Milky Way is largely a matter of conjecture. We shrink from
+thinking it an infinite void, endless emptiness, and our intellectual
+sympathies go out to Lambert's speculation of a universe filled with
+stellar systems, of which ours, bounded by the galaxy, is only one.
+There is, indeed, little direct evidence that other such systems exist,
+but the Andromeda nebula is not altogether unlike a galaxy with a
+central cloud of stars, and in the southern hemisphere, invisible in our
+latitudes, are two remarkable stellar bodies like the Milky Way in
+appearance, but cut off from all apparent connection with it, much as we
+might expect to find independent stellar systems, if such there be.
+
+These two bodies are known as the Magellanic clouds, and individually
+bear the names of Major and Minor Nubecula. According to Sir John
+Herschel, "the Nubecula Major, like the Minor, consists partly of large
+tracts and ill-defined patches of irresolvable nebula, and of nebulosity
+in every stage of resolution up to perfectly resolved stars like the
+Milky Way, as also of regular and irregular nebulƦ ... of globular
+clusters in every stage of resolvability, and of clustering groups
+sufficiently insulated and condensed to come under the designation of
+clusters of stars." Its outlines are vague and somewhat uncertain, but
+surely include an area of more than 40 square degrees--i. e., as much as
+the bowl of the Big Dipper--and within this area Herschel counted
+several hundred nebulƦ and clusters "which far exceeds anything that is
+to be met with in any other region of the heavens." Although its
+excessive complexity of detail baffled Herschel's attempts at artistic
+delineation, it has yielded to the modern photographic processes, which
+show the Nubecula Major to be an enormous spiral nebula made up of
+subordinate stars, nebulƦ, and clusters, as is the Milky Way.
+
+Compared with the Andromeda nebula, its greater angular extent suggests
+a smaller distance, although for the present all efforts at determining
+the parallax of either seem hopeless. But the spiral form which is
+common to both suggests that the Milky Way itself may be a gigantic
+spiral nebula near whose center lies the sun, a humble member of a great
+cluster of stars which is roughly globular in shape, but flattened at
+the poles of the galaxy and completely encircled by its coils. However
+plausible such a view may appear, it is for the present, at least, pure
+hypothesis, although vigorously advocated by Easton, who bases his
+argument upon the appearance of the galaxy itself.
+
+225. ABSORPTION OF STARLIGHT.--We have had abundant occasion to learn
+that at least within the confines of the solar system meteoric matter,
+cosmic dust, is profusely scattered, and it appears not improbable that
+the same is true, although in smaller degree, in even the remoter parts
+of space. In this case the light which comes from the farther stars over
+a path requiring many centuries to travel, must be in some measure
+absorbed and enfeebled by the obstacles which it encounters on the way.
+Unless celestial space is transparent to an improbable degree the
+remoter stars do not show their true brightness; there is a certain
+limit beyond which no star is able to send its light, and beyond which
+the universe must be to us a blank. A lighthouse throws into the fog its
+beams only to have them extinguished before a single mile is passed, and
+though the celestial lights shine farther, a limit to their reach is
+none the less certain if meteoric dust exists outside the solar system.
+If there is such an absorption of light in space, as seems plausible,
+the universe may well be limitless and the number of stellar systems
+infinite, although the most attenuated of dust clouds suffices to
+conceal from us and to shut off from our investigation all save a minor
+fraction of it and them.
+
+
+
+
+CHAPTER XV
+
+GROWTH AND DECAY
+
+
+226. NATURE OF THE PROBLEM.--To use a common figure of speech, the
+universe is alive. We have found it filled with an activity that
+manifests itself not only in the motions of the heavenly bodies along
+their orbits, but which extends to their minutest parts, the molecules
+and atoms, whose vibrations furnish the radiant energy given off by sun
+and stars. Some of these activities, such as the motions of the heavenly
+bodies in their orbits, seem fitted to be of endless duration; while
+others, like the radiation of light and heat, are surely temporary, and
+sooner or later must come to an end and be replaced by something
+different. The study of things as they are thus leads inevitably to
+questions of what has been and what is to be. A sound science should
+furnish some account of the universe of yesterday and to-morrow as well
+as of to-day, and we need not shrink from such questions, although
+answers to them must be vague and in great measure speculative.
+
+The historian of America finds little difficulty with events of the
+nineteenth century or even the eighteenth, but the sources of
+information about America in the fifteenth century are much less
+definite; the tenth century presents almost a blank, and the history of
+American mankind in the first century of the Christian era is wholly
+unknown. So, as we attempt to look into the past or the future of the
+heavens, we must expect to find the mists of obscurity grow denser with
+remoter periods until even the vaguest outlines of its development are
+lost, and we are compelled to say, beyond this lies the unknown. Our
+account of growth and decay in the universe, therefore, can not aspire
+to cover the whole duration of things, but must be limited in its scope
+to certain chapters whose epochs lie near to the time in which we live,
+and even for these we need to bear constantly in mind the logical bases
+of such an inquiry and the limitations which they impose upon us.
+
+227. LOGICAL BASES AND LIMITATIONS.--The first of these bases is: An
+adequate knowledge of the present universe. Our only hope of reading the
+past and future lies in an understanding of the present; not necessarily
+a complete knowledge of it, but one which is sound so far as it goes.
+Our position is like that of a detective who is called upon to unravel a
+mystery or crime, and who must commence with the traces that have been
+left behind in its commission. The foot print, the blood stain, the
+broken glass must be examined and compared, and fashioned into a theory
+of how they came to be; and as a wrong understanding of these elements
+is sure to vitiate the theories based upon them, so a false science of
+the universe as it now is, will surely give a false account of what it
+has been; while a correct but incomplete knowledge of the present does
+not wholly bar an understanding of the past, but only puts us in the
+position of the detective who correctly understands what he sees but
+fails to take note of other facts which might greatly aid him.
+
+The second basis of our inquiry is: The assumed permanence of natural
+laws. The law of gravitation certainly held true a century ago as well
+as a year ago, and for aught we know to the contrary it may have been a
+law of the universe for untold millions of years; but that it has
+prevailed for so long a time is a pure assumption, although a necessary
+one for our purpose. So with those other laws of mathematics and
+mechanics and physics and chemistry to which we must appeal; if there
+was ever a time or place in which they did not hold true, that time and
+place lie beyond the scope of our inquiry, and are in the domain
+inaccessible to scientific research. It is for this reason that science
+knows nothing and can know nothing of a creation or an end of the
+universe, but considers only its orderly development within limited
+periods of time. What kind of a past universe would, under the operation
+of known laws, develop into the present one, is the question with which
+we have to deal, and of it we may say with Helmholtz: "From the
+standpoint of science this is no idle speculation but an inquiry
+concerning the limitations of its methods and the scope of its known
+laws."
+
+To ferret out the processes by which the heavenly bodies have been
+brought to their present condition we seek first of all for lines of
+development now in progress which tend to change the existing order of
+things into something different, and, having found these, to trace their
+effects into both past and future. Any force, however small, or any
+process, however slow, may produce great results if it works always and
+ceaselessly in the same direction, and it is in these processes, whose
+trend is never reversed, that we find a partial clew to both past and
+future.
+
+228. THE SUN'S DEVELOPMENT.--The first of these to claim our attention
+is the shrinking of the sun's diameter which, as we have seen in Chapter
+X, is the means by which the solar output of radiant energy is
+maintained from year to year. Its amount, only a few feet per annum, is
+far too small to be measured with any telescope; but it is cumulative,
+working century after century in the same direction, and, given time
+enough, it will produce in the future, and must have produced in the
+past, enormous transformations in the sun's bulk and equally significant
+changes in its physical condition.
+
+Thus, as we attempt to trace the sun's history into the past, the
+farther back we go the greater shall we expect to find its diameter and
+the greater the space (volume) through which its molecules are spread.
+By reason of this expansion its density must have been less then than
+now, and by going far enough back we may even reach a time at which the
+density was comparable with what we find in the nebulƦ of to-day. If our
+ideas of the sun's present mechanism are sound, then, as a necessary
+consequence of these, its past career must have been a process of
+condensation in which its component particles were year by year packed
+closer together by their own attraction for each other. As we have seen
+in Ā§ 126, this condensation necessarily developed heat, a part of which
+was radiated away as fast as produced, while the remainder was stored
+up, and served to raise the temperature of the sun to what we find it
+now. At the present time this temperature is a chief obstacle to further
+shrinkage, and so powerfully opposes the gravitative forces as to
+maintain nearly an equilibrium with them, thus causing a very slow rate
+of further condensation. But it is not probable that this was always so.
+In the early stages of the sun's history, when the temperature was low,
+contraction of its bulk must have been more rapid, and attempts have
+been made by the mathematicians to measure its rate of progress and to
+determine how long a time has been consumed in the development of the
+present sun from a primitive nebulous condition in which it filled a
+space of greater diameter than Neptune's orbit. Of course, numerical
+precision is not to be expected in results of this kind, but, from a
+consideration of the greatest amount of heat that could be furnished by
+the shrinkage of a mass equal to that of the sun, it seems that the
+period of this development is to be measured in tens of millions or
+possibly hundreds of millions of years, but almost certainly does not
+reach a thousand millions.
+
+229. THE SUN'S FUTURE.--The future duration of the sun as a source of
+radiant energy is surely to be measured in far smaller numbers than
+these. Its career as a dispenser of light and heat is much more than
+half spent, for the shrinkage results in an ever-increasing density,
+which makes its gaseous substance approximate more and more toward the
+behavior of a liquid or solid, and we recall that these forms of matter
+can not by any further condensation restore the heat whose loss through
+radiation caused them to contract. They may continue to shrink, but
+their temperature must fall, and when the sun's substance becomes too
+dense to obey the laws of gaseous matter its surface must cool rapidly
+as a consequence of the radiation into surrounding space, and must
+congeal into a crust which, although at first incandescent, will
+speedily become dark and opaque, cutting off the light of the central
+portions, save as it may be rent from time to time by volcanic outbursts
+of the still incandescent mass beneath. But such outbursts can be of
+short duration only, and its final condition must be that of a dark
+body, like the earth or moon, no longer available as a source of radiant
+energy. Even before the formation of a solid crust it is quite possible
+that the output of light and heat may be seriously diminished by the
+formation of dense vapors completely enshrouding it, as is now the case
+with Jupiter and Saturn. It is believed that these planets were formerly
+incandescent, and at the present time are in a state of development
+through which the earth has passed and toward which the sun is moving.
+According to Newcomb, the future during which the sun can continue to
+furnish light and heat at its present rate is not likely to exceed
+10,000,000 years.
+
+This idea of the sun as a developing body whose present state is only
+temporary, furnishes a clew to some of the vexing problems of solar
+physics. Thus the sun-spot period, the distribution of the spots in
+latitude, and the peculiar law of rotation of the sun in different
+latitudes, may be, and very probably are, results not of anything now
+operating beneath its photosphere, but of something which happened to it
+in the remote past--e. g., an unsymmetrical shrinkage or possibly a
+collision with some other body. At sea the waves continue to toss long
+after the storm which produced them has disappeared, and, according to
+the mathematical researches of Wilsing, a profound agitation of the
+sun's mass might well require tens of thousands, or even hundreds of
+thousands of years to subside, and during this time its effects would be
+visible, like the waves, as phenomena for which the actual condition of
+things furnishes no apparent cause.
+
+230. THE NEBULAR HYPOTHESIS.--The theory of the sun's progressive
+contraction as a necessary result of its radiation of energy is
+comparatively modern, but more than a century ago philosophic students
+of Nature had been led in quite a different way to the belief that in
+the earlier stages of its career the sun must have been an enormously
+extended body whose outer portions reached even beyond the orbit of the
+remotest planet. Laplace, whose speculations upon this subject have had
+a dominant influence during the nineteenth century, has left, in a
+popular treatise upon astronomy, an admirable statement of the phenomena
+of planetary motion, which suggest and lead up to the nebular theory of
+the sun's development, and in presenting this theory we shall follow
+substantially his line of thought, but with some freedom of translation
+and many omissions.
+
+He says: "To trace out the primitive source of the planetary movements,
+we have the following five phenomena: (1) These movements all take place
+in the same direction and nearly in the same plane. (2) The movements of
+the satellites are in the same direction as those of the planets. (3)
+The rotations of the planets and the sun are in the same direction as
+the orbital motions and nearly in the same plane. (4) Planets and
+satellites alike have nearly circular orbits. (5) The orbits of comets
+are wholly unlike these by reason of their great eccentricities and
+inclinations to the ecliptic." That these coincidences should be purely
+the result of chance seemed to Laplace incredible, and, seeking a cause
+for them, he continues: "Whatever its nature may be, since it has
+produced or controlled the motions of the planets, it must have reached
+out to all these bodies, and, in view of the prodigious distances which
+separate them, the cause can have been nothing else than a fluid of
+great extent which must have enveloped the sun like an atmosphere. A
+consideration of the planetary motions leads us to think that ... the
+sun's atmosphere formerly extended far beyond the orbits of all the
+planets and has shrunk by degrees to its present dimensions." This is
+not very different from the idea developed in Ā§ 228 from a consideration
+of the sun's radiant energy; but in Laplace's day the possibility of
+generating the sun's heat by contraction of its bulk was unknown, and he
+was compelled to assume a very high temperature for the primitive
+nebulous sun, while we now know that this is unnecessary. Whether the
+primitive nebula was hot or cold the shrinkage would take place in much
+the same way, and would finally result in a star or sun of very high
+temperature, but its development would be slower if it were hot in the
+beginning than if it were cold.
+
+But again Laplace: "How did the sun's atmosphere determine the rotations
+and revolutions of planets and satellites? If these bodies had been
+deeply immersed in this atmosphere its resistance to their motion would
+have made them fall into the sun, and we may therefore conjecture that
+the planets were formed, one by one, at the outer limits of the solar
+atmosphere by the condensation of zones of vapor which were cast off in
+the plane of the sun's equator." Here he proceeds to show by an appeal
+to dynamical principles that something of this kind must happen, and
+that the matter sloughed off by the nebula in the form of a ring,
+perhaps comparable to the rings of Saturn or the asteroid zone, would
+ultimately condense into a planet, which in its turn might shrink and
+cast off rings to produce satellites.
+
+[Illustration: PIERRE SIMON LAPLACE (1749-1827).]
+
+Planets and satellites would then all have similar motions, as noted at
+the beginning of this section, since in every case this motion is an
+inheritance from a common source, the rotation of the primitive
+nebula about its own axis. "All the bodies which circle around a planet
+having been thus formed from rings which its atmosphere successively
+abandoned as rotation became more and more rapid, this rotation should
+take place in less time than is required for the orbital revolution of
+any of the bodies which have been cast off, and this holds true for the
+sun as compared with the planets."
+
+231. OBJECTIONS TO THE NEBULAR HYPOTHESIS.--In Laplace's time this
+slower rate of motion was also supposed to hold true for Saturn's rings
+as compared with the rotation of Saturn itself, but, as we have seen in
+Chapter XI, this ring is made up of a great number of independent
+particles which move at different rates of speed, and comparing, through
+Kepler's Third Law, the motion of the inner edge of the ring with the
+known periodic time of the satellites, we may find that these particles
+must rotate about Saturn more rapidly than the planet turns upon its
+axis. Similarly the inner satellite of Mars completes its revolution in
+about one third of a Martian day, and we find in cases like this grounds
+for objection to the nebular theory. Compare also Laplace's argument
+with the peculiar rotations of Uranus, Neptune, and their satellites
+(Chapter XI). Do these fortify or weaken his case?
+
+Despite these objections and others equally serious that have been
+raised, the nebular theory agrees with the facts of Nature at so many
+points that astronomers upon the whole are strongly inclined to accept
+its major outlines as being at least an approximation to the course of
+development actually followed by the solar system; but at some
+points--e. g., the formation of planets and satellites through the
+casting off of nebulous rings--the objections are so many and strong as
+to call for revision and possibly serious modification of the theory.
+
+One proposed modification, much discussed in recent years, consists in
+substituting for the primitive _gaseous_ nebula imagined by Laplace, a
+very diffuse cloud of meteoric matter which in the course of its
+development would become transformed into the gaseous state by rising
+temperature. From this point of view much of the meteoric dust still
+scattered throughout the solar system may be only the fragments left
+over in fashioning the sun and planets. Chamberlin and Moulton, who have
+recently given much attention to this subject, in dissenting from some
+of Laplace's views, consider that the primitive nebulous condition must
+have been one in which the matter of the system was "so brought together
+as to give low mass, high momentum, and irregular distribution to the
+outer part, and high mass, low momentum, and sphericity to the central
+part," and they suggest a possible oblique collision of a small nebula
+with the outer parts of a large one.
+
+232. BODE'S LAW.--We should not leave the theory of Laplace without
+noting the light it casts upon one point otherwise obscure--the meaning
+of Bode's law (Ā§ 134). This law, stated in mathematical form, makes a
+geometrical series, and similar geometrical series apply to the
+distances of the satellites of Jupiter and Saturn from these planets.
+Now, Roche has shown by the application of physical laws to the
+shrinkage of a gaseous body that its radius at any time may be expressed
+by means of a certain mathematical formula very similar to Bode's law,
+save that it involves the amount of time that has elapsed since the
+beginning of the shrinking process. By comparing this formula with the
+one corresponding to Bode's law he reaches the conclusion that the
+peculiar spacing of the planets expressed by that law means that they
+were formed at successive _equal_ intervals of time--i. e., that Mars is
+as much older than the earth as the earth is older than Venus, etc. The
+failure of Bode's law in the case of Neptune would then imply that the
+interval of time between the formation of Neptune and Uranus was shorter
+than that which has prevailed for the other planets. But too much
+stress should not be placed upon this conclusion. So long as the manner
+in which the planets came into being continues an open question,
+conclusions about their time of birth must remain of doubtful validity.
+
+233. TIDAL FRICTION BETWEEN EARTH AND MOON.--An important addition to
+theories of development within the solar system has been worked out by
+Prof. G. H. Darwin, who, starting with certain very simple assumptions
+as to the present condition of things in earth and moon, derives from
+these, by a strict process of mathematical reasoning, far-reaching
+conclusions of great interest and importance. The key to these
+conclusions lies in recognition of the fact that through the influence
+of the tides (Ā§ 42) there is now in progress and has been in progress
+for a very long time, a gradual transfer of motion (moment of momentum)
+from the earth to the moon. The earth's motion of rotation is being
+slowly destroyed by the friction of the tides, as the motion of a
+bicycle is destroyed by the friction of a brake, and, in consequence of
+this slowing down, the moon is pushed farther and farther away from the
+earth, so that it now moves in a larger orbit than it had some millions
+of years ago.
+
+Fig. 24 has been used to illustrate the action of the moon in raising
+tides upon the earth, but in accordance with the third law of motion
+(Ā§ 36) this action must be accompanied by an equal and contrary reaction
+whose nature may readily be seen from the same figure. The moon moves
+about its orbit from west to east and the earth rotates about its axis
+in the same direction, as shown by the curved arrow in the figure. The
+tidal wave, _I_, therefore points a little _in advance_ of the moon's
+position in its orbit and by its attraction must tend to pull the moon
+ahead in its orbital motion a little faster than it would move if the
+whole substance of the earth were placed inside the sphere represented
+by the broken circle in the figure. It is true that the tidal wave at
+_IĀ“Ā“_ pulls back and tends to neutralize the effect of the wave at _I_,
+but on the whole the tidal wave nearer the moon has the stronger
+influence, and the moon on the whole moves a very little faster, and by
+virtue of this added impetus draws continually a little farther away
+from the earth than it would if there were no tides.
+
+234. CONSEQUENCES OF TIDAL FRICTION UPON THE EARTH.--This process of
+moving the moon away from the earth is a cumulative one, going on
+century after century, and with reference to it the moon's orbit must be
+described not as a circle or ellipse, or any other curve which returns
+into itself, but as a spiral, like the balance spring of a watch, each
+of whose coils is a little larger than the preceding one, although this
+excess is, to be sure, very small, because the tides themselves are
+small and the tidal influence feeble when compared with the whole
+attraction of the earth for the moon. But, given time enough, even this
+small force may accomplish great results, and something like 100,000,000
+years of past opportunity would have sufficed for the tidal forces to
+move the moon from close proximity with the earth out to its present
+position.
+
+For millions of years to come, if moon and earth endure so long, the
+distance between them must go on increasing, although at an ever slower
+rate, since the farther away the moon goes the smaller will be the tides
+and the slower the working out of their results. On the other hand, when
+the moon was nearer the earth than now, tidal influences must have been
+greater and their effects more rapidly produced than at the present
+time, particularly if, as seems probable, at some past epoch the earth
+was hot and plastic like Jupiter and Saturn. Then, instead of tides in
+the water of the sea, such as we now have, the whole substance of the
+earth would respond to the moon's attraction in _bodily tides_ of
+semi-fluid matter not only higher, but with greater internal friction of
+their molecules one upon another, and correspondingly greater effect in
+checking the earth's rotation.
+
+But, whether the tide be a bodily one or confined to the waters of the
+sea, so long as the moon causes it to flow there will be a certain
+amount of friction which will affect the earth much as a brake affects a
+revolving wheel, slowing down its motion, and producing thus a longer
+day as well as a longer month on account of the moon's increased
+distance. Slowing down the earth's rotation is the direct action of the
+moon upon the earth. Pushing the moon away is the form in which the
+earth's equal and contrary reaction manifests itself.
+
+235. CONSEQUENCES OF TIDAL FRICTION UPON THE MOON.--When the moon was
+plastic the earth must have raised in it a bodily tide manifold greater
+than the lunar tides upon the earth, and, as we have seen in Chapter IX,
+this tide has long since worn out the greater part of the moon's
+rotation and brought our satellite to the condition in which it presents
+always the same face toward the earth.
+
+These two processes, slowing down the rotation and pushing away the
+disturbing body, are inseparable--one requires the other; and it is
+worth noting in this connection that when for any reason the tide ceases
+to flow, and the tidal wave takes up a permanent position, as it has in
+the moon (Ā§ 99), its work is ended, for when there is no motion of the
+wave there can be no friction to further reduce the rate of rotation of
+the one body, and no reaction to that friction to push away the other.
+But this permanent and stationary tidal wave in the moon, or elsewhere,
+means that the satellite presents always the same face toward its
+planet, moving once about its orbit in the time required for one
+revolution upon its axis, and the tide raised by the moon upon the earth
+tends to produce here the result long since achieved in our satellite,
+to make our day and month of equal length, and to make the earth turn
+always the same side toward the moon. But the moon's tidal force is
+small compared with that of the earth, and has a vastly greater momentum
+to overcome, so that its work upon the earth is not yet complete.
+According to Thomson and Tait, the moon must be pushed off another
+hundred thousand miles, and the day lengthened out by tidal influence to
+seven of our present weeks before the day and the lunar month are made
+of equal length, and the moon thereby permanently hidden from one
+hemisphere of the earth.
+
+236. THE EARTH-MOON SYSTEM.--Retracing into the past the course of
+development of the earth and moon, it is possible to reach back by means
+of the mathematical theory of tidal friction to a time at which these
+bodies were much nearer to each other than now, but it has not been
+found possible to trace out the mode of their separation from one body
+into two, as is supposed in the nebular theory. In the earliest part of
+their history accessible to mathematical analysis they are distinct
+bodies at some considerable distance from each other, with the earth
+rotating about an axis more nearly perpendicular to the moon's orbit and
+to the ecliptic than is now the case. Starting from such a condition,
+the lunar tides, according to Darwin, have been instrumental in tipping
+the earth's rotation axis into its present oblique position, and in
+determining the eccentricity of the moon's orbit and its position with
+respect to the ecliptic as well as the present length of day and month.
+
+337. TIDAL FRICTION UPON THE PLANETS.--The satellites of the outer
+planets are equally subject to influences of this kind, and there
+appears to be independent evidence that some of them, at least, turn
+always the same face toward their respective planets, indicating that
+the work of tidal friction has here been accomplished. We saw in Chapter
+XI that it is at present an open question whether the inner planets,
+Venus and Mercury, do not always turn the same face toward the sun,
+their day and year being of equal length. In addition to the direct
+observational evidence upon this point, Schiaparelli has sought to show
+by an appeal to tidal theory that such is probably the case, at least
+for Mercury, since the tidal forces which tend to bring about this
+result in that planet are about as great as the forces which have
+certainly produced it in the case of the moon and Saturn's satellite,
+Japetus. The same line of reasoning would show that every satellite in
+the solar system, save possibly the newly discovered ninth satellite of
+Saturn, must, as a consequence of tidal friction, turn always the same
+face toward its planet.
+
+238. THE SOLAR TIDE.--The sun also raises tides in the earth, and their
+influence must be similar in character to that of the lunar tides,
+checking the rotation of the earth and thrusting earth and sun apart,
+although quantitatively these effects are small compared with those of
+the moon. They must, however, continue so long as the solar tide lasts,
+possibly until the day and year are made of equal length--i. e., they
+may continue long after the lunar tidal influence has ceased to push
+earth and moon apart. Should this be the case, a curious inverse effect
+will be produced. The day being then longer than the month, the moon
+will again raise a tide in the earth which will run around it _from west
+to east_, opposite to the course of the present tide, thus tending to
+accelerate the earth's rotation, and by its reaction to bring the moon
+back toward the earth again, and ultimately to fall upon it.
+
+We may note that an effect of this kind must be in progress now between
+Mars and its inner satellite, Phobos, whose time of orbital revolution
+is only one third of a Martian day. It seems probable that this
+satellite is in the last stages of its existence as an independent body,
+and must ultimately fall into Mars.
+
+239. ROCHE'S LIMIT.--In looking forward to such a catastrophe, however,
+due regard must be paid to a dynamical principle of a different
+character. The moon can never be precipitated upon the earth entire,
+since before it reaches us it will have been torn asunder by the excess
+of the earth's attraction for the near side of its satellite over that
+which it exerts upon the far side. As the result of Roche's mathematical
+analysis we are able to assign a limiting distance between any planet
+and its satellite within which the satellite, if it turns always the
+same face toward the planet, can not come without being broken into
+fragments. If we represent the radius of the planet by _r_, and the
+quotient obtained by dividing the density of the planet by the density
+of the satellite by _q_, then
+
+    Roche's limit = 2.44 r āˆ›q.
+
+Thus in the case of earth and moon we find from the densities given in
+Ā§ 95, _q_ = 1.65, and with _r_ = 3,963 miles we obtain 11,400 miles as
+the nearest approach which the moon could make to the earth without
+being broken up by the difference of the earth's attractions for its
+opposite sides.
+
+We must observe, however, that Roche's limit takes no account of
+molecular forces, the adhesion of one molecule to another, by virtue of
+which a stick or stone resists fracture, but is concerned only with the
+gravitative forces by which the molecules are attracted toward the
+moon's center and toward the earth. Within a stone or rock of moderate
+size these gravitative forces are insignificant, and cohesion is the
+chief factor in preserving its integrity, but in a large body like the
+moon, the case is just reversed, cohesion plays a small part and
+gravitation a large one in holding the body together. We may conclude,
+therefore, that at a proper distance these forces are capable of
+breaking up the moon, or any other large body, into fragments of a size
+such that molecular cohesion instead of gravitation is the chief agent
+in preserving them from further disintegration.
+
+240. SATURN'S RINGS.--Saturn's rings are of peculiar interest in this
+connection. The outer edge of the ring system lies just inside of
+Roche's limit for this planet, and we have already seen that the rings
+are composed of small fragments independent of each other. Whatever may
+have been the process by which the nine satellites of Saturn came into
+existence, we have in Roche's limit the explanation why the material of
+the ring was not worked up into satellites; the forces exerted by Saturn
+would tear into pieces any considerable satellite thus formed and
+equally would prevent the formation of one from raw material.
+
+Saturn's rings present the only case within the solar system where
+matter is known to be revolving about a planet at a distance less than
+Roche's limit, and it is an interesting question whether these rings can
+remain as a permanent part of the planet's system or are only a
+temporary feature. The drawings of Saturn made two centuries ago agree
+among themselves in representing the rings as larger than they now
+appear, and there is some reason to suppose that as a consequence of
+mutual disturbances--collisions--their momentum is being slowly wasted
+so that ultimately they must be precipitated into the planet. But the
+direct evidence of such a progress that can be drawn from present data
+is too scanty to justify positive conclusions in the matter. On the
+other hand, Nolan suggests that in the outer parts of the ring small
+satellites might be formed whose tidal influence upon Saturn would
+suffice to push them away from the ring beyond Roche's limit, and that
+the very small inner satellites of Saturn may have been thus formed at
+the expense of the ring.
+
+The inner satellite of Mars is very close to Roche's limit for that
+planet, and, as we have seen above, must be approaching still nearer to
+the danger line.
+
+241. THE MOON'S DEVELOPMENT.--The fine series of photographs of the moon
+obtained within the last few years at Paris, have been used by the
+astronomers of that observatory for a minute study of the lunar
+formations, much as geologists study the surface of the earth to
+determine something about the manner in which it was formed. Their
+conclusions are, in general, that at some past time the moon was a hot
+and fluid body which, as it cooled and condensed, formed a solid crust
+whose further shrinkage compressed the liquid nucleus and led to a long
+series of fractures in the crust and outbursts of liquid matter, whose
+latest and feeblest stages produced the lunar craters, while traces of
+the earlier ones, connected with a general settling of the crust,
+although nearly obliterated, are still preserved in certain large but
+vague features of the lunar topography, such as the distribution of the
+seas, etc. They find also in certain markings of the surface what they
+consider convincing evidence of the existence in past times of a lunar
+atmosphere. But this seems doubtful, since the force of gravity at the
+moon's surface is so small that an atmosphere similar to that of the
+earth, even though placed upon the moon, could not permanently endure,
+but would be lost by the gradual escape of its molecules into the
+surrounding space.
+
+The molecules of a gas are quite independent one of another, and are in
+a state of ceaseless agitation, each one darting to and fro, colliding
+with its neighbors or with whatever else opposes its forward motion, and
+traveling with velocities which, on the average, amount to a good many
+hundreds of feet per second, although in the case of any individual
+molecule they may be much less or much greater than the average value,
+an occasional molecule having possibly a velocity several times as great
+as the average. In the upper regions of our own atmosphere, if one of
+these swiftly moving particles of oxygen or nitrogen were headed away
+from the earth with a velocity of seven miles per second, the whole
+attractive power of the earth would be insufficient to check its motion,
+and it would therefore, unless stopped by some collision, escape from
+the earth and return no more. But, since this velocity of seven miles
+per second is more than thirty times as great as the average velocity of
+the molecules of air, it must be very seldom indeed that one is found to
+move so swiftly, and the loss of the earth's atmosphere by leakage of
+this sort is insignificant. But upon the moon, or any other body where
+the force of gravity is small, conditions are quite different, and in
+our satellite a velocity of little more than one mile per second would
+suffice to carry a molecule away from the outer limits of its
+atmosphere. This velocity, only five times the average, would be
+frequently attained, particularly in former times when the moon's
+temperature was high, for then the average velocity of all the molecules
+would be considerably increased, and the amount of leakage might become,
+and probably would become, a serious matter, steadily depleting the
+moon's atmosphere and leading finally to its present state of
+exhaustion. It is possible that the moon may at one time have had an
+atmosphere, but if so it could have been only a temporary possession,
+and the same line of reasoning may be applied to the asteroids and to
+most of the satellites of the solar system, and also, though in less
+degree, to the smaller planets, Mercury and Mars.
+
+242. STELLAR DEVELOPMENT.--We have already considered in this chapter
+the line of development followed by one star, the sun, and treating this
+as a typical case, it is commonly believed that the life history of a
+star, in so far as it lies within our reach, begins with a condition in
+which its matter is widely diffused, and presumably at a low
+temperature. Contracting in bulk under the influence of its own
+gravitative forces, the star's temperature rises to a maximum, and then
+falls off in later stages until the body ceases to shine and passes over
+to the list of dark stars whose existence can only be detected in
+exceptional cases, such as are noted in Chapter XIII. The most
+systematic development of this idea is due to Lockyer, who looks upon
+all the celestial bodies--sun, moon and planets, stars, nebulƦ, and
+comets--as being only collections of meteoric matter in different stages
+of development, and who has sought by means of their spectra to classify
+these bodies and to determine their stage of advancement. While the
+fundamental ideas involved in this "meteoritic hypothesis" are not
+seriously controverted, the detailed application of its principles is
+open to more question, and for the most part those astronomers who hold
+that in the present state of knowledge stellar spectra furnish a key to
+a star's age or degree of advancement do not venture beyond broad
+general statements.
+
+[Illustration: FIG. 151.--Types of stellar spectra substantially
+according to SECCHI.]
+
+243. STELLAR SPECTRA.--Thus the types of stellar spectra shown in Fig.
+151 are supposed to illustrate successive stages in the development of
+an average star. Type I corresponds to the period in which its
+temperature is near the maximum; Type II belongs to a later stage in
+which the temperature has commenced to fall; and Type III to the period
+immediately preceding extinction.
+
+While human life, or even the duration of the human race, is too short
+to permit a single star to be followed through all the stages of its
+career, an adequate picture of that development might be obtained by
+examining many stars, each at a different stage of progress, and,
+following this idea, numerous subdivisions of the types of stellar
+spectra shown in Fig. 151 have been proposed in order to represent with
+more detail the process of stellar growth and decay; but for the most
+part these subdivisions and their interpretation are accepted by
+astronomers with much reserve.
+
+It is significant that there are comparatively few stars with spectra of
+Type III, for this is what we should expect to find if the development
+of a star through the last stages of its visible career occupied but a
+small fraction of its total life. From the same point of view the great
+number of stars with spectra of the first type would point to a long
+duration of this stage of life. The period in which the sun belongs,
+represented by Type II, probably has a duration intermediate between the
+others. Since most of the variable stars, save those of the Algol class,
+have spectra of the third type, we conclude that variability, with its
+associated ruddy color and great atmospheric absorption of light, is a
+sign of old age and approaching extinction. The Algol or eclipse
+variables, on the other hand, having spectra of the first type, are
+comparatively young stars, and, as we shall see a little later, the
+shortness of their light periods in some measure confirms this
+conclusion drawn from their spectra.
+
+We have noted in Ā§ 196 that the sun's near neighbors are prevailingly
+stars with spectra of the second type, while the Milky Way is mainly
+composed of first-type stars, and from this we may now conclude that in
+our particular part of the entire celestial space the stars are, as a
+rule, somewhat further developed than is the case elsewhere.
+
+244. DOUBLE STARS.--The double stars present special problems of
+development growing out of the effects of tidal friction, which must
+operate in them much as it does between earth and moon, tending steadily
+to increase the distance between the components of such a star. So, too,
+in such a system as is shown in Fig. 132, gravity must tend to make each
+component of the double star shrink to smaller dimensions, and this
+shrinkage must result in faster rotation and increased tidal friction,
+which in turn must push the components apart, so that in view of the
+small density and close proximity of those particular stars we may
+fairly regard a star like Ī² LyrƦ as in the early stages of its
+career and destined with increasing age to lose its variability of
+light, since the eclipses which now take place must cease with
+increasing distance between the components unless the orbit is turned
+exactly edgewise toward the earth. Close proximity and the resulting
+shortness of periodic time in a double star seem, therefore, to be
+evidence of its youth, and since this shortness of periodic time is
+characteristic of both Algol variables and spectroscopic binaries as a
+class, we may set them down as being, upon the whole, stars in the early
+stages of their career. On the other hand, it is generally true that the
+larger the orbit, and the greater the periodic time in the orbit, the
+farther is the star advanced in its development.
+
+In his theory of tidal friction, Darwin has pointed out that whenever
+the periodic time in the orbit is more than twice as long as the time
+required for rotation about the axis, the effect of the tides is to
+increase the eccentricity of the orbit, and, following this indication,
+See has urged that with increasing distance between the components of a
+double star their orbits about the common center of gravity must grow
+more and more eccentric, so that we have in the shape of such orbits a
+new index of stellar development; the more eccentric the orbit, the
+farther advanced are the stars. It is important to note in this
+connection that among the double stars whose orbits have been computed
+there seems to run a general rule--the larger the orbit the greater is
+its eccentricity--a relation which must hold true if tidal friction
+operates as above supposed, and which, being found to hold true,
+confirms in some degree the criteria of stellar age which are furnished
+by the theory of tidal friction.
+
+245. NEBULƆ.--The nebular hypothesis of Laplace has inclined astronomers
+to look upon nebulƦ in general as material destined to be worked up into
+stars, but which is now in a very crude and undeveloped stage. Their
+great bulk and small density seem also to indicate that gravitation has
+not yet produced in them results at all comparable with what we see in
+sun and stars. But even among nebulƦ there are to be found very
+different stages of development. The irregular nebula, shapeless and
+void like that of Orion; the spiral, ring, and planetary nebulƦ and the
+star cluster, clearly differ in amount of progress toward their final
+goal. But it is by no means sure that these several types are different
+stages in one line of development; for example, the primitive nebula
+which grows into a spiral may never become a ring or planetary nebula,
+and _vice versa_. So too there is no reason to suppose that a star
+cluster will ever break up into isolated stars such as those whose
+relation to each other is shown in Fig. 122.
+
+246. CLASSIFICATION.--Considering the heavenly bodies with respect to
+their stage of development, and arranging them in due order, we should
+probably find lowest down in the scale of progress the irregular nebulƦ
+of chaotic appearance such as that represented in Fig. 146. Above these
+in point of development stand the spiral, ring, and planetary nebulƦ,
+although the exact sequence in which they should be arranged remains a
+matter of doubt. Still higher up in the scale are star clusters whose
+individual members, as well as isolated stars, are to be classified by
+means of their spectra, as shown in Fig. 151, where the order of
+development of each star is probably from Type I, through II, into III
+and beyond, to extinction of its light and the cutting off of most of
+its radiant energy. Jupiter and Saturn are to be regarded as stars which
+have recently entered this dark stage. The earth is further developed
+than these, but it is not so far along as are Mars and Mercury; while
+the moon is to be looked upon as the most advanced heavenly body
+accessible to our research, having reached a state of decrepitude which
+may almost be called death--a stage typical of that toward which all the
+others are moving.
+
+Meteors and comets are to be regarded as fragments of celestial matter,
+chips, too small to achieve by themselves much progress along the normal
+lines of development, but destined sooner or later, by collision with
+some larger body, to share thenceforth in its fortunes.
+
+247. STABILITY OF THE UNIVERSE.--It was considered a great achievement
+in the mathematical astronomy of a century ago when Laplace showed that
+the mutual attractions of sun and planets might indeed produce endless
+perturbations in the motions and positions of these bodies, but could
+never bring about collisions among them or greatly alter their existing
+orbits. But in the proof of this great theorem two influences were
+neglected, either of which is fatal to its validity. One of these--tidal
+friction--as we have already seen, tends to wreck the systems of
+satellites, and the same effect must be produced upon the planets by any
+other influence which tends to impede their orbital motion. It is the
+inertia of the planet in its forward movement that balances the sun's
+attraction, and any diminution of the planet's velocity will give this
+attraction the upper hand and must ultimately precipitate the planet
+into the sun. The meteoric matter with which the earth comes ceaselessly
+into collision must have just this influence, although its effects are
+very small, and something of the same kind may come from the medium
+which transmits radiant energy through the interstellar spaces.
+
+It seems incredible that the luminiferous ether, which is supposed to
+pervade all space, should present absolutely no resistance to the motion
+of stars and planets rushing through it with velocities which in many
+cases exceed 50,000 miles per hour. If there is a resistance to this
+motion, however small, we may extend to the whole visible universe the
+words of Thomson and Tait, who say in their great Treatise on Natural
+Philosophy, "We have no data in the present state of science for
+estimating the relative importance of tidal friction and of the
+resistance of the resisting medium through which the earth and moon
+move; but, whatever it may be, there can be but one ultimate result for
+such a system as that of the sun and planets, if continuing long enough
+under existing laws and not disturbed by meeting with other moving
+masses in space. That result is the falling together of all into one
+mass, which, although rotating for a time, must in the end come to rest
+relatively to the surrounding medium."
+
+Compare with this the words of a great poet who in The Tempest puts into
+the mouth of Prospero the lines:
+
+    "The cloud-capp'd towers, the gorgeous palaces,
+    The solemn temples, the great globe itself,
+    Yea, all which it inherit, shall dissolve;
+    And, like this insubstantial pageant faded,
+    Leave not a rack behind."
+
+248. THE FUTURE.--In spite of statements like these, it lies beyond the
+scope of scientific research to affirm that the visible order of things
+will ever come to naught, and the outcome of present tendencies, as
+sketched above, may be profoundly modified in ages to come, by
+influences of which we are now ignorant. We have already noted that the
+farther our speculation extends into either past or future, the more
+insecure are its conclusions, and the remoter consequences of present
+laws are to be accepted with a corresponding reserve. But the one great
+fact which stands out clear in this connection is that of _change_. The
+old concept of a universe created in finished form and destined so to
+abide until its final dissolution, has passed away from scientific
+thought and is replaced by the idea of slow development. A universe
+which is ever becoming something else and is never finished, as shadowed
+forth by Goethe in the lines:
+
+    "Thus work I at the roaring loom of Time,
+    And weave for Deity a living robe sublime."
+
+
+
+
+APPENDIX
+
+
+THE GREEK ALPHABET
+
+The Greek letters are so much used by astronomers in connection with the
+names of the stars, and for other purposes, that the Greek alphabet is
+printed below--not necessarily to be learned, but for convenient
+reference:
+
+    Greek.          Name.  English.
+
+    Ī‘  Ī±            Alpha    a
+    Ī’  Ī²            Beta     b
+    Ī“  Ī³            Gamma    g
+    Ī”  Ī“            Delta    d
+    Ī•  Īµ or Ļµ       Epsilon  ĕ
+    Ī–  Ī¶            Zeta     z
+    Ī—  Ī·            Eta      ē
+    Ī˜  Ļ‘ or Īø       Theta     th
+    Ī™  Ī¹            Iota      i
+    Īš  Īŗ            Kappa     k
+    Ī›  Ī»            Lambda    l
+    Īœ  Ī¼            Mu        m
+    Ī  Ī½            Nu        n
+    Īž  Ī¾            Xi        x
+    ĪŸ  Īæ            Omicron   ŏ
+    Ī   Ļ€            Pi        p
+    Ī”  Ļ            Rho       r
+    Ī£  Ļƒ or Ļ‚       Sigma     s
+    Ī¤  Ļ„            Tau       t
+    Ī„  Ļ…            Upsilon   u
+    Ī¦  Ļ†            Phi       ph
+    Ī§  Ļ‡            Chi       ch
+    ĪØ  Ļˆ            Psi       ps
+    Ī©  Ļ‰            Omega     ō
+
+
+POPULAR LITERATURE OF ASTRONOMY
+
+The following brief bibliography, while making no pretense at
+completeness, may serve as a useful guide to supplementary reading:
+
+_General Treatises_
+
+    YOUNG. _General Astronomy._ An admirable general survey of the
+    entire field.
+
+    NEWCOMB. _Popular Astronomy._ The second edition of a German
+    translation of this work by Engelmann and Vogel is especially
+    valuable.
+
+    BALL. _Story of the Heavens._ Somewhat easier reading than
+    either of the preceding.
+
+    CHAMBERS. _Descriptive Astronomy._ An elaborate but elementary
+    work in three volumes.
+
+    LANGLEY. _The New Astronomy._ Treats mainly of the physical
+    condition of the celestial bodies.
+
+    PROCTOR and RANYARD. _Old and New Astronomy._
+
+_Special Treatises_
+
+    PROCTOR. _The Moon._ A general treatment of the subject.
+
+    NASMYTH and CARPENTER. _The Moon._ An admirably illustrated but
+    expensive work dealing mainly with the topography and physical
+    conditions of the moon. There is a cheaper and very good edition
+    in German.
+
+    YOUNG. _The Sun._ International Scientific Series. The most
+    recent and authoritative treatise on this subject.
+
+    PROCTOR. _Other Worlds than Ours._ An account of planets,
+    comets, etc.
+
+    NEWTON. _Meteor._ EncyclopƦdia Britannica.
+
+    AIRY. _Gravitation._ A non-mathematical exposition of the laws
+    of planetary motion.
+
+    STOKES. _On Light as a Means of Investigation._ Burnett
+    Lectures. II. The basis of spectrum analysis.
+
+    SCHELLEN. _Spectrum Analysis._
+
+    THOMSON (Sir W., Lord KELVIN), _Popular Lectures, etc._ Lectures
+    on the Tides, The Sun's Heat, etc.
+
+    BALL. _Time and Tide._ An exposition of the researches of G. H.
+    Darwin upon tidal friction.
+
+    GORE. _The Visible Universe._ Deals with a class of problems
+    inadequately treated in most popular astronomies.
+
+    DARWIN. _The Tides._ An admirable elementary exposition.
+
+    CLERKE. _The System of the Stars._ Stellar astronomy.
+
+    NEWCOMB. Chapters on the Stars, in _Popular Science Monthly_ for
+    1900.
+
+    CLERKE. _History of Astronomy during the Nineteenth Century._ An
+    admirable work.
+
+    WOLF. _Geschichte der Astronomie._ MĆ¼nchen, 1877. An excellent
+    German work.
+
+
+A LIST OF STARS FOR TIME OBSERVATIONS
+
+See Ā§ 20.
+
+ ----------------+---------------+------------------+-------------+
+ NAME.           |  Magnitude.   | Right Ascension. | Declination.|
+ ----------------+---------------+------------------+-------------+
+                 |               |                  |             |
+                 |               |     h. m.        |      Ā°      |
+ Ī² Ceti          |       2       |     0 38.6       |    - 18.5   |
+ Ī· Ceti          |       3       |     1  3.6       |    - 10.7   |
+ Ī± Ceti          |       3       |     2 57.1       |    +  3.7   |
+ Ī³ Eridani       |       3       |     3 53.4       |    - 13.8   |
+ _Aldebaran_     |       1       |     4 30.2       |    + 16.3   |
+                 |               |                  |             |
+ _Rigel_         |       0       |     5  9.7       |    -  8.3   |
+ Īŗ Orionis       |       2       |     5 43.0       |    -  9.7   |
+ Ī² Canis Majoris |       2       |     6 18.3       |    - 17.9   |
+ _Sirius_        |      -1       |     6 40.7       |    - 16.6   |
+ _Procyon_       |       0       |     7 34.1       |    +  5.5   |
+                 |               |                  |             |
+ Ī± HydrƦ         |       2       |     9 22.7       |    -  8.2   |
+ _Regulus_       |       1       |    10  3.0       |    + 12.5   |
+ Ī½ HydrƦ         |       3       |    10 44.7       |    - 15.7   |
+ Īµ Corvi         |       3       |    12  5.0       |    - 22.1   |
+ Ī³ Corvi         |       3       |    12 10.7       |    - 17.0   |
+                 |               |                  |             |
+ _Spica_         |       1       |    13 19.9       |    - 10.6   |
+ Ī¶ Virginis      |       3       |    13 29.6       |    -  0.1   |
+ Ī± LibrƦ         |       3       |    14 45.3       |    - 15.6   |
+ Ī² LibrƦ         |       3       |    15 11.6       |    -  9.0   |
+ _Antares_       |       1       |    16 23.3       |    - 26.2   |
+                 |               |                  |             |
+ Ī± Ophiuchi      |       2       |    17 30.3       |    + 12.6   |
+ Īµ Sagittarii    |       2       |    18 17.5       |    - 34.4   |
+ Ī“ AquilƦ        |       3       |    19 20.5       |    +  2.9   |
+ _Altair_        |       1       |    19 45.9       |    +  8.6   |
+ Ī² Aquarii       |       3       |    21 26.3       |    -  6.0   |
+                 |               |                  |             |
+ Ī± Aquarii       |       3       |    22  0.6       |    -  0.8   |
+ _Fomalhaut_     |       1       |    22 52.1       |    - 30.2   |
+ ----------------+---------------+------------------+-------------+
+
+
+
+
+INDEX
+
+
+The references are to section numbers.
+
+
+  Absorption of starlight, 225.
+
+  Absorption spectra, 87.
+
+  Accelerating force, 35.
+
+  Adjustment of observations, 2.
+
+  Albedo of moon, 97.
+    of Venus, 148.
+
+  Algol, 205.
+
+  Altitudes, 4, 21.
+
+  Andromeda nebula, 214.
+
+  Angles, measurement of, 2.
+
+  Angular diameter, 7.
+
+  Annular eclipse, 64.
+
+  Asteroids, 156.
+
+  Atmosphere of the earth, 49.
+    of the moon, 103.
+    of Jupiter, 139.
+    of Mars, 153.
+
+  Aurora, 51.
+
+  Azimuth, 5, 21.
+
+
+  Biela's comet, 181.
+
+  Bode's law, 134, 232.
+
+  Bredichin's theory of comet tails, 180.
+
+
+  Calendar, O. S. and N. S., 61.
+
+  Capture of comets and meteors, 176.
+
+  Canals of Mars, 154.
+
+  Celestial mechanics, 32.
+
+  Changes upon the moon, 108.
+
+  Chemical constitution of sun, 116.
+    of stars, 210.
+
+  Chromosphere, the sun's, 124.
+
+  Chronology, 59.
+
+  Classification of stars, 212.
+
+  Clocks and watches, 74.
+    sidereal clock, 12.
+
+  Collisions with comets, 183.
+
+  Colors of stars, 209.
+
+  Comets, general characteristics, 158-164.
+    development of, 179, 181.
+    groups, 177.
+    orbits, 161.
+    periodic, 176.
+    spectra, 182.
+    tails, 180.
+
+  Comets and meteors, relation of, 175.
+
+  Conic sections, 38.
+
+  Constellations, 184.
+
+  Corona, the sun's, 123.
+
+  Craters, lunar, 105.
+
+
+  Dark stars, 201.
+
+  Day, 52, 62.
+
+  Declination, 21.
+
+  Development of comet, 179.
+    of moon, 241.
+    of nebulƦ, 245.
+    of stars, 242, 244.
+    of sun, 228.
+  of universe, 226.
+
+  Distribution of stars and nebulƦ, 220.
+
+  Diurnal motion, 10, 15.
+
+  Doppler principle, 89.
+
+  Double nebulƦ, 215.
+
+  Double stars, 198.
+    development of, 244.
+
+  Driving clock, 80.
+
+
+  Earth, atmosphere, 48.
+    mass, 45.
+    size and shape, 44.
+    warming of the earth, 47.
+
+  Eclipses, nature of, 63.
+    annular eclipse, 64.
+    eclipse limits, 68.
+    eclipse maps, 70, 71.
+    number of, in a year, 69.
+    partial eclipse, 64.
+    prediction of, 70, 71.
+    recurrence of, 72.
+    shadow cone, 64, 66.
+    total eclipse, 64.
+    uses of, 73.
+
+  Eclipses of Jupiter's satellites, 141.
+
+  Eclipse theory of variable stars, 205.
+
+  Ecliptic, 26.
+    obliquity of, 25.
+
+  Ellipse, 33.
+
+  Epochs for planetary motion, 30.
+
+  Energy, radiant, 75.
+    condensation of, 76.
+
+  Epicycle, 32.
+
+  Equation of time, 53.
+
+  Equator, 16, 21.
+
+  Equatorial mounting, 80.
+
+  Equinoxes, 25.
+
+  Ether, 75.
+
+  Evening star, 31.
+
+
+  FaculƦ, 122.
+
+  Falling bodies, law of, 35.
+
+  Finding the stars, 14.
+
+  Fraunhofer lines, 87.
+
+
+  Galaxy, 219.
+
+  Geography of the sky, 16.
+
+  Graphical representation, 6.
+
+  Grating, diffraction, 84.
+
+  Gravitation, law of, 37.
+
+
+  Harvest moon, 93.
+
+  Heat of the sun, 118, 126.
+
+  Helmholtz, contraction theory of the sun, 126, 228.
+
+  Horizon, 4, 21.
+
+  Hour angle, 21.
+
+  Hour circle, 21.
+
+  Hyperbola, 38.
+
+
+  Japetus, satellite of Saturn, 145.
+
+  Jupiter, 136.
+    atmosphere, 139.
+    belts, 137.
+    invisible from fixed stars, 197.
+    orbit of, 29.
+    physical condition, 139.
+    rotation and flattening, 138.
+    satellites, 140.
+    surface markings, 137.
+
+
+  Kepler's laws, 33, 111.
+
+
+  Latitude, determination of, 18.
+
+  Leap year, 61.
+
+  Lenses, 77.
+
+  Leonid meteor shower, 172.
+    perturbations of, 174.
+
+  Librations of moon, 98.
+
+  Life upon the planets, 157.
+
+  Light curves, 205.
+
+  Light, nature of, 75.
+
+  Light year, 190.
+
+  Limits of eclipses, 68.
+
+  Longitude, 56.
+    determination of, 58.
+
+  Lunation, 60.
+
+
+  Magnifying power of telescope, 79.
+
+  Magnitude, stellar, 9, 186.
+
+  Mars, atmosphere, temperature, 150.
+    canals, 154.
+    orbit, 30.
+    polar caps, 152.
+    rotation, 151.
+    satellites, 155.
+    surface markings, 150.
+
+  Mass, determination of, 37.
+    of comets, 164.
+    of double stars, 200.
+    of moon, 94.
+    of planets, 40, 133.
+
+  Measurements, accurate, 1.
+
+  Mercury, 149.
+    motion of its perihelion, 43.
+    orbit of, 30.
+
+  Meridian, 19, 21.
+
+  Meteors, nature of, 165, 169.
+    number of, 167.
+    velocity, 170.
+
+  Meteors and comets, relation of, 175.
+
+  Meteor showers, radiant, 171.
+    Leonids, capture of, 172, 173.
+    perturbations, 174.
+
+  Milky Way, 219.
+
+  Mira, Īæ Ceti, 204.
+
+  Mirrors, 77.
+
+  Month, 60.
+
+  Moon, 91.
+    albedo, 97.
+    atmosphere, 103.
+    changes in, 108.
+    density, surface gravity, 95.
+    development of, 241.
+    harvest moon, 93.
+    influence upon the earth, 109, 233.
+    librations, 98.
+    map of, 101.
+    mass and size, 94.
+    motion, 24, 92.
+    mountains and craters, 104.
+    phases, 91, 92.
+    physical condition, 100, 107.
+
+  Month, 60.
+
+  Morning star, 31.
+
+  Motion in line of sight, 89, 193.
+
+  Multiple stars, 202.
+
+
+  Names of stars, 8.
+
+  NebulƦ, 214.
+    density, 217.
+    development of, 245.
+    motion, 218.
+    spectra, 216.
+    types and classes of, 215.
+
+  Nebular hypothesis, 230.
+    objections to, 231.
+
+  Neptune, 146.
+    discovery of, 41.
+
+  Newton's laws of motion, 34.
+    law of gravitation, 37, 43.
+
+  Nodes, 39.
+    relation to eclipses, 67, 71.
+
+  Nucleus, of comet, 160.
+
+
+  Objective, of telescope, 78.
+
+  Obliquity of ecliptic, 25.
+
+  Observations, of stars, 10.
+
+  Occultation of stars, 103.
+
+  Orbits, of comets, 161.
+    of double stars, 199.
+    of moon, 92.
+    of planets, 28.
+
+  Orion nebula, 215.
+
+
+  Parabola, 35, 38, 161.
+
+  Parabolic velocity, 38.
+
+  Parallax, 114, 188.
+
+  Penumbra, 64, 121.
+
+  Perihelion, 38.
+
+  Periodic comets, 176.
+
+  Personal equation, 82.
+
+  Perturbations, 39.
+    of meteors, 174.
+
+  Phases, of the moon, 91, 92.
+
+  Photography, 81.
+    of stars, 13.
+
+  Photosphere, of sun, 121.
+
+  Planets, 26, 133.
+    distances from the sun, 134.
+    how to find, 29.
+    mass, density, size, 133.
+    motion of, 27, 38.
+    periodic times of, 30.
+
+  Planetary nebulƦ, 215.
+
+  Pleiades, 16, 215.
+
+  Plumb-line apparatus, 11, 18.
+
+  Poles, 21.
+
+  Precession, 46.
+
+  Prisms, 84.
+
+  Problem of three bodies, 39.
+
+  Prominences, solar, 125.
+
+  Proper motions, 191.
+
+  Protractor, 2.
+
+  Ptolemaic system, 32.
+
+
+  Radiant energy, 75.
+
+  Radiant, of meteor shower, 171.
+
+  Radius victor, 33.
+
+  Reference lines and circles, 17.
+
+  Refraction, 50.
+
+  Right ascension, 16, 20, 21.
+
+  Roche's limit, 239.
+
+  Rotation, of earth, 55.
+    of Mars, 151.
+    of moon, 99.
+    of Jupiter, 138.
+    of Saturn, 144.
+    of sun, 120, 132.
+
+
+  Saros, 72.
+
+  Satellites, of Jupiter, 136, 140.
+    of Mars, 155.
+    of Saturn, 145.
+
+  Saturn, 142.
+    ball of, 144.
+    orbit, 29.
+    rings, 142.
+    rotation, 144.
+    satellites, 145.
+
+  Seasons, on the earth, 47.
+    on Mars, 151.
+
+  Shadow cone, 64, 66.
+
+  Sidereal time, 20, 54.
+
+  Shooting stars, 158. (See Meteor.)
+
+  Spectroscope, 84.
+
+  Spectroscopic binaries, 203.
+
+  Spectrum, 84, 87.
+    of comets, 182.
+    of nebulƦ, 216.
+    of stars, 211.
+    types of, 88.
+
+  Spectrum analysis, 85.
+
+  Spiral nebulƦ, 215.
+
+  Standard time, 57.
+
+  Stars, 8, 184.
+    classes of, 212.
+    clusters, 213.
+    colors, 209.
+    dark stars, 201.
+    development of, 242.
+    distances from the sun, 188, 196.
+    distribution of, 220.
+    double stars, 198, 203.
+    drift, 194.
+    magnitudes, 9, 196.
+    number of, 185.
+    spectra, 211.
+    temporary, 208.
+    variable, 204.
+
+  Starlight, absorption of, 225.
+
+  Star maps, construction of, 23.
+
+  Stellar system, extent of, 223.
+
+  Sun's apparent motion, 25.
+    real motion, 195.
+
+  Sun, 110.
+    chemical composition, 116.
+    chromosphere, 124.
+    corona, 123.
+    distance from the earth, 111.
+    faculƦ, 119, 122.
+    gaseous constitution, 127.
+    heat of, 117.
+    mechanism of, 126.
+    physical properties, 115-120.
+    prominences, 125.
+    rotation, 120, 132.
+    surface of, 119.
+    temperature, 118.
+
+  Sun spots, 119, 121.
+    period, 129, 131.
+    zones, 130.
+
+
+  Telescopes, 78.
+    equatorial mounting for, 80.
+    magnifying power of, 79.
+
+  Temperature of Jupiter, 139.
+    of Mars, 152.
+    of Mercury, 149.
+    of moon, 107.
+    of sun, 118.
+
+  Temporary stars, 208.
+
+  Terminator, 91.
+
+  Tenth meter, 75.
+
+  Tidal friction, 233-238.
+
+  Tides, 42.
+
+  Time, sidereal, 20, 54.
+    solar, 52.
+    determination of, 20.
+    equation of, 53.
+    standard, 57.
+
+  Triangulation, 3.
+
+  Trifid nebula, 215.
+
+  Twilight, 51.
+
+  Twinkling, of stars, 48.
+
+
+  Universe, development of, 226.
+    stability of, 247.
+
+  Uranus, 146.
+
+
+  Variable stars, 204.
+
+  Velocity, its relation to orbital motion, 38.
+
+  Venus, 148.
+    orbit of, 30.
+
+  Vernal equinox, 21, 25.
+
+  Vertical circle, 21.
+
+
+  Wave front, 76.
+
+  Wave lengths, 75, 86.
+
+
+  Year, 25.
+    leap year, 61.
+    sidereal year, 59.
+    tropical year, 60.
+
+
+  Zenith, 21.
+
+  Zodiac, 26.
+
+  Zodiacal light, 168.
+
+
+
+
+THE END
+
+
+
+
+[Illustration: PROTRACTOR TO ACCOMPANY COMSTOCK'S ASTRONOMY]
+
+
+
+
+
+End of Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock
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+<pre>
+
+Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Text-Book of Astronomy
+
+Author: George C. Comstock
+
+Release Date: January 3, 2011 [EBook #34834]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY ***
+
+
+
+
+Produced by Chris Curnow, Iris Schimandle, Lindy Walsh and
+the Online Distributed Proofreading Team at
+http://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+
+
+
+<p class="center">TWENTIETH CENTURY TEXT-BOOKS</p>
+
+
+<p class="center">EDITED BY<br />
+A. F. NIGHTINGALE, <span class="smcap">Ph.D.</span>, LL.D.<br />
+FORMERLY SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO
+</p>
+
+
+<hr style="width: 65%;" />
+
+
+<div class="figcenter" style="width: 500px;"><a name="Frontispiece" id="Frontispiece"></a>
+<a href="images/i005-full.jpg"><img src="images/i005.jpg" width="500" height="329" alt="A TOTAL SOLAR ECLIPSE.
+
+After Burckhalter&#39;s photographs of the eclipse of May 28, 1900." title="A TOTAL SOLAR ECLIPSE.
+
+After Burckhalter&#39;s photographs of the eclipse of May 28, 1900." /></a>
+<span class="caption">A TOTAL SOLAR ECLIPSE.<br />
+
+After Burckhalter&#39;s photographs of the eclipse of May 28, 1900.</span>
+</div>
+
+
+
+<hr style="width: 65%;" />
+
+<p class="center">TWENTIETH CENTURY TEXT-BOOKS</p>
+
+
+
+
+
+<h1>A TEXT-BOOK OF
+ASTRONOMY</h1>
+
+
+<h3>BY</h3>
+<h2>GEORGE C. COMSTOCK</h2>
+
+<p class="center">DIRECTOR OF THE WASHBURN OBSERVATORY AND<br />
+PROFESSOR OF ASTRONOMY IN THE<br />
+UNIVERSITY OF WISCONSIN</p>
+
+
+<div class="figcenter" style="width: 110px;">
+<img src="images/i006.jpg" width="110" height="110" alt="" title="" />
+</div>
+
+
+<p class="center">NEW YORK<br />
+D. APPLETON AND COMPANY<br />
+1903
+</p>
+
+
+<hr style="width: 65%;" />
+<p class="center"><span class="smcap">Copyright</span>, 1901</p>
+
+<p class="center"><span class="smcap">By</span> D. APPLETON AND COMPANY</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum">[Pg v]</span></p>
+<h2>PREFACE</h2>
+
+
+<p>The present work is not a compendium of astronomy
+or an outline course of popular reading in that science. It
+has been prepared as a text-book, and the author has purposely
+omitted from it much matter interesting as well as
+important to a complete view of the science, and has endeavored
+to concentrate attention upon those parts of the
+subject that possess special educational value. From this
+point of view matter which permits of experimental treatment
+with simple apparatus is of peculiar value and is
+given a prominence in the text beyond its just due in a
+well-balanced exposition of the elements of astronomy,
+while topics, such as the results of spectrum analysis,
+which depend upon elaborate apparatus, are in the experimental
+part of the work accorded much less space than
+their intrinsic importance would justify.</p>
+
+<p>Teacher and student are alike urged to magnify the
+observational side of the subject and to strive to obtain in
+their work the maximum degree of precision of which their
+apparatus is capable. The instruments required are few
+and easily obtained. With exception of a watch and a protractor,
+all of the apparatus needed may be built by any
+one of fair mechanical talent who will follow the illustrations
+and descriptions of the text. In order that proper
+opportunity for observations may be had, the study should
+be pursued during the milder portion of the year, between
+April and November in northern latitudes, using clear
+<span class="pagenum">[Pg vi]</span>
+weather for a direct study of the sky and cloudy days for
+book work.</p>
+
+<p>The illustrations contained in the present work are
+worthy of as careful study as is the text, and many of
+them are intended as an aid to experimental work and
+accurate measurement, e.&nbsp;g., the star maps, the diagrams
+of the planetary orbits, pictures of the moon, sun, etc. If
+the school possesses a projection lantern, a set of astronomical
+slides to be used in connection with it may be
+made of great advantage, if the pictures are studied as an
+auxiliary to Nature. Mere display and scenic effect are of
+little value.</p>
+
+<p>A brief bibliography of popular literature upon astronomy
+may be found at the end of this book, and it will be
+well if at least a part of these works can be placed in the
+school library and systematically used for supplementary
+reading. An added interest may be given to the study if
+one or more of the popular periodicals which deal with
+astronomy are taken regularly by the school and kept
+within easy reach of the students. From time to time
+the teacher may well assign topics treated in these periodicals
+to be read by individual students and presented
+to the class in the form of an essay.</p>
+
+<p>The author is under obligations to many of his professional
+friends who have contributed illustrative matter for
+his text, and his thanks are in an especial manner due to
+the editors of the Astrophysical Journal, Astronomy and
+Astrophysics, and Popular Astronomy for permission to
+reproduce here plates which have appeared in those periodicals,
+and to Dr. Charles Boynton, who has kindly read
+and criticised the proofs.</p>
+
+<div style="margin-left: 75%;"><p><span class="smcap">George C. Comstock.</span><br /></p></div>
+
+<div style="margin-left: 2em;"><p><span class="smcap">University of Wisconsin</span>, <i>February, 1901</i>.<span class="pagenum">[Pg vii]</span><br /></p></div>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum">[Pg viii]</span></p>
+<h2>CONTENTS</h2>
+
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">CHAPTER</td><td align="right">PAGE</td></tr>
+<tr><td align="left"><a href="#CHAPTER_I">I.&mdash;<span class="smcap">Different kinds of measurement</span></a></td><td align="right"><a href="#Page_1">1</a></td></tr>
+<tr><td align="left"><div class="indent">The measurement of angles and time.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_II">II.&mdash;<span class="smcap">The stars and their diurnal motion</span></a></td><td align="right"><a href="#Page_10">10</a></td></tr>
+<tr><td align="left"><div class="indent">Finding the stars&mdash;Their apparent motion&mdash;Latitude&mdash;Direction of the meridian&mdash;Sidereal time&mdash;Definitions.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_III">III.&mdash;<span class="smcap">Fixed and wandering stars</span></a></td><td align="right"><a href="#Page_29">29</a></td></tr>
+<tr><td align="left"><div class="indent">Apparent motion of the sun, moon, and planets&mdash;Orbits of the planets&mdash;How to find the planets.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_IV">IV.&mdash;<span class="smcap">Celestial mechanics</span></a></td><td align="right"><a href="#Page_46">46</a></td></tr>
+<tr><td align="left"><div class="indent">Kepler's laws&mdash;Newton's laws of motion&mdash;The law of gravitation&mdash;Orbital motion&mdash;Perturbations&mdash;Masses of the planets&mdash;Discovery of Neptune&mdash;The tides.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_V">V.&mdash;<span class="smcap">The earth as a planet</span></a></td><td align="right"><a href="#Page_70">70</a></td></tr>
+<tr><td align="left"><div class="indent">Size&mdash;Mass&mdash;Precession&mdash;The warming of the earth&mdash;The atmosphere&mdash;Twilight.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_VI">VI.&mdash;<span class="smcap">The measurement of time</span></a></td><td align="right"><a href="#Page_86">86</a></td></tr>
+<tr><td align="left"><div class="indent">Solar and sidereal time&mdash;Longitude&mdash;The calendar&mdash;Chronology.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_VII">VII.&mdash;<span class="smcap">Eclipses</span></a></td><td align="right"><a href="#Page_101">101</a></td></tr>
+<tr><td align="left"><div class="indent">Their cause and nature&mdash;Eclipse limits&mdash;Eclipse maps&mdash;Recurrence and prediction of eclipses.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_VIII">VIII.&mdash;<span class="smcap">Instruments and the principles involved in their use</span></a></td><td align="right"><a href="#Page_121">121</a></td></tr>
+<tr><td align="left"><div class="indent">The clock&mdash;Radiant energy&mdash;Mirrors and lenses&mdash;The telescope&mdash;Camera&mdash;Spectroscope&mdash;Principles of spectrum analysis.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_IX">IX.&mdash;<span class="smcap">The moon</span></a></td><td align="right"><a href="#Page_150">150</a></td></tr>
+<tr><td align="left"><div class="indent">Numerical data&mdash;Phases&mdash;Motion&mdash;Librations&mdash;Lunar topography&mdash;Physical condition.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_X">X.&mdash;<span class="smcap">The sun</span></a></td><td align="right"><a href="#Page_178">178</a></td></tr>
+<tr><td align="left"><div class="indent">Numerical data&mdash;Chemical nature&mdash;Temperature&mdash;Visible and invisible parts&mdash;Photosphere&mdash;Spots&mdash;Faculę&mdash;Chromosphere&mdash;Prominences&mdash;Corona&mdash;The sun-spot period&mdash;The sun's rotation&mdash;Mechanical theory of the sun.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_XI">XI.&mdash;<span class="smcap">The planets</span></a></td><td align="right"><a href="#Page_212">212</a></td></tr>
+<tr><td align="left"><div class="indent">Arrangement of the solar system&mdash;Bode's law&mdash;Physical condition of the planets&mdash;Jupiter&mdash;Saturn&mdash;Uranus and Neptune&mdash;Venus&mdash;Mercury&mdash;Mars&mdash;The asteroids.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_XII">XII.&mdash;<span class="smcap">Comets and meteors</span></a></td><td align="right"><a href="#Page_251">251</a></td></tr>
+<tr><td align="left"><div class="indent">Motion, size, and mass of comets&mdash;Meteors&mdash;Their number and distribution&mdash;Meteor showers&mdash;Relation of comets and meteors&mdash;Periodic comets&mdash;Comet families and groups&mdash;Comet tails&mdash;Physical nature of comets&mdash;Collisions.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_XIII">XIII.&mdash;<span class="smcap">The fixed stars</span></a></td><td align="right"><a href="#Page_291">291</a></td></tr>
+<tr><td align="left"><div class="indent">Number of the stars&mdash;Brightness&mdash;Distance&mdash;Proper motion&mdash;Motion in line of sight&mdash;Double stars&mdash;Variable stars&mdash;New stars.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_XIV">XIV.&mdash;<span class="smcap">Stars and nebulę</span></a></td><td align="right"><a href="#Page_330">330</a></td></tr>
+<tr><td align="left"><div class="indent">Stellar colors and spectra&mdash;Classes of stars&mdash;Clusters&mdash;Nebulę&mdash;Their spectra and physical condition&mdash;The Milky Way&mdash;Construction of the heavens&mdash;Extent of the stellar system.</div></td><td></td></tr>
+<tr><td align="left"><a href="#CHAPTER_XV">XV.&mdash;<span class="smcap">Growth and decay</span></a></td><td align="right"><a href="#Page_358">358</a></td></tr>
+<tr><td align="left"><div class="indent">Logical bases and limitations&mdash;Development of the sun&mdash;The nebular hypothesis&mdash;Tidal friction&mdash;Roche's limit&mdash;Development of the moon&mdash;Development of stars and nebulę&mdash;The future.</div></td><td></td></tr>
+<tr><td align="left"><a href="#APPENDIX"><span class="smcap">Appendix</span></a></td><td align="right"><a href="#Page_383">383</a></td></tr>
+<tr><td align="left"><a href="#INDEX"><span class="smcap">Index</span></a></td><td align="right"><a href="#Page_387">387</a></td></tr>
+</table></div>
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum">[Pg ix]</span></p>
+<h2>LIST OF LITHOGRAPHIC PLATES</h2>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"></td><td align="right">FACING PAGE</td></tr>
+<tr><td align="left"><a href="#PLATE_I">I.&mdash;Northern Constellations</a></td><td align="right"><a href="#Page_124">124</a></td></tr>
+<tr><td align="left"><a href="#PLATE_II">II.&mdash;Equatorial Constellations</a></td><td align="right"><a href="#Page_190">190</a></td></tr>
+<tr><td align="left"><a href="#PLATE_III">III.&mdash;Map of Mars</a></td><td align="right"><a href="#Page_246">246</a></td></tr>
+<tr><td align="left"><a href="#PLATE_IV">IV.&mdash;The Pleiades</a></td><td align="right"><a href="#Page_344">344</a></td></tr>
+<tr><td align="left"><a href="#PROTRACTOR">Protractor</a></td><td align="right"><a href="#PROTRACTOR"><i>In pocket at back of book</i></a></td></tr>
+</table></div>
+
+
+
+<hr style="width: 65%;" />
+<h2>LIST OF FULL-PAGE ILLUSTRATIONS</h2>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"></td><td align="right">FACING PAGE</td></tr>
+<tr><td align="left"><a href="#Frontispiece">A Total Solar Eclipse</a></td><td align="right"><a href="#Frontispiece"><i>Frontispiece</i></a></td></tr>
+<tr><td align="left"><a href="#THE_HARVARD_COLLEGE_OBSERVATORY">The Harvard College Observatory, Cambridge, Mass.</a></td><td align="right"><a href="#Page_24">24</a></td></tr>
+<tr><td align="left"><a href="#ISAAC_NEWTON">Isaac Newton</a></td><td align="right"><a href="#Page_46">46</a></td></tr>
+<tr><td align="left"><a href="#GALILEO_GALILEI">Galileo Galilei</a></td><td align="right"><a href="#Page_52">52</a></td></tr>
+<tr><td align="left"><a href="#LICK_OBSERVATORY">The Lick Observatory, Mount Hamilton, Cal.</a></td><td align="right"><a href="#Page_60">60</a></td></tr>
+<tr><td align="left"><a href="#YERKES_OBSERVATORY">The Yerkes Observatory, Williams Bay, Wis.</a></td><td align="right"><a href="#Page_100">100</a></td></tr>
+<tr><td align="left"><a href="#THE_MOON">The Moon, one day after First Quarter</a></td><td align="right"><a href="#Page_150">150</a></td></tr>
+<tr><td align="left"><a href="#WILLIAM_HERSCHEL">William Herschel</a></td><td align="right"><a href="#Page_234">234</a></td></tr>
+<tr><td align="left"><a href="#LAPLACE">Pierre Simon Laplace</a></td><td align="right"><a href="#Page_364">364</a></td></tr>
+</table></div>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<h1>ASTRONOMY</h1>
+
+
+
+<hr style="width: 65%;" />
+<h2><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I</h2>
+
+<h3>DIFFERENT KINDS OF MEASUREMENT</h3>
+
+
+<p><a name="S_1" id="S_1"></a>1. <b>Accurate measurement.</b>&mdash;Accurate measurement is the
+foundation of exact science, and at the very beginning of
+his study in astronomy the student should learn something
+of the astronomer's kind of measurement. He should practice
+measuring the stars with all possible care, and should
+seek to attain the most accurate results of which his instruments
+and apparatus are capable. The ordinary affairs of
+life furnish abundant illustration of some of these measurements,
+such as finding the length of a board in inches or
+the weight of a load of coal in pounds and measurements
+of both length and weight are of importance in astronomy,
+but of far greater astronomical importance than these are
+the measurement of angles and the measurement of time.
+A kitchen clock or a cheap watch is usually thought of as
+a machine to tell the "time of day," but it may be used to
+time a horse or a bicycler upon a race course, and then it
+becomes an instrument to measure the amount of time
+required for covering the length of the course. Astronomers
+use a clock in both of these ways&mdash;to tell the time at
+which something happens or is done, and to measure the
+amount of time required for something; and in using a
+clock for either purpose the student should learn to take
+the time from it to the nearest second or better, if it has a<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span>
+seconds hand, or to a small fraction of a minute, by estimating
+the position of the minute hand between the minute
+marks on the dial. Estimate the fraction in tenths of
+a minute, not in halves or quarters.</p>
+
+<p><span class="smcap">Exercise 1.</span>&mdash;If several watches are available, let one
+person tap sharply upon a desk with a pencil and let each
+of the others note the time by the minute hand to the
+nearest tenth of a minute and record the observations as
+follows:</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">2h. 44.5m.</td><td align="left">First tap.</td><td align="left">2h. 46.4m.</td><td align="left">1.9m.</td></tr>
+<tr><td align="left">2h. 44.9m.</td><td align="left">Second tap.</td><td align="left">2h. 46.7m.</td><td align="left">1.8m.</td></tr>
+<tr><td align="left">2h. 46.6m.</td><td align="left">Third tap.</td><td align="left">2h. 48.6m.</td><td align="left">2.0m.</td></tr>
+</table></div>
+
+<p>The letters h and m are used as abbreviations for hour and
+minute. The first and second columns of the table are the
+record made by one student, and second and third the record
+made by another. After all the observations have been
+made and recorded they should be brought together and
+compared by taking the differences between the times recorded
+for each tap, as is shown in the last column. This
+difference shows how much faster one watch is than the
+other, and the agreement or disagreement of these differences
+shows the degree of accuracy of the observations.
+Keep up this practice until tenths of a minute can be estimated
+with fair precision.</p>
+
+<p><a name="S_2" id="S_2"></a>2. <b>Angles and their use.</b>&mdash;An angle is the amount of
+opening or difference of direction between two lines that
+cross each other. At twelve o'clock the hour and minute
+hand of a watch point in the same direction and the angle
+between them is zero. At one o'clock the minute hand is
+again at XII, but the hour hand has moved to&nbsp;I, one
+twelfth part of the circumference of the dial, and the angle
+between the hands is one twelfth of a circumference. It is
+customary to imagine the circumference of a dial to be cut
+up into 360 equal parts&mdash;i.&nbsp;e., each minute space of an ordinary
+dial to be subdivided into six equal parts, each of<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span>
+which is called a degree, and the measurement of an angle
+consists in finding how many of these degrees are included
+in the opening between its sides. At one o'clock the angle
+between the hands of a watch is thirty degrees, which is
+usually written 30°, at three o'clock it is 90°, at six o'clock
+180°, etc.</p>
+
+<p>A watch may be used to measure angles. How? But
+a more convenient instrument is the protractor, which is
+shown in <a href="#Fig_1">Fig.&nbsp;1</a>, applied to the angle <i>A&nbsp;B&nbsp;&nbsp;C</i> and showing
+that <i>A&nbsp;B&nbsp;C</i>&nbsp;=&nbsp;85° as nearly
+as the protractor scale
+can be read.</p>
+
+<p>The student should
+have and use a protractor,
+such as is furnished
+with this book,
+for the numerous exercises
+which are to follow.</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_1" id="Fig_1"></a>
+<img src="images/i016.png" width="300" height="223" alt="Fig. 1.&mdash;A protractor." title="Fig. 1.&mdash;A protractor." />
+<span class="caption"><span class="smcap">Fig. 1.</span>&mdash;A protractor.</span>
+</div>
+
+<p><a name="Exercise_2" id="Exercise_2"></a><span class="smcap">Exercise 2.</span>&mdash;Draw
+neatly a triangle with
+sides about 100 millimeters long, measure each of its angles
+and take their sum. No matter what may be the
+shape of the triangle, this sum should be very nearly 180°&mdash;exactly
+180° if the work were perfect&mdash;but perfection
+can seldom be attained and one of the first lessons to
+be learned in any science which deals with measurement
+is, that however careful we may be in our work some
+minute error will cling to it and our results can be only
+approximately correct. This, however, should not be
+taken as an excuse for careless work, but rather as a stimulus
+to extra effort in order that the unavoidable errors
+may be made as small as possible. In the present case
+the measured angles may be improved a little by adding
+(algebraically) to each of them one third of the amount by
+which their sum falls short of 180°, as in the following
+example:<span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><th align="left"></th><th align="center">Measured angles.</th><th align="center">Correction</th><th align="center">Corrected angles.</th></tr>
+<tr><td align="left"></td><td align="right">°&nbsp;</td><td align="right">°&nbsp;</td><td align="right">°&nbsp;</td></tr>
+<tr><td align="left">A</td><td align="right">73.4</td><td align="right">+ 0.1</td><td align="right">73.5</td></tr>
+<tr><td align="left">B</td><td align="right">49.3</td><td align="right">+ 0.1</td><td align="right">49.4</td></tr>
+<tr><td align="left">C</td><td align="right">57.0</td><td align="right">+ 0.1</td><td align="right">57.1</td></tr>
+<tr><td align="left">Sum</td><td align="right"><span class="bt">179.7</span></td><td>&nbsp;</td><td align="right"><span class="bt">180.0</span></td></tr>
+<tr><td align="left">Defect</td><td align="right">+ 0.3</td><td></td><td></td></tr>
+</table></div>
+
+<p>This process is in very common use among astronomers,
+and is called "adjusting" the observations.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_2" id="Fig_2"></a>
+<img src="images/i017.png" width="350" height="208" alt="Fig. 2.&mdash;Triangulation." title="Fig. 2.&mdash;Triangulation." />
+<span class="caption"><span class="smcap">Fig. 2.</span>&mdash;Triangulation.</span>
+</div>
+
+<p><a name="S_3" id="S_3"></a>3. <b>Triangles.</b>&mdash;The instruments used by astronomers for
+the measurement of angles are usually provided with a
+telescope, which may be pointed at different objects, and
+with a scale, like that of the protractor, to measure the
+angle through which the telescope is turned in passing
+from one object to another. In this way it is possible to
+measure the angle between lines drawn from the instrument
+to two distant objects,
+such as two church
+steeples or the sun and
+moon, and this is usually
+called the angle between
+the objects. By measuring
+angles in this way
+it is possible to determine
+the distance to an
+inaccessible point, as shown in <a href="#Fig_2">Fig.&nbsp;2</a>. A surveyor at&nbsp;<i>A</i>
+desires to know the distance to&nbsp;<i>C</i>, on the opposite side of a
+river which he can not cross. He measures with a tape line
+along his own side of the stream the distance <i>A&nbsp;B</i>&nbsp;=&nbsp;100
+yards and then, with a suitable instrument, measures the
+angle at&nbsp;<i>A</i> between the points&nbsp;<i>C</i> and&nbsp;<i>B</i>, and the angle at
+<i>B</i> between <i>C</i> and <i>A</i>, finding <i>B&nbsp;A&nbsp;C</i>&nbsp;=&nbsp;73.4°, <i>A&nbsp;B&nbsp;C</i>&nbsp;=&nbsp;49.3°.
+To determine the distance <i>A&nbsp;C</i> he draws upon paper a line
+100 millimeters long, and marks the ends <i>a</i> and <i>b</i>; with a
+protractor he constructs at <i>a</i> the angle <i>b&nbsp;a&nbsp;c</i>&nbsp;=&nbsp;73.4°, and at
+<i>b</i> the angle <i>a&nbsp;b&nbsp;c</i>&nbsp;=&nbsp;49.3°, and marks by <i>c</i> the point where<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span>
+the two lines thus drawn meet. With the millimeter scale
+he now measures the distance <i>a&nbsp;c</i>&nbsp;=&nbsp;90.2 millimeters, which
+determines the distance <i>A&nbsp;C</i> across the river to be 90.2
+yards, since the triangle on paper has been made similar
+to the one across the river, and millimeters on the one
+correspond to yards on the other. What is the proposition
+of geometry upon which this depends? The measured
+distance <i>A&nbsp;B</i> in the surveyor's problem is called a base line.</p>
+
+<p><a name="Exercise_3" id="Exercise_3"></a><span class="smcap">Exercise 3.</span>&mdash;With a foot rule and a protractor measure
+a base line and the angles necessary to determine the
+length of the schoolroom. After the length has been thus
+found, measure it directly with the foot rule and compare
+the measured length with the one found from the angles.
+If any part of the work has been carelessly done, the student
+need not expect the results to agree.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_3" id="Fig_3"></a>
+<img src="images/i018.png" width="500" height="230" alt="Fig. 3.&mdash;Finding the moon&#39;s distance from the earth." title="Fig. 3.&mdash;Finding the moon&#39;s distance from the earth." />
+<span class="caption"><span class="smcap">Fig. 3.</span>&mdash;Finding the moon&#39;s distance from the earth.</span>
+</div>
+
+<p>In the same manner, by sighting at the moon from
+widely different parts of the earth, as in <a href="#Fig_3">Fig.&nbsp;3</a>, the moon's
+distance from us is found to be about a quarter of a million
+miles. What is the base line in this case?</p>
+
+<p><a name="S_4" id="S_4"></a>4. <b>The horizon</b>&mdash;<b>altitudes.</b>&mdash;In their observations astronomers
+and sailors make much use of the <i>plane of the horizon</i>,
+and practically any flat and level surface, such as that
+of a smooth pond, may be regarded as a part of this plane
+and used as such. A very common observation relating to<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span>
+the plane of the horizon is called "taking the sun's altitude,"
+and consists in measuring the angle between the
+sun's rays and the plane of the horizon upon which they
+fall. This angle between a line and a plane appears slightly
+different from the angle between two lines, but is really the
+same thing, since it means the angle between the sun's rays
+and a line drawn in the plane of the horizon toward the
+point directly under the sun. Compare this with the definition
+given in the geographies, "The latitude of a point
+on the earth's surface is its angular distance north or south
+of the equator," and note that the latitude is the angle
+between the plane of the equator and a line drawn from
+the earth's center to the given point on its surface.</p>
+
+<p>A convenient method of obtaining a part of the plane
+of the horizon for use in observation is as follows: Place
+a slate or a pane of glass upon a table in the sunshine.
+Slightly moisten its whole surface and then pour a little
+more water upon it near the center. If the water runs
+toward one side, thrust the edge of a thin wooden wedge
+under this side and block it up until the water shows no
+tendency to run one way rather than another; it is then
+level and a part of the plane of the horizon. Get several
+wedges ready before commencing the experiment. After
+they have been properly placed, drive a pin or tack behind
+each one so that it may not slip.</p>
+
+<p><a name="S_5" id="S_5"></a>5. <b>Taking the sun's altitude.</b> <a name="Exercise_4" id="Exercise_4"></a><span class="smcap">Exercise 4.</span>&mdash;Prepare a
+piece of board 20 centimeters, or more, square, planed
+smooth on one face and one edge. Drive a pin perpendicularly
+into the face of the board, near the middle of the
+planed edge. Set the board on edge on the horizon plane
+and turn it edgewise toward the sun so that a shadow of
+the pin is cast on the plane. Stick another pin into the
+board, near its upper edge, so that its shadow shall fall
+exactly upon the shadow of the first pin, and with a watch
+or clock observe the time at which the two shadows coincide.
+Without lifting the board from the plane, turn it<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>
+around so that the opposite edge is directed toward the sun
+and set a third pin just as the second one was placed, and
+again take the time. Remove the pins and draw fine pencil
+lines, connecting the holes, as shown in <a href="#Fig_4">Fig.&nbsp;4</a>, and with
+the protractor measure the angle
+thus marked. The student
+who has studied elementary geometry
+should be able to demonstrate
+that at the mean of the
+two recorded times the sun's altitude
+was equal to one half of the
+angle measured in the figure.</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_4" id="Fig_4"></a>
+<img src="images/i020.png" width="300" height="203" alt="Fig. 4.&mdash;Taking the sun&#39;s
+altitude." title="Fig. 4.&mdash;Taking the sun&#39;s
+altitude." />
+<span class="caption"><span class="smcap">Fig. 4.</span>&mdash;Taking the sun&#39;s
+altitude.</span>
+</div>
+
+<p>When the board is turned
+edgewise toward the sun so that its shadow is as thin as
+possible, rule a pencil line alongside it on the horizon plane.
+The angle which this line makes with a line pointing due
+south is called the sun's <i>azimuth</i>. When the sun is south,
+its azimuth is zero; when west, it is 90°; when east,
+270°, etc.</p>
+
+<p><span class="smcap">Exercise 5.</span>&mdash;Let a number of different students take
+the sun's altitude during both the morning and afternoon
+session and note the time of each observation, to the nearest
+minute. Verify the setting of the plane of the horizon
+from time to time, to make sure that no change has occurred
+in it.</p>
+
+<p><a name="S_6" id="S_6"></a>6. <b>Graphical representations.</b>&mdash;Make a graph (drawing)
+of all the observations, similar to <a href="#Fig_5">Fig.&nbsp;5</a>, and find by bisecting
+a set of chords <i>g</i> to <i>g</i>, <i>e</i> to <i>e</i>, <i>d</i> to <i>d</i>, drawn parallel to
+<i>B&nbsp;B</i>, the time at which the sun's altitude was greatest. In
+<a href="#Fig_5">Fig.&nbsp;5</a> we see from the intersection of <i>M&nbsp;M</i> with <i>B&nbsp;B</i> that
+this time was 11h. 50m.</p>
+
+<p>The method of graphs which is here introduced is of
+great importance in physical science, and the student
+should carefully observe in <a href="#Fig_5">Fig.&nbsp;5</a> that the line <i>B&nbsp;B</i> is a
+scale of times, which may be made long or short, provided
+only the intervals between consecutive hours 9 to 10, 10 to<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span>
+11, 11 to 12, etc., are equal. The distance of each little
+circle from <i>B&nbsp;B</i> is taken proportional to the sun's altitude,
+and may be upon any desired scale&mdash;e.&nbsp;g., a millimeter to
+a degree&mdash;provided the same scale is used for all observations.
+Each circle is placed accurately over that part of
+the base line which corresponds to the time at which the
+altitude was taken. Square ruled paper is very convenient,
+although not necessary, for such diagrams. It is especially
+to be noted that from the few observations which are represented
+in the figure a smooth curve has been drawn
+through the circles which represent the sun's altitude, and
+this curve shows the altitude of the sun at every moment
+between 9 <span class="smcap">A.&nbsp;M.</span> and 3 <span class="smcap">P.&nbsp;M.</span> In <a href="#Fig_5">Fig.&nbsp;5</a> the sun's altitude at
+noon was 57°. What was it at half past two?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_5" id="Fig_5"></a>
+<img src="images/i021.png" width="500" height="211" alt="Fig. 5.&mdash;A graph of the sun&#39;s altitude." title="Fig. 5.&mdash;A graph of the sun&#39;s altitude." />
+<span class="caption"><span class="smcap">Fig. 5.</span>&mdash;A graph of the sun&#39;s altitude.</span>
+</div>
+
+<p><a name="S_7" id="S_7"></a>7. <b>Diameter of a distant object.</b>&mdash;By sighting over a protractor,
+measure the angle between imaginary lines drawn
+from it to the opposite sides of a window. Carry the protractor
+farther away from the window and repeat the experiment,
+to see how much the angle changes. The angle
+thus measured is called "the angle subtended" by the window
+at the place where the measurement was made. If
+this place was squarely in front of the window we may
+draw upon paper an angle equal to the measured one and
+lay off from the vertex along its sides a distance proportional
+to the distance of the window&mdash;e.&nbsp;g., a millimeter for<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>
+each centimeter of real distance. If a cross line be now
+drawn connecting the points thus found, its length will be
+proportional to the width of the window, and the width
+may be read off to scale, a centimeter for every millimeter
+in the length of the cross line.</p>
+
+<p>The astronomer who measures with an appropriate instrument
+the angle subtended by the moon may in an
+entirely similar manner find the moon's diameter and has,
+in fact, found it to be 2,163 miles. Can the same method
+be used to find the diameter of the sun? A planet? The
+earth?</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span></p>
+<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II</h2>
+
+<h3>THE STARS AND THEIR DIURNAL MOTION</h3>
+
+
+<p><a name="S_8" id="S_8"></a>8. <b>The stars.</b>&mdash;From the very beginning of his study in
+astronomy, and as frequently as possible, the student should
+practice watching the stars by night, to become acquainted
+with the constellations and their movements. As an introduction
+to this study he may face toward the north, and
+compare the stars which he sees in that part of the sky with
+the map of the northern heavens, given on <a href="#PLATE_I">Plate&nbsp;I</a>, opposite
+<a href="#Page_124">page&nbsp;124</a>. Turn the map around, upside down if
+necessary, until the stars upon it match the brighter ones
+in the sky. Note how the stars are grouped in such conspicuous
+constellations as the Big Dipper (Ursa Major), the
+Little Dipper (Ursa Minor), and Cassiopeia. These three
+constellations should be learned so that they can be recognized
+at any time.</p>
+
+<p><i>The names of the stars.</i>&mdash;Facing the star map is a key
+which contains the names of the more important constellations
+and the names of the brighter stars in their constellations.
+These names are for the most part a Greek letter
+prefixed to the genitive case of the Latin name of the constellation.
+(See the Greek alphabet printed at the end of
+the book.)</p>
+
+<p><a name="S_9" id="S_9"></a>9. <b>Magnitudes of the stars.</b>&mdash;Nearly nineteen centuries
+ago St. Paul noted that "one star differeth from another
+star in glory," and no more apt words can be found to mark
+the difference of brightness which the stars present. Even
+prior to St. Paul's day the ancient Greek astronomers had
+divided the stars in respect of brightness into six groups,<span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>
+which the modern astronomers still use, calling each group
+a <i>magnitude</i>. Thus a few of the brightest stars are said to
+be of the first magnitude, the great mass of faint ones
+which are just visible to the unaided eye are said to be of
+the sixth magnitude, and intermediate degrees of brilliancy
+are represented by the intermediate magnitudes, second,
+third, fourth, and fifth. The student must not be misled
+by the word magnitude. It has no reference to the size of
+the stars, but only to their brightness, and on the star maps
+of this book the larger and smaller circles by which the
+stars are represented indicate only the brightness of the
+stars according to the system of magnitudes. Following
+the indications of these maps, the student should, in learning
+the principal stars and constellations, learn also to
+recognize how bright is a star of the second, fourth, or
+other magnitude.</p>
+
+<p><a name="S_10" id="S_10"></a>10. <b>Observing the stars.</b>&mdash;Find on the map and in the
+sky the stars &alpha;&nbsp;Ursę Minoris, &alpha;&nbsp;Ursę Majoris, &beta;&nbsp;Ursę Majoris.
+What geometrical figure will fit on to these stars?
+In addition to its regular name, &alpha;&nbsp;Ursę Minoris is frequently
+called by the special name Polaris, or the pole star.
+Why are the other two stars called "the Pointers"? What
+letter of the alphabet do the five bright stars in Cassiopeia
+suggest?</p>
+
+<p><a name="Exercise_6" id="Exercise_6"></a><span class="smcap">Exercise 6.</span>&mdash;Stand in such a position that Polaris is
+just hidden behind the corner of a building or some other
+vertical line, and mark upon the key map as accurately as
+possible the position of this line with respect to the other
+stars, showing which stars are to the right and which are
+to the left of it. Record the time (date, hour, and minute)
+at which this observation was made. An hour or two later
+repeat the observation at the same place, draw the line and
+note the time, and you will find that the line last drawn
+upon the map does not agree with the first one. The stars
+have changed their positions, and with respect to the vertical
+line the Pointers are now in a different direction from<span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>
+Polaris. Measure with a protractor the angle between the
+two lines drawn in the map, and use this angle and the
+recorded times of the observation to find how many degrees
+per hour this direction is changing. It should be about 15°
+per hour. If the observation were repeated 12 hours after
+the first recorded time, what would be the position of the
+vertical line among the stars? What would it be 24 hours
+later? A week later? Repeat the observation on the next
+clear night, and allowing for the number of whole revolutions
+made by the stars between the two dates, again determine
+from the time interval a more accurate value of the
+rate at which the stars move.</p>
+
+<p>The motion of the stars which the student has here detected
+is called their "diurnal" motion. What is the significance
+of the word diurnal?</p>
+
+<p>In the preceding paragraph there is introduced a method
+of great importance in astronomical practice&mdash;i.&nbsp;e., determining
+something&mdash;in this case the rate per hour, from observations
+separated by a long interval of time, in order to get
+a more accurate value than could be found from a short
+interval. Why is it more accurate? To determine the
+rate at which the planet Mars rotates about its axis, astronomers
+use observations separated by an interval of more
+than 200 years, during which the planet made more than
+75,000 revolutions upon its axis. If we were to write out
+in algebraic form an equation for determining the length
+of one revolution of Mars about its axis, the large number,
+75,000, would appear in the equation as a divisor, and in
+the final result would greatly reduce whatever errors existed
+in the observations employed.</p>
+
+<p>Repeat <a href="#Exercise_6">Exercise&nbsp;6</a> night after night, and note whether
+the stars come back to the same position at the same hour
+and minute every night.</p>
+
+
+<div class="figcenter" style="width: 650px">
+
+<div class="figleft" style="width: 300px;"><a name="Fig_6" id="Fig_6"></a>
+<img src="images/i026a.jpg" width="300" height="580" alt="Fig. 6.
+The plumb-line apparatus." title="Fig. 6.
+The plumb-line apparatus." />
+<span class="caption"><span class="smcap">Fig. 6.</span></span>
+</div>
+
+<div class="figright" style="width: 300px;"><a name="Fig_7" id="Fig_7"></a>
+<img src="images/i026b.jpg" width="300" height="578" alt="Fig. 7.
+The plumb-line apparatus." title="Fig. 7.
+The plumb-line apparatus." />
+<span class="caption"><span class="smcap">Fig. 7.</span></span>
+</div>
+<div style="clear: both;"></div>
+<span class="caption">The plumb-line apparatus.</span>
+</div>
+
+<p><a name="S_11" id="S_11"></a>11. <b>The plumb-line apparatus.</b>&mdash;This experiment, and
+many others, may be conveniently and accurately made
+with no other apparatus than a plumb line, and a device<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>
+for sighting past it. In Figs.&nbsp;<a href="#Fig_6">6</a> and&nbsp;<a href="#Fig_7">7</a> there is shown a
+simple form of such apparatus, consisting essentially of a
+board which rests in a horizontal position upon the points
+of three screws that pass through it. This board carries
+a small box, to one side of which is nailed in vertical position
+another board 5 or 6 feet long to carry the plumb line.
+This consists of a wire or fish line with any heavy weight&mdash;e.&nbsp;g.,
+a brick or flatiron&mdash;tied to its lower end and immersed
+in a vessel of water placed inside the box, so as to check
+any swinging motion of the weight. In the cover of the
+box is a small hole through which the wire passes, and by
+turning the screws in the baseboard the apparatus may be
+readily leveled, so that the wire shall swing freely in the
+center of the hole without touching the cover of the box.<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span>
+Guy wires, shown in the figure, are applied so as to stiffen
+the whole apparatus. A board with a screw eye at each
+end may be pivoted to the upright, as in <a href="#Fig_6">Fig.&nbsp;6</a>, for measuring
+altitudes; or to the box, as in <a href="#Fig_7">Fig.&nbsp;7</a>, for observing the
+time at which a star in its diurnal motion passes through
+the plane determined by the plumb line and the center of
+the screw eye through which the observer looks.</p>
+
+<p>The whole apparatus may be constructed by any person
+of ordinary mechanical skill at a very small cost, and it or
+something equivalent should be provided for every class beginning
+observational astronomy. To use the apparatus for
+the experiment of <a href="#S_10">§&nbsp;10</a>, it should be leveled, and the board
+with the screw eyes, attached as in <a href="#Fig_7">Fig.&nbsp;7</a>, should be turned
+until the observer, looking through the screw eye, sees
+Polaris exactly behind the wire. Use a bicycle lamp to
+illumine the wire by night. The apparatus is now adjusted,
+and the observer has only to wait for the stars which he
+desires to observe, and to note by his watch the time at
+which they pass behind the wire. It will be seen that the
+wire takes the place of the vertical edge of the building,
+and that the board with the screw eyes is introduced solely
+to keep the observer in the right place relative to the
+wire.</p>
+
+<p><a name="S_12" id="S_12"></a>12. <b>A sidereal clock.</b>&mdash;Clocks are sometimes so made and
+regulated that they show always the same hour and minute
+when the stars come back to the same place, and such a
+timepiece is called a sidereal clock&mdash;i.&nbsp;e., a star-time clock.
+Would such a clock gain or lose in comparison with an ordinary
+watch? Could an ordinary watch be turned into a
+sidereal watch by moving the regulator?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_8" id="Fig_8"></a>
+<a href="images/i028-full.jpg"><img src="images/i028.jpg" width="500" height="502" alt="Fig. 8.&mdash;Photographing the circumpolar stars.&mdash;Barnard." title="Fig. 8.&mdash;Photographing the circumpolar stars.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 8.</span>&mdash;Photographing the circumpolar stars.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_13" id="S_13"></a>13. <b>Photographing the stars.</b>&mdash;<a name="Exercise_7" id="Exercise_7"></a><span class="smcap">Exercise 7.</span>&mdash;For any student
+who uses a camera. Upon some clear and moonless
+night point the camera, properly focused, at Polaris, and
+expose a plate for three or four hours. Upon developing
+the plate you should find a series of circular trails such as
+are shown in <a href="#Fig_8">Fig.&nbsp;8</a>, only longer. Each one of these is produced<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span>
+by a star moving slowly over the plate, in consequence
+of its changing position in the sky. The center
+indicated by these curved trails is called the pole of the
+heavens. It is that part of the sky toward which is pointed
+the axis about which the earth rotates, and the motion of
+the stars around the center is only an apparent motion due
+to the rotation of the earth which daily carries the observer
+and his camera around this axis while the stars stand still,
+just as trees and fences and telegraph poles stand still,
+although to the passenger upon a railway train they appear
+to be in rapid motion. So far as simple observations are
+concerned, there is no method by which the pupil can tell
+for himself that the motion of the stars is an apparent
+rather than a real one, and, following the custom of astronomers,
+we shall habitually speak as if it were a real movement
+of the stars. How long was the plate exposed in
+photographing <a href="#Fig_8">Fig.&nbsp;8</a>?<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p>
+
+<p><a name="S_14" id="S_14"></a>14. <b>Finding the stars.</b>&mdash;On <a href="#PLATE_I">Plate&nbsp;I</a>, opposite <a href="#Page_124">page&nbsp;124</a>,
+the pole of the heavens is at the center of the map, near
+Polaris, and the heavy trail near the center of <a href="#Fig_8">Fig.&nbsp;8</a> is
+made by Polaris. See if you can identify from the map
+any of the stars whose trails show in the photograph. The
+brighter the star the bolder and heavier its trail.</p>
+
+<p>Find from the map and locate in the sky the two bright
+stars Capella and Vega, which are on opposite sides of
+Polaris and nearly equidistant from it. Do these stars
+share in the motion around the pole? Are they visible on
+every clear night, and all night?</p>
+
+<p>Observe other bright stars farther from Polaris than
+are Vega and Capella and note their movement. Do they
+move like the sun and moon? Do they rise and set?</p>
+
+<p>In what part of the sky do the stars move most rapidly,
+near the pole or far from it?</p>
+
+<p>How long does it take the fastest moving stars to make
+the circuit of the sky and come back to the same place?
+How long does it take the slow stars?</p>
+
+<p><a name="S_15" id="S_15"></a>15. <b>Rising and setting of the stars.</b>&mdash;A study of the sky
+along the lines indicated in these questions will show that
+there is a considerable part of it surrounding the pole
+whose stars are visible on every clear night. The same
+star is sometimes high in the sky, sometimes low, sometimes
+to the east of the pole and at other times west of it,
+but is always above the horizon. Such stars are said to
+be circumpolar. A little farther from the pole each star,
+when at the lowest point of its circular path, dips for a
+time below the horizon and is lost to view, and the farther
+it is away from the pole the longer does it remain invisible,
+until, in the case of stars 90° away from the pole, we find
+them hidden below the horizon for twelve hours out of
+every twenty-four (see <a href="#Fig_9">Fig.&nbsp;9</a>). The sun is such a star,
+and in its rising and setting acts precisely as does every
+other star at a similar distance from the pole&mdash;only, as we
+shall find later, each star keeps always at (nearly) the same<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span>
+distance from the pole, while the sun in the course of a
+year changes its distance from the pole very greatly, and
+thus changes the amount of time it spends above and below
+the horizon, producing in this way the long days of
+summer and the short ones of winter.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_9" id="Fig_9"></a>
+<a href="images/i030-full.jpg"><img src="images/i030.jpg" width="500" height="472" alt="Fig. 9.&mdash;Diurnal motion of the northern constellations." title="Fig. 9.&mdash;Diurnal motion of the northern constellations." /></a>
+<span class="caption"><span class="smcap">Fig. 9.</span>&mdash;Diurnal motion of the northern constellations.</span>
+</div>
+
+<p>How much time do stars which are more than 90° from
+the pole spend above the horizon?</p>
+
+<p>We say in common speech that the sun rises in the
+east, but this is strictly true only at the time when it is 90°
+distant from the pole&mdash;i.&nbsp;e., in March and September. At
+other seasons it rises north or south of east according as
+its distance from the pole is less or greater than 90°, and
+the same is true for the stars.<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span></p>
+
+<p><a name="S_16" id="S_16"></a>16. <b>The geography of the sky.</b>&mdash;Find from a map the
+latitude and longitude of your schoolhouse. Find on the
+map the place whose latitude is 39° and longitude 77° west
+of the meridian of Greenwich. Is there any other place in
+the world which has the same latitude and longitude as
+your schoolhouse?</p>
+
+<p>The places of the stars in the sky are located in exactly
+the manner which is illustrated by these geographical
+questions, only different names are used. Instead of latitude
+the astronomer says <i>declination</i>, in place of longitude
+he says <i>right ascension</i>, in place of meridian he says <i>hour
+circle</i>, but he means by these new names the same ideas
+that the geographer expresses by the old ones.</p>
+
+<p>Imagine the earth swollen up until it fills the whole
+sky; the earth's equator would meet the sky along a line
+(a great circle) everywhere 90° distant from the pole, and
+this line is called the <i>celestial equator</i>. Trace its position
+along the middle of the map opposite <a href="#Page_190">page&nbsp;190</a> and
+notice near what stars it runs. Every meridian of the
+swollen earth would touch the sky along an hour circle&mdash;i.&nbsp;e.,
+a great circle passing through the pole and therefore
+perpendicular to the equator. Note that in the map one of
+these hour circles is marked&nbsp;0. It plays the same part in
+measuring right ascensions as does the meridian of Greenwich
+in measuring longitudes; it is the beginning, from
+which they are reckoned. Note also, at the extreme left
+end of the map, the four bright stars in the form of a
+square, one side of which is parallel and close to the hour
+circle, which is marked 0. This is familiarly called the
+Great Square in Pegasus, and may be found high up in the
+southern sky whenever the Big Dipper lies below the pole.
+Why can it not be seen when Ursa Major is above the
+pole?</p>
+
+<p>Astronomers use the right ascensions of the stars not
+only to tell in what part of the sky the star is placed, but
+also in time reckonings, to regulate their sidereal clocks, and<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>
+with regard to this use they find it convenient to express
+right ascension not in degrees but in hours, 24 of which
+fill up the circuit of the sky and each of which is equal to
+15° of arc, 24&nbsp;×&nbsp;15 =&nbsp;360. The right ascension of Capella
+is 5h. 9m. =&nbsp;77.2°, but the student should accustom himself
+to using it in hours and minutes as given and not to
+change it into degrees. He should also note that some
+stars lie on the side of the celestial equator toward Polaris,
+and others are on the opposite side, so that the astronomer
+has to distinguish between north declinations and south
+declinations, just as the geographer distinguishes between
+north latitudes and south latitudes. This is done by the
+use of the +&nbsp;and&nbsp;- signs, a&nbsp;+ denoting that the star lies
+north of the celestial equator, i.&nbsp;e., toward Polaris.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_10" id="Fig_10"></a>
+<a href="images/i032-full.jpg"><img src="images/i032.jpg" width="500" height="432" alt="Fig. 10.&mdash;From a photograph of the Pleiades." title="Fig. 10.&mdash;From a photograph of the Pleiades." /></a>
+<span class="caption"><span class="smcap">Fig. 10.</span>&mdash;From a photograph of the Pleiades.</span>
+</div>
+
+<p>Find on <a href="#PLATE_II">Plate&nbsp;II</a>, opposite <a href="#Page_190">page&nbsp;190</a>, the Pleiades<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>
+(Pl&#275;ad&#275;s), R.&nbsp;A.&nbsp;=&nbsp;3h. 42m., Dec.&nbsp;=&nbsp;+23.8°. Why do
+they not show on <a href="#PLATE_I">Plate&nbsp;I</a>, opposite <a href="#Page_124">page&nbsp;124</a>? In what
+direction are they from Polaris? This is one of the
+finest star clusters in the sky, but it needs a telescope to
+bring out its richness. See how many stars you can count
+in it with the naked eye, and afterward examine it with
+an opera glass. Compare what you see with <a href="#Fig_10">Fig.&nbsp;10</a>. Find
+Antares, R.&nbsp;A.&nbsp;=&nbsp;16h. 23m. Dec.&nbsp;=&nbsp;-26.2°. How far is
+it, in degrees, from the pole? Is it visible in your sky?
+If so, what is its color?</p>
+
+<p>Find the R.&nbsp;A. and Dec. of &alpha;&nbsp;Ursę Majoris; of &beta;&nbsp;Ursę
+Majoris; of Polaris. Find the Northern Crown, <i>Corona
+Borealis</i>, R.&nbsp;A.&nbsp;=&nbsp;15h. 30m., Dec.&nbsp;=&nbsp;+27.0°; the Beehive,
+<i>Pręsepe</i>, R.&nbsp;A.&nbsp;=&nbsp;8h. 33m., Dec.&nbsp;=&nbsp;+20.4°.</p>
+
+<p>These should be looked up, not only on the map, but
+also in the sky.</p>
+
+<p><a name="S_17" id="S_17"></a>17. <b>Reference lines and circles.</b>&mdash;As the stars move across
+the sky in their diurnal motion, they carry the framework
+of hour circles and equator with them, so that the right
+ascension and declination of each star remain unchanged
+by this motion, just as longitudes and latitudes remain unchanged
+by the earth's rotation. They are the same when
+a star is rising and when it is setting; when it is above the
+pole and when it is below it. During each day the hour
+circle of every star in the heavens passes overhead, and at
+the moment when any particular hour circle is exactly
+overhead all the stars which lie upon it are said to be "on
+the meridian"&mdash;i.&nbsp;e., at that particular moment they stand
+directly over the observer's geographical meridian and upon
+the corresponding celestial meridian.</p>
+
+<p>An eye placed at the center of the earth and capable of
+looking through its solid substance would see your geographical
+meridian against the background of the sky exactly covering
+your celestial meridian and passing from one pole
+through your zenith to the other pole. In <a href="#Fig_11">Fig.&nbsp;11</a> the inner
+circle represents the terrestrial meridian of a certain place,<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span>
+<i>O</i>, as seen from the center of the earth, <i>C</i>, and the outer
+circle represents the celestial meridian of <i>O</i> as seen from
+<i>C</i>, only we must imagine, what can not be shown on the
+figure, that the outer circle is so large that the inner one
+shrinks to a mere point in
+comparison with it. If <i>C&nbsp;P</i>
+represents the direction in
+which the earth's axis passes
+through the center, then <i>C&nbsp;E</i>
+at right angles to it must
+be the direction of the equator
+which we suppose to be
+turned edgewise toward us;
+and if <i>C&nbsp;O</i> is the direction of
+some particular point on the
+earth's surface, then <i>Z</i> directly
+overhead is called the
+<i>zenith</i> of that point, upon
+the celestial sphere. The line <i>C&nbsp;H</i> represents a direction
+parallel to the horizon plane at <i>O</i>, and <i>H&nbsp;C&nbsp;P</i> is the angle
+which the axis of the earth makes with this horizon plane.
+The arc <i>O&nbsp;E</i> measures the latitude of <i>O</i>, and the arc <i>Z&nbsp;E</i>
+measures the declination of <i>Z</i>, and since by elementary
+geometry each of these arcs contains the same number of
+degrees as the angle <i>E&nbsp;C&nbsp;Z</i>, we have the</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_11" id="Fig_11"></a>
+<img src="images/i034.png" width="300" height="303" alt="Fig. 11.&mdash;Reference lines and circles." title="Fig. 11.&mdash;Reference lines and circles." />
+<span class="caption"><span class="smcap">Fig. 11.</span>&mdash;Reference lines and circles.</span>
+</div>
+
+<p><i>Theorem.</i>&mdash;The latitude of any place is equal to the
+declination of its zenith.</p>
+
+<p><i>Corollary.</i>&mdash;Any star whose declination is equal to your
+latitude will once in each day pass through your zenith.</p>
+
+<p><a name="S_18" id="S_18"></a>18. <b>Latitude.</b>&mdash;From the construction of the figure</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">&#8736; <i>E&nbsp;C&nbsp;Z</i> + &#8736; <i>Z&nbsp;C&nbsp;P</i></td><td align="center">=</td><td align="left">90°</td></tr>
+<tr><td align="right">&#8736; <i>H&nbsp;C&nbsp;P</i> + &#8736; <i>Z&nbsp;C&nbsp;P</i></td><td align="center">=</td><td align="left">90°</td></tr>
+</table></div>
+
+<p>from which we find by subtraction and transposition</p>
+
+<p class="center">&#8736; <i>E&nbsp;C&nbsp;Z</i> = &#8736; <i>H&nbsp;C&nbsp;P</i></p>
+
+<p>and this gives the further<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span></p>
+
+<p><i>Theorem.</i>&mdash;The latitude of any place is equal to the
+elevation of the pole above its horizon plane.</p>
+
+<p>An observer who travels north or south over the earth
+changes his latitude, and therefore changes the angle between
+his horizon plane and the axis of the earth. What
+effect will this have upon the position of stars in his sky?
+If you were to go to the earth's equator, in what part of
+the sky would you look for Polaris? Can Polaris be seen
+from Australia? From South America? If you were to
+go from Minnesota to Texas, in what
+respect would the appearance of
+stars in the northern sky be changed?
+How would the appearance of stars
+in the southern sky be changed?</p>
+
+<div class="figleft" style="width: 300px;"><a name="Fig_12" id="Fig_12"></a>
+<img src="images/i035.png" width="300" height="305" alt="Fig. 12.&mdash;Diurnal path of
+Polaris." title="Fig. 12.&mdash;Diurnal path of
+Polaris." />
+<span class="caption"><span class="smcap">Fig. 12.</span>&mdash;Diurnal path of
+Polaris.</span>
+</div>
+
+<p><a name="Exercise_8" id="Exercise_8"></a><span class="smcap">Exercise 8.</span>&mdash;Determine your
+latitude by taking the altitude of
+Polaris when it is at some one of the
+four points of its diurnal path, shown
+in <a href="#Fig_12">Fig.&nbsp;12</a>. When it is at&nbsp;<i>1</i> it is
+said to be at upper culmination, and
+the star &zeta;&nbsp;Ursę Majoris in the handle of the Big Dipper
+will be directly below it. When at <i>2</i> it is at western elongation,
+and the star Castor is near the meridian. When it
+is at&nbsp;<i>3</i> it is at lower culmination, and the star Spica is on
+the meridian. When it is at&nbsp;<i>4</i> it is at eastern elongation,
+and Altair is near the meridian. All of these stars are
+conspicuous ones, which the student should find upon the
+map and learn to recognize in the sky. The altitude observed
+at either <i>2</i>&nbsp;or&nbsp;<i>4</i> may be considered equal to the latitude
+of the place, but the altitude observed when Polaris
+is at the positions marked <i>1</i>&nbsp;and&nbsp;<i>3</i> must be corrected for
+the star's distance from the pole, which may be assumed
+equal to 1.3°.</p>
+
+<p>The plumb-line apparatus described at <a href="#Page_12">page&nbsp;12</a> is shown
+in <a href="#Fig_6">Fig.&nbsp;6</a> slightly modified, so as to adapt it to measuring
+the altitudes of stars. Note that the board with the screw<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>
+eye at one end has been transferred from the box to the
+vertical standard, and has a screw eye at each end. When
+the apparatus has been properly leveled, so that the plumb
+line hangs at the middle of the hole in the box cover, the
+board is to be pointed at the star by sighting through the
+centers of the two screw eyes, and a pencil line is to be
+ruled along its edge upon the face of the vertical standard.
+After this has been done turn the apparatus halfway around
+so that what was the north side now points south, level it
+again and revolve the board about the screw which holds it
+to the vertical standard, until the screw eyes again point to
+the star. Rule another line along the same edge of the
+board as before and with a protractor measure the angle
+between these lines. Use a bicycle lamp if you need artificial
+light for your work. The student who has studied
+plane geometry should be able to prove that one half of the
+angle between these lines is equal to the altitude of the
+star.</p>
+
+<p>After you have determined your latitude from Polaris,
+compare the result with your position as shown upon the
+best map available. With a little practice and considerable
+care the latitude may be thus determined within one tenth
+of a degree, which is equivalent to about 7 miles. If
+you go 10 miles north or south from your first station you
+should find the pole higher up or lower down in the sky by
+an amount which can be measured with your apparatus.</p>
+
+<p><a name="S_19" id="S_19"></a>19. <b>The meridian line.</b>&mdash;To establish a true north and
+south line upon the ground, use the apparatus as described
+at <a href="#Page_13">page&nbsp;13</a>, and when Polaris is at upper or lower culmination
+drive into the ground two stakes in line with the star
+and the plumb line. Such a meridian line is of great convenience
+in observing the stars and should be laid out and
+permanently marked in some convenient open space from
+which, if possible, all parts of the sky are visible. June and
+November are convenient months for this exercise, since
+Polaris then comes to culmination early in the evening.<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span></p>
+
+<p><a name="S_20" id="S_20"></a>20. <b>Time.</b>&mdash;What is <i>the time</i> at which school begins in
+the morning? What do you mean by "<i>the time</i>"?</p>
+
+<p>The sidereal time at any moment is the right ascension
+of the hour circle which at that moment coincides with the
+meridian. When the hour circle passing through Sirius
+coincides with the meridian, the sidereal time is 6h. 40m.,
+since that is the right ascension of Sirius, and in astronomical
+language Sirius is "<i>on the meridian</i>" at 6h. 40m.
+sidereal time. As may be seen from the map, this 6h. 40m.
+is the right ascension of Sirius, and if a clock be set to indicate
+6h. 40m. when Sirius crosses the meridian, it will
+show sidereal time. If the clock is properly regulated,
+every other star in the heavens will come to the meridian
+at the moment when the time shown by the clock is equal
+to the right ascension of the star. A clock properly regulated
+for this purpose will gain about four minutes per
+day in comparison with ordinary clocks, and when so regulated
+it is called a sidereal clock. The student should
+be provided with such a clock for his future work, but
+one such clock will serve for several persons, and a nutmeg
+clock or a watch of the cheapest kind is quite sufficient.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="THE_HARVARD_COLLEGE_OBSERVATORY" id="THE_HARVARD_COLLEGE_OBSERVATORY"></a>
+<a href="images/i038-full.jpg"><img src="images/i038.jpg" width="600" height="341" alt="THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS." title="THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS." /></a>
+<span class="caption">THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.</span>
+</div>
+
+<p><a name="Exercise_9" id="Exercise_9"></a><span class="smcap">Exercise 9.</span>&mdash;Set such a clock to sidereal time by
+means of the transit of a star over your meridian. For this
+experiment it is presupposed that a meridian line has been
+marked out on the ground as in <a href="#S_19">§&nbsp;19</a>, and the simplest
+mode of performing the experiment required is for the
+observer, having chosen a suitable star in the southern part
+of the sky, to place his eye accurately over the northern end
+of the meridian line and to estimate as nearly as possible
+the beginning and end of the period during which the star
+appears to stand exactly above the southern end of the
+line. The middle of this period may be taken as the time
+at which the star crossed the meridian and at this moment
+the sidereal time is equal to the right ascension of the star.
+The difference between this right ascension and the observed<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span>
+middle instant is the error of the clock or the
+amount by which its hands must be set back or forward in
+order to indicate true sidereal time.</p>
+
+<p>A more accurate mode of performing the experiment
+consists in using the plumb-line apparatus carefully adjusted,
+as in <a href="#Fig_7">Fig.&nbsp;7</a>, so that the line joining the wire to
+the center of the screw eye shall be parallel to the meridian
+line. Observe the time by the clock at which the star disappears
+behind the wire as seen through the center of the
+screw eye. If the star is too high up in the sky for convenient
+observation, place a mirror, face up, just north of
+the screw eye and observe star, wire and screw eye by reflection
+in it.</p>
+
+<p>The numerical right ascension of the observed star is
+needed for this experiment, and it may be measured from
+the star map, but it will usually be best to observe one of
+the stars of the table at the end of the book, and to obtain
+its right ascension as follows: The table gives the right
+ascension and declination of each star as they were at the
+beginning of the year 1900, but on account of the precession
+(see <a href="#CHAPTER_V">Chapter&nbsp;V</a>), these numbers all change slowly with
+the lapse of time, and on the average the right ascension
+of each star of the table must be increased by one twentieth
+of a minute for each year after 1900&mdash;i.&nbsp;e., in 1910
+the right ascension of the first star of the table will be
+0h. 38.6m. + (10/20)m. =&nbsp;0h. 39.1m. The declinations also
+change slightly, but as they are only intended to help in
+finding the star on the star maps, their change may be
+ignored.</p>
+
+<p>Having set the clock approximately to sidereal time,
+observe one or two more stars in the same way as above.
+The difference between the observed time and the right
+ascension, if any is found, is the "correction" of the
+clock. This correction ought not to exceed a minute if due
+care has been taken in the several operations prescribed.
+The relation of the clock to the right ascension of the stars<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>
+is expressed in the following equation, with which the
+student should become thoroughly familiar:</p>
+
+<p class="center"><i>A</i> = <i>T</i> ± <i>U</i></p>
+
+<p><i>T</i> stands for the time by the clock at which the star crossed
+the meridian. <i>A</i> is the right ascension of the star, and <i>U</i>
+is the correction of the clock. Use the +&nbsp;sign in the equation
+whenever the clock is too slow, and the -&nbsp;sign when
+it is too fast. <i>U</i> may be found from this equation when <i>A</i>
+and <i>T</i> are given, or <i>A</i> may be found when <i>T</i> and <i>U</i> are
+given. It is in this way that astronomers measure the right
+ascensions of the stars and planets.</p>
+
+<p>Determine <i>U</i> from each star you have observed, and
+note how the several results agree one with another.</p>
+
+<p><a name="S_21" id="S_21"></a>21. <b>Definitions.</b>&mdash;To define a thing or an idea is to give
+a description sufficient to identify it and distinguish it
+from every other possible thing or idea. If a definition
+does not come up to this standard it is insufficient. Anything
+beyond this requirement is certainly useless and
+probably mischievous.</p>
+
+<p>Let the student define the following geographical terms,
+and let him also criticise the definitions offered by his fellow-students:
+Equator, poles, meridian, latitude, longitude,
+north, south, east, west.</p>
+
+<p>Compare the following astronomical definitions with
+your geographical definitions, and criticise them in the
+same way. If you are not able to improve upon them, commit
+them to memory:</p>
+
+<p><i>The Poles</i> of the heavens are those points in the sky
+toward which the earth's axis points. How many are
+there? The one near Polaris is called the north pole.</p>
+
+<p><i>The Celestial Equator</i> is a great circle of the sky distant
+90° from the poles.</p>
+
+<p><i>The Zenith</i> is that point of the sky, overhead, toward
+which a plumb line points. Why is the word overhead
+placed in the definition? Is there more than one zenith?<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span></p>
+
+<p><i>The Horizon</i> is a great circle of the sky 90° distant
+from the zenith.</p>
+
+<p><i>An Hour Circle</i> is any great circle of the sky which
+passes through the poles. Every star has its own hour
+circle.</p>
+
+<p><i>The Meridian</i> is that hour circle which passes through
+the zenith.</p>
+
+<p><i>A Vertical Circle</i> is any great circle that passes through
+the zenith. Is the meridian a vertical circle?</p>
+
+<p><i>The Declination</i> of a star is its angular distance north
+or south of the celestial equator.</p>
+
+<p><i>The Right Ascension</i> of a star is the angle included between
+its hour circle and the hour circle of a certain point
+on the equator which is called the <i>Vernal Equinox</i>. From
+spherical geometry we learn that this angle is to be measured
+either at the pole where the two hour circles intersect,
+as is done in the star map opposite <a href="#Page_124">page&nbsp;124</a>, or
+along the equator, as is done in the map opposite page
+190. Right ascension is always measured from the vernal
+equinox in the direction opposite to that in which the
+stars appear to travel in their diurnal motion&mdash;i.&nbsp;e., from
+west toward east.</p>
+
+<p><i>The Altitude</i> of a star is its angular distance above the
+horizon.</p>
+
+<p><i>The Azimuth</i> of a star is the angle between the meridian
+and the vertical circle passing through the star. A star
+due south has an azimuth of 0°. Due west, 90°. Due
+north, 180°. Due east, 270°.</p>
+
+<p>What is the azimuth of Polaris in degrees?</p>
+
+<p>What is the azimuth of the sun at sunrise? At sunset?
+At noon? Are these azimuths the same on different days?</p>
+
+<p><i>The Hour Angle</i> of a star is the angle between its hour
+circle and the meridian. It is measured from the meridian
+in the direction in which the stars appear to travel in their
+diurnal motion&mdash;i.&nbsp;e., from east toward west.</p>
+
+<p>What is the hour angle of the sun at noon? What is<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>
+the hour angle of Polaris when it is at the lowest point in
+its daily motion?</p>
+
+<p><a name="S_22" id="S_22"></a>22. <b>Exercises.</b>&mdash;The student must not be satisfied with
+merely learning these definitions. He must learn to see
+these points and lines in his mind as if they were visibly
+painted upon the sky. To this end it will help him to note
+that the poles, the zenith, the meridian, the horizon, and
+the equator seem to stand still in the sky, always in the
+same place with respect to the observer, while the hour
+circles and the vernal equinox move with the stars and
+keep the same place among them. Does the apparent motion
+of a star change its declination or right ascension?
+What is the hour angle of the sun when it has the greatest
+altitude? Will your answer to the preceding question be
+true for a star? What is the altitude of the sun after sunset?
+In what direction is the north pole from the zenith?
+From the vernal equinox? Where are the points in which
+the meridian and equator respectively intersect the horizon?</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p>
+<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III</h2>
+
+<h3>FIXED AND WANDERING STARS</h3>
+
+
+<p><a name="S_23" id="S_23"></a>23. <b>Star maps.</b>&mdash;Select from the map some conspicuous
+constellation that will be conveniently placed for observation
+in the evening, and make on a large scale a copy of all
+the stars of the constellation that are shown upon the map.
+At night compare this copy with the sky, and mark in upon
+your paper all the stars of the constellation which are not
+already there. Both the original drawing and the additions
+made to it by night should be carefully done, and for
+the latter purpose what is called the method of allineations
+may be used with advantage&mdash;i.&nbsp;e., the new star is in line
+with two already on the drawing and is midway between
+them, or it makes an equilateral triangle with two others,
+or a square with three others, etc.</p>
+
+<p>A series of maps of the more prominent constellations,
+such as Ursa Major, Cassiopea, Pegasus, Taurus, Orion,
+Gemini, Canis Major, Leo, Corvus, Bootes, Virgo, Hercules,
+Lyra, Aquila, Scorpius, should be constructed in this manner
+upon a uniform scale and preserved as a part of the
+student's work. Let the magnitude of the stars be represented
+on the maps as accurately as may be, and note the
+peculiarity of color which some stars present. For the
+most part their color is a very pale yellow, but occasionally
+one may be found of a decidedly ruddy hue&mdash;e.&nbsp;g., Aldebaran
+or Antares. Such a star map, not quite complete, is
+shown in <a href="#Fig_13">Fig.&nbsp;13</a>.</p>
+
+<p>So, too, a sharp eye may detect that some stars do not
+remain always of the same magnitude, but change their<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+brightness from night to night, and this not on account of
+cloud or mist in the atmosphere, but from something in the
+star itself. Algol is one of the most conspicuous of these
+<i>variable stars</i>, as they are called.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_13" id="Fig_13"></a>
+<img src="images/i045.png" width="500" height="514" alt="Fig. 13.&mdash;Star map of the region about Orion." title="" />
+<span class="caption"><span class="smcap">Fig. 13.</span>&mdash;Star map of the region about Orion.</span>
+</div>
+
+<p><a name="S_24" id="S_24"></a>24. <b>The moon's motion among the stars.</b>&mdash;Whenever the
+moon is visible note its position among the stars by allineations,
+and plot it on the key map opposite <a href="#Page_190">page&nbsp;190</a>. Keep
+a record of the day and hour corresponding to each such
+observation. You will find, if the work is correctly done,
+that the positions of the moon all fall near the curved line
+shown on the map. This line is called the ecliptic.<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span></p>
+
+<p>After several such observations have been made and
+plotted, find by measurement from the map how many
+degrees per day the moon moves. How long would it require
+to make the circuit of the heavens and come back to
+the starting point?</p>
+
+<p>On each night when you observe the moon, make on a
+separate piece of paper a drawing of it about 10 centimeters
+in diameter and show in the drawing every feature of
+the moon's face which you can see&mdash;e.&nbsp;g., the shape of the
+illuminated surface (phase); the direction among the stars
+of the line joining the horns; any spots which you can see
+upon the moon's face, etc. An opera glass will prove of
+great assistance in this work.</p>
+
+<p>Use your drawings and the positions of the moon plotted
+upon the map to answer the following questions: Does
+the direction of the line joining the horns have any special
+relation to the ecliptic? Does the amount of illuminated
+surface of the moon have any relation to the moon's angular
+distance from the sun? Does it have any relation to the
+time at which the moon sets? Do the spots on the moon
+when visible remain always in the same place? Do they
+come and go? Do they change their position with relation
+to each other? Can you determine from these spots that
+the moon rotates about an axis, as the earth does? In
+what direction does its axis point? How long does it take
+to make one revolution about the axis? Is there any day
+and night upon the moon?</p>
+
+<p>Each of these questions can be correctly answered from
+the student's own observations without recourse to any
+book.</p>
+
+<p><a name="S_25" id="S_25"></a>25. <b>The sun and its motion.</b>&mdash;Examine the face of the
+sun through a smoked glass to see if there is anything
+there that you can sketch.</p>
+
+<p>By day as well as by night the sky is studded with stars,
+only they can not be seen by day on account of the overwhelming
+glare of sunlight, but the position of the sun<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>
+among the stars may be found quite as accurately as was
+that of the moon, by observing from day to day its right
+ascension and declination, and this should be practiced at
+noon on clear days by different members of the class.</p>
+
+<p><span class="smcap">Exercise 10.</span>&mdash;The right ascension of the sun may be
+found by observing with the sidereal clock the time of its
+transit over the meridian. Use the equation in <a href="#S_20">§&nbsp;20</a>, and
+substitute in place of <i>U</i> the value of the clock correction
+found from observations of stars on a preceding or following
+night. If the clock gains or loses <i>with respect to
+sidereal time</i>, take this into account in the value of <i>U</i>.</p>
+
+<p><a name="Exercise_11" id="Exercise_11"></a><span class="smcap">Exercise 11.</span>&mdash;To determine the sun's declination,
+measure its altitude at the time it crosses the meridian.
+Use either the method of <a href="#Exercise_4">Exercise&nbsp;4</a>, or that used with
+Polaris in <a href="#Exercise_8">Exercise&nbsp;8</a>. The student should be able to show
+from <a href="#Fig_11">Fig.&nbsp;11</a> that the declination is equal to the sum of
+the altitude and the latitude of the place diminished by
+90°, or in an equation</p>
+
+<p class="center">Declination = Altitude + Latitude - 90°.</p>
+
+<p>If the declination as found from this equation is a negative
+number it indicates that the sun is on the south side of the
+equator.</p>
+
+<p>The right ascension and declination of the sun as observed
+on each day should be plotted on the map and the
+date, written opposite it. If the work has been correctly
+done, the plotted points should fall upon the curved line
+(ecliptic) which runs lengthwise of the map. This line, in
+fact, represents the sun's path among the stars.</p>
+
+<p>Note that the hours of right ascension increase from 0
+up to 24, while the numbers on the clock dial go only from
+0 to 12, and then repeat 0 to 12 again during the same
+day. When the sidereal time is 13 hours, 14 hours, etc.,
+the clock will indicate 1 hour, 2 hours, etc., and 12 hours
+must then be added to the time shown on the dial.</p>
+
+<p>If observations of the sun's right ascension and declination<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>
+are made in the latter part of either March or September
+the student will find that the sun crosses the equator
+at these times, and he should determine from his observations,
+as accurately as possible, the date and hour of this
+crossing and the point on the equator at which the sun
+crosses it. These points are called the equinoxes, Vernal
+Equinox and Autumnal Equinox for the spring and autumn
+crossings respectively, and the student will recall that the
+vernal equinox is the point from which right ascensions
+are measured. Its position among the stars is found by
+astronomers from observations like those above described,
+only made with much more elaborate apparatus.</p>
+
+<p>Similar observations made in June and December show
+that the sun's midday altitude is about 47° greater in summer
+than in winter. They show also that the sun is as far
+north of the equator in June as he is south of it in December,
+from which it is easily inferred that his path, the
+ecliptic, is inclined to the equator at an angle of 23°.5, one
+half of 47°. This angle is called the obliquity of the ecliptic.
+The student may recall that in the geographies the
+torrid zone is said to extend 23°.5 on either side of the
+earth's equator. Is there any connection between these
+limits and the obliquity of the ecliptic? Would it be correct
+to define the torrid zone as that part of the earth's
+surface within which the sun may at some season of the
+year pass through the zenith?</p>
+
+<p><a name="Exercise_12" id="Exercise_12"></a><span class="smcap">Exercise 12.</span>&mdash;After a half dozen observations of the
+sun have been plotted upon the map, find by measurement
+the rate, in degrees per day, at which the sun moves along
+the ecliptic. How many days will be required for it to
+move completely around the ecliptic from vernal equinox
+back to vernal equinox again? Accurate observations with
+the elaborate apparatus used by professional astronomers
+show that this period, which is called a <i>tropical year</i>, is 365
+days 5 hours 48 minutes 46 seconds. Is this the same as
+the ordinary year of our calendars?<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span></p>
+
+<p><a name="S_26" id="S_26"></a>26. <b>The planets.</b>&mdash;Any one who has watched the sky and
+who has made the drawings prescribed in this chapter can
+hardly fail to have found in the course of his observations
+some bright stars not set down on the printed star maps,
+and to have found also that these stars do not remain fixed
+in position among their fellows, but wander about from
+one constellation to another. Observe the motion of one
+of these planets from night to night and plot its positions
+on the star map, precisely as was done for the moon.
+What kind of path does it follow?</p>
+
+<p>Both the ancient Greeks and the modern Germans have
+called these bodies wandering stars, and in English we name
+them planets, which is simply the Greek word for wanderer,
+bent to our use. Besides the sun and moon there are in
+the heavens five planets easily visible to the naked eye and,
+as we shall see later, a great number of smaller ones visible
+only in the telescope. More than 2,000 years ago astronomers
+began observing the motion of sun, moon, and
+planets among the stars, and endeavored to account for
+these motions by the theory that each wandering star
+moved in an orbit about the earth. Classical and medięval
+literature are permeated with this idea, which was displaced
+only after a long struggle begun by Copernicus (1543 <span class="smcap">A.&nbsp;D.</span>),
+who taught that the moon alone of these bodies revolves
+about the earth, while the earth and the other planets revolve
+around the sun. The ecliptic is the intersection of
+the plane of the earth's orbit with the sky, and the sun appears
+to move along the ecliptic because, as the earth moves
+around its orbit, the sun is always seen projected against
+the opposite side of it. The moon and planets all appear
+to move near the ecliptic because the planes of their orbits
+nearly coincide with the plane of the earth's orbit, and a
+narrow strip on either side of the ecliptic, following its
+course completely around the sky, is called the <i>zodiac</i>, a
+word which may be regarded as the name of a narrow street
+(16° wide) within which all the wanderings of the visible<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>
+planets are confined and outside of which they never venture.
+Indeed, Mars is the only planet which ever approaches
+the edge of the street, the others traveling near the middle
+of the road.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_14" id="Fig_14"></a>
+<img src="images/i050.png" width="500" height="487" alt="Fig. 14.&mdash;The apparent motion of a planet." title="Fig. 14.&mdash;The apparent motion of a planet." />
+<span class="caption"><span class="smcap">Fig. 14.</span>&mdash;The apparent motion of a planet.</span>
+</div>
+
+<p><a name="S_27" id="S_27"></a>27. <b>A typical case of planetary motion.</b>&mdash;The Copernican
+theory, enormously extended and developed through the
+Newtonian law of gravitation (see <a href="#CHAPTER_IV">Chapter&nbsp;IV</a>), has completely
+supplanted the older Ptolemaic doctrine, and an
+illustration of the simple manner in which it accounts for
+the apparently complicated motions of a planet among the
+stars is found in Figs.&nbsp;<a href="#Fig_14">14</a> and&nbsp;<a href="#Fig_15">15</a>, the first of which represents
+the apparent motion of the planet Mars through the
+constellations Aries and Pisces during the latter part of the<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>
+year 1894, while the second shows the true motions of Mars
+and the earth in their orbits about the sun during the same
+period. The straight line in <a href="#Fig_14">Fig.&nbsp;14</a>, with cross ruling upon
+it, is a part of the ecliptic, and the numbers placed opposite
+it represent the distance, in degrees, from the vernal equinox.
+In <a href="#Fig_15">Fig.&nbsp;15</a> the straight line represents the direction
+from the sun toward the vernal equinox, and the angle
+which this line makes with the line joining earth and sun is
+called the earth's longitude. The imaginary line joining
+the earth and sun is called the earth's radius vector, and
+the pupil should note that the longitude and length of the
+radius vector taken together show the direction and distance
+of the earth from the sun&mdash;i.&nbsp;e., they fix the relative
+positions of the two bodies. The same is nearly true for
+Mars and would be wholly true if the orbit of Mars lay in
+the same plane with that of the earth. How does <a href="#Fig_14">Fig.&nbsp;14</a>
+show that the orbit of Mars does not lie exactly in the same
+plane with the orbit of the earth?</p>
+
+<p><a name="Exercise_13" id="Exercise_13"></a><span class="smcap">Exercise 13.</span>&mdash;Find from <a href="#Fig_15">Fig.&nbsp;15</a> what ought to have
+been the apparent course of Mars among the stars during
+the period shown in the two figures, and compare what you
+find with <a href="#Fig_14">Fig.&nbsp;14</a>. The apparent position of Mars among
+the stars is merely its direction from the earth, and this
+direction is represented in <a href="#Fig_14">Fig.&nbsp;14</a> by the distance of the
+planet from the ecliptic and by its longitude.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_15" id="Fig_15"></a>
+<img src="images/i052.png" width="500" height="605" alt="Fig. 15.&mdash;The real motion of a planet." title="Fig. 15.&mdash;The real motion of a planet." />
+<span class="caption"><span class="smcap">Fig. 15.</span>&mdash;The real motion of a planet.</span>
+</div>
+
+<p>The longitude of Mars for each date can be found from
+<a href="#Fig_15">Fig.&nbsp;15</a> by measuring the angle between the straight line
+<i>S&nbsp;V</i> and the line drawn from the earth to Mars. Thus for
+October 12th we may find with the protractor that the angle
+between the line <i>S&nbsp;V</i> and the line joining the earth to Mars
+is a little more than 30°, and in <a href="#Fig_14">Fig.&nbsp;14</a> the position of
+Mars for this date is shown nearly opposite the cross line
+corresponding to 30° on the ecliptic. Just how far below
+the ecliptic this position of Mars should fall can not be
+told from <a href="#Fig_15">Fig.&nbsp;15</a>, which from necessity is constructed as if
+the orbits of Mars and the earth lay in the same plane, and<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>
+Mars in this case would always appear to stand exactly on
+the ecliptic and to oscillate back and forth as shown in <a href="#Fig_14">Fig.&nbsp;14</a>,
+but without the up-and-down motion there shown. In
+this way plot in <a href="#Fig_14">Fig.&nbsp;14</a> the longitudes of Mars as seen from
+the earth for other dates and observe how the forward motion
+of the two planets in their orbits accounts for the apparently
+capricious motion of Mars to and fro among the stars.<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_16" id="Fig_16"></a>
+<img src="images/i053.png" width="500" height="491" alt="Fig. 16.&mdash;The orbits of Jupiter and Saturn." title="Fig. 16.&mdash;The orbits of Jupiter and Saturn." />
+<span class="caption"><span class="smcap">Fig. 16.</span>&mdash;The orbits of Jupiter and Saturn.</span>
+</div>
+
+<p><a name="S_28" id="S_28"></a>28. <b>The orbits of the planets.</b>&mdash;Each planet, great or
+small, moves in its own appropriate orbit about the sun,
+and the exact determination of these orbits, their sizes,
+shapes, positions, etc., has been one of the great problems
+of astronomy for more than 2,000 years, in which successive
+generations of astronomers have striven to push to a
+still higher degree of accuracy the knowledge attained by
+their predecessors. Without attempting to enter into the
+details of this problem we may say, generally, that every<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>
+planet moves in a plane passing through the sun, and for
+the six planets visible to the naked eye these planes nearly
+coincide, so that the six orbits may all be shown without
+much error as lying in the flat surface of one map. It is,
+however, more convenient to use two maps, such as Figs.&nbsp;<a href="#Fig_16">16</a>
+and&nbsp;<a href="#Fig_17">17</a>, one of which shows the group of planets, Mercury,
+Venus, the earth, and Mars, which are near the sun, and
+on this account are sometimes called the inner planets,
+while the other shows the more distant planets, Jupiter and
+Saturn, together with the earth, whose orbit is thus made
+to serve as a connecting link between the two diagrams.
+These diagrams are accurately drawn to scale, and are intended
+to be used by the student for accurate measurement
+in connection with the exercises and problems which
+follow.</p>
+
+<p>In addition to the six planets shown in the figures the
+solar system contains two large planets and several hundred
+small ones, for the most part invisible to the naked eye,
+which are omitted in order to avoid confusing the diagrams.</p>
+
+<p><a name="S_29" id="S_29"></a>29. <b>Jupiter and Saturn.</b>&mdash;In <a href="#Fig_16">Fig.&nbsp;16</a> the sun at the center
+is encircled by the orbits of the three planets, and inclosing
+all of these is a circular border showing the directions from
+the sun of the constellations which lie along the zodiac.
+The student must note carefully that it is only the directions
+of these constellations that are correctly shown, and
+that in order to show them at all they have been placed
+very much too close to the sun. The cross lines extending
+from the orbit of the earth toward the sun with Roman
+numerals opposite them show the positions of the earth in
+its orbit on the first day of January (<i>I</i>), first day of February
+(<i>II</i>), etc., and the similar lines attached to the orbits
+of Jupiter and Saturn with Arabic numerals show the positions
+of those planets on the first day of January of each
+year indicated, so that the figure serves to show not only
+the orbits of the planets, but their actual positions in their<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>
+orbits for something more than the first decade of the twentieth
+century.</p>
+
+<p>The line drawn from the sun toward the right of the
+figure shows the direction to the vernal equinox. It forms
+one side of the angle which measures a planet's longitude.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_17" id="Fig_17"></a>
+<img src="images/i055.png" width="500" height="489" alt="Fig. 17.&mdash;The orbits of the inner planets." title="Fig. 17.&mdash;The orbits of the inner planets." />
+<span class="caption"><span class="smcap">Fig. 17.</span>&mdash;The orbits of the inner planets.</span>
+</div>
+
+<p><a name="Exercise_14" id="Exercise_14"></a><span class="smcap">Exercise 14.</span>&mdash;Measure with your protractor the longitude
+of the earth on January 1st. Is this longitude the
+same in all years? Measure the longitude of Jupiter on
+January&nbsp;1, 1900; on July 1, 1900; on September 25, 1906.<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span></p>
+
+<p>Draw neatly on the map a pencil line connecting the
+position of the earth for January&nbsp;1, 1900, with the position
+of Jupiter for the same date, and produce the line beyond
+Jupiter until it meets the circle of the constellations. This
+line represents the direction of Jupiter from the earth, and
+points toward the constellation in which the planet appears
+at that date. But this representation of the place of Jupiter
+in the sky is not a very accurate one, since on the scale
+of the diagram the stars are in fact more than 100,000 times
+as far off as they are shown in the figure, and the pencil
+mark does not meet the line of constellations at the same
+intersection it would have if this line were pushed back
+to its true position. To remedy this defect we must draw
+another line from the sun parallel to the one first drawn,
+and its intersection with the constellations will give very
+approximately the true position of Jupiter in the sky.</p>
+
+<p><a name="Exercise_15" id="Exercise_15"></a><span class="smcap">Exercise 15.</span>&mdash;Find the present positions of Jupiter
+and Saturn, and look them up in the sky by means of your
+star maps. The planets will appear in the indicated constellations
+as very bright stars not shown on the map.</p>
+
+<p>Which of the planets, Jupiter and Saturn, changes its
+direction from the sun more rapidly? Which travels the
+greater number of miles per day? When will Jupiter and
+Saturn be in the same constellation? Does the earth move
+faster or slower than Jupiter?</p>
+
+<p>The distance of Jupiter or Saturn from the earth at any
+time may be readily obtained from the figure. Thus, by
+direct measurement with the millimeter scale we find for
+January 1, 1900, the distance of Jupiter from the earth is 6.1
+times the distance of the sun from the earth, and this may
+be turned into miles by multiplying it by 93,000,000, which
+is approximately the distance of the sun from the earth.
+For most purposes it is quite as well to dispense with this
+multiplication and call the distance 6.1 astronomical units,
+remembering that the astronomical unit is the distance of
+the sun from the earth.<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span></p>
+
+<p><a name="Exercise_16" id="Exercise_16"></a><span class="smcap">Exercise 16.</span>&mdash;What is Jupiter's distance from the earth
+at its nearest approach? What is the greatest distance it
+ever attains? Is Jupiter's least distance from the earth
+greater or less than its least distance from Saturn?</p>
+
+<p>On what day in the year 1906 will the earth be on
+line between Jupiter and the sun? On this day Jupiter
+is said to be in <i>opposition</i>&mdash;i.&nbsp;e., the planet and the sun
+are on opposite sides of the earth, and Jupiter then comes
+to the meridian of any and every place at midnight. When
+the sun is between the earth and Jupiter (at what date in
+1906?) the planet is said to be in <i>conjunction</i> with the
+sun, and of course passes the meridian with the sun at
+noon. Can you determine from the figure the time at
+which Jupiter comes to the meridian at other dates than
+opposition and conjunction? Can you determine when it
+is visible in the evening hours? Tell from the figure what
+constellation is on the meridian at midnight on January
+1st. Will it be the same constellation in every year?</p>
+
+<p><a name="S_30" id="S_30"></a>30. <b>Mercury, Venus, and Mars.</b>&mdash;<a href="#Fig_17">Fig.&nbsp;17</a>, which represents
+the orbits of the inner planets, differs from <a href="#Fig_16">Fig.&nbsp;16</a>
+only in the method of fixing the positions of the planets
+in their orbits at any given date. The motion of these planets
+is so rapid, on account of their proximity to the sun, that
+it would not do to mark their positions as was done for
+Jupiter and Saturn, and with the exception of the earth they
+do not always return to the same place on the same day in
+each year. It is therefore necessary to adopt a slightly different
+method, as follows: The straight line extending from
+the sun toward the vernal equinox, <i>V</i>, is called the prime
+radius, and we know from past observations that the earth
+in its motion around the sun crosses this line on September
+23d in each year, and to fix the earth's position for September
+23d in the diagram we have only to take the point at
+which the prime radius intersects the earth's orbit. A
+month later, on October 23d, the earth will no longer be at
+this point, but will have moved on along its orbit to the<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span>
+point marked 30 (thirty days after September 23d). Sixty
+days after September 23d it will be at the point marked 60,
+etc., and for any date we have only to find the number of
+days intervening between it and the preceding September
+23d, and this number will show at once the position of the
+earth in its orbit. Thus for the date July 4, 1900, we find</p>
+
+<p class="center">1900, July 4 - 1899, September 23 = 284 days,</p>
+
+<p>and the little circle marked upon the earth's orbit between
+the numbers 270 and 300 shows the position of the earth on
+that date.</p>
+
+<p>In what constellation was the sun on July 4, 1900?
+What zodiacal constellation came to the meridian at midnight
+on that date? What other constellations came to
+the meridian at the same time?</p>
+
+<p>The positions of the other planets in their orbits are
+found in the same manner, save that they do not cross the
+prime radius on the same date in each year, and the times
+at which they do cross it must be taken from the following
+table:</p>
+
+<h3><span class="smcap">Table of Epochs</span></h3>
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" rules="groups" frame="hsides">
+<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup>
+<thead>
+<tr><th align="center">A.&nbsp;D.</th><th align="center">Mercury.</th><th align="center">Venus.</th><th align="center">Earth.</th><th align="center">Mars.</th></tr>
+</thead>
+<tbody>
+<tr><td align="left">Period</td><td align="left">88.0 days.</td><td align="left">224.7 days.</td><td align="left">365.25 days.</td><td align="left">687.1 days.</td></tr>
+<tr><td align="left">1900</td><td align="left">Feb. 18th.</td><td align="left">Jan. 11th.</td><td align="left">Sept. 23d.</td><td align="left">April 28th.</td></tr>
+<tr><td align="left">1901</td><td align="left">Feb. 5th.</td><td align="left">April 5th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr>
+<tr><td align="left">1902</td><td align="left">Jan. 23d.</td><td align="left">June 29th.</td><td align="left">Sept. 23d.</td><td align="left">March 16th.</td></tr>
+<tr><td align="left">1903</td><td align="left">April 8th.</td><td align="left">Feb. 8th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr>
+<tr><td align="left">1904</td><td align="left">March 25th.</td><td align="left">May 3d.&nbsp;</td><td align="left">Sept. 23d.</td><td align="left">Feb. 1st.</td></tr>
+<tr><td align="left">1905</td><td align="left">March 12th.</td><td align="left">July 26th.</td><td align="left">Sept. 23d.</td><td align="left">Dec. 19th.</td></tr>
+<tr><td align="left">1906</td><td align="left">Feb. 27th.</td><td align="left">March 8th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr>
+<tr><td align="left">1907</td><td align="left">Feb. 14th.</td><td align="left">May 31st.</td><td align="left">Sept. 23d.</td><td align="left">Nov. 6th.</td></tr>
+<tr><td align="left">1908</td><td align="left">Feb. 1st.</td><td align="left">Jan. 11th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr>
+<tr><td align="left">1909</td><td align="left">Jan. 18th.</td><td align="left">April 4th.</td><td align="left">Sept. 23d.</td><td align="left">Sept. 23d.</td></tr>
+<tr><td align="left">1910</td><td align="left">Jan. 5th.</td><td align="left">June 28th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr>
+</tbody>
+</table></div>
+
+<p>The first line of figures in this table shows the number
+of days that each of these planets requires to make
+a complete revolution about the sun, and it appears from
+these numbers that Mercury makes about four revolutions<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>
+in its orbit per year, and therefore crosses the prime radius
+four times in each year, while the other planets are decidedly
+slower in their movements. The following lines of
+the table show for each year the date at which each planet
+first crossed the prime radius in that year; the dates of
+subsequent crossings in any year can be found by adding
+once, twice, or three times the period to the given date,
+and the table may be extended to later years, if need be, by
+continuously adding multiples of the period. In the case
+of Mars it appears that there is only about one year out of
+two in which this planet crosses the prime radius.</p>
+
+<p>After the date at which the planet crosses the prime
+radius has been determined its position for any required
+date is found exactly as in the case of the earth, and the
+constellation in which the planet will appear from the
+earth is found as explained above in connection with Jupiter
+and Saturn.</p>
+
+<p>The broken lines in the figure represent the construction
+for finding the places in the sky occupied by Mercury,
+Venus, and Mars on July 4, 1900. Let the student make a
+similar construction and find the positions of these planets
+at the present time. Look them up in the sky and see if
+they are where your work puts them.</p>
+
+<p><a name="S_31" id="S_31"></a>31. <b>Exercises.</b>&mdash;The "evening star" is a term loosely
+applied to any planet which is visible in the western sky
+soon after sunset. It is easy to see that such a planet must
+be farther toward the east in the sky than is the sun, and
+in either <a href="#Fig_16">Fig.&nbsp;16</a> or <a href="#Fig_17">Fig.&nbsp;17</a> any planet which viewed from
+the position of the earth lies to the left of the sun and
+not more than 50° away from it will be an evening star.
+If to the right of the sun it is a morning star, and may be
+seen in the eastern sky shortly before sunrise.</p>
+
+<p>What planet is the evening star <i>now</i>? Is there more
+than one evening star at a time? What is the morning
+star now?</p>
+
+<p>Do Mercury, Venus, or Mars ever appear in opposition?<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>
+What is the maximum angular distance from the sun at
+which Venus can ever be seen? Why is Mercury a more
+difficult planet to see than Venus? In what month of the
+year does Mars come nearest to the earth? Will it always
+be brighter in this month than in any other? Which of
+all the planets comes nearest to the earth?</p>
+
+<p>The earth always comes to the same longitude on the
+same day of each year. Why is not this true of the other
+planets?</p>
+
+<p>The student should remember that in one respect Figs.&nbsp;<a href="#Fig_16">16</a>
+and&nbsp;<a href="#Fig_17">17</a> are not altogether correct representations, since
+they show the orbits as all lying in the same plane. If this
+were strictly true, every planet would move, like the sun,
+always along the ecliptic; but in fact all of the orbits are
+tilted a little out of the plane of the ecliptic and every
+planet in its motion deviates a little from the ecliptic, first
+to one side then to the other; but not even Mars, which is
+the most erratic in this respect, ever gets more than eight
+degrees away from the ecliptic, and for the most part all
+of them are much closer to the ecliptic than this limit.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span></p>
+<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV</h2>
+
+<h3>CELESTIAL MECHANICS</h3>
+
+
+<p><a name="S_32" id="S_32"></a>32. <b>The beginnings of celestial mechanics.</b>&mdash;From the earliest
+dawn of civilization, long before the beginnings of
+written history, the motions of sun and moon and planets
+among the stars from constellation to constellation had
+commanded the attention of thinking men, particularly of
+the class of priests. The religions of which they were the
+guardians and teachers stood in closest relations with the
+movements of the stars, and their own power and influence
+were increased by a knowledge of them.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="ISAAC_NEWTON" id="ISAAC_NEWTON"></a>
+<img src="images/i062.jpg" width="500" height="619" alt="ISAAC NEWTON (1643-1727)." title="ISAAC NEWTON (1643-1727)." />
+<span class="caption">ISAAC NEWTON (1643-1727).</span>
+</div>
+
+<p>Out of these professional needs, as well as from a spirit
+of scientific research, there grew up and flourished for
+many centuries a study of the motions of the planets, simple
+and crude at first, because the observations that could
+then be made were at best but rough ones, but growing
+more accurate and more complex as the development of the
+mechanic arts put better and more precise instruments into
+the hands of astronomers and enabled them to observe with
+increasing accuracy the movements of these bodies. It was
+early seen that while for the most part the planets, including
+the sun and moon, traveled through the constellations
+from west to east, some of them sometimes reversed their
+motion and for a time traveled in the opposite way. This
+clearly can not be explained by the simple theory which
+had early been adopted that a planet moves always in the
+same direction around a circular orbit having the earth at
+its center, and so it was said to move around in a small
+circular orbit, called an epicycle, whose center was situated<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>
+upon and moved along a circular orbit, called the deferent,
+within which the earth was placed, as is shown in <a href="#Fig_18">Fig.&nbsp;18</a>,
+where the small circle is the epicycle, the large circle is the
+deferent, <i>P</i> is the planet, and <i>E</i> the earth. When this
+proved inadequate to account for the really complicated
+movements of the planets, another epicycle was put on top
+of the first one, and then another and another, until the
+supposed system became so complicated that Copernicus, a
+Polish astronomer, repudiated
+its fundamental theorem and
+taught that the motions of
+the planets take place in circles
+around the sun instead
+of about the earth, and that
+the earth itself is only one of
+the planets moving around
+the sun in its own appropriate
+orbit and itself largely responsible
+for the seemingly
+erratic movements of the
+other planets, since from day to day we see them and observe
+their positions from different points of view.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_18" id="Fig_18"></a>
+<img src="images/i064.png" width="350" height="333" alt="Fig. 18.&mdash;Epicycle and deferent." title="Fig. 18.&mdash;Epicycle and deferent." />
+<span class="caption"><span class="smcap">Fig. 18.</span>&mdash;Epicycle and deferent.</span>
+</div>
+
+<p><a name="S_33" id="S_33"></a>33. <b>Kepler's laws.</b>&mdash;Two generations later came Kepler
+with his three famous laws of planetary motion:</p>
+
+<p>I. Every planet moves in an ellipse which has the sun
+at one of its foci.</p>
+
+<p>II. The radius vector of each planet moves over equal
+areas in equal times.</p>
+
+<p>III. The squares of the periodic times of the planets
+are proportional to the cubes of their mean distances from
+the sun.</p>
+
+<p>These laws are the crowning glory, not only of Kepler's
+career, but of all astronomical discovery from the beginning
+up to his time, and they well deserve careful study
+and explanation, although more modern progress has shown
+that they are only approximately true.<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span></p>
+
+<p><a name="Exercise_17" id="Exercise_17"></a><span class="smcap">Exercise 17.</span>&mdash;Drive two pins into a smooth board an
+inch apart and fasten to them the ends of a string a foot
+long. Take up the slack of the string with the point of a
+lead pencil and, keeping the string drawn taut, move the
+pencil point over the board into every possible position.
+The curve thus traced will be an ellipse having the pins at
+the two points which are called its foci.</p>
+
+<p>In the case of the planetary orbits one focus of the
+ellipse is vacant, and, in accordance with the first law, the
+center of the sun is at the other focus. In <a href="#Fig_17">Fig.&nbsp;17</a> the dot,
+inside the orbit of Mercury, which is marked <i>a</i>, shows the
+position of the vacant focus of the orbit of Mars, and the
+dot <i>b</i> is the vacant focus of Mercury's orbit. The orbits of
+Venus and the earth are so nearly circular that their vacant
+foci lie very close to the sun and are not marked in the
+figure. The line drawn from the sun to any point of the
+orbit (the string from pin to pencil point) is a <i>radius vector</i>.
+The point midway between the pins is the <i>center</i> of the
+ellipse, and the distance of either pin from the center measures
+the <i>eccentricity</i> of the ellipse.</p>
+
+<p>Draw several ellipses with the same length of string,
+but with the pins at different distances apart, and note that
+the greater the eccentricity the flatter is the ellipse, but
+that all of them have the same length.</p>
+
+<p>If both pins were driven into the same hole, what kind
+of an ellipse would you get?</p>
+
+<p>The Second Law was worked out by Kepler as his answer
+to a problem suggested by the first law. In <a href="#Fig_17">Fig.&nbsp;17</a> it is
+apparent from a mere inspection of the orbit of Mercury
+that this planet travels much faster on one side of its orbit
+than on the other, the distance covered in ten days between
+the numbers 10 and 20 being more than fifty per cent greater
+than that between 50 and 60. The same difference is found,
+though usually in less degree, for every other planet, and
+Kepler's problem was to discover a means by which to
+mark upon the orbit the figures showing the positions of<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span>
+the planet at the end of equal intervals of time. His solution
+of this problem, contained in the second law, asserts
+that if we draw radii vectors from the sun to each of the
+marked points taken at equal time intervals around the
+orbit, then the area of the sector formed by two adjacent
+radii vectores and the arc included between them is equal
+to the area of each and every other such sector, the short
+radii vectores being spread apart so as to include a long
+arc between them while the long radii vectores have a short
+arc. In Kepler's form of stating the law the radius vector
+is supposed to travel with the planet and in each day to
+sweep over the same fractional part of the total area of the
+orbit. The spacing of the numbers in <a href="#Fig_17">Fig.&nbsp;17</a> was done by
+means of this law.</p>
+
+<p>For the proper understanding of Kepler's Third Law we
+must note that the "mean distance" which appears in it is
+one half of the long diameter of the orbit and that the
+"periodic time" means the number of days or years required
+by the planet to make a complete circuit in its orbit.
+Representing the first of these by <i>a</i> and the second by <i>T</i>,
+we have, as the mathematical equivalent of the law,</p>
+
+<p class="center"><i>a</i><sup>3</sup> ÷ <i>T</i><sup>2</sup> = <i>C</i></p>
+
+<p>where the quotient, <i>C</i>, is a number which, as Kepler found,
+is the same for every planet of the solar system. If we take
+the mean distance of the earth from the sun as the unit of
+distance, and the year as the unit of time, we shall find by
+applying the equation to the earth's motion, <i>C</i>&nbsp;=&nbsp;1. Applying
+this value to any other planet we shall find in the
+same units, <i>a</i>&nbsp;=&nbsp;<i>T</i><sup>2/3</sup>, by means of which we may determine
+the distance of any planet from the sun when its periodic
+time, <i>T</i>, has been learned from observation.</p>
+
+<p><a name="Exercise_18" id="Exercise_18"></a><span class="smcap">Exercise 18.</span>&mdash;Uranus requires 84 years to make a
+revolution in its orbit. What is its mean distance from the
+sun? What are the mean distances of Mercury, Venus, and
+Mars? (See <a href="#CHAPTER_III">Chapter&nbsp;III</a> for their periodic times.) Would<span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span>
+it be possible for two planets at different distances from
+the sun to move around their orbits in the same time?</p>
+
+<p>A circle is an ellipse in which the two foci have been
+brought together. Would Kepler's laws hold true for such
+an orbit?</p>
+
+<p><a name="S_34" id="S_34"></a>34. <b>Newton's laws of motion.</b>&mdash;Kepler studied and described
+the motion of the planets. Newton, three generations
+later (1727 <span class="smcap">A.&nbsp;D.</span>), studied and described the mechanism
+which controls that motion. To Kepler and his age the
+heavens were supernatural, while to Newton and his successors
+they are a part of Nature, governed by the same
+laws which obtain upon the earth, and we turn to the ordinary
+things of everyday life as the foundation of celestial
+mechanics.</p>
+
+<p>Every one who has ridden a bicycle knows that he can
+coast farther upon a level road if it is smooth than if it is
+rough; but however smooth and hard the road may be and
+however fast the wheel may have been started, it is sooner
+or later stopped by the resistance which the road and the
+air offer to its motion, and when once stopped or checked
+it can be started again only by applying fresh power. We
+have here a familiar illustration of what is called</p>
+
+<p><b>The first law of motion.</b>&mdash;"Every body continues in its
+state of rest or of uniform motion in a straight line except
+in so far as it may be compelled by force to change that
+state." A gust of wind, a stone, a careless movement of
+the rider may turn the bicycle to the right or the left, but
+unless some disturbing force is applied it will go straight
+ahead, and if all resistance to its motion could be removed
+it would go always at the speed given it by the last power
+applied, swerving neither to the one hand nor the other.</p>
+
+<p>When a slow rider increases his speed we recognize at
+once that he has applied additional power to the wheel, and
+when this speed is slackened it equally shows that force has
+been applied against the motion. It is force alone which
+can produce a change in either velocity or direction of<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>
+motion; but simple as this law now appears it required the
+genius of Galileo to discover it and of Newton to give it the
+form in which it is stated above.</p>
+
+<p><a name="S_35" id="S_35"></a>35. <b>The second law of motion</b>, which is also due to Galileo
+and Newton, is:</p>
+
+<p>"Change of motion is proportional to force applied and
+takes place in the direction of the straight line in which
+the force acts." Suppose a man to fall from a balloon at
+some great elevation in the air; his own weight is the force
+which pulls him down, and that force operating at every
+instant is sufficient to give him at the end of the first second
+of his fall a downward velocity of 32 feet per second&mdash;i.&nbsp;e.,
+it has changed his state from rest, to motion at this
+rate, and the motion is toward the earth because the force
+acts in that direction. During the next second the ceaseless
+operation of this force will have the same effect as in
+the first second and will add another 32 feet to his velocity,
+so that two seconds from the time he commenced to
+fall he will be moving at the rate of 64 feet per second, etc.
+The column of figures marked <i>v</i> in the table below shows
+what his velocity will be at the end of subsequent seconds.
+The changing velocity here shown is the change of motion
+to which the law refers, and the velocity is proportional to
+the time shown in the first column of the table, because the
+amount of force exerted in this case is proportional to the
+time during which it operated. The distance through
+which the man will fall in each second is shown in the column
+marked <i>d</i>, and is found by taking the average of his
+velocity at the beginning and end of this second, and the
+total distance through which he has fallen at the end of
+each second, marked <i>s</i> in the table, is found by taking the
+sum of all the preceding values of <i>d</i>. The velocity, 32 feet
+per second, which measures the change of motion in each
+second, also measures the <i>accelerating force</i> which produces
+this motion, and it is usually represented in formulę by
+the letter <i>g</i>. Let the student show from the numbers in<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>
+the table that the accelerating force, the time, <i>t</i>, during
+which it operates, and the space, <i>s</i>, fallen through, satisfy
+the relation</p>
+
+<p class="center"><i>s</i> = 1/2 <i>gt</i><sup>2</sup>,</p>
+
+<p>which is usually called the law of falling bodies. How does
+the table show that <i>g</i> is equal to 32?</p>
+
+<h3><span class="smcap">Table</span></h3>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><th align="center"><i>t</i></th><th align="center"><i>v</i></th><th align="center"><i>d</i></th><th align="center"><i>s</i></th></tr>
+<tr><td align="center">0</td><td align="right">0</td><td align="right">0</td><td align="right">0</td></tr>
+<tr><td align="center">1</td><td align="right">32</td><td align="right">16</td><td align="right">16</td></tr>
+<tr><td align="center">2</td><td align="right">64</td><td align="right">48</td><td align="right">64</td></tr>
+<tr><td align="center">3</td><td align="right">96</td><td align="right">80</td><td align="right">144</td></tr>
+<tr><td align="center">4</td><td align="right">128</td><td align="right">112</td><td align="right">256</td></tr>
+<tr><td align="center">5</td><td align="right">160</td><td align="right">144</td><td align="right">400</td></tr>
+<tr><td align="center">etc.</td><td align="center">etc.</td><td align="center">etc.</td><td align="center">etc.</td></tr>
+</table></div>
+
+<p>If the balloon were half a mile high how long would it
+take to fall to the ground? What would be the velocity
+just before reaching the ground?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="GALILEO_GALILEI" id="GALILEO_GALILEI"></a>
+<a href="images/i070-full.jpg"><img src="images/i070.jpg" width="500" height="674" alt="GALILEO GALILEI (1564-1642)." title="GALILEO GALILEI (1564-1642)." /></a>
+<span class="caption">GALILEO GALILEI (1564-1642).</span>
+</div>
+
+<p><a href="#Fig_19">Fig.&nbsp;19</a> shows the path through the air of a ball which
+has been struck by a bat at the point <i>A</i>, and started off in
+the direction <i>A&nbsp;B</i> with a velocity of 200 feet per second.
+In accordance with the first law of motion, if it were acted
+upon by no other force than the impulse given by the bat,
+it should travel along the straight line <i>A&nbsp;B</i> at the uniform
+rate of 200 feet per second, and at the end of the fourth
+second it should be 800 feet from <i>A</i>, at the point marked 4,
+but during these four seconds its weight has caused it to
+fall 256 feet, and its actual position, 4', is 256 feet below
+the point 4. In this way we find its position at the end of
+each second, 1', 2', 3', 4', etc., and drawing a line through
+these points we shall find the actual path of the ball under
+the influence of the two forces to be the curved line <i>A&nbsp;C</i>.
+No matter how far the ball may go before striking the
+ground, it can not get back to the point <i>A</i>, and the curve<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>
+<i>A&nbsp;C</i> therefore can not be a part of a circle, since that curve
+returns into itself. It is, in fact, a part of a <i>parabola</i>,
+which, as we shall see later, is a kind of orbit in which
+comets and some other heavenly bodies move. A skyrocket
+moves in the same kind of a path, and so does a stone, a
+bullet, or any other object hurled through the air.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_19" id="Fig_19"></a>
+<img src="images/i072.png" width="500" height="449" alt="Fig. 19.&mdash;The path of a ball." title="Fig. 19.&mdash;The path of a ball." />
+<span class="caption"><span class="smcap">Fig. 19.</span>&mdash;The path of a ball.</span>
+</div>
+
+<p><a name="S_36" id="S_36"></a>36. <b>The third law of motion.</b>&mdash;"To every action there is
+always an equal and contrary reaction; or the mutual actions
+of any two bodies are always equal and oppositely
+directed." This is well illustrated in the case of a man
+climbing a rope hand over hand. The direct force or action
+which he exerts is a downward pull upon the rope, and it is
+the reaction of the rope to this pull which lifts him along
+it. We shall find in a later chapter a curious application
+of this law to the history of the earth and moon.<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span></p>
+
+<p>It is the great glory of Sir Isaac Newton that he first of
+all men recognized that these simple laws of motion hold
+true in the heavens as well as upon the earth; that the
+complicated motion of a planet, a comet, or a star is determined
+in accordance with these laws by the forces
+which act upon the bodies, and that these forces are
+essentially the same as that which we call weight. The
+formal statement of the principle last named is included
+in&mdash;</p>
+
+<p><a name="S_37" id="S_37"></a>37. <b>Newton's law of gravitation.</b>&mdash;"Every particle of
+matter in the universe attracts every other particle with a
+force whose direction is that of a line joining the two, and
+whose magnitude is directly as the product of their masses,
+and inversely as the square of their distance from each
+other." We know that we ourselves and the things about
+us are pulled toward the earth by a force (weight) which is
+called, in the Latin that Newton wrote, <i>gravitas</i>, and the
+word marks well the true significance of the law of gravitation.
+Newton did not discover a new force in the heavens,
+but he extended an old and familiar one from a limited
+terrestrial sphere of action to an unlimited and celestial
+one, and furnished a precise statement of the way in which
+the force operates. Whether a body be hot or cold, wet or
+dry, solid, liquid, or gaseous, is of no account in determining
+the force which it exerts, since this depends solely
+upon mass and distance.</p>
+
+<p>The student should perhaps be warned against straining
+too far the language which it is customary to employ in
+this connection. The law of gravitation is certainly a far-reaching
+one, and it may operate in every remotest corner
+of the universe precisely as stated above, but additional
+information about those corners would be welcome to supplement
+our rather scanty stock of knowledge concerning
+what happens there. We may not controvert the words of
+a popular preacher who says, "When I lift my hand I move
+the stars in Ursa Major," but we should not wish to stand<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span>
+sponsor for them, even though they are justified by a rigorous
+interpretation of the Newtonian law.</p>
+
+<p>The word <i>mass</i>, in the statement of the law of gravitation,
+means the quantity of matter contained in the body,
+and if we represent by the letters <i>m'</i> and <i>m''</i> the respective
+quantities of matter contained in the two bodies whose distance
+from each other is <i>r</i>, we shall have, in accordance
+with the law of gravitation, the following mathematical
+expression for the force, <i>F</i>, which acts between them:</p>
+
+<p class="center"><i>F</i> = <i>k</i> (<i>m'm''</i>)/<i>r</i><sup>2</sup>.</p>
+
+<p>This equation, which is the general mathematical expression
+for the law of gravitation, may be made to yield
+some curious results. Thus, if we select two bullets, each
+having a mass of 1&nbsp;gram, and place them so that their centers
+are 1 centimeter apart, the above expression for the
+force exerted between them becomes</p>
+
+<p class="center"><i>F</i> = <i>k</i> {(1 × 1)/1<sup>2</sup>} = <i>k</i>,</p>
+
+<p>from which it appears that the coefficient <i>k</i> is the force
+exerted between these bodies. This is called the gravitation
+constant, and it evidently furnishes a measure of the
+specific intensity with which one particle of matter attracts
+another. Elaborate experiments which have been made to
+determine the amount of this force show that it is surprisingly
+small, for in the case of the two bullets whose
+mass of 1 gram each is supposed to be concentrated into
+an indefinitely small space, gravity would have to operate
+between them continuously for more than forty minutes in
+order to pull them together, although they were separated
+by only 1 centimeter to start with, and nothing save their
+own inertia opposed their movements. It is only when one
+or both of the masses <i>m'</i>, <i>m''</i> are very great that the force
+of gravity becomes large, and the weight of bodies at the<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>
+surface of the earth is considerable because of the great
+quantity of matter which goes to make up the earth.
+Many of the heavenly bodies are much more massive than
+the earth, as the mathematical astronomers have found by
+applying the law of gravitation to determine numerically
+their masses, or, in more popular language, to "weigh"
+them.</p>
+
+<p>The student should observe that the two terms mass
+and weight are not synonymous; mass is defined above as
+the quantity of matter contained in a body, while weight
+is the force with which the earth attracts that body, and
+in accordance with the law of gravitation its weight depends
+upon its distance from the center of the earth, while
+its mass is quite independent of its position with respect
+to the earth.</p>
+
+<p>By the third law of motion the earth is pulled toward a
+falling body just as strongly as the body is pulled toward
+the earth&mdash;i.&nbsp;e., by a force equal to the weight of the body.
+How much does the earth rise toward the body?</p>
+
+<p><a name="S_38" id="S_38"></a>38. <b>The motion of a planet.</b>&mdash;In <a href="#Fig_20">Fig.&nbsp;20</a> <i>S</i> represents the
+sun and <i>P</i> a planet or other celestial body, which for the
+moment is moving along the straight line <i>P&nbsp;1</i>. In accordance
+with the first law of motion it would continue to move
+along this line with uniform velocity if no external force
+acted upon it; but such a force, the sun's attraction, is
+acting, and by virtue of this attraction the body is pulled
+aside from the line <i>P&nbsp;1</i>.</p>
+
+<p>Knowing the velocity and direction of the body's motion
+and the force with which the sun attracts it, the mathematician
+is able to apply Newton's laws of motion so as to
+determine the path of the body, and a few of the possible
+orbits are shown in the figure where the short cross stroke
+marks the point of each orbit which is nearest to the sun.
+This point is called the <i>perihelion</i>.</p>
+
+<p>Without any formal application of mathematics we may
+readily see that the swifter the motion of the body at <i>P</i><span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>
+the shorter will be the time during which it is subjected to
+the sun's attraction at close range, and therefore the force
+exerted by the sun, and the resulting change of motion, will
+be small, as in the orbits <i>P&nbsp;1</i> and <i>P&nbsp;2</i>.</p>
+
+<p>On the other hand, <i>P&nbsp;5</i> and <i>P&nbsp;6</i> represent orbits in which
+the velocity at <i>P</i> was comparatively small, and the resulting
+change of motion greater
+than would be possible for
+a more swiftly moving body.</p>
+
+<p>What would be the orbit
+if the velocity at <i>P</i> were
+reduced to nothing at all?</p>
+
+<p>What would be the effect
+if the body starting at <i>P</i>
+moved directly away from&nbsp;<i>1</i>?</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_20" id="Fig_20"></a>
+<img src="images/i076.png" width="350" height="411" alt="Fig. 20.&mdash;Different kinds of orbits." title="Fig. 20.&mdash;Different kinds of orbits." />
+<span class="caption"><span class="smcap">Fig. 20.</span>&mdash;Different kinds of orbits.</span>
+</div>
+
+<p>The student should not
+fail to observe that the sun's
+attraction tends to pull the
+body at&nbsp;<i>P</i> forward along its
+path, and therefore increases
+its velocity, and that this
+influence continues until
+the planet reaches perihelion, at which point it attains its
+greatest velocity, and the force of the sun's attraction is
+wholly expended in changing the direction of its motion.
+After the planet has passed perihelion the sun begins to
+pull backward and to retard the motion in just the same
+measure that before perihelion passage it increased it, so
+that the two halves of the orbit on opposite sides of a line
+drawn from the perihelion through the sun are exactly
+alike. We may here note the explanation of Kepler's second
+law: when the planet is near the sun it moves faster,
+and the radius vector changes its direction more rapidly
+than when the planet is remote from the sun on account
+of the greater force with which it is attracted, and the exact
+relation between the rates at which the radius vector<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>
+turns in different parts of the orbit, as given by the second
+law, depends upon the changes in this force.</p>
+
+<p>When the velocity is not too great, the sun's backward
+pull, after a planet has passed perihelion, finally overcomes
+it and turns the planet toward the sun again, in such a way
+that it comes back to the point <i>P</i>, moving in the same direction
+and with the same speed as before&mdash;i.&nbsp;e., it has gone
+around the sun in an orbit like <i>P&nbsp;6</i> or <i>P&nbsp;4</i>, an ellipse, along
+which it will continue to move ever after. But we must
+not fail to note that this return into the same orbit is a
+consequence of the last line in the statement of the law of
+gravitation (p. 54), and that, if the magnitude of this force
+were inversely as the cube of the distance or any other proportion
+than the square, the orbit would be something very
+different. If the velocity is too great for the sun's attraction
+to overcome, the orbit will be a hyperbola, like <i>P&nbsp;2</i>,
+along which the body will move away never to return, while
+a velocity just at the limit of what the sun can control gives
+an orbit like <i>P&nbsp;3</i>, a parabola, along which the body moves
+with <i>parabolic velocity</i>, which is ever diminishing as the
+body gets farther from the sun, but is always just sufficient
+to keep it from returning. If the earth's velocity could be
+increased 41 per cent, from 19 up to 27 miles per second, it
+would have parabolic velocity, and would quit the sun's
+company.</p>
+
+<p>The summation of the whole matter is that the orbit in
+which a body moves around the sun, or past the sun, depends
+upon its velocity and if this velocity and the direction
+of the motion at any one point in the orbit are known
+the whole orbit is determined by them, and the position of
+the planet in its orbit for past as well as future times can
+be determined through the application of Newton's laws;
+and the same is true for any other heavenly body&mdash;moon,
+comet, meteor, etc. It is in this way that astronomers are
+able to predict, years in advance, in what particular part of
+the sky a given planet will appear at a given time.<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span></p>
+
+<p>It is sometimes a source of wonder that the planets
+move in ellipses instead of circles, but it is easily seen from
+<a href="#Fig_20">Fig.&nbsp;20</a> that the planet, <i>P</i>, could not by any possibility
+move in a circle, since the direction of its motion at <i>P</i> is
+not at right angles with the line joining it to the sun as it
+must be in a circular orbit, and even if it were perpendicular
+to the radius vector the planet must needs have
+exactly the right velocity given to it at this point, since
+either more or less speed would change the circle into an
+ellipse. In order to produce circular motion there must be
+a balancing of conditions as nice as is required to make a
+pin stand upon its point, and the really surprising thing is
+that the orbits of the planets should be so nearly circular
+as they are. If the orbit of the earth were drawn accurately
+to scale, the untrained eye would not detect the
+slightest deviation from a true circle, and even the orbit of
+Mercury (<a href="#Fig_17">Fig.&nbsp;17</a>), which is much more
+eccentric than that of the earth, might almost
+pass for a circle.</p>
+
+<div class="figright" style="width: 200px;"><a name="Fig_21" id="Fig_21"></a>
+<img src="images/i078.png" width="200" height="331" alt="Fig. 21.
+An impossible orbit." title="Fig. 21.
+An impossible orbit." />
+<span class="caption"><span class="smcap">Fig. 21.</span>
+An impossible orbit.</span>
+</div>
+
+<p>The orbit <i>P&nbsp;2</i>, which lies between the
+parabola and the straight line, is called in
+geometry a hyperbola, and Newton succeeded
+in proving from the law of gravitation
+that a body might move under the
+sun's attraction in a hyperbola as well as
+in a parabola or ellipse; but it must move
+in some one of these curves; no other orbit
+is possible.<a name="FNanchor_A_1" id="FNanchor_A_1"></a><a href="#Footnote_A_1" class="fnanchor">[A]</a> Thus it would not be
+possible for a body moving under the law
+of gravitation to describe about the sun any such orbit
+as is shown in <a href="#Fig_21">Fig.&nbsp;21</a>. If the body passes a second time
+through any point of its orbit, such as <i>P</i> in the figure, then
+it must retrace, time after time, the whole path that it first<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>
+traversed in getting from <i>P</i> around to <i>P</i> again&mdash;i.&nbsp;e., the
+orbit must be an ellipse.</p>
+
+<p>Newton also proved that Kepler's three laws are mere
+corollaries from the law of gravitation, and that to be
+strictly correct the third law must be slightly altered so as
+to take into account the masses of the planets. These are,
+however, so small in comparison with that of the sun, that
+the correction is of comparatively little moment.</p>
+
+<p><a name="S_39" id="S_39"></a>39. <b>Perturbations.</b>&mdash;In what precedes we have considered
+the motion of a planet under the influence of no other
+force than the sun's attraction, while in fact, as the law of
+gravitation asserts, every other body in the universe is in
+some measure attracting it and changing its motion. The
+resulting disturbances in the motion of the attracted body
+are called <i>perturbations</i>, but for the most part these are
+insignificant, because the bodies by whose disturbing attractions
+they are caused are either very small or very remote,
+and it is only when our moving planet, <i>P</i>, comes under the
+influence of some great disturbing power like Jupiter or
+one of the other planets that the perturbations caused by
+their influence need to be taken into account.</p>
+
+<p>The problem of the motion of three bodies&mdash;sun, Jupiter,
+planet&mdash;which must then be dealt with is vastly more complicated
+than that which we have considered, and the ablest
+mathematicians and astronomers have not been able to furnish
+a complete solution for it, although they have worked
+upon the problem for two centuries, and have developed an
+immense amount of detailed information concerning it.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="LICK_OBSERVATORY" id="LICK_OBSERVATORY"></a>
+<a href="images/i080-full.jpg"><img src="images/i080.jpg" width="600" height="338" alt="THE LICK OBSERVATORY, MOUNT HAMILTON, CAL." title="" /></a>
+<span class="caption">THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.</span>
+</div>
+
+<p>In general each planet works ceaselessly upon the orbit
+of every other, changing its size and shape and position,
+backward and forward in accordance with the law of gravitation,
+and it is a question of serious moment how far this
+process may extend. If the diameter of the earth's orbit
+were very much increased or diminished by the perturbing
+action of the other planets, the amount of heat received
+from the sun would be correspondingly changed, and the<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>
+earth, perhaps, be rendered unfit for the support of life.
+The tipping of the plane of the earth's orbit into a new
+position might also produce serious consequences; but the
+great French mathematician of a century ago, Laplace,
+succeeded in proving from the law of gravitation that although
+both of these changes are actually in progress they
+can not, at least for millions of years, go far enough to
+prove of serious consequence, and the same is true for all
+the other planets, unless here and there an asteroid may
+prove an exception to the rule.</p>
+
+<p>The precession (<a href="#CHAPTER_V">Chapter&nbsp;V</a>) is a striking illustration
+of a perturbation of slightly different character from the
+above, and another is found in connection with the plane
+of the moon's orbit. It will be remembered that the moon
+in its motion among the stars never goes far from the
+ecliptic, but in a complete circuit of the heavens crosses it
+twice, once in going from south to north and once in the
+opposite direction. The points at which it crosses the
+ecliptic are called the <i>nodes</i>, and under the perturbing influence
+of the sun these nodes move westward along the
+ecliptic about twenty degrees per year, an extraordinarily
+rapid perturbation, and one of great consequence in the
+theory of eclipses.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_22" id="Fig_22"></a>
+<img src="images/i083.png" width="350" height="335" alt="Fig. 22.&mdash;A planet subject to great perturbations
+by Jupiter." title="Fig. 22.&mdash;A planet subject to great perturbations
+by Jupiter." />
+<span class="caption"><span class="smcap">Fig. 22.</span>&mdash;A planet subject to great perturbations
+by Jupiter.</span>
+</div>
+
+<p><a name="S_40" id="S_40"></a>40. <b>Weighing the planets.</b>&mdash;Although these perturbations
+can not be considered dangerous, they are interesting since
+they furnish a method for weighing the planets which produce
+them. From the law of gravitation we learn that the
+ability of a planet to produce perturbations depends directly
+upon its mass, since the force <i>F</i> which it exerts contains
+this mass, <i>m'</i>, as a factor. So, too, the divisor <i>r</i><sup>2</sup> in
+the expression for the force shows that the distance between
+the disturbing and disturbed bodies is a matter of
+great consequence, for the smaller the distance the greater
+the force. When, therefore, the mass of a planet such as
+Jupiter is to be determined from the perturbations it produces,
+it is customary to select some such opportunity as<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>
+is presented in <a href="#Fig_22">Fig.&nbsp;22</a>, where one of the small planets,
+called asteroids, is represented as moving in a very eccentric
+orbit, which at one point approaches close to the orbit
+of Jupiter, and at another place comes near to the orbit of
+the earth. For the most part
+Jupiter will not exert any
+very great disturbing influence
+upon a planet moving in
+such an orbit as this, since it
+is only at rare intervals that
+the asteroid and Jupiter approach
+so close to each other,
+as is shown in the figure.
+The time during which the
+asteroid is little affected by
+the attraction of Jupiter is
+used to study the motion given
+to it by the sun's attraction&mdash;that
+is, to determine carefully the undisturbed orbit
+in which it moves; but there comes a time at which the
+asteroid passes close to Jupiter, as shown in the figure, and
+the orbital motion which the sun imparts to it will then be
+greatly disturbed, and when the planet next comes round
+to the part of its orbit near the earth the effect of these
+disturbances upon its apparent position in the sky will be
+exaggerated by its close proximity to the earth. If now
+the astronomer observes the actual position of the asteroid
+in the sky, its right ascension and declination, and compares
+these with the position assigned to the planet by the
+law of gravitation when the attraction of Jupiter is ignored,
+the differences between the observed right ascensions and
+declinations and those computed upon the theory of undisturbed
+motion will measure the influence that Jupiter has
+had upon the asteroid, and the amount by which Jupiter has
+shifted it, compared with the amount by which the sun has
+moved it&mdash;that is, with the motion in its orbit&mdash;furnishes<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>
+the mass of Jupiter expressed as a fractional part of the
+mass of the sun.</p>
+
+<p>There has been determined in this manner the mass of
+every planet in the solar system which is large enough to
+produce any appreciable perturbation, and all these masses
+prove to be exceedingly small fractions of the mass of the
+sun, as may be seen from the following table, in which is
+given opposite the name of each planet the number by
+which the mass of the sun must be divided in order to
+get the mass of the planet:</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">Mercury</td><td align="right">7,000,000 (?)</td></tr>
+<tr><td align="left">Venus</td><td align="right">408,000</td></tr>
+<tr><td align="left">Earth</td><td align="right">329,000</td></tr>
+<tr><td align="left">Mars</td><td align="right">3,093,500</td></tr>
+<tr><td align="left">Jupiter</td><td align="right">1,047.4</td></tr>
+<tr><td align="left">Saturn</td><td align="right">3,502</td></tr>
+<tr><td align="left">Uranus</td><td align="right">22,800</td></tr>
+<tr><td align="left">Neptune</td><td align="right">19,700</td></tr>
+</table></div>
+
+<p>It is to be especially noted that the mass given for each
+planet includes the mass of all the satellites which attend
+it, since their influence was felt in the perturbations from
+which the mass was derived. Thus the mass assigned to
+the earth is the combined mass of earth and moon.</p>
+
+<p><a name="S_41" id="S_41"></a>41. <b>Discovery of Neptune.</b>&mdash;The most famous example of
+perturbations is found in connection with the discovery,
+in the year 1846, of Neptune, the outermost planet of the
+solar system. For many years the motion of Uranus, his
+next neighbor, had proved a puzzle to astronomers. In
+accordance with Kepler's first law this planet should move
+in an ellipse having the sun at one of its foci, but no ellipse
+could be found which exactly fitted its observed path among
+the stars, although, to be sure, the misfit was not very pronounced.
+Astronomers surmised that the small deviations
+of Uranus from the best path which theory combined with
+observation could assign, were due to perturbations in its<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span>
+motion caused by an unknown planet more remote from
+the sun&mdash;a thing easy to conjecture but hard to prove, and
+harder still to find the unknown disturber. But almost
+simultaneously two young men, Adams in England and
+Le Verrier in France, attacked the problem quite independently
+of each other, and carried it to a successful solution,
+showing that if the irregularities in the motion of
+Uranus were indeed caused by an unknown planet, then
+that planet must, in September, 1846, be in the direction
+of the constellation Aquarius; and there it was found on
+September 23d by the astronomers of the Berlin Observatory
+whom Le Verrier had invited to search for it, and found
+within a degree of the exact point which the law of gravitation
+in his hands had assigned to it.</p>
+
+<p>This working backward from the perturbations experienced
+by Uranus to the cause which produced them is justly
+regarded as one of the greatest scientific achievements of
+the human intellect, and it is worthy of note that we are
+approaching the time at which it may be repeated, for Neptune
+now behaves much as did Uranus three quarters of a
+century ago, and the most plausible explanation which can
+be offered for these anomalies in its path is that the bounds
+of the solar system must be again enlarged to include another
+disturbing planet.</p>
+
+<p><a name="S_42" id="S_42"></a>42. <b>The shape of a planet.</b>&mdash;There is an effect of gravitation
+not yet touched upon, which is of considerable interest
+and wide application in astronomy&mdash;viz., its influence in determining
+the shape of the heavenly bodies. The earth is
+a globe because every part of it is drawn toward the center
+by the attraction of the other parts, and if this attraction
+on its surface were everywhere of equal force the material
+of the earth would be crushed by it into a truly spherical
+form, no matter what may have been the shape in which it
+was originally made. But such is not the real condition of
+the earth, for its diurnal rotation develops in every particle
+of its body a force which is sometimes called <i>centrifugal</i>,<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span>
+but which is really nothing more than the inertia of its
+particles, which tend at every moment to keep unchanged
+the direction of their motion and which thus resist the attraction
+that pulls them into a circular path marked out
+by the earth's rotation, just as a stone tied at the end of
+a string and swung swiftly in a circle pulls upon the
+string and opposes the constraint which keeps it moving
+in a circle. A few experiments with such a stone will
+show that the faster it goes the harder does it pull upon
+the string, and the same is true of each particle of the
+earth, the swiftly moving ones near the equator having
+a greater centrifugal force than the slow ones near the
+poles. At the equator the centrifugal force is directly
+opposed to the force of gravity, and in effect diminishes it,
+so that, comparatively, there is an excess of gravity at the
+poles which compresses the earth along its axis and causes
+it to bulge out at the equator until a balance is thus restored.
+As we have learned from the study of geography,
+in the case of the earth, this compression amounts to about
+27 miles, but in the larger planets, Jupiter and Saturn, it
+is much greater, amounting to several thousand miles.</p>
+
+<p>But rotation is not the only influence that tends to
+pull a planet out of shape. The attraction which the earth
+exerts upon the moon is stronger on the near side and
+weaker on the far side of our satellite than at its center,
+and this difference of attraction tends to warp the moon, as
+is illustrated in <a href="#Fig_23">Fig.&nbsp;23</a> where <i>1</i>, <i>2</i>, and <i>3</i> represent pieces
+of iron of equal mass placed in line on a table near a horseshoe
+magnet, <i>H</i>. Each piece of iron is attracted by the
+magnet and is held back by a weight to which it is
+fastened by means of a cord running over a pulley, <i>P</i>,
+at the edge of the table. These weights are all to be
+supposed equally heavy and each of them pulls upon its
+piece of iron with a force just sufficient to balance the
+attraction of the magnet for the middle piece, No.&nbsp;<i>2</i>.
+It is clear that under this arrangement No.&nbsp;<i>2</i> will move<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span>
+neither to the right nor to the left, since the forces exerted
+upon it by the magnet and the weight just balance each
+other. Upon No.&nbsp;<i>1</i>, however, the magnet pulls harder
+than upon No.&nbsp;<i>2</i>, because it is nearer and its pull therefore
+more than balances the force exerted by the weight,
+so that No.&nbsp;<i>1</i> will be pulled away from No.&nbsp;<i>2</i> and will
+stretch the elastic cords, which are represented by the
+lines joining <i>1</i> and <i>2</i>, until their tension, together with the
+force exerted by the weight, just balances the attraction
+of the magnet. For No.&nbsp;<i>3</i>, the force exerted by the magnet
+is less than that of the weight, and it will also be pulled
+away from No.&nbsp;<i>2</i> until its elastic cords are stretched to the
+proper tension. The net result is that the three blocks
+which, without the magnet's influence, would be held close
+together by the elastic cords, are pulled apart by this outside
+force as far as the resistance of the cords will permit.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_23" id="Fig_23"></a>
+<img src="images/i087.png" width="500" height="258" alt="Fig. 23.&mdash;Tide-raising forces." title="Fig. 23.&mdash;Tide-raising forces." />
+<span class="caption"><span class="smcap">Fig. 23.</span>&mdash;Tide-raising forces.</span>
+</div>
+
+<p>An entirely analogous set of forces produces a similar
+effect upon the shape of the moon. The elastic cords of
+<a href="#Fig_23">Fig.&nbsp;23</a> stand for the attraction of gravitation by which all
+the parts of the moon are bound together. The magnet
+represents the earth pulling with unequal force upon different
+parts of the moon. The weights are the inertia of the
+moon in its orbital motion which, as we have seen in a<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span>
+previous section, upon the whole just balances the earth's
+attraction and keeps the moon from falling into it. The
+effect of these forces is to stretch out the moon along a line
+pointing toward the earth, just as the blocks were stretched
+out along the line of the magnet, and to make this diameter
+of the moon slightly but permanently longer than
+the others.</p>
+
+<div class="figright" style="width: 200px;"><a name="Fig_24" id="Fig_24"></a>
+<img src="images/i088.png" width="200" height="581" alt="Fig. 24.&mdash;The tides." title="Fig. 24.&mdash;The tides." />
+<span class="caption"><span class="smcap">Fig. 24.</span>&mdash;The tides.</span>
+</div>
+
+<p><b>The tides.</b>&mdash;Similarly the moon and the sun attract opposite
+sides of the earth with different forces and feebly
+tend to pull it out of shape. But here
+a new element comes into play: the
+earth turns so rapidly upon its axis
+that its solid parts have no time in
+which to yield sensibly to the strains,
+which shift rapidly from one diameter
+to another as different parts of the
+earth are turned toward the moon, and
+it is chiefly the waters of the sea which
+respond to the distorting effect of the
+sun's and moon's attraction. These are
+heaped up on opposite sides of the
+earth so as to produce a slight elongation
+of its diameter, and <a href="#Fig_24">Fig.&nbsp;24</a> shows
+how by the earth's rotation this swelling
+of the waters is swept out from
+under the moon and is pulled back by
+the moon until it finally takes up some
+such position as that shown in the figure
+where the effect of the earth's rotation
+in carrying it one way is just balanced
+by the moon's attraction urging
+it back on line with the moon. This heaping up of the
+waters is called a <i>tide</i>. If <i>I</i> in the figure represents a little
+island in the sea the waters which surround it will of
+course accompany it in its diurnal rotation about the
+earth's axis, but whenever the island comes back to the<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span>
+position <i>I</i>, the waters will swell up as a part of the tidal
+wave and will encroach upon the land in what is called
+high tide or flood tide. So too when they reach <i>I''</i>, half a
+day later, they will again rise in flood tide, and midway
+between these points, at <i>I'</i>, the waters must subside, giving
+low or ebb tide.</p>
+
+<p>The height of the tide raised by the moon in the open
+sea is only a very few feet, and the tide raised by the sun is
+even less, but along the coast of a continent, in bays and
+angles of the shore, it often happens that a broad but low
+tidal wave is forced into a narrow corner, and then the rise
+of the water may be many feet, especially when the solar
+tide and the lunar tide come in together, as they do twice
+in every month, at new and full moon. Why do they come
+together at these times instead of some other?</p>
+
+<p>Small as are these tidal effects, it is worth noting that
+they may in certain cases be very much greater&mdash;e.&nbsp;g., if
+the moon were as massive as is the sun its tidal effect
+would be some millions of times greater than it now is and
+would suffice to grind the earth into fragments. Although
+the earth escapes this fate, some other bodies are not so
+fortunate, and we shall see in later chapters some evidence
+of their disintegration.</p>
+
+<p><a name="S_43" id="S_43"></a>43. <b>The scope of the law of gravitation.</b>&mdash;In all the domain
+of physical science there is no other law so famous as
+the Newtonian law of gravitation; none other that has been
+so dwelt upon, studied, and elaborated by astronomers and
+mathematicians, and perhaps none that can be considered
+so indisputably proved. Over and over again mathematical
+analysis, based upon this law, has pointed out conclusions
+which, though hitherto unsuspected, have afterward
+been found true, as when Newton himself derived as a corollary
+from this law that the earth ought to be flattened at
+the poles&mdash;a thing not known at that time, and not proved
+by actual measurement until long afterward. It is, in fact,
+this capacity for predicting the unknown and for explaining<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>
+in minutest detail the complicated phenomena of the
+heavens and the earth that constitutes the real proof of the
+law of gravitation, and it is therefore worth while to note
+that at the present time there are a very few points at
+which the law fails to furnish a satisfactory account of
+things observed. Chief among these is the case of the planet
+Mercury, the long diameter of whose orbit is slowly turning
+around in a way for which the law of gravitation as yet furnishes
+no explanation. Whether this is because the law itself
+is inaccurate or incomplete, or whether it only marks a case
+in which astronomers have not yet properly applied the
+law and traced out its consequences, we do not know; but
+whether it be the one or the other, this and other similar
+cases show that even here, in its most perfect chapter,
+astronomy still remains an incomplete science.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span></p>
+<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V</h2>
+
+<h3>THE EARTH AS A PLANET</h3>
+
+
+<p><a name="S_44" id="S_44"></a>44. <b>The size of the earth.</b>&mdash;The student is presumed to
+have learned, in his study of geography, that the earth is a
+globe about 8,000 miles in diameter and, without dwelling
+upon the "proofs" which are commonly given for these
+statements, we proceed to consider the principles upon
+which the measurement of
+the earth's size and shape
+are based.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_25" id="Fig_25"></a>
+<img src="images/i091.png" width="350" height="367" alt="Fig. 25.&mdash;Measuring the size of the earth." title="Fig. 25.&mdash;Measuring the size of the earth." />
+<span class="caption"><span class="smcap">Fig. 25.</span>&mdash;Measuring the size of the earth.</span>
+</div>
+
+<p>In <a href="#Fig_25">Fig.&nbsp;25</a> the circle represents
+a meridian section
+of the earth; <i>P&nbsp;P'</i> is the
+axis about which it rotates,
+and the dotted lines represent
+a beam of light coming
+from a star in the plane
+of the meridian, and so distant
+that the dotted lines
+are all practically parallel
+to each other. The several
+radii drawn through the points <i>1</i>, <i>2</i>, <i>3</i>, represent the direction
+of the vertical at these points, and the angles which
+these radii produced, make with the rays of starlight are
+each equal to the angular distance of the star from the
+zenith of the place at the moment the star crosses the meridian.
+We have already seen, in <a href="#CHAPTER_II">Chapter&nbsp;II</a>, how these
+angles may be measured, and it is apparent from the figure
+that the difference between any two of these angles&mdash;e.&nbsp;g.,<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>
+the angles at <i>1</i> and <i>2</i>&mdash;is equal to the angle at the center,
+<i>O</i>, between the points <i>1</i> and <i>2</i>. By measuring these angular
+distances of the star from the zenith, the astronomer
+finds the angles at the center of the earth between the stations
+<i>1</i>, <i>2</i>, <i>3</i>, etc., at which his observations are made. If
+the meridian were a perfect circle the change of zenith distance
+of the star, as one traveled along a meridian from the
+equator to the pole, would be perfectly uniform&mdash;the same
+number of degrees for each hundred miles traveled&mdash;and
+observations made in many parts of the earth show that
+this is very nearly true, but that, on the whole, as we approach
+the pole it is necessary to travel a little greater distance
+than is required for a given change in the angle at
+the equator. The earth is, in fact, flattened at the poles to
+the amount of about 27 miles in the length of its diameter,
+and by this amount, as well as by smaller variations due to
+mountains and valleys, the shape of the earth differs from
+a perfect sphere. These astronomical measurements of the
+curvature of the earth's surface furnish by far the most satisfactory
+proof that it is very approximately a sphere, and
+furnish as its equatorial diameter 7,926 miles.</p>
+
+<p>Neglecting the <i>compression</i>, as it is called, i.&nbsp;e., the 27
+miles by which the equatorial diameter exceeds the polar,
+the size of the earth may easily be found by measuring the
+distance <i>1</i>&nbsp;-&nbsp;<i>2</i> along the surface and by combining with this
+the angle <i>1&nbsp;O&nbsp;2</i> obtained through measuring the meridian
+altitudes of any star as seen from <i>1</i> and <i>2</i>. Draw on paper
+an angle equal to the measured difference of altitude and
+find how far you must go from its vertex in order to have
+the distance between the sides, measured along an arc of
+a circle, equal to the measured distance between <i>1</i> and <i>2</i>.
+This distance from the vertex will be the earth's radius.</p>
+
+<p><a name="Exercise_19" id="Exercise_19"></a><span class="smcap">Exercise 19.</span>&mdash;Measure the diameter of the earth by
+the method given above. In order that this may be done
+satisfactorily, the two stations at which observations are
+made must be separated by a considerable distance&mdash;i.&nbsp;e.,<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>
+200 miles. They need not be on the same meridian, but if
+they are on different meridians in place of the actual distance
+between them, there must be used the projection of
+that distance upon the meridian&mdash;i.&nbsp;e., the north and south
+part of the distance.</p>
+
+<p>By co-operation between schools in the Northern and
+Southern States, using a good map to obtain the required
+distances, the diameter of the earth
+may be measured with the plumb-line
+apparatus described in <a href="#CHAPTER_II">Chapter&nbsp;II</a>
+and determined within a small
+percentage of its true value.</p>
+
+<p><a name="S_45" id="S_45"></a>45. <b>The mass of the earth.</b>&mdash;We
+have seen in <a href="#CHAPTER_IV">Chapter&nbsp;IV</a> the possibility
+of determining the masses of
+the planets as fractional parts of
+the sun's mass, but nothing was
+there shown, or could be shown,
+about measuring these masses after
+the common fashion in kilogrammes
+or tons. To do this we must first
+get the mass of the earth in tons or
+kilogrammes, and while the principles
+involved in this determination
+are simple enough, their actual application
+is delicate and difficult.</p>
+
+<div class="figleft" style="width: 225px;"><a name="Fig_26" id="Fig_26"></a>
+<img src="images/i093.png" width="225" height="458" alt="Fig. 26.&mdash;Illustrating the principles
+involved in weighing
+the earth." title="Fig. 26.&mdash;Illustrating the principles
+involved in weighing
+the earth." />
+<span class="caption"><span class="smcap">Fig. 26.</span>&mdash;Illustrating the principles
+involved in weighing
+the earth.</span>
+</div>
+
+<p>In <a href="#Fig_26">Fig.&nbsp;26</a> we suppose a long
+plumb line to be suspended above
+the surface of the earth and to be attracted toward the
+center of the earth, <i>C</i>, by a force whose intensity is (<a href="#CHAPTER_IV">Chapter&nbsp;IV</a>)</p>
+
+<p class="center"><i>F</i> = <i>k</i> <i>mE</i>/<i>R</i><sup>2</sup>,</p>
+
+<p>where <i>E</i> denotes the mass of the earth, which is to be determined
+by experiment, and <i>R</i> is the radius of the earth,
+3,963 miles. If there is no disturbing influence present,<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>
+the plumb line will point directly downward, but if a massive
+ball of lead or other heavy substance is placed at one
+side, <i>1</i>, it will attract the plumb line with a force equal to</p>
+
+<p class="center"><i>f</i> = <i>k</i> <i>mB</i>/<i>r</i><sup>2</sup>,</p>
+
+<p>where <i>r</i> is the distance of its center from the plumb bob
+and <i>B</i> is its mass which we may suppose, for illustration,
+to be a ton. In consequence of this attraction the plumb
+line will be pulled a little to one side, as shown by the dotted
+line, and if we represent by <i>l</i> the length of the plumb
+line and by <i>d</i> the distance between the original and the
+disturbed positions of the plumb bob we may write the proportion</p>
+
+<p class="center"><i>F</i> : <i>f</i> :: <i>l</i> : <i>d</i>;</p>
+
+<p>and introducing the values of <i>F</i> and <i>f</i> given above, and
+solving for <i>E</i> the proportion thus transformed, we find</p>
+
+<p class="center"><i>E</i> = <i>B</i> · <i>l</i>/<i>d</i> · (<i>R</i>/<i>r</i>)<sup>2</sup>.</p>
+
+<p>In this equation the mass of the ball, <i>B</i>, the length of the
+plumb line, <i>l</i>, the distance between the center of the ball
+and the center of the plumb bob, <i>r</i>, and the radius of the
+earth, <i>R</i>, can all be measured directly, and <i>d</i>, the amount
+by which the plumb bob is pulled to one side by the ball, is
+readily found by shifting the ball over to the other side, at
+<i>2</i>, and measuring with a microscope how far the plumb
+bob moves. This distance will, of course, be equal to <i>2&nbsp;d</i>.</p>
+
+<p>By methods involving these principles, but applied in a
+manner more complicated as well as more precise, the mass
+of the earth is found to be, in tons, 6,642&nbsp;×&nbsp;10<sup>18</sup>&mdash;i.&nbsp;e., 6,642
+followed by 18 ciphers, or in kilogrammes 60,258&nbsp;×&nbsp;10<sup>20</sup>.
+The earth's atmosphere makes up about a millionth part
+of this mass.</p>
+
+<p>If the length of the plumb line were 100 feet, the
+weight of the ball a ton, and the distance between the two<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>
+positions of the ball, <i>1</i> and <i>2</i>, six feet, how many inches, <i>d</i>,
+would the plumb bob be pulled out of place?</p>
+
+<p>Find from the mass of the earth and the data of <a href="#S_40">§&nbsp;40</a>
+the mass of the sun in tons. Find also the mass of Mars.
+The computation can be very greatly abridged by the use
+of logarithms.</p>
+
+<p><a name="S_46" id="S_46"></a>46. <b>Precession.</b>&mdash;That the earth is isolated in space and
+has no support upon which to rest, is sufficiently shown by
+the fact that the stars are visible upon every side of it, and
+no support can be seen stretching out toward them. We
+must then consider the earth to be a globe traveling freely
+about the sun in a circuit which it completes once every
+year, and rotating once in every twenty-four hours about
+an axis which remains at all seasons directed very nearly
+toward the star Polaris. The student should be able to
+show from his own observations of the sun that, with reference
+to the stars, the direction of the sun from the earth
+changes about a degree a day. Does this prove that the
+earth revolves about the sun?</p>
+
+<p>But it is only in appearance that the pole maintains its
+fixed position among the stars. If photographs are taken
+year after year, after the manner of <a href="#Exercise_7">Exercise&nbsp;7</a>, it will be
+found that slowly the pole is moving (nearly) toward Polaris,
+and making this star describe a smaller and smaller
+circle in its diurnal path, while stars on the other side of
+the pole (in right ascension 12h.) become more distant
+from it and describe larger circles in their diurnal motion;
+but the process takes place so slowly that the space of a
+lifetime is required for the motion of the pole to equal the
+angular diameter of the full moon.</p>
+
+<p>Spin a top and note how its rapid whirl about its axis
+corresponds to the earth's diurnal rotation. When the axis
+about which the top spins is truly vertical the top "sleeps";
+but if the axis is tipped ever so little away from the vertical
+it begins to wobble, so that if we imagine the axis prolonged
+out to the sky and provided with a pencil point as<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span>
+a marker, this would trace a circle around the zenith, along
+which the pole of the top would move, and a little observation
+will show that the more the top is tipped from the
+vertical the larger does this circle become and the more
+rapidly does the wobbling take place. Were it not for the
+spinning of the top about its axis, it would promptly fall
+over when tipped from the vertical position, but the spin
+combines with the force which pulls the top over and produces
+the wobbling motion. Spin the top in opposite
+directions, with the hands of a watch and contrary to the
+hands of a watch, and note the effect which is produced
+upon the wobbling.</p>
+
+<p>The earth presents many points of resemblance to the
+top. Its diurnal rotation is the spin about the axis. This
+axis is tipped 23.5° away from the perpendicular to its
+orbit (obliquity of the ecliptic) just as the axis of the top
+is tipped away from the vertical line. In consequence of
+its rapid spin, the body of the earth bulges out at the equator
+(27 miles), and the sun and moon, by virtue of their attraction
+(see <a href="#CHAPTER_IV">Chapter&nbsp;IV</a>), lay hold of this protuberance and
+pull it down toward the plane of the earth's orbit, so that if
+it were not for the spin this force would straighten the axis
+up and set it perpendicular to the orbit plane. But here, as
+in the case of the top, the spin and the tipping force combine
+to produce a wobble which is called precession, and
+whose effect we recognize in the shifting position of the
+pole among the stars. The motion of precession is very
+much slower than the wobbling of the top, since the tipping
+force for the earth is relatively very small, and a period
+of nearly 26,000 years is required for a complete circuit
+of the pole about its center of motion. Friction ultimately
+stops both the spin and the wobble of the top, but
+this influence seems wholly absent in the case of the earth,
+and both rotation and precession go on unchanged from
+century to century, save for certain minor forces which for
+a time change the direction or rate of the precessional<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span>
+motion, first in one way and then in another, without in
+the long run producing any results of consequence.</p>
+
+<p>The center of motion, about which the pole travels in a
+small circle having an angular radius of 23.5°, is at that
+point of the heavens toward which a perpendicular to the
+plane of the earth's orbit points, and may be found on the
+star map in right ascension 18h. 0m. and declination 66.5°.</p>
+
+<p><a name="Exercise_20" id="Exercise_20"></a><span class="smcap">Exercise 20.</span>&mdash;Find this point on the map, and draw
+as well as you can the path of the pole about it. The motion
+of the pole along its path is toward the constellation
+Cepheus. Mark the position of the pole along this path
+at intervals of 1,000 years, and refer to these positions in
+dealing with some of the following questions:</p>
+
+<p>Does the wobbling of the top occur in the same direction
+as the motion of precession? Do the tipping forces
+applied to the earth and top act in the same direction?
+What will be the polar star 12,000 years hence? The
+Great Pyramid of Egypt is thought to have been used
+as an observatory when Alpha Draconis was the bright star
+nearest the pole. How long ago was that?</p>
+
+<p>The motion of the pole of course carries the equator
+and the equinoxes with it, and thus slowly changes the
+right ascensions and declinations of all the stars. On this
+account it is frequently called the precession of the equinoxes,
+and this motion of the equinox, slow though it is,
+is a matter of some consequence in connection with chronology
+and the length of the year.</p>
+
+<p>Will the precession ever bring back the right ascensions
+and declinations to be again what they now are?</p>
+
+<p>In what direction is the pole moving with respect to
+the Big Dipper? Will its motion ever bring it exactly to
+Polaris? How far away from Polaris will the precession
+carry the pole? What other bright stars will be brought
+near the pole by the precession?</p>
+
+<p><a name="S_47" id="S_47"></a>47. <b>The warming of the earth.</b>&mdash;Winter and summer alike
+the day is on the average warmer than the night, and it is<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span>
+easy to see that this surplus of heat comes from the sun by
+day and is lost by night through radiation into the void
+which surrounds the earth; just as the heat contained in a
+mass of molten iron is radiated away and the iron cooled
+when it is taken out from the furnace and placed amid
+colder surroundings. The earth's loss of heat by radiation
+goes on ceaselessly day and night, and were it not for the
+influx of solar heat this radiation would steadily diminish
+the temperature toward what is called the "absolute zero"&mdash;i.&nbsp;e.,
+a state in which all heat has been taken away and
+beyond which there can be no greater degree of cold. This
+must not be confounded with the zero temperatures shown
+by our thermometers, since it lies nearly 500° below the zero
+of the Fahrenheit scale (-273° Centigrade), a temperature
+which by comparison makes the coldest winter weather
+seem warm, although the ordinary thermometer may register
+many degrees below its zero. The heat radiated by the
+sun into the surrounding space on every side of it is another
+example of the same cooling process, a hot body giving up
+its heat to the colder space about it, and it is the minute
+fraction of this heat poured out by the sun, and in small
+part intercepted by the earth, which warms the latter and
+produces what we call weather, climate, the seasons, etc.</p>
+
+<p>Observe the fluctuations, the ebb and flow, which are
+inherent in this process. From sunset to sunrise there is
+nothing to compensate the steady outflow of heat, and
+air and ground grow steadily colder, but with the sunrise
+there comes an influx of solar heat, feeble at first because
+it strikes the earth's surface very obliquely, but becoming
+more and more efficient as the sun rises higher in the sky.
+But as the air and the ground grow warm during the morning
+hours they part more and more readily and rapidly with
+their store of heat, just as a steam pipe or a cup of coffee
+radiates heat more rapidly when very hot. The warmest
+hour of the day is reached when these opposing tendencies
+of income and expenditure of heat are just balanced; and<span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span>
+barring such disturbing factors as wind and clouds, the gain
+in temperature usually extends to the time&mdash;an hour or two
+beyond noon&mdash;at which the diminishing altitude of the sun
+renders his rays less efficient, when radiation gains the
+upper hand and the temperature becomes for a short time
+stationary, and then commences to fall steadily until the
+next sunrise.</p>
+
+<p>We have here an example of what is called a periodic
+change&mdash;i.&nbsp;e., one which, within a definite and uniform
+period (24 hours), oscillates from a minimum up to a
+maximum temperature and then back again to a minimum,
+repeating substantially the same variation day after day.
+But it must be understood that minor causes not taken
+into account above, such as winds, water, etc., produce
+other fluctuations from day to day which sometimes obscure
+or even obliterate the diurnal variation of temperature
+caused by the sun.</p>
+
+<p>Expose the back of your hand to the sun, holding the
+hand in such a position that the sunlight strikes perpendicularly
+upon it; then turn the hand so that the light
+falls quite obliquely upon it and note how much more vigorous
+is the warming effect of the sun in the first position
+than in the second. It is chiefly this difference of angle
+that makes the sun's warmth more effective when he is
+high up in the sky than when he is near the horizon, and
+more effective in summer than in winter.</p>
+
+<p>We have seen in <a href="#CHAPTER_III">Chapter&nbsp;III</a> that the sun's motion
+among the stars takes place along a path which carries it
+alternately north and south of the equator to a distance
+of 23.5°, and the stars show by their earlier risings and
+later settings, as we pass from the equator toward the
+north pole of the heavens, that as the sun moves northward
+from the equator, each day in the northern hemisphere
+will become a little longer, each night a little shorter,
+and every day the sun will rise higher toward the zenith
+until this process culminates toward the end of June, when<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span>
+the sun begins to move southward, bringing shorter days
+and smaller altitudes until the Christmas season, when
+again it is reversed and the sun moves northward. We
+have here another periodic variation, which runs its complete
+course in a period of a year, and it is easy to see that
+this variation must have a marked effect on the warming
+of the earth, the long days and great altitudes of summer
+producing the greater warmth of that season, while the
+shorter days and lower altitudes of December, by diminishing
+the daily supply of solar heat, bring on the winter's
+cold. The succession of the seasons, winter following summer
+and summer winter, is caused by the varying altitude
+of the sun, and this in turn is due to the obliquity of the
+ecliptic, or, what is the same thing, the amount by which
+the axis of the earth is tipped from being perpendicular to
+the plane of its orbit, and the seasons are simply a periodic
+change in the warming of the earth, quite comparable with
+the diurnal change but of longer period.</p>
+
+<p>It is evident that the period within which the succession
+of winter and summer is completed, the year, as we commonly
+call it, must equal the time required by the sun to
+go from the vernal equinox around to the vernal equinox
+again, since this furnishes a complete cycle of the sun's
+motions north and south from the equator. On account
+of the westward motion of the equinox (precession) this
+is not quite the same as the time required for a complete
+revolution of the earth in its orbit, but is a little
+shorter (20m. 23s.), since the equinox moves back to meet
+the sun.</p>
+
+<p><a name="S_48" id="S_48"></a>48. <b>Relation of the sun to climate.</b>&mdash;It is clear that both
+the northern and southern hemispheres of the earth must
+have substantially the same kind of seasons, since the motion
+of the sun north and south affects both alike; but
+when the sun is north of the equator and warming our
+hemisphere most effectively, his light falls more obliquely
+upon the other hemisphere, the days there are short and<span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>
+winter reigns at the time we are enjoying summer, while
+six months later the conditions are reversed.</p>
+
+<p>In those parts of the earth near the equator&mdash;the torrid
+zone&mdash;there is no such marked change from cold to warm
+as we experience, because, as the sun never gets more than
+23.5° away from the celestial equator, on every day of the
+year he mounts high in the tropic skies, always coming
+within 23.5° of the zenith, and usually closer than this, so
+that there is no such periodic change in the heat supply as
+is experienced in higher latitudes, and within the tropics
+the temperature is therefore both higher and more uniform
+than in our latitude.</p>
+
+<p>In the frigid zones, on the contrary, the sun never rises
+high in the sky; at the poles his greatest altitude is only
+23.5°, and during the winter season he does not rise at all,
+so that the temperature is here low the whole year round,
+and during the winter season, when for weeks or months at
+a time the supply of solar light is entirely cut off, the temperature
+falls to a degree unknown in more favored climes.</p>
+
+<p>If the obliquity of the ecliptic were made 10° greater,
+what would be the effect upon the seasons in the temperate
+zones? What if it were made 10° less?</p>
+
+<p>Does the precession of the equinoxes have any effect
+upon the seasons or upon the climate of different parts of
+the earth?</p>
+
+<p>If the axis of the earth pointed toward Arcturus instead
+of Polaris, would the seasons be any different from what
+they are now?</p>
+
+<p><a name="S_49" id="S_49"></a>49. <b>The atmosphere.</b>&mdash;Although we live upon its surface,
+we are not outside the earth, but at the bottom of a sea of
+air which forms the earth's outermost layer and extends
+above our heads to a height of many miles. The study of
+most of the phenomena of the atmosphere belongs to that
+branch of physics called meteorology, but there are a few
+matters which fairly come within our consideration of the
+earth as a planet.<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> We can not see the stars save as we look through this
+atmosphere, and the light which comes through it is bent
+and oftentimes distorted so as to present serious obstacles
+to any accurate telescopic study of the heavenly bodies.
+Frequently this disturbance is visible to the naked eye, and
+the stars are said to twinkle&mdash;i.&nbsp;e., to quiver and change
+color many times per second, solely in consequence of a disturbed
+condition of the air and not from anything which
+goes on in the star. This effect is more marked low down
+in the sky than near the zenith, and it is worth noting that
+the planets show very little of it because the light they
+send to the earth comes from a disk of sensible area, while
+a star, being much smaller and farther from the earth, has
+its disk reduced practically to a mere point whose light is
+more easily affected by local disturbances in the atmosphere
+than is the broader beam which comes from the planets'
+disk.</p>
+
+<p><a name="S_50" id="S_50"></a>50. <b>Refraction.</b>&mdash;At all times, whether the stars twinkle
+or not, their light is bent in its passage through the atmosphere,
+so that the stars appear to stand higher up in the
+sky than their true positions. This effect, which the astronomer
+calls refraction, must be allowed for in observations
+of the more precise class, although save at low altitudes
+its amount is a very small fraction of a degree, but
+near the horizon it is much exaggerated in amount and
+becomes easily visible to the naked eye by distorting the
+disks of the sun and moon from circles into ovals with
+their long diameters horizontal. The refraction lifts both
+upper and lower edge of the sun, but lifts the lower edge
+more than the upper, thus shortening the vertical diameter.
+See <a href="#Fig_27">Fig.&nbsp;27</a>, which shows not only this effect, but also the
+reflection of the sun from the curved surface of the sea,
+still further flattening the image. If the surface of the
+water were flat, the reflected image would have the same
+shape as the sun's disk, and its altered appearance is sometimes
+cited as a proof that the earth's surface is curved.<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span></p>
+
+<p>The total amount of the refraction at the horizon is a
+little more than half a degree, and since the diameters of
+the sun and moon subtend an angle of about half a degree,
+we have the remarkable result that in reality the whole
+disk of either sun or moon is below the horizon at the
+instant that the lower edge appears to touch the horizon
+and sunset or moonset begins. The same effect exists at
+sunrise, and as a consequence the duration of sunshine or
+of moonshine is on the average about six minutes longer
+each day than it would be if there were no atmosphere and
+no refraction. A partial offset to this benefit is found in
+the fact that the atmosphere absorbs the light of the heavenly
+bodies, so that stars appear much less bright when
+near the horizon than when they are higher up in the sky,
+and by reason of this absorption the setting sun can be
+looked at with the naked eye without the discomfort which
+its dazzling luster causes at noon.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_27" id="Fig_27"></a>
+<a href="images/i103-full.jpg"><img src="images/i103.jpg" width="500" height="317" alt="Fig. 27.&mdash;Flattening of the sun&#39;s disk by refraction and by reflection from the
+surface of the sea." title="Fig. 27.&mdash;Flattening of the sun&#39;s disk by refraction and by reflection from the
+surface of the sea." /></a>
+<span class="caption"><span class="smcap">Fig. 27.</span>&mdash;Flattening of the sun&#39;s disk by refraction and by reflection from the
+surface of the sea.</span>
+</div>
+
+<p><a name="S_51" id="S_51"></a>51. <b>The twilight.</b>&mdash;Another effect of the atmosphere,
+even more marked than the preceding, is the twilight. As<span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span>
+at sunrise the mountain top catches the rays of the coming
+sun before they reach the lowland, and at sunset it keeps
+them after they have faded from the regions below, so the
+particles of dust and vapor, which always float in the atmosphere,
+catch the sunlight and reflect it to the surface of the
+earth while the sun is still below the horizon, giving at the
+beginning and end of day that vague and diffuse light which
+we call twilight.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_28" id="Fig_28"></a>
+<img src="images/i104.png" width="350" height="170" alt="Fig. 28.&mdash;Twilight phenomena." title="Fig. 28.&mdash;Twilight phenomena." />
+<span class="caption"><span class="smcap">Fig. 28.</span>&mdash;Twilight phenomena.</span>
+</div>
+
+<p><a href="#Fig_28">Fig.&nbsp;28</a> shows a part of the earth surrounded by such a
+dust-laden atmosphere, which is illuminated on the left by
+the rays of the sun, but which, on the right of the figure,
+lies in the shadow cast
+by the earth. To an
+observer placed at <i>1</i> the
+sun is just setting, and
+all the atmosphere
+above him is illumined
+with its rays, which
+furnish a bright twilight.
+When, by the earth's rotation, this observer has been
+carried to <i>2</i>, all the region to the east of his zenith lies in
+the shadow, while to the west there is a part of the atmosphere
+from which there still comes a twilight, but now comparatively
+faint, because the lower part of the atmosphere
+about our observer lies in the shadow, and it is mainly
+its upper regions from which the light comes, and here the
+dust and moisture are much less abundant than in the lower
+strata. Still later, when the observer has been carried by the
+earth's rotation to the point&nbsp;<i>3</i>, every vestige of twilight will
+have vanished from his sky, because all of the illuminated
+part of the atmosphere is now below his horizon, which is
+represented by the line <i>3&nbsp;L</i>. In the figure the sun is represented
+to be 78° below this horizon line at the end of twilight,
+but this is a gross exaggeration, made for the sake of
+clearness in the drawing&mdash;in fact, twilight is usually said
+to end when the sun is 18° below the horizon.<span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span></p>
+
+<p>Let the student redraw <a href="#Fig_28">Fig.&nbsp;28</a> on a large scale, so that
+the points <i>1</i> and <i>3</i> shall be only 18° apart, as seen from the
+earth's center. He will find that the point <i>L</i> is brought
+down much closer to the surface of the earth, and measuring
+the length of the line <i>2&nbsp;L</i>, he should find for the "height
+of the atmosphere" about one-eightieth part of the radius
+of the earth&mdash;i.&nbsp;e., a little less than 50 miles. This, however,
+is not the true height of the atmosphere. The air
+extends far beyond this, but the particles of dust and vapor
+which are capable of sending sunlight down to the earth
+seem all to lie below this limit.</p>
+
+<p>The student should not fail to watch the eastern sky
+after sunset, and see the shadow of the earth rise up and
+fill it while the twilight arch retreats steadily toward the
+west.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_29" id="Fig_29"></a>
+<img src="images/i105.png" width="500" height="191" alt="Fig. 29.&mdash;The cause of long and short twilights." title="Fig. 29.&mdash;The cause of long and short twilights." />
+<span class="caption"><span class="smcap">Fig. 29.</span>&mdash;The cause of long and short twilights.</span>
+</div>
+
+<p><i>Duration of twilight.</i>&mdash;Since twilight ends when the sun
+is 18° below the horizon, any circumstance which makes
+the sun go down rapidly will shorten the duration of twilight,
+and anything which retards the downward motion
+of the sun will correspondingly prolong it. Chief among
+influences of this kind is the angle which the sun's course
+makes with the horizon. If it goes straight down, as at
+<i>a</i>, <a href="#Fig_29">Fig.&nbsp;29</a>, a much shorter time will suffice to carry it to
+a depression of 18° than is needed in the case shown at
+<i>b</i> in the same figure, where the motion is very oblique to
+the horizon. If we consider different latitudes and different
+seasons of the year, we shall find every possible variety
+<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span>
+of circumstance from <i>a</i> to <i>b</i>, and corresponding to these,
+the duration of twilight varies from an all-night duration
+in the summers of Scotland and more northern lands to an
+hour or less in the mountains of Peru. For the sake of
+graphical effect, the shortness of tropical twilight is somewhat
+exaggerated by Coleridge in the lines,</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"The sun's rim dips; the stars rush out:<br /></span>
+<span class="i0">At one stride comes the dark."<br /></span>
+<span class="i24"><i>The Ancient Mariner.</i><br /></span>
+</div></div>
+
+<p>In the United States the longest twilights come at the
+end of June, and last for a little more than two hours,
+while the shortest ones are in March and September,
+amounting to a little more than an hour and a half; but
+at all times the last half hour of twilight is hardly to be
+distinguished from night, so small is the quantity of reflecting
+matter in the upper regions of the atmosphere.
+For practical convenience it is customary to assume in
+the courts of law that twilight ends an hour after sunset.</p>
+
+<p>How long does twilight last at the north pole?</p>
+
+<p><i>The Aurora.</i>&mdash;One other phenomenon of the atmosphere
+may be mentioned, only to point out that it is not
+of an astronomical character. The Aurora, or northern
+lights, is as purely an affair of the earth as is a thunderstorm,
+and its explanation belongs to the subject of terrestrial
+magnetism.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p>
+<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI</h2>
+
+<h3>THE MEASUREMENT OF TIME</h3>
+
+
+<p><a name="S_52" id="S_52"></a>52. <b>Solar time.</b>&mdash;To measure any quantity we need a unit
+in terms of which it must be expressed. Angles are measured
+in degrees, and the degree is the unit for angular measurement.
+For most scientific purposes the centimeter is
+adopted as the unit with which to measure distances, and
+similarly a day is the fundamental unit for the measurement
+of time. Hours, minutes, and seconds are aliquot
+parts of this unit convenient for use in dealing with shorter
+periods than a day, and the week, month, and year which
+we use in our calendars are multiples of the day.</p>
+
+<p>Strictly speaking, a day is not the time required by the
+earth to make one revolution upon its axis, but it is best
+defined as the amount of time required for a particular part
+of the sky to make the complete circuit from the meridian
+of a particular place through west and east back to the
+meridian again. The day begins at the moment when this
+specified part of the sky is on the meridian, and "the time"
+at any moment is the hour angle of this particular part of
+the sky&mdash;i.&nbsp;e., the number of hours, minutes, etc., that have
+elapsed since it was on the meridian.</p>
+
+<p>The student has already become familiar with the kind
+of day which is based upon the motion of the vernal equinox,
+and which furnishes sidereal time, and he has seen
+that sidereal time, while very convenient in dealing with
+the motions of the stars, is decidedly inconvenient for the
+ordinary affairs of life since in the reckoning of the hours
+it takes no account of daylight and darkness. One can not<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span>
+tell off-hand whether 10 hours, sidereal time, falls in the day
+or in the night. We must in some way obtain a day and a
+system of time reckoning based upon the apparent diurnal
+motion of the sun, and we may, if we choose, take the sun
+itself as the point in the heavens whose transit over the
+meridian shall mark the beginning and the end of the day.
+In this system "the time" is the number of hours, minutes,
+etc., which have elapsed since the sun was on the meridian,
+and this is the kind of time which is shown by a sun dial,
+and which was in general use, years ago, before clocks and
+watches became common. Since the sun moves among the
+stars about a degree per day, it is easily seen that the rotating
+earth will have to turn farther in order to carry any
+particular meridian from the sun around to the sun again,
+than to carry it from a star around to the same star, or
+from the vernal equinox around to the vernal equinox
+again; just as the minute hand of a clock turns farther
+in going from the hour hand round to the hour hand again
+than it turns in going from XII to XII. These solar days
+and hours and minutes are therefore a little longer than
+the corresponding sidereal ones, and this furnishes the explanation
+why the stars come to the meridian a little earlier,
+by solar time, every night than on the night before, and
+why sidereal time gains steadily upon solar time, this gain
+amounting to approximately 3m. 56.5s. per day, or exactly
+one day per year, since the sun makes the complete circuit
+of the constellations once in a year.</p>
+
+<p>With the general introduction of clocks and watches
+into use about a century ago this kind of solar time went
+out of common use, since no well-regulated clock could
+keep the time correctly. The earth in its orbital motion
+around the sun goes faster in some parts of its orbit than
+in others, and in consequence the sun appears to move
+more rapidly among the stars in winter than in summer;
+moreover, on account of the convergence of hour circles
+as we go away from the equator, the same amount of motion<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span>
+along the ecliptic produces more effect in winter and
+summer when the sun is north or south, than it does in the
+spring and autumn when the sun is near the equator, and
+as a combined result of these causes and other minor ones
+true solar time, as it is called, is itself not uniform, but
+falls behind the uniform lapse of sidereal time at a variable
+rate, sometimes quicker, sometimes slower. A true solar
+day, from noon to noon, is 51 seconds shorter in September
+than in December.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_30" id="Fig_30"></a>
+<img src="images/i109.png" width="500" height="242" alt="Fig. 30.&mdash;The equation of time." title="" />
+<span class="caption"><span class="smcap">Fig. 30.</span>&mdash;The equation of time.</span>
+</div>
+
+<p><a name="S_53" id="S_53"></a>53. <b>Mean solar time.</b>&mdash;To remedy these inconveniences
+there has been invented and brought into common use
+what is called <i>mean solar time</i>, which is perfectly uniform
+in its lapse and which, by comparison with sidereal time,
+loses exactly one day per year. "The time" in this system
+never differs much from true solar time, and the difference
+between the two for any particular day may be found in
+any good almanac, or may be read from the curve in <a href="#Fig_30">Fig.&nbsp;30</a>,
+in which the part of the curve above the line marked
+<i>0m</i> shows how many minutes mean solar time is faster than
+true solar time. The correct name for this difference between
+the two kinds of solar time is the <i>equation of time</i>, but
+in the almanacs it is frequently marked "sun fast" or "sun
+slow." In sidereal time and true solar time the distinction<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span>
+between <span class="smcap">A.&nbsp;M.</span> hours (<i>ante meridiem</i> =&nbsp;before the sun reaches
+the meridian) and <span class="smcap">P.&nbsp;M.</span> hours (<i>post meridiem</i> =&nbsp;after the
+sun has passed the meridian) is not observed, "the time"
+being counted from 0 hours to 24 hours, commencing when
+the sun or vernal equinox is on the meridian. Occasionally
+the attempt is made to introduce into common use
+this mode of reckoning the hours, beginning the day
+(date) at midnight and counting the hours consecutively
+up to 24, when the next date is reached and a new start
+made. Such a system would simplify railway time tables
+and similar publications; but the American public is slow
+to adopt it, although the system has come into practical
+use in Canada and Spain.</p>
+
+<p><a name="S_54" id="S_54"></a>54. <b>To find (approximately) the sidereal time at any moment.</b>&mdash;<span class="smcap">Rule
+I.</span> When the mean solar time is known. Let
+<i>W</i> represent the time shown by an ordinary watch, and
+represent by <i>S</i> the corresponding sidereal time and by <i>D</i>
+the number of days that have elapsed from March 23d to
+the date in question. Then</p>
+
+<p class="center"><i>S</i> = <i>W</i> + 69/70 × <i>D</i> × 4.</p>
+
+<p>The last term is expressed in minutes, and should be reduced
+to hours and minutes. Thus at 4 <span class="smcap">P.&nbsp;M.</span> on July 4th&mdash;</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"><i>D</i></td><td align="center">=</td><td align="left">103 days.</td></tr>
+<tr><td align="right">69/70 × <i>D</i> × 4</td><td align="center">=</td><td align="left">406m.</td></tr>
+<tr><td align="right"></td><td align="center">=</td><td align="left">6h. 46m.</td></tr>
+<tr><td align="right"><i>W</i></td><td align="center">=</td><td align="left">4h. 0m.</td></tr>
+<tr><td align="right"><i>S</i></td><td align="center">=</td><td align="left">10h. 46m.</td></tr>
+</table></div>
+
+<p>The daily gain of sidereal upon mean solar time is 69/70 of 4
+minutes, and March 23d is the date on which sidereal and
+mean solar time are together, taking the average of one year
+with another, but it varies a little from year to year on
+account of the extra day introduced in leap years.</p>
+
+<p><span class="smcap">Rule II.</span> When the stars in the northern sky can be
+seen. Find &beta;&nbsp;Cassiopeię, and imagine a line drawn from it<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span>
+to Polaris, and another line from Polaris to the zenith.
+The sidereal time is equal to the angle between these lines,
+provided that that angle must be measured from the zenith
+toward the west. Turn the angle from degrees into hours
+by dividing by 15.</p>
+
+<p><a name="S_55" id="S_55"></a>55. <b>The earth's rotation.</b>&mdash;We are familiar with the fact
+that a watch may run faster at one time than at another,
+and it is worth while to inquire if the same is not true of
+our chief timepiece&mdash;the earth. It is assumed in the sections
+upon the measurement of time that the earth turns
+about its axis with absolute uniformity, so that mean solar
+time never gains or loses even the smallest fraction of a
+second. Whether this be absolutely true or not, no one has
+ever succeeded in finding convincing proof of a variation
+large enough to be measured, although it has recently been
+shown that the axis about which it rotates is not perfectly
+fixed within the body of the earth. The solid body of the
+earth wriggles about this axis like a fish upon a hook, so
+that the position of the north pole upon the earth's surface
+changes within a year to the extent of 40 or 50 feet
+(15 meters) without ever getting more than this distance
+away from its average position. This is probably caused
+by the periodical shifting of masses of air and water from
+one part of the earth to another as the seasons change,
+and it seems probable that these changes will produce
+some small effect upon the rotation of the earth. But in
+spite of these, for any such moderate interval of time as a
+year or a century, so far as present knowledge goes, we may
+regard the earth's rotation as uniform and undisturbed.
+For longer intervals&mdash;e.&nbsp;g., 1,000,000 or 10,000,000 years&mdash;the
+question is a very different one, and we shall have to
+meet it again in another connection.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_31" id="Fig_31"></a>
+<img src="images/i112.png" width="350" height="252" alt="Fig. 31.&mdash;Longitude and time" title="Fig. 31.&mdash;Longitude and time" />
+<span class="caption"><span class="smcap">Fig. 31.</span>&mdash;Longitude and time</span>
+</div>
+
+<p><a name="S_56" id="S_56"></a>56. <b>Longitude and time.</b>&mdash;In what precedes there has
+been constant reference to the meridian. The day begins
+when the sun is on the meridian. Solar time is the angular
+distance of the sun past the meridian. Sidereal time<span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span>
+was determined by observing transits of stars over a meridian
+line actually laid out upon the ground, etc. But
+every place upon the earth has its own meridian from
+which "the time" may be reckoned, and in <a href="#Fig_31">Fig.&nbsp;31</a>, where
+the rays of sunlight
+are represented as
+falling upon a part
+of the earth's equator
+through which
+the meridians of
+New York, Chicago,
+and San Francisco
+pass, it is evident
+that these rays make
+different angles with
+the meridians, and
+that the sun is farther from the meridian of New York
+than from that of San Francisco by an amount just equal
+to the angle at <i>O</i> between these meridians. This angle is
+called by geographers the difference of longitude between
+the two places, and the student should note that the word
+longitude is here used in a different sense from that on
+<a href="#Page_36">page&nbsp;36</a>. From <a href="#Fig_31">Fig.&nbsp;31</a> we obtain the</p>
+
+<p><i>Theorem.</i>&mdash;The difference between "the times" at any
+two meridians is equal to their difference of longitude, and
+the time at the eastern meridian is greater than at the
+western meridian. Astronomers usually express differences
+of longitude in hours instead of degrees. 1h.&nbsp;=&nbsp;15°.</p>
+
+<p>The name given to any kind of time should distinguish
+all the elements which enter into it&mdash;e.&nbsp;g., New York
+sidereal time means the hour angle of the vernal equinox
+measured from the meridian of New York, Chicago true
+solar time is the hour angle of the sun reckoned from the
+meridian of Chicago, etc.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_32" id="Fig_32"></a>
+<a href="images/i113-full.png"><img src="images/i113.png" width="600" height="422" alt="Fig. 32.&mdash;Standard time." title="Fig. 32.&mdash;Standard time." /></a>
+<span class="caption"><span class="smcap">Fig. 32.</span>&mdash;Standard time.</span>
+</div>
+
+<p><a name="S_57" id="S_57"></a>57. <b>Standard time.</b>&mdash;The requirements of railroad traffic
+have led to the use throughout the United States and<span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span>
+Canada of four "standard times," each of which is a mean
+solar time some integral number of hours slower than the
+time of the meridian passing through the Royal Observatory
+at Greenwich, England.</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">Eastern</td><td align="center">time is</td><td align="center">5</td><td align="center">hours</td><td align="center">slower</td><td align="center">than</td><td align="center">that</td><td align="center">of Greenwich.</td></tr>
+<tr><td align="left">Central</td><td align="center">"</td><td align="center">6</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr>
+<tr><td align="left">Mountain</td><td align="center">"</td><td align="center">7</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr>
+<tr><td align="left">Pacific</td><td align="center">"</td><td align="center">8</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr>
+</table></div>
+
+<p>In <a href="#Fig_32">Fig.&nbsp;32</a> the broken lines indicate roughly the parts of
+the United States and Canada in which these several kinds
+of time are used, and illustrate how irregular are the boundaries
+of these parts.</p>
+
+<p>Standard time is sent daily into all of the more important
+telegraph offices of the United States, and serves to
+regulate watches and clocks, to the almost complete exclusion
+of local time.</p>
+
+<p><a name="S_58" id="S_58"></a>58. <b>To determine the longitude.</b>&mdash;With an ordinary watch
+observe the time of the sun's transit over your local meridian,
+and correct the observed time for the equation of
+time by means of the curve in <a href="#Fig_30">Fig.&nbsp;30</a>. The difference
+between the corrected time and 12 o'clock will be the correction
+of your watch referred to local mean solar time.
+Compare your watch with the time signals in the nearest
+telegraph office and find its correction referred to standard
+time. The difference between the two corrections is the
+difference between your longitude and that of the standard
+meridian.</p>
+
+<p>N.&nbsp;B.&mdash;Don't tamper with the watch by trying to "set it
+right." No harm will be done if it is wrong, provided you
+take due account of the correction as indicated above.</p>
+
+<p>If the correction of the watch changed between your
+observation and the comparison in the telegraph office,
+what effect would it have upon the longitude determination?
+How can you avoid this effect?</p>
+
+<p><a name="S_59" id="S_59"></a>59. <b>Chronology.</b>&mdash;The Century Dictionary defines chronology
+as "the science of time"&mdash;that is, "the method of<span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span>
+measuring or computing time by regular divisions or periods
+according to the revolutions of the sun or moon."</p>
+
+<p>We have already seen that for the measurement of short
+intervals of time the day and its subdivisions&mdash;hours,
+minutes, seconds&mdash;furnish a very complete and convenient
+system. But for longer periods, extending to hundreds and
+thousands of days, a larger unit of time is required, and for
+the most part these longer units have in all ages and among
+all peoples been based upon astronomical considerations.
+But to this there is one marked exception. The week is a
+simple multiple of the day, as the dime is a multiple of the
+cent, and while it may have had its origin in the changing
+phases of the moon this is at best doubtful, since it does
+not follow these with any considerable accuracy. If the
+still longer units of time&mdash;the month and the year&mdash;had
+equally been made to consist of an integral number of days
+much confusion and misunderstanding might have been
+avoided, and the annals of ancient times would have presented
+fewer pitfalls to the historian than is now the case.
+The month is plainly connected with the motion of the
+moon among the stars. The year is, of course, based upon
+the motion of the sun through the heavens and the change
+of seasons which is thus produced; although, as commonly
+employed, it is not quite the same as the time required by
+the earth to make one complete revolution in its orbit.
+This time of one revolution is called a sidereal year, while,
+as we have already seen in <a href="#CHAPTER_V">Chapter&nbsp;V</a>, the year which
+measures the course of the seasons is shorter than this on
+account of the precession of the equinoxes. It is called a
+tropical year with reference to the circuit which the sun
+makes from one tropic to the other and back again.</p>
+
+<p>We can readily understand why primitive peoples should
+adopt as units of time these natural periods, but in so
+doing they incurred much the same kind of difficulty that
+we should experience in trying to use both English and
+American money in the ordinary transactions of life. How<span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span>
+many dollars make a pound sterling? How shall we make
+change with English shillings and American dimes, etc.?
+How much is one unit worth in terms of the other?</p>
+
+<p>One of the Greek poets<a name="FNanchor_B_2" id="FNanchor_B_2"></a><a href="#Footnote_B_2" class="fnanchor">[B]</a> has left us a quaint account of
+the confusion which existed in his time with regard to the
+place of months and moons in the calendar:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"The moon by us to you her greeting sends,<br /></span>
+<span class="i0">But bids us say that she's an ill-used moon<br /></span>
+<span class="i0">And takes it much amiss that you will still<br /></span>
+<span class="i0">Shuffle her days and turn them topsy-turvy,<br /></span>
+<span class="i0">So that when gods, who know their feast days well,<br /></span>
+<span class="i0">By your false count are sent home supperless,<br /></span>
+<span class="i0">They scold and storm at her for your neglect."<br /></span>
+</div></div>
+
+
+<p><a name="S_60" id="S_60"></a>60. <b>Day, month, and year.</b>&mdash;If the day, the month, and
+the year are to be used concurrently, it is necessary to
+determine how many days are contained in the month and
+year, and when this has been done by the astronomer the
+numbers are found to be very awkward and inconvenient
+for daily use; and much of the history of chronology
+consists in an account of the various devices by which ingenious
+men have sought to use integral numbers to replace
+the cumbrous decimal fractions which follow.</p>
+
+<p>According to Professor Harkness, for the epoch 1900
+<span class="smcap">A.&nbsp;D.</span>&mdash;</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center">One</td><td align="center">tropical</td><td align="center">year</td><td align="center">=</td><td align="left">365.242197 mean solar days.</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">=</td><td align="left">365d. 5h. 48m. 45.8s.</td></tr>
+</table></div>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center">One</td><td align="center">lunation</td><td align="center">=</td><td align="left">29.530588 mean solar days.</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">=</td><td align="left">29d. 12h. 44m. 2.8s.</td></tr>
+</table></div>
+
+<p>The word <i>lunation</i> means the average interval from one
+new moon to the next one&mdash;i.&nbsp;e., the time required by the
+moon to go from conjunction with the sun round to conjunction
+again.</p>
+
+<p>A very ancient device was to call a year equal to 365<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span>
+days, and to have months alternately of 29 and 30 days in
+length, but this was unsatisfactory in more than one way.
+At the end of four years this artificial calendar would be
+about one day ahead of the true one, at the end of forty
+years ten days in error, and within a single lifetime the
+seasons would have appreciably changed their position in
+the year, April weather being due in March, according to
+the calendar. So, too, the year under this arrangement
+did not consist of any integral number of months, 12
+months of the average length of 29.5 days being 354 days,
+and 13 months 383.5 days, thus making any particular
+month change its position from the beginning to the middle
+and the end of the year within a comparatively short
+time. Some peoples gave up the astronomical year as an
+independent unit and adopted a conventional year of 12
+lunar months, 354 days, which is now in use in certain
+Mohammedan countries, where it is known as the wandering
+year, with reference to the changing positions of the
+seasons in such a year. Others held to the astronomical
+year and adopted a system of conventional months, such
+that twelve of them would just make up a year, as is done
+to this day in our own calendar, whose months of arbitrary
+length we are compelled to remember by some such jingle
+as the following:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Thirty days hath September,<br /></span>
+<span class="i0">April, June, and November;<br /></span>
+<span class="i0">All the rest have thirty-one<br /></span>
+<span class="i0">Save February,<br /></span>
+<span class="i0">Which alone hath twenty-eight,<br /></span>
+<span class="i0">Till leap year gives it twenty-nine."<br /></span>
+</div></div>
+
+
+<p><a name="S_61" id="S_61"></a>61. <b>The calendar.</b>&mdash;The foundations of our calendar may
+fairly be ascribed to Julius Cęsar, who, under the advice
+of the Egyptian astronomer Sosigines, adopted the old
+Egyptian device of a leap year, whereby every fourth year
+was to consist of 366 days, while ordinary years were only
+365 days long. He also placed the beginning of the year<span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span>
+at the first of January, instead of in March, where it had
+formerly been, and gave his own name, Julius, to the month
+which we now call July. August was afterward named in
+honor of his successor, Augustus. The names of the earlier
+months of the year are drawn from Roman mythology;
+those of the later months, September, October, etc., meaning
+seventh month, eighth month, represent the places of
+these months in the year, before Cęsar's reformation, and
+also their places in some of the subsequent calendars, for
+the widest diversity of practice existed during medięval
+times with regard to the day on which the new year should
+begin, Christmas, Easter, March 25th, and others having been
+employed at different times and places.</p>
+
+<p>The system of leap years introduced by Cęsar makes
+the average length of a year 365.25 days, which differs by
+about eleven minutes from the true length of the tropical
+year, a difference so small that for ordinary purposes no
+better approximation to the true length of the year need
+be desired. But <i>any</i> deviation from the true length, however
+small, must in the course of time shift the seasons, the
+vernal and autumnal equinox, to another part of the year,
+and the ecclesiastical authorities of medięval Europe found
+here ground for objection to Cęsar's calendar, since the
+great Church festival of Easter has its date determined
+with reference to the vernal equinox, and with the lapse of
+centuries Easter became more and more displaced in the
+calendar, until Pope Gregory XIII, late in the sixteenth
+century, decreed another reformation, whereby ten days
+were dropped from the calendar, the day after March 11th
+being called March 21st, to bring back the vernal equinox
+to the date on which it fell in <span class="smcap">A.&nbsp;D.</span> 325, the time of the
+Council of Nicęa, which Gregory adopted as the fundamental
+epoch of his calendar.</p>
+
+<p>The calendar having thus been brought back into agreement
+with that of old time, Gregory purposed to keep it in
+such agreement for the future by modifying Cęsar's leap-year<span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span>
+rule so that it should run: Every year whose number
+is divisible by&nbsp;4 shall be a leap year except those years
+whose numbers are divisible by 100 but not divisible by
+400. These latter years&mdash;e.&nbsp;g., 1900&mdash;are counted as common
+years. The calendar thus altered is called Gregorian
+to distinguish it from the older, Julian calendar, and it
+found speedy acceptance in those civilized countries whose
+Church adhered to Rome; but the Protestant powers were
+slow to adopt it, and it was introduced into England and
+her American colonies by act of Parliament in the year
+1752, nearly two centuries after Gregory's time. In Russia
+the Julian calendar has remained in common use to
+our own day, but in commercial affairs it is there customary
+to write the date according to both calendars&mdash;e.&nbsp;g.,
+July 4/16, and at the present time strenuous exertions
+are making in that country for the adoption of the Gregorian
+calendar to the complete exclusion of the Julian
+one.</p>
+
+<p>The Julian and Gregorian calendars are frequently represented
+by the abbreviations O.&nbsp;S. and N.&nbsp;S., old style,
+new style, and as the older historical dates are usually expressed
+in O.&nbsp;S., it is sometimes convenient to transform a
+date from the one calendar to the other. This is readily
+done by the formula</p>
+
+<p class="center"><i>G</i> = <i>J</i> + (<i>N</i> - 2) - <i>N</i>/4,</p>
+
+<p>where <i>G</i> and <i>J</i> are the respective dates, <i>N</i> is the number
+of the century, and the remainder is to be neglected in the
+division by 4. For September 3, 1752, O.&nbsp;S., we have</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void">
+<tfoot>
+<tr><td align="right"><i>G</i></td><td align="center">=</td><td align="left">Sept. 14</td></tr>
+</tfoot>
+<tbody>
+<tr><td align="right"><i>J</i></td><td align="center">=</td><td align="left">Sept. 3</td></tr>
+<tr><td align="right"><i>N</i> - 2</td><td align="center">=</td><td align="left">+ 15</td></tr>
+<tr><td align="right">- <i>N</i>/4</td><td align="center">=</td><td align="left">- 4</td></tr>
+</tbody>
+</table>
+</div>
+
+<p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p>
+
+<p>and September 14 is the date fixed by act of Parliament to
+correspond to September 3, 1752, O.&nbsp;S. Columbus discovered
+America on October 12, 1492, O.&nbsp;S. What is the corresponding
+date in the Gregorian calendar?</p>
+
+<p><a name="S_62" id="S_62"></a>62. <b>The day of the week.</b>&mdash;A problem similar to the
+above but more complicated consists in finding the day of
+the week on which any given date of the Gregorian calendar
+falls&mdash;e.&nbsp;g., October 21, 1492.</p>
+
+<p>The formula for this case is</p>
+
+<p class="center">7<i>q</i> + <i>r</i> = <i>Y</i> + <i>D</i> + (<i>Y</i> - 1)/4 - (<i>Y</i> - 1)/100 + (<i>Y</i> - 1)/400</p>
+
+<p>where <i>Y</i> denotes the given year, <i>D</i> the number of the day
+(date) in that year, and <i>q</i> and <i>r</i> are respectively the quotient
+and the remainder obtained by dividing the second
+member of the equation by&nbsp;7. If <i>r</i>&nbsp;=&nbsp;1 the date falls on
+Sunday, etc., and if <i>r</i>&nbsp;=&nbsp;0 the day is Saturday. For the
+example suggested above we have</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void">
+<tfoot>
+<tr><td align="right">D =</td><td align="right">295</td></tr>
+</tfoot>
+<tbody>
+<tr><td align="left">Jan.</td><td align="right">31</td></tr>
+<tr><td align="left">Feb.</td><td align="right">29</td></tr>
+<tr><td align="left">Mch.</td><td align="right">31</td></tr>
+<tr><td align="left">April</td><td align="right">30</td></tr>
+<tr><td align="left">May</td><td align="right">31</td></tr>
+<tr><td align="left">June</td><td align="right">30</td></tr>
+<tr><td align="left">July</td><td align="right">31</td></tr>
+<tr><td align="left">Aug.</td><td align="right">31</td></tr>
+<tr><td align="left">Sept.</td><td align="right">30</td></tr>
+<tr><td align="left">Oct.</td><td align="right">21</td></tr>
+</tbody>
+</table></div>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void">
+<tfoot>
+<tr><td align="center"></td><td align="right"><i>q</i></td><td align="center">=</td><td align="right">306</td></tr>
+<tr><td align="center"></td><td align="right"><i>r</i></td><td align="center">=</td><td align="right">6</td><td align="left">= Friday.</td></tr>
+</tfoot>
+<tbody>
+<tr><td align="center"><i>Y</i></td><td align="right"></td><td align="center">=</td><td align="right">1492</td></tr>
+<tr><td align="center">+ <i>D</i></td><td align="right"></td><td align="center">=</td><td align="right">+ 295</td></tr>
+<tr><td align="center">+ (<i>Y</i> - 1) ÷</td><td align="right">4</td><td align="center">=</td><td align="right">+ 372</td></tr>
+<tr><td align="center">- (<i>Y</i> - 1) ÷</td><td align="right">100</td><td align="center">=</td><td align="right">- 14</td></tr>
+<tr><td align="center">+ (<i>Y</i> - 1) ÷</td><td align="right">400</td><td align="center">=</td><td align="right">+ 3</td></tr>
+</tbody>
+<tbody>
+<tr><td align="center"></td><td align="right"></td><td align="center">&nbsp;</td><td align="right">7 )<span class="overline"> 2148</span></td></tr>
+</tbody>
+</table></div>
+
+<p>Find from some history the day of the week on which
+Columbus first saw America, and compare this with the
+above.</p>
+
+<p>On what day of the week did last Christmas fall? On
+what day of the week were you born? In the formula for
+the day of the week why does <i>q</i> have the coefficient&nbsp;7?<span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span>
+What principles in the calendar give rise to the divisors 4,
+100, 400?</p>
+
+<p>For much curious and interesting information about
+methods of reckoning the lapse of time the student may
+consult the articles Calendar and Chronology in any good
+encyclopędia.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="YERKES_OBSERVATORY" id="YERKES_OBSERVATORY"></a>
+<a href="images/i122-full.jpg"><img src="images/i122.jpg" width="600" height="321" alt="THE YERKES OBSERVATORY, WILLIAMS BAY, WIS." title="THE YERKES OBSERVATORY, WILLIAMS BAY, WIS." /></a>
+<span class="caption">THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.</span>
+</div>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span></p>
+<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII</h2>
+
+<h3>ECLIPSES</h3>
+
+
+<p><a name="S_63" id="S_63"></a>63. <b>The nature of eclipses.</b>&mdash;Every planet has a shadow
+which travels with the planet along its orbit, always pointing
+directly away from the sun, and cutting off from a certain
+region of space the sunlight which otherwise would fill
+it. For the most part these shadows are invisible, but occasionally
+one of them falls upon a planet or some other body
+which shines by reflected sunlight, and, cutting off its supply
+of light, produces the striking phenomenon which we
+call an eclipse. The satellites of Jupiter, Saturn, and Mars
+are eclipsed whenever they plunge into the shadows cast by
+their respective planets, and Jupiter himself is partially
+eclipsed when one of his own satellites passes between him
+and the sun, and casts upon his broad surface a shadow too
+small to cover more than a fraction of it.</p>
+
+<p>But the eclipses of most interest to us are those of the
+sun and moon, called respectively solar and lunar eclipses.
+In <a href="#Fig_33">Fig.&nbsp;33</a> the full moon, <i>M'</i>, is shown immersed in the
+shadow cast by the earth, and therefore eclipsed, and in the
+same figure the new moon, <i>M</i>, is shown as casting its shadow
+upon the earth and producing an eclipse of the sun. From
+a mere inspection of the figure we may learn that an eclipse
+of the sun can occur only at new moon&mdash;i.&nbsp;e., when the
+moon is on line between the earth and sun&mdash;and an eclipse
+of the moon can occur only at full moon. Why? Also, the
+eclipsed moon, <i>M'</i>, will present substantially the same appearance
+from every part of the earth where it is at all visible&mdash;the
+same from North America as from South America&mdash;but<span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span>
+the eclipsed sun will present very
+different aspects from different parts of
+the earth. Thus, at <i>L</i>, within the moon's
+shadow, the sunlight will be entirely cut
+off, producing what is called a total eclipse.
+At points of the earth's surface near <i>J</i> and
+<i>K</i> there will be no interference whatever
+with the sunlight, and no eclipse, since the
+moon is quite off the line joining these regions
+to any part of the sun. At places between
+<i>J</i> and <i>L</i> or <i>K</i> and <i>L</i> the moon will
+cut off a part of the sun's light, but not all
+of it, and will produce what is called a partial
+eclipse, which, as seen from the northern
+parts of the earth, will be an eclipse of
+the lower (southern) part of the sun, and
+as seen from the southern hemisphere will
+be an eclipse of the northern part of the
+sun.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_33" id="Fig_33"></a>
+<img src="images/i125.png" width="600" height="91" alt="Fig. 33.&mdash;Different kinds of eclipse." title="Fig. 33.&mdash;Different kinds of eclipse." />
+<span class="caption"><span class="smcap">Fig. 33.</span>&mdash;Different kinds of eclipse.</span>
+</div>
+
+<p>The moon revolves around the earth in
+a plane, which, in the figure, we suppose to
+be perpendicular to the surface of the paper,
+and to pass through the sun along the
+line <i>M'&nbsp;M</i> produced. But it frequently
+happens that this plane is turned to one
+side of the sun, along some such line as
+<i>P&nbsp;Q</i>, and in this case the full moon would
+cut through the edge of the earth's shadow
+without being at any time wholly immersed
+in it, giving a partial eclipse of the moon,
+as is shown in the figure.</p>
+
+<p>In what parts of the earth would this
+eclipse be visible? What kinds of solar
+eclipse would be produced by the new moon
+at&nbsp;<i>Q</i>? In what parts of the earth would
+they be visible?<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p>
+
+<p><a name="S_64" id="S_64"></a>64. <b>The shadow cone.</b>&mdash;The shape and position of the
+earth's shadow are indicated in <a href="#Fig_33">Fig.&nbsp;33</a> by the lines drawn
+tangent to the circles which represent the sun and earth,
+since it is only between these lines that the earth interferes
+with the free radiation of sunlight, and since both sun and
+earth are spheres, and the earth is much the smaller of the
+two, it is evident that the earth's shadow must be, in geometrical
+language, a cone whose base is at the earth, and
+whose vertex lies far to the right of the figure&mdash;in other
+words, the earth's shadow, although very long, tapers off
+finally to a point and ends. So, too, the shadow of the
+moon is a cone, having its base at the moon and its vertex
+turned away from the sun, and, as shown in the figure, just
+about long enough to reach the earth.</p>
+
+<p>It is easily shown, by the theorem of similar triangles in
+connection with the known size of the earth and sun, that
+the distance from the center of the earth to the vertex of
+its shadow is always equal to the distance of the earth from
+the sun divided by 108, and, similarly, that the length of
+the moon's shadow is equal to the distance of the moon
+from the sun divided by 400, the moon's shadow being the
+smaller and shorter of the two, because the moon is smaller
+than the earth. The radius of the moon's orbit is just about
+1/400th part of the radius of the earth's orbit&mdash;i.&nbsp;e., the distance
+of the moon from the earth is 1/400th part of the distance
+of the earth from the sun, and it is this "chance"
+agreement between the length of the moon's shadow and
+the distance of the moon from the earth which makes the
+tip of the moon's shadow fall very near the earth at the
+time of solar eclipses. Indeed, the elliptical shape of the
+moon's orbit produces considerable variations in the distance
+of the moon from the earth, and in consequence of
+these variations the vertex of the shadow sometimes falls
+short of reaching the earth, and sometimes even projects
+considerably beyond its farther side. When the moon's
+distance is too great for the shadow to bridge the space between<span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>
+earth and moon there can be no total eclipse of the
+sun, for there is no shadow which can fall upon the earth,
+even though the moon does come directly between earth
+and sun. But there is then produced a peculiar kind of
+partial eclipse called <i>annular</i>, or ring-shaped, because the
+moon, although eclipsing the central parts of the sun, is
+not large enough to cover the whole of it, but leaves the
+sun's edge visible as a ring of light, which completely surrounds
+the moon. Although, strictly speaking, this is only
+a partial eclipse, it is customary to put total and annular
+eclipses together in one class, which is called central eclipses,
+since in these eclipses the line of centers of sun and moon
+strikes the earth, while in ordinary partial eclipses it passes
+to one side of the earth without striking it. In this latter
+case we have to consider another cone called the <i>penumbra</i>&mdash;i.&nbsp;e.,
+partial shadow&mdash;which is shown in <a href="#Fig_33">Fig.&nbsp;33</a> by the
+broken lines tangent to the sun and moon, and crossing at
+the point <i>V</i>, which is the vertex of this cone. This penumbral
+cone includes within its surface all that region of space
+within which the moon cuts off any of the sunlight, and
+of course it includes the shadow cone which produces total
+eclipses. Wherever the penumbra falls there will be a solar
+eclipse of some kind, and the nearer the place is to the axis
+of the penumbra, the more nearly total will be the eclipse.
+Since the moon stands about midway between the earth and
+the vertex of the penumbra, the diameter of the penumbra
+where it strikes the earth will be about twice as great as
+the diameter of the moon, and the student should be able
+to show from this that the region of the earth's surface
+within which a partial solar eclipse is visible extends in a
+straight line about 2,100 miles on either side of the region
+where the eclipse is total. Measured along the curved
+surface of the earth, this distance is frequently much
+greater.</p>
+
+<p>Is it true that if at any time the axis of the shadow cone
+comes within 2,100 miles of the earth's surface a partial<span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span> eclipse will be visible in those parts of the earth nearest the
+axis of the shadow?</p>
+
+<p><a name="S_65" id="S_65"></a>65. <b>Different characteristics of lunar and solar eclipses.</b>&mdash;One
+marked difference between lunar and solar eclipses
+which has been already suggested, may be learned from <a href="#Fig_33">Fig.&nbsp;33</a>.
+The full moon, <i>M'</i>, will be seen eclipsed from every
+part of the earth where it is visible at all at the time of the
+eclipse&mdash;that is, from the whole night side of the earth;
+while the eclipsed sun will be seen eclipsed only from those
+parts of the day side of the earth upon which the moon's
+shadow or penumbra falls. Since the point of the shadow
+at best but little more than reaches to the earth, the
+amount of space upon the earth which it can cover at any
+one moment is very small, seldom more than 100 to 200
+miles in length, and it is only within the space thus actually
+covered by the shadow that the sun is at any given
+moment totally eclipsed, but within this region the sun
+disappears, absolutely, behind the solid body of the moon,
+leaving to view only such outlying parts and appendages as
+are too large for the moon to cover. At a lunar eclipse, on
+the other hand, the earth coming between sun and moon
+cuts off the light from the latter, but, curiously enough,
+does not cut it off so completely that the moon disappears
+altogether from sight even in mid-eclipse. The explanation
+of this continued visibility is furnished by the broken
+lines extending, in <a href="#Fig_33">Fig.&nbsp;33</a>, from the earth through the
+moon. These represent sunlight, which, entering the
+earth's atmosphere near the edge of the earth (edge as seen
+from sun and moon), passes through it and emerges in a
+changed direction, refracted, into the shadow cone and
+feebly illumines the moon's surface with a ruddy light like
+that often shown in our red sunsets. Eclipse and sunset
+alike show that when the sun's light shines through dense
+layers of air it is the red rays which come through most
+freely, and the attentive observer may often see at a clear
+sunset something which corresponds exactly to the bending<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span>
+of the sunlight into the shadow cone; just before the sun
+reaches the horizon its disk is distorted from a circle into
+an oval whose horizontal diameter is longer than the vertical
+one (see <a href="#S_50">§&nbsp;50</a>).</p>
+
+<p><span class="smcap">Query.</span>&mdash;At a total lunar eclipse what would be the
+effect upon the appearance of the moon if the atmosphere
+around the edge of the earth were heavily laden with
+clouds?</p>
+
+<p><a name="S_66" id="S_66"></a>66. <b>The track of the shadow.</b>&mdash;We may regard the moon's
+shadow cone as a huge pencil attached to the moon, moving
+with it along its orbit in the direction of the arrowhead
+(<a href="#Fig_34">Fig.&nbsp;34</a>), and as it moves drawing a black line across
+the face of the earth at the time of total eclipse. This black
+line is the path of the shadow and marks out those regions
+within which the eclipse will be total at some stage of its
+progress. If the point of the shadow just reaches the
+earth its trace will have no sensible width, while, if the
+moon is nearer, the point of the cone will be broken off,
+and, like a blunt pencil, it will draw a broad streak across
+the earth, and this under the most favorable circumstances
+may have a breadth of a little more than 160 miles and a
+length of 10,000 or 12,000 miles. The student should
+be able to show from the known distance of the moon
+(240,000 miles) and the known interval between consecutive
+new moons (29.5 days) that on the average the moon's
+shadow sweeps past the earth at the rate of 2,100 miles per
+hour, and that in a general way this motion is from west
+to east, since that is the direction of the moon's motion in
+its orbit. The actual velocity with which the moon's shadow
+moves past a given station may, however, be considerably
+greater or less than this, since on the one hand when the
+shadow falls very obliquely, as when the eclipse occurs near
+sunrise or sunset, the shifting of the shadow will be very
+much greater than the actual motion of the moon which
+produces it, and on the other hand the earth in revolving
+upon its axis carries the spectator and the ground upon<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span>
+which he stands along the same direction in which the
+shadow is moving. At the equator, with the sun and moon
+overhead, this motion of the earth subtracts about 1,000
+miles per hour from the velocity with which the shadow
+passes by. It is chiefly on this account, the diminished
+velocity with which the shadow passes by, that total solar
+eclipses last longer in the tropics than in higher latitudes,
+but even under the most favorable circumstances the duration
+of totality does not reach eight minutes at any one
+place, although it may take the shadow several hours to
+sweep the entire length of its path across the earth.</p>
+
+<p>According to Whitmell the greatest possible duration of
+a total solar eclipse is 7m. 40s., and it can attain this limit
+only when the eclipse occurs near the beginning of July
+and is visible at a place 5° north of the equator.</p>
+
+<p>The duration of a lunar eclipse depends mainly upon
+the position of the moon with respect to the earth's shadow.
+If it strikes the shadow centrally, as at <i>M'</i>, <a href="#Fig_33">Fig.&nbsp;33</a>, a total
+eclipse may last for about two hours, with an additional
+hour at the beginning and end, during which the moon is
+entering and leaving the earth's shadow. If the moon
+meets the shadow at one side of the axis, as at <i>P</i>, the total
+phase of the eclipse may fail altogether, and between these
+extremes the duration of totality may be anything from
+two hours downward.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_34" id="Fig_34"></a>
+<img src="images/i131.png" width="500" height="248" alt="Fig. 34.&mdash;Relation of the lunar nodes to eclipses." title="Fig. 34.&mdash;Relation of the lunar nodes to eclipses." />
+<span class="caption"><span class="smcap">Fig. 34.</span>&mdash;Relation of the lunar nodes to eclipses.</span>
+</div>
+
+<p><a name="S_67" id="S_67"></a>67. <b>Relation of the lunar nodes to eclipses.</b>&mdash;To show why
+the moon sometimes encounters the earth's shadow centrally
+and more frequently at full moon passes by without
+touching it at all, we resort to <a href="#Fig_34">Fig.&nbsp;34</a>, which represents a
+part of the orbit of the earth about the sun, with dates
+showing the time in each year at which the earth passes
+the part of its orbit thus marked. The orbit of the moon
+about the earth, <i>M&nbsp;M'</i>, is also shown, with the new moon,
+<i>M</i>, casting its shadow toward the earth and the full moon,
+<i>M'</i>, apparently immersed in the earth's shadow. But here
+appearances are deceptive, and the student who has made<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>
+the observations set forth in <a href="#CHAPTER_III">Chapter&nbsp;III</a> has learned for
+himself a fact of which careful account must now be taken.
+The apparent paths of the moon and sun among the stars
+are great circles which lie near each other, but are not
+exactly the same; and since these great circles are only the
+intersections of the sky with the planes of the earth's orbit
+and the moon's orbit, we see that these planes are slightly
+inclined to each other and must therefore intersect along
+some line passing through the center of the earth. This
+line, <i>N'&nbsp;N''</i>, is shown in the figure, and if we suppose the
+surface of the paper to represent the plane of the earth's
+orbit, we shall have to suppose the moon's orbit to be tipped
+around this line, so that the left side of the orbit lies above
+and the right side below the surface of the paper. But
+since the earth's shadow lies in the plane of its orbit&mdash;i.&nbsp;e.,
+in the surface of the paper&mdash;the full moon of March, <i>M'</i>,
+must have passed below the shadow, and the new moon, <i>M</i>,
+must have cast its shadow above the earth, so that neither
+a lunar nor a solar eclipse could occur in that month. But
+toward the end of May the earth and moon have reached
+a position where the line <i>N'&nbsp;N''</i> points almost directly
+toward the sun, in line with the shadow cones which hide
+it. Note that the line <i>N'&nbsp;N''</i> remains very nearly parallel
+to its original position, while the earth is moving along<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span>
+its orbit. The full moon will now be very near this line
+and therefore very close to the plane of the earth's orbit, if
+not actually in it, and must pass through the shadow of the
+earth and be eclipsed. So also the new moon will cast its
+shadow in the plane of the ecliptic, and this shadow, falling
+upon the earth, produced the total solar eclipse of May 28,
+1900.</p>
+
+<p><i>N'&nbsp;N''</i> is called the line of nodes of the moon's orbit (<a href="#S_39">§&nbsp;39</a>),
+and the two positions of the earth in its orbit, diametrically
+opposite each other, at which <i>N'&nbsp;N''</i> points exactly toward
+the sun, we shall call the <i>nodes</i> of the lunar orbit. Strictly
+speaking, the nodes are those points of the sky against
+which the moon's center is projected at the moment when
+in its orbital motion it cuts through the plane of the earth's
+orbit. Bearing in mind these definitions, we may condense
+much of what precedes into the proposition: Eclipses of
+either sun or moon can occur only when the earth is at or
+near one of the nodes of the moon's orbit. Corresponding
+to these positions of the earth there are in each year two
+seasons, about six months apart, at which times, and at
+these only, eclipses can occur. Thus in the year 1900 the
+earth passed these two points on June 2d and November
+24th respectively, and the following list of eclipses which
+occurred in that year shows that all of them were within a
+few days of one or the other of these dates:</p>
+
+<h4><i>Eclipses of the Year 1900</i></h4>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">Total solar eclipse</td><td align="left">May 28th.</td></tr>
+<tr><td align="left">Partial lunar eclipse</td><td align="left">June 12th.</td></tr>
+<tr><td align="left">Annular (solar) eclipse</td><td align="left">November 21st.</td></tr>
+</table></div>
+
+<p><a name="S_68" id="S_68"></a>68. <b>Eclipse limits.</b>&mdash;If the earth is exactly at the node at
+the time of new moon, the moon's shadow will fall centrally
+upon it and will produce an eclipse visible within the
+torrid zone, since this is that part of the earth's surface
+nearest the plane of its orbit. If the earth is near but not
+at the node, the new moon will stand a little north or south<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span>
+of the plane of the earth's orbit, and its shadow will strike
+the earth farther north or south than before, producing an
+eclipse in the temperate or frigid zones; or the shadow may
+even pass entirely above or below the earth, producing no
+eclipse whatever, or at most a partial eclipse visible near
+the north or south pole. Just how many days' motion the
+earth may be away from the node and still permit an eclipse
+is shown in the following brief table of eclipse limits, as
+they are called:</p>
+
+<h4><i>Solar Eclipse Limits</i></h4>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" colspan="5">If at any new moon the earth is</td></tr>
+<tr><td align="left">Less than 10 days away</td><td align="center">from</td><td align="center">a</td><td align="center">node,</td><td align="left">a central eclipse is certain.</td></tr>
+<tr><td align="left">Between 10 and 16 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">some kind of eclipse is certain.</td></tr>
+<tr><td align="left">Between 16 and 19 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">a partial eclipse is possible.</td></tr>
+<tr><td align="left">More than 19 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">no eclipse is possible.</td></tr>
+</table></div>
+
+<h4><i>Lunar Eclipse Limits</i></h4>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" colspan="5">If at any full moon the earth is</td></tr>
+<tr><td align="left">Less than 4 days away</td><td align="center">from</td><td align="center">a</td><td align="center">node,</td><td align="left">a total eclipse is certain.</td></tr>
+<tr><td align="left">Between 4 and 10 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">some kind of eclipse is certain.</td></tr>
+<tr><td align="left">Between 10 and 14 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">a partial eclipse is possible.</td></tr>
+<tr><td align="left">More than 14 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">no eclipse is possible.</td></tr>
+</table></div>
+
+<p>From this table of eclipse limits we may draw some
+interesting conclusions about the frequency with which
+eclipses occur.</p>
+
+<p><a name="S_69" id="S_69"></a>69. <b>Number of eclipses in a year.</b>&mdash;Whenever the earth
+passes a node of the moon's orbit a new moon must occur at
+some time during the 2&nbsp;×&nbsp;16 days that the earth remains
+inside the limits where some kind of eclipse is certain, and
+there must therefore be an eclipse of the sun every time the
+earth passes a node of the moon's orbit. But, since there
+are two nodes past which the earth moves at least once in
+each year, there must be at least two solar eclipses every
+year. Can there be more than two? On the average, will
+central or partial eclipses be the more numerous?</p>
+
+<p>A similar line of reasoning will not hold true for
+eclipses of the moon, since it is quite possible that no full<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span>
+moon should occur during the 20 days required by the
+earth to move past the node from the western to the eastern
+limit. This omission of a full moon while the earth is
+within the eclipse limits sometimes happens at both nodes
+in the same year, and then we have a year with no eclipse
+of the moon. The student may note in the list of eclipses
+for 1900 that the partial lunar eclipse of June 12th occurred
+10 days after the earth passed the node, and was
+therefore within the doubtful zone where eclipses may
+occur and may fail, and corresponding to this position the
+eclipse was a very small one, only a thousandth part of the
+moon's diameter dipping into the shadow of the earth.
+By so much the year 1900 escaped being an illustration of
+a year in which no lunar eclipse occurred.</p>
+
+<p>A partial eclipse of the moon will usually occur about a
+fortnight before or after a total eclipse of the sun, since
+the full moon will then be within the eclipse limit at the
+opposite node. A partial eclipse of the sun will always
+occur about a fortnight before or after a total eclipse of the
+moon.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_35" id="Fig_35"></a>
+<a href="images/i135-full.png"><img src="images/i135.png" width="600" height="404" alt="Fig. 35.&mdash;The eclipse of May 28, 1900." title="Fig. 35.&mdash;The eclipse of May 28, 1900." /></a>
+<span class="caption"><span class="smcap">Fig. 35.</span>&mdash;The eclipse of May 28, 1900.</span>
+</div>
+
+<p><a name="S_70" id="S_70"></a>70. <b>Eclipse maps.</b>&mdash;It is the custom of astronomers to
+prepare, in advance of the more important eclipses, maps
+showing the trace of the moon's shadow across the earth,
+and indicating the times of beginning and ending of the
+eclipses, as is shown in <a href="#Fig_35">Fig.&nbsp;35</a>. While the actual construction
+of such a map requires much technical knowledge, the
+principles involved are simple enough: the straight line
+passed through the center of sun and moon is the axis of
+the shadow cone, and the map contains little more than a
+graphical representation of when and where this cone meets
+the surface of the earth. Thus in the map, the "Path of
+Total Eclipse" is the trace of the shadow cone across the
+face of the earth, and the width of this path shows that the
+earth encountered the shadow considerably inside the vertex
+of the cone. The general direction of the path is from
+west to east, and the slight sinuousities which it present<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span><span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>s
+are for the most part due to unavoidable distortion of the
+map caused by the attempt to represent the curved surface
+of the earth upon the flat surface of the paper. On either
+side of the Path of Total Eclipse is the region within which
+the eclipse was only partial, and the broken lines marked Begins
+at 3h., Ends at 3h., show the intersection of the penumbral
+cone with the surface of the earth at 3 <span class="smcap">P.&nbsp;M.</span>, Greenwich
+time. These two lines inclose every part of the earth's
+surface from which at that time any eclipse whatever could
+be seen, and at this moment the partial eclipse was just beginning
+at every point on the eastern edge of the penumbra
+and just ending at every point on the western edge, while
+at the center of the penumbra, on the Path of Total Eclipse,
+lay the shadow of the moon, an oval patch whose greatest
+diameter was but little more than 60 miles in length, and
+within which lay every part of the earth where the eclipse
+was total at that moment.</p>
+
+<p>The position of the penumbra at other hours is also
+shown on the map, although with more distortion, because
+it then meets the surface of the earth more obliquely, and
+from these lines it is easy to obtain the time of beginning
+and end of the eclipse at any desired place, and to estimate
+by the distance of the place from the Path of Total Eclipse
+how much of the sun's face was obscured.</p>
+
+<p>Let the student make these "predictions" for Washington,
+Chicago, London, and Algiers.</p>
+
+<p>The points in the map marked First Contact, Last Contact,
+show the places at which the penumbral cone first
+touched the earth and finally left it. According to computations
+made as a basis for the construction of the map the
+Greenwich time of First Contact was 0h. 12.5m. and of Last
+Contact 5h. 35.6m., and the difference between these two
+times gives the total duration of the eclipse upon the earth&mdash;i.&nbsp;e.,
+5 hours 23.1 minutes.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_36" id="Fig_36"></a>
+<a href="images/i137-full.jpg"><img src="images/i137.jpg" width="500" height="500" alt="Fig. 36.&mdash;Central eclipses for the first two decades of the twentieth century.
+Oppolzer." title="Fig. 36.&mdash;Central eclipses for the first two decades of the twentieth century.
+Oppolzer." /></a>
+<span class="caption"><span class="smcap">Fig. 36.</span>&mdash;Central eclipses for the first two decades of the twentieth century.
+<span class="smcap">Oppolzer.</span></span>
+</div>
+
+<p><a name="S_71" id="S_71"></a>71. <b>Future eclipses.</b>&mdash;An eclipse map of a different kind
+is shown in <a href="#Fig_36">Fig.&nbsp;36</a>, which represents the shadow paths of<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>
+all the central eclipses of the sun, visible during the period
+1900-1918 <span class="smcap">A.&nbsp;D.</span>, in those parts of the earth north of the
+south temperate zone. Each continuous black line shows
+the path of the shadow in a total eclipse, from its beginning,
+at sunrise, at the western end of the line to its end,
+sunset, at the eastern end, the little circle near the middle
+of the line showing the place at which the eclipse
+was total at noon. The broken lines represent similar
+data for the annular eclipses. This map is one of a series
+prepared by the Austrian astronomer, Oppolzer, showing
+the path of every such eclipse from the year 1200<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span>
+<span class="smcap">B.&nbsp;C.</span> to 2160 <span class="smcap">A.&nbsp;D.</span>, a period of more than three thousand
+years.</p>
+
+<p>If we examine the dates of the eclipses shown in this
+map we shall find that they are not limited to the particular
+seasons, May and November, in which those of the year
+1900 occurred, but are scattered through all the months of
+the year, from January to December. This shows at once
+that the line of nodes, <i>N'&nbsp;N''</i>, of <a href="#Fig_34">Fig.&nbsp;34</a>, does not remain
+in a fixed position, but turns round in the plane of the
+earth's orbit so that in different years the earth reaches the
+node in different months. The precession has already furnished
+us an illustration of a similar change, the slow rotation
+of the earth's axis, producing a corresponding shifting
+of the line in which the planes of the equator and ecliptic
+intersect; and in much the same way, through the disturbing
+influence of the sun's attraction, the line <i>N'&nbsp;N''</i> is made
+to revolve westward, opposite to the arrowheads in <a href="#Fig_34">Fig.&nbsp;34</a>,
+at the rate of nearly 20° per year, so that the earth
+comes to each node about 19 days earlier in each year than
+in the year preceding, and the eclipse season in each year
+comes on the average about 19 days earlier than in the year
+before, although there is a good deal of irregularity in the
+amount of change in particular years.</p>
+
+<p><a name="S_72" id="S_72"></a>72. <b>Recurrence of eclipses.</b>&mdash;Before the beginning of the
+Christian era astronomers had found out a rough-and-ready
+method of predicting eclipses, which is still of interest and
+value. The substance of the method is that if we start
+with any eclipse whatever&mdash;e.&nbsp;g., the eclipse of May 28, 1900&mdash;and
+reckon forward or backward from that date a period of
+18 years and 10 or 11 days, we shall find another eclipse quite
+similar in its general characteristics to the one with which
+we started. Thus, from the map of eclipses (<a href="#Fig_36">Fig.&nbsp;36</a>), we
+find that a total solar eclipse will occur on June 8, 1918,
+18 years and 11 days after the one illustrated in <a href="#Fig_35">Fig.&nbsp;35</a>.
+This period of 18 years and 11 days is called <i>saros</i>, an
+ancient word which means cycle or repetition, and since<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>
+every eclipse is repeated after the lapse of a saros, we may
+find the dates of all the eclipses of 1918 by adding 11
+days to the dates given in the table of eclipses for 1900
+(<a href="#S_67">§&nbsp;67</a>), and it is to be especially noted that each eclipse of
+1918 will be like its predecessor of 1900 in character&mdash;lunar,
+solar, partial, total, etc. The eclipses of any year
+may be predicted by a similar reference to those which
+occurred eighteen years earlier. Consult a file of old
+almanacs.</p>
+
+<p>The exact length of a saros is 223 lunar months, each of
+which is a little more than 29.5 days long, and if we multiply
+the exact value of this last number (see <a href="#S_60">§&nbsp;60</a>) by 223,
+we shall find for the product 6,585.32 days, which is equal
+to 18 years 11.32 days when there are four leap years included
+in the 18, or 18 years 10.32 days when the number
+of leap years is five; and in applying the saros to the
+prediction of eclipses, due heed must be paid to the number
+of intervening leap years. To explain why eclipses are
+repeated at the end of the saros, we note that the occurrence
+of an eclipse depends solely upon the relative positions of
+the earth, moon, and node of the moon's orbit, and the
+eclipse will be repeated as often as these three come back
+to the position which first produced it. This happens at
+the end of every saros, since the saros is, approximately, the
+least common multiple of the length of the year, the length
+of the lunar month, and the length of time required by the
+line of nodes to make a complete revolution around the
+ecliptic. If the saros were exactly a multiple of these
+three periods, every eclipse would be repeated over and
+over again for thousands of years; but such is not the
+case, the saros is not an exact multiple of a year, nor
+is it an exact multiple of the time required for a revolution
+of the line of nodes, and in consequence the
+restitution which comes at the end of the saros is not a
+perfect one. The earth at the 223d new moon is in fact
+about half a day's motion farther west, relative to the node,<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span>
+than it was at the beginning, and the resulting
+eclipse, while very similar, is not
+precisely the same as before. After another
+18 years, at the second repetition, the earth
+is a day farther from the node than at first,
+and the eclipse differs still more in character,
+etc. This is shown in <a href="#Fig_37">Fig.&nbsp;37</a>, which
+represents the apparent positions of the
+disks of the sun and moon as seen from the
+center of the earth at the end of each sixth
+saros, 108 years, where the upper row of
+figures represents the number of repetitions
+of the eclipse from the beginning, marked
+<i>0</i>, to the end, <i>72</i>. The solar eclipse limits,
+10, 16, 19 days, are also shown, and all those
+eclipses which fall between the 10-day limits
+will be central as seen from some part of
+the earth, those between 16 and 19 partial
+wherever seen, while between 10 and 16
+they may be either total or partial. Compare
+the figure with the following description
+given by Professor Newcomb: "A series
+of such eclipses commences with a very
+small eclipse near one pole of the earth.
+Gradually increasing for about eleven recurrences,
+it will become central near the same
+pole. Forty or more central eclipses will
+then recur, the central line moving slowly
+toward the other pole. The series will then
+become partial, and finally cease. The entire
+duration of the series will be more than
+a thousand years. A new series commences,
+on the average, at intervals of thirty years."</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_37" id="Fig_37"></a>
+<img src="images/i140.png" width="600" height="77" alt="Fig. 37.&mdash;Graphical illustration of the saros." title="Fig. 37.&mdash;Graphical illustration of the saros." />
+<span class="caption"><span class="smcap">Fig. 37.</span>&mdash;Graphical illustration of the saros.</span>
+</div>
+
+<p>A similar figure may be constructed to
+represent the recurrence of lunar eclipses;
+but here, in consequence of the smaller<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>
+eclipse limits, we shall find that a series is of shorter duration,
+a little over eight centuries as compared with twelve
+centuries, which is the average duration of a series of solar
+eclipses.</p>
+
+<p>One further matter connected with the saros deserves
+attention. During the period of 6,585.32 days the earth
+has 6,585 times turned toward the sun the same face upon
+which the moon's shadow fell at the beginning of the saros,
+but at the end of the saros the odd 0.32 of a day gives the
+earth time to make about a third of a revolution more
+before the eclipse is repeated, and in consequence the
+eclipse is seen in a different region of the earth, on the
+average about 116° farther west in longitude. Compare in
+<a href="#Fig_36">Fig.&nbsp;36</a> the regions in which the eclipses of 1900 and 1918
+are visible.</p>
+
+<p>Is this change in the region where the repeated eclipse
+is visible, true of lunar eclipses as well as solar?</p>
+
+<p><a name="S_73" id="S_73"></a>73. <b>Use of eclipses.</b>&mdash;At all times and among all peoples
+eclipses, and particularly total eclipses of the sun, have
+been reckoned among the most impressive phenomena of
+Nature. In early times and among uncultivated people
+they were usually regarded with apprehension, often amounting
+to a terror and frenzy, which civilized travelers have
+not scrupled to use for their own purposes with the aid of
+the eclipse predictions contained in their almanacs, threatening
+at the proper time to destroy the sun or moon, and
+pointing to the advancing eclipse as proof that their
+threats were not vain. In our own day and our own land
+these feelings of awe have not quite disappeared, but for
+the most part eclipses are now awaited with an interest and
+pleasure which, contrasted with the former feelings of mankind,
+furnish one of the most striking illustrations of the
+effect of scientific knowledge in transforming human fear
+and misery into a sense of security and enjoyment.</p>
+
+<p>But to the astronomer an eclipse is more than a beautiful
+illustration of the working of natural laws; it is in<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span>
+varying degree an opportunity of adding to his store of
+knowledge respecting the heavenly bodies. The region
+immediately surrounding the sun is at most times closed to
+research by the blinding glare of the sun's own light, so
+that a planet as large as the moon might exist here unseen
+were it not for the occasional opportunity presented by a
+total eclipse which shuts off the excessive light and permits
+not only a search for unknown planets but for anything
+and everything which may exist around the sun. More
+than one astronomer has reported the discovery of such
+planets, and at least one of these has found a name and a
+description in some of the books, but at the present time
+most astronomers are very skeptical about the existence of
+any such object of considerable size, although there is
+some reason to believe that an enormous number of little
+bodies, ranging in size from grains of sand upward, do
+move in this region, as yet unseen and offering to the
+future problems for investigation.</p>
+
+<p>But in other directions the study of this region at the
+times of total eclipse has yielded far larger returns, and in
+the chapter on the sun we shall have to consider the marvelous
+appearances presented by the solar prominences and
+by the corona, an appendage of the sun which reaches out
+from his surface for millions of miles but is never seen
+save at an eclipse. Photographs of the corona are taken
+by astronomers at every opportunity, and reproductions of
+some of these may be found in <a href="#CHAPTER_X">Chapter&nbsp;X</a>.</p>
+
+<p>Annular eclipses and lunar eclipses are of comparatively
+little consequence, but any recorded eclipse may become of
+value in connection with chronology. We date our letters
+in a particular year of the twentieth century, and commonly
+suppose that the years are reckoned from the birth of
+Christ; but this is an error, for the eclipses which were observed
+of old and by the chroniclers have been associated
+with events of his life, when examined by the astronomers
+are found quite inconsistent with astronomic theory.<span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span>
+They are, however, reconciled with it if we assume that our
+system of dates has its origin four years after the birth of
+Christ, or, in other words, that Christ was born in the
+year 4 <span class="smcap">B.&nbsp;C.</span> A mistake was doubtless made at the time
+the Christian era was introduced into chronology. At
+many other points the chance record of an eclipse in
+the early annals of civilization furnishes a similar means of
+controlling and correcting the dates assigned by the historian
+to events long past.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span></p>
+<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII</h2>
+
+<h3>INSTRUMENTS AND THE PRINCIPLES INVOLVED
+IN THEIR USE</h3>
+
+
+<p><a name="S_74" id="S_74"></a>74. <b>Two familiar instruments.</b>&mdash;In previous chapters we
+have seen that a clock and a divided circle (protractor) are
+needed for the observations which an astronomer makes,
+and it is worth while to note here that the geography of
+the sky and the science of celestial motions depend fundamentally
+upon these two instruments. The protractor is a
+simple instrument, a humble member of the family of
+divided circles, but untold labor and ingenuity have been
+expended on this family to make possible the construction
+of a circle so accurately divided that with it angles may be
+measured to the tenth of a second instead of to the tenth
+of a degree&mdash;i.&nbsp;e., 3,600 times as accurate as the protractor
+furnishes.</p>
+
+<p>The building of a good clock is equally important and
+has cost a like amount of labor and pains, so that it is a far
+cry from Galileo and his discovery that a pendulum "keeps
+time" to the modern clock with its accurate construction
+and elaborate provision against disturbing influences of
+every kind. Every such timepiece, whether it be of the
+nutmeg variety which sells for a dollar, or whether it be the
+standard clock of a great national observatory, is made up
+of the same essential parts that fall naturally into four
+classes, which we may compare with the departments of a
+well-ordered factory: I.&nbsp;A timekeeping department, the
+pendulum or balance spring, whose oscillations must all be
+of equal duration. II.&nbsp;A power department, the weights or<span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span>
+mainspring, which, when wound, store up the power applied
+from outside and give it out piecemeal as required to keep
+the first department running. III.&nbsp;A publication department,
+the dial and hands, which give out the time furnished
+by Department&nbsp;I. IV.&nbsp;A transportation department,
+the wheels, which connect the other three and serve as a
+means of transmitting power and time from one to the
+other. The case of either clock or watch is merely the
+roof which shelters it and forms no department of its industry.
+Of these departments the first is by far the most
+important, and its good or bad performance makes or mars
+the credit of the clock. Beware of meddling with the
+balance wheel of your watch.</p>
+
+<p><a name="S_75" id="S_75"></a>75. <b>Radiant energy.</b>&mdash;But we have now to consider other
+instruments which in practice supplement or displace the
+simple apparatus hitherto employed. Among the most important
+of these modern instruments are the telescope, the
+spectroscope, and the photographic camera; and since all
+these instruments deal with the light which comes from
+the stars to the earth, we must for their proper understanding
+take account of the nature of that light, or, more strictly
+speaking, we must take account of the radiant energy emitted
+by the sun and stars, which energy, coming from the
+sun, is translated by our nerves into the two different sensations
+of light and heat. The radiant energy which comes
+from the stars is not fundamentally different from that of
+the sun, but the amount of energy furnished by any star is
+so small that it is unable to produce through our nerves
+any sensible perception of heat, and for the same reason
+the vast majority of stars are invisible to the unaided eye;
+they do not furnish a sufficient amount of energy to affect
+the optic nerves. A hot brick taken into the hand reveals
+its presence by the two different sensations of heat and
+pressure (weight); but as there is only one brick to produce
+the two sensations, so there is only one energy to produce
+through its action upon different nerves the two sensations<span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span>
+of light and heat, and this energy is called <i>radiant</i> because
+it appears to stream forth radially from everything which
+has the capacity of emitting it. For the detailed study
+of radiant energy the student is referred to that branch
+of science called physics; but some of its elementary principles
+may be learned through the following simple experiment,
+which the student should not fail to perform for
+himself:</p>
+
+<p>Drop a bullet or other similar object into a bucket
+of water and observe the circular waves which spread
+from the place where it enters the water. These waves
+are a form of radiant energy, but differing from light or
+heat in that they are visibly confined to a single plane,
+the surface of the water, instead of filling the entire surrounding
+space. By varying the size of the bucket, the
+depth of the water, the weight of the bullet, etc., different
+kinds of waves, big and little, may be produced; but
+every such set of waves may be described and defined in
+all its principal characteristics by means of three numbers&mdash;viz.,
+the vertical height of the waves from hollow
+to crest; the distance of one wave from the next; and
+the velocity with which the waves travel across the water.
+The last of these quantities is called the velocity of propagation;
+the second is called the wave length; one half
+of the first is called the amplitude; and all these terms
+find important applications in the theory of light and
+heat.</p>
+
+<p>The energy of the falling bullet, the disturbance which
+it produced on entering the water, was carried by the
+waves from the center to the edge of the bucket but not
+beyond, for the wave can go only so far as the water
+extends. The transfer of energy in this way requires a
+perfectly continuous medium through which the waves
+may travel, and the whole visible universe is supposed to
+be filled with something called <i>ether</i>, which serves everywhere
+as a medium for the transmission of radiant energy<span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span>
+just as the water in the experiment served as a medium
+for transmitting in waves the energy furnished to it by the
+falling bullet. The student may think of this energy as being
+transmitted in spherical waves through the ether, every
+glowing body, such as a star, a candle flame, an arc lamp, a
+hot coal, etc., being the origin and center of such systems
+of waves, and determining by its own physical and chemical
+properties the wave length and amplitude of the wave
+systems given off.</p>
+
+<p>The intensity of any light depends upon the amplitude
+of the corresponding vibration, and its color depends upon
+the wave length. By ingenious devices which need not be
+here described it has been found possible to measure the
+wave length corresponding to different colors&mdash;e.&nbsp;g., all of
+the colors of the rainbow, and some of these wave lengths
+expressed in tenth meters are as follows: A tenth meter is
+the length obtained by dividing a meter into 10<sup>10</sup> equal
+parts. 10<sup>10</sup> =&nbsp;10,000,000,000.</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><th align="center" colspan="3">Color.</th><th align="center">Wave length.</th></tr>
+<tr><td align="left">Extreme</td><td align="left">limit</td><td align="left">of visible violet</td><td align="center">3,900</td></tr>
+<tr><td align="left">Middle</td><td align="left">of the</td><td align="left">violet</td><td align="center">4,060</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="left">blue</td><td align="center">4,730</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="left">green</td><td align="center">5,270</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="left">yellow</td><td align="center">5,810</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="left">orange</td><td align="center">5,970</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="left">red</td><td align="center">7,000</td></tr>
+<tr><td align="left">Extreme</td><td align="left">limit</td><td align="left">of visible red</td><td align="center">7,600</td></tr>
+</table></div>
+
+<div class="figcenter" style="width: 500px;"><a name="PLATE_I" id="PLATE_I"></a>
+<a href="images/i148-full.jpg"><img src="images/i148.jpg" width="500" height="817" alt="PLATE I.
+THE NORTHERN CONSTELLATIONS" title="PLATE I.
+THE NORTHERN CONSTELLATIONS" /></a>
+<span class="caption">PLATE I.
+THE NORTHERN CONSTELLATIONS</span>
+</div>
+
+<p>The phrase "extreme limit of visible violet" or red
+used above must be understood to mean that in general the
+eye is not able to detect radiant energy having a wave
+length less than 3,900 or greater than 7,600 tenth meters.
+Radiant energy, however, exists in waves of both greater
+and shorter length than the above, and may be readily
+detected by apparatus not subject to the limitations of the
+human eye&mdash;e.&nbsp;g., a common thermometer will show a rise
+of temperature when its bulb is exposed to radiant energy
+of wave length much greater than 7,600 tenth meters, and<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>
+a photographic plate will be strongly affected by energy of
+shorter wave length than 3,900 tenth meters.</p>
+
+<p><a name="S_76" id="S_76"></a>76. <b>Reflection and condensation of waves.</b>&mdash;When the
+waves produced by dropping a bullet into a bucket of
+water meet the sides of the bucket, they appear to rebound
+and are reflected back toward the center, and if the bullet is
+dropped very near the center of the bucket the reflected
+waves will meet simultaneously at this point and produce
+there by their combined action a wave higher than that
+which was reflected at the walls of the bucket. There has
+been a condensation of energy produced by the reflection,
+and this increased energy is shown by the greater amplitude
+of the wave. The student should not fail to notice that
+each portion of the wave has traveled out and back over
+the radius of the bucket, and that they meet simultaneously
+at the center because of this equality of the paths over which
+they travel, and the resulting equality of time required to
+go out and back. If the bullet were dropped at one side of
+the center, would the reflected waves produce <i>at any point</i>
+a condensation of energy?</p>
+
+<p>If the bucket were of elliptical instead of circular cross
+section and the bullet were dropped at one focus of the
+ellipse there would be produced a condensation of reflected
+energy at the other focus, since the sum of the paths traversed
+by each portion of the wave before and after reflection
+is equal to the sum of the paths traversed by every
+other portion, and all parts of the wave reach the second
+focus at the same time. Upon what geometrical principle
+does this depend?</p>
+
+<p>The condensation of wave energy in the circular and
+elliptical buckets are special cases under the general principle
+that such a condensation will be produced at any
+point which is so placed that different parts of the wave
+front reach it simultaneously, whether by reflection or by
+some other means, as shown below.</p>
+
+<p>The student will note that for the sake of greater precision<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>
+we here say <i>wave front</i> instead of wave. If in any
+wave we imagine a line drawn along the crest, so as to touch
+every drop which at that moment is exactly at the crest, we
+shall have what is called a wave front, and similarly a line
+drawn through the trough between two waves, or through
+any set of drops similarly placed on a wave, constitutes a
+wave front.</p>
+
+<p><a name="S_77" id="S_77"></a>77. <b>Mirrors and lenses.</b>&mdash;That form of radiant energy
+which we recognize as light and heat may be reflected and
+condensed precisely as are the waves of water in the exercise
+considered above, but owing to the extreme shortness
+of the wave length in this case the reflecting surface should
+be very smooth and highly polished. A piece of glass hollowed
+out in the center by grinding, and with a light film
+of silver chemically deposited upon the hollow surface and
+carefully polished, is often used by astronomers for this purpose,
+and is called a concave mirror.</p>
+
+<p>The radiant energy coming from a star or other distant
+object and falling upon the silvered face of such a mirror
+is reflected and condensed at a point a little in front of the
+mirror, and there forms an image of the star, which may be
+seen with the unaided eye, if it is held in the right place, or
+may be examined through a magnifying glass. Similarly,
+an image of the sun, a planet, or a distant terrestrial object
+is formed by the mirror, which condenses at its appropriate
+place the radiant energy proceeding from each and every
+point in the surface of the object, and this, in common
+phrase, produces an image of the object.</p>
+
+<p>Another device more frequently used by astronomers
+for the production of images (condensation of energy) is a
+lens which in its simplest form is a round piece of glass,
+thick in the center and thin at the edge, with a cross section,
+such as is shown at <i>A&nbsp;B</i> in <a href="#Fig_38">Fig.&nbsp;38</a>. If we suppose
+<i>E&nbsp;G&nbsp;D</i> to represent a small part of a wave front coming from
+a very distant source of radiant energy, such as a star, this
+wave front will be practically a plane surface represented<span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span>
+by the straight line <i>E&nbsp;D</i>, but in passing through the lens
+this surface will become warped, since light travels slower
+in glass than in air, and the central part of the beam, <i>G</i>,
+in its onward motion will be retarded by the thick center
+of the lens, more than <i>E</i> or <i>D</i> will be retarded by the comparatively
+thin outer edges of <i>A&nbsp;B</i>. On the right of the
+lens the wave front therefore will be transformed into a
+curved surface whose exact character depends upon the
+shape of the lens and the kind of glass of which it is made.
+By properly choosing these the new wave front may be
+made a part of a sphere having its center at the point <i>F</i> and
+the whole energy of the wave front, <i>E&nbsp;G&nbsp;D</i>, will then be condensed
+at <i>F</i>, because this point is equally distant from all
+parts of the warped wave front, and therefore is in a position
+to receive them simultaneously. The distance of <i>F</i>
+from <i>A&nbsp;B</i> is called the focal length of the lens, and <i>F</i> itself
+is called the focus. The significance of this last word
+(Latin, <i>focus</i> =&nbsp;fireplace) will become painfully apparent to
+the student if he will hold a common reading glass between
+his hand and the sun in such a way that the focus falls
+upon his hand.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_38" id="Fig_38"></a>
+<img src="images/i152.png" width="500" height="141" alt="Fig. 38.&mdash;Illustrating the theory of lenses." title="Fig. 38.&mdash;Illustrating the theory of lenses." />
+<span class="caption"><span class="smcap">Fig. 38.</span>&mdash;Illustrating the theory of lenses.</span>
+</div>
+
+<p>All the energy transmitted by the lens in the direction
+<i>G&nbsp;F</i> is concentrated upon a very small area at <i>F</i>, and
+an image of the object&mdash;e.&nbsp;g., a star, from which the light
+came&mdash;is formed here. Other stars situated near the one in
+question will also send beams of light along slightly different
+directions to the lens, and these will be concentrated,
+each in its appropriate place, in the <i>focal plane</i>, <i>F&nbsp;H</i>, passed
+through the focus, <i>F</i>, perpendicular to the line, <i>F&nbsp;G</i>, and<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span>
+we shall find in this plane a picture of all the stars or other
+objects within the range of the lens.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_39" id="Fig_39"></a>
+<img src="images/i153a.png" width="350" height="214" alt="Fig. 39.&mdash;Essential parts of a reflecting
+telescope." title="Fig. 39.&mdash;Essential parts of a reflecting
+telescope." />
+<span class="caption"><span class="smcap">Fig. 39.</span>&mdash;Essential parts of a reflecting
+telescope.</span>
+</div>
+
+<p><a name="S_78" id="S_78"></a>78. <b>Telescopes.</b>&mdash;The simplest kind of telescope consists
+of a concave mirror to produce images, and a magnifying
+glass, called an <i>eyepiece</i>, through which to examine them;
+but for convenience'
+sake, so that the observer
+may not stand in his
+own light, a small mirror
+is frequently added
+to this combination, as
+at&nbsp;<i>H</i> in <a href="#Fig_39">Fig.&nbsp;39</a>, where
+the lines represent the
+directions along which
+the energy is propagated.
+By reflection from this mirror the focal plane and the
+images are shifted to <i>F</i>, where they may be examined from
+one side through the magnifying glass <i>E</i>.</p>
+
+<p>Such a combination of parts is called a <i>reflecting</i> telescope,
+while one in which the images are produced by a
+lens or combination of lenses is called a <i>refracting</i> telescope,
+the adjective having reference to the bending, refraction,
+produced by the glass upon the direction in which
+the energy is propagated. The customary arrangement of
+parts in such a telescope is shown in <a href="#Fig_40">Fig.&nbsp;40</a>, where the
+part marked <i>O</i> is called the objective and <i>V&nbsp;E</i> (the magnifying
+glass) is the eyepiece, or ocular, as it is sometimes
+called.</p>
+
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_40" id="Fig_40"></a>
+<img src="images/i153b.png" width="500" height="96" alt="Fig. 40.&mdash;A simple form of refracting telescope." title="Fig. 40.&mdash;A simple form of refracting telescope." />
+<span class="caption"><span class="smcap">Fig. 40.</span>&mdash;A simple form of refracting telescope.</span>
+</div>
+
+<p>Most objects with which we have to deal in using a
+telescope send to it not light of one color only, but a mixture
+<span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span>
+of light of many colors, many different wave lengths,
+some of which are refracted more than others by the glass
+of which the lens is composed, and in consequence of these
+different amounts of refraction a single lens does not furnish
+a single image of a star, but gives a confused jumble of
+red and yellow and blue images much inferior in sharpness
+of outline (definition) to the images made by a good concave
+mirror. To remedy this defect it is customary to
+make the objective of two or more pieces of glass of different
+densities and ground to different shapes as is shown at <i>O</i>
+in <a href="#Fig_40">Fig.&nbsp;40</a>. The two pieces of glass thus mounted in one
+frame constitute a compound lens having its own focal
+plane, shown at <i>F</i> in the figure, and similarly the lenses
+composing the eyepiece have a focal plane between the
+eyepiece and the objective which must also fall at <i>F</i>, and
+in the use of a telescope the eyepiece must be pushed out
+or in until its focal plane coincides with that of the objective.
+This process, which is called focusing, is what is
+accomplished in the ordinary opera glass by turning a screw
+placed between the two tubes, and it must be carefully
+done with every telescope in order to obtain distinct vision.</p>
+
+<p><a name="S_79" id="S_79"></a>79. <b>Magnifying power.</b>&mdash;The amount by which a given
+telescope magnifies depends upon the focal length of the objective
+(or mirror) and the focal length of the eyepiece, and
+is equal to the ratio of these two quantities. Thus in <a href="#Fig_40">Fig.&nbsp;40</a>
+the distance of the objective from the focal plane <i>F</i> is
+about 16 times as great as the distance of the eyepiece
+from the same plane, and the magnifying power of this
+telescope is therefore 16 diameters. A magnifying power
+of 16 diameters means that the diameter of any object seen
+in the telescope looks 16 times as large as it appears without
+the telescope, and is nearly equivalent to saying that
+the object appears only one sixteenth as far off. Sometimes
+the magnifying power is assumed to be the number
+of times that the <i>area</i> of an object seems increased; and
+since areas are proportional to the squares of lines, the<span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span>
+magnifying power of 16 diameters might be called a power
+of 256. Every large telescope is provided with several eyepieces
+of different focal lengths, ranging from a quarter of
+an inch to two and a half inches, which are used to furnish
+different magnifying powers as may be required for
+the different kinds of work undertaken with the instrument.
+Higher powers can be used with large telescopes
+than with small ones, but it is seldom advantageous to
+use with any telescope an eyepiece giving a higher power
+than 60 diameters for each inch of diameter of the objective.</p>
+
+<p>The part played by the eyepiece in determining magnifying
+power will be readily understood from the following
+experiment:</p>
+
+<p>Make a pin hole in a piece of cardboard. Bring a
+printed page so close to one eye that you can no longer see
+the letters distinctly, and then place the pin hole between
+the eye and the page. The letters which were before
+blurred may now be seen plainly through the pin hole,
+even when the page is brought nearer to the eye than before.
+As it is brought nearer, notice how the letters seem
+to become larger, solely because they are nearer. A pin
+hole is the simplest kind of a magnifier, and the eyepiece
+in a telescope plays the same part as does the pin hole in
+the experiment; it enables the eye to be brought nearer to
+the image, and the shorter the focal length of the eyepiece
+the nearer is the eye brought to the image and the higher
+is the magnifying power.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_41" id="Fig_41"></a>
+<img src="images/i156.png" width="350" height="585" alt="Fig. 41.&mdash;A simple equatorial mounting." title="Fig. 41.&mdash;A simple equatorial mounting." />
+<span class="caption"><span class="smcap">Fig. 41.</span>&mdash;A simple equatorial mounting.</span>
+</div>
+
+<p><a name="S_80" id="S_80"></a>80. <b>The equatorial mounting.</b>&mdash;Telescopes are of all sizes,
+from the modest opera glass which may be carried in the
+pocket and which requires no other support than the hand,
+to the giant which must have a special roof to shelter it
+and elaborate machinery to support and direct it toward
+the sky. But for even the largest telescopes this machinery
+consists of the following parts, which are illustrated, with
+exception of the last one, in the small equatorial telescope<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span>
+shown in <a href="#Fig_41">Fig.&nbsp;41</a>. It is not customary to place a driving
+clock on so small a telescope as this:</p>
+
+<p>(<i>a</i>) A supporting pier or tripod.</p>
+
+<p>(<i>b</i>) An axis placed parallel to the axis of the earth.</p>
+
+<p>(<i>c</i>) Another axis at
+right angles to <i>b</i> and
+capable of revolving
+upon <i>b</i> as an axle.</p>
+
+<p>(<i>d</i>) The telescope
+tube attached to <i>c</i> and capable
+of revolving about <i>c</i>.</p>
+
+<p>(<i>e</i>) Graduated circles
+attached to <i>c</i> and <i>b</i> to
+measure the amount by
+which the telescope is
+turned on these axes.</p>
+
+<p>(<i>f</i>) A driving clock so
+connected with <i>b</i> as to
+make <i>c</i> (and <i>d</i>) revolve
+about <i>b</i> with an angular
+velocity equal and opposite
+to that with which the
+earth turns upon its axis.</p>
+
+<p>Such a support is called
+an equatorial mounting,
+and the student should
+note from the figure that
+the circles, <i>e</i>, measure the
+hour angle and declination
+of any star toward which
+the telescope is directed,
+and conversely if the telescope be so set that these circles
+indicate the hour angle and declination of any given star,
+the telescope will then point toward that star. In this
+way it is easy to find with the telescope any moderately
+bright star, even in broad daylight, although it is then
+<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span>
+absolutely invisible to the naked eye. The rotation of the
+earth about its axis will speedily carry the telescope away
+from the star, but if the driving clock be started, its effect
+is to turn the telescope toward the west just as fast as the
+earth's rotation carries it toward the east, and by these
+compensating motions
+to keep it directed toward
+the star. In <a href="#Fig_42">Fig.&nbsp;42</a>,
+which represents
+the largest and one of
+the most perfect refracting
+telescopes
+ever built, let the student
+pick out and identify
+the several parts
+of the mounting above
+described. A part of
+the driving clock may
+be seen within the head
+of the pier. In <a href="#Fig_43">Fig.&nbsp;43</a>
+trace out the corresponding
+parts in
+the mounting of a reflecting
+telescope.</p>
+
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_42" id="Fig_42"></a>
+<a href="images/i157-full.jpg"><img src="images/i157.jpg" width="600" height="370" alt="Fig. 42.&mdash;Equatorial mounting of the great telescope of the Yerkes Observatory." title="Fig. 42.&mdash;Equatorial mounting of the great telescope of the Yerkes Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 42.</span>&mdash;Equatorial mounting of the great telescope of the Yerkes Observatory.</span>
+</div>
+
+
+<div class="figright" style="width: 350px;"><a name="Fig_43" id="Fig_43"></a>
+<img src="images/i158.jpg" width="350" height="582" alt="Fig. 43.&mdash;The reflecting telescope of the
+Paris Observatory." title="Fig. 43.&mdash;The reflecting telescope of the
+Paris Observatory." />
+<span class="caption"><span class="smcap">Fig. 43.</span>&mdash;The reflecting telescope of the
+Paris Observatory.</span>
+</div>
+
+<p>A telescope is often
+only a subordinate part
+of some instrument or
+apparatus, and then its
+style of mounting is
+determined by the requirements of the special case; but
+when the telescope is the chief thing, and the remainder
+of the apparatus is subordinate to it, the equatorial mounting
+is almost always adopted, although sometimes the arrangement
+of the parts is very different in appearance from
+any of those shown above. Beware of the popular error that
+an object held close in front of a telescope can be seen by an<span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span>
+observer at the eyepiece. The numerous stories of astronomers
+who saw spiders crawling over the objective of their
+telescope, and imagined they were beholding strange objects
+in the sky, are all fictitious, since nothing on or near
+the objective could possibly be seen through the telescope.</p>
+
+<p><a name="S_81" id="S_81"></a>81. <b>Photography.</b>&mdash;A photographic camera consists of a
+lens and a device for holding at its focus a specially prepared
+plate or film. This
+plate carries a chemical
+deposit which is very
+sensitive to the action
+of light, and which may
+be made to preserve the
+imprint of any picture
+which the lens forms
+upon it. If such a sensitive
+plate is placed at
+the focus of a reflecting
+telescope, the combination
+becomes a camera
+available for astronomical
+photography, and at
+the present time the
+tendency is strong in
+nearly every branch of
+astronomical research to
+substitute the sensitive
+plate in place of the observer
+at a telescope. A
+refracting telescope may also be used for astronomical photography,
+and is very much used, but some complications
+occur here on account of the resolution of the light into
+its constituent colors in passing through the objective.
+<a href="#Fig_44">Fig.&nbsp;44</a> shows such a telescope, or rather two telescopes, one
+photographic, the other visual, supported side by side upon
+the same equatorial mounting.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_44" id="Fig_44"></a>
+<img src="images/i159.png" width="350" height="539" alt="Fig. 44.&mdash;Photographic telescope of the Paris
+Observatory." title="Fig. 44.&mdash;Photographic telescope of the Paris
+Observatory." />
+<span class="caption"><span class="smcap">Fig. 44.</span>&mdash;Photographic telescope of the Paris
+Observatory.</span>
+</div><p><span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span></p>
+
+<p>One of the great advantages of photography is found in
+connection with what is called&mdash;</p>
+
+<p><a name="S_82" id="S_82"></a>82. <b>Personal equation.</b>&mdash;It is a remarkable fact, first investigated
+by the German astronomer Bessel, three quarters
+of a century ago, that where extreme accuracy is required
+the human senses can not be implicitly relied upon.
+The most skillful observers will not agree exactly in their
+measurement of an angle or in estimating the exact instant
+at which a star crossed the meridian; the most skillful
+artists can not draw identical pictures of the same object,
+etc.</p>
+
+<p>These minor deceptions of the senses are included in
+the term <i>personal equation</i>, which is a famous phrase in
+astronomy, denoting that the observations of any given
+person require to be corrected by means of some equation
+involving his personality.</p>
+
+<p>General health, digestion, nerves, fatigue, all influence
+the personal equation, and it was in reference to such matters
+that one of the most eminent of living astronomers has
+given this description of his habits of observing:</p>
+
+<p>"In order to avoid every physiological disturbance, I
+have adopted the rule to abstain for one or two hours before
+commencing observations from every laborious occupation;
+never to go to the telescope with stomach loaded with
+food; to abstain from everything which could affect the
+nervous system, from narcotics and alcohol, and especially
+from the abuse of coffee, which I have found to be exceedingly
+prejudicial to the accuracy of observation."<a name="FNanchor_C_3" id="FNanchor_C_3"></a><a href="#Footnote_C_3" class="fnanchor">[C]</a> A
+regimen suggestive of preparation for an athletic contest
+rather than for the more quiet labors of an astronomer.</p>
+
+<p><a name="S_83" id="S_83"></a>83. <b>Visual and photographic work.</b>&mdash;The photographic
+plate has no stomach and no nerves, and is thus free from
+many of the sources of error which inhere in visual observations,
+and in special classes of work it possesses other<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>
+marked advantages, such as rapidity when many stars are
+to be dealt with simultaneously, permanence of record, and
+owing to the cumulative effect of long exposure of the plate
+it is possible to photograph with a given telescope stars far
+too faint to be seen through it. On the other hand, the
+eye has the advantage in some respects, such as studying
+the minute details of a fairly bright object&mdash;e.&nbsp;g., the surface
+of a planet, or the sun's corona and, for the present at
+least, neither method of observing can exclude the other.
+For a remarkable case of discordance between the results
+of photographic and visual observations compare the pictures
+of the great nebula in the constellation Andromeda,
+which are given in <a href="#CHAPTER_XIV">Chapter&nbsp;XIV</a>. A partial explanation
+of these discordances and other similar ones is that the
+eye is most strongly affected by greenish-yellow light,
+while the photographic plate responds most strongly to
+violet light; the photograph, therefore, represents things
+which the eye has little capacity for seeing, and <i>vice versa</i>.</p>
+
+<p><a name="S_84" id="S_84"></a>84. <b>The spectroscope.</b>&mdash;In some respects the spectroscope
+is the exact counterpart of the telescope. The latter condenses
+radiant energy and the former disperses it. As a
+measuring instrument the telescope is mainly concerned
+with the direction from which light comes, and the different
+colors of which that light is composed affect it only as
+an obstacle to be overcome in its construction. On the
+other hand, with the spectroscope the direction from which
+the radiant energy comes is of minor consequence, and the
+all-important consideration is the intrinsic character of
+that radiation. What colors are present in the light and
+in what proportions? What can these colors be made to
+tell about the nature and condition of the body from which
+they come, be it sun, or star, or some terrestrial source of
+light, such as an arc lamp, a candle flame, or a furnace in
+blast? These are some of the characteristic questions of
+the spectrum analysis, and, as the name implies, they are
+solved by analyzing the radiant energy into its component<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span>
+parts, setting down the blue light in one place, the yellow
+in another, the red in still another, etc., and interpreting
+this array of colors by means of principles which we shall
+have to consider. Something of this process of color
+analysis may be seen in the brilliant hues shown by a soap
+bubble, or reflected from a piece of mother-of-pearl, and
+still more strikingly exhibited in the rainbow, produced by
+raindrops which break up the sunlight into its component
+colors and arrange them each in its appropriate place.
+Any of these natural methods of decomposing light might
+be employed in the construction of a spectroscope, but in
+spectroscopes which are used for analyzing the light from
+feeble sources, such as a star, or a candle flame, a glass
+prism of triangular cross section is usually employed to resolve
+the light into its component colors, which it does by
+refracting it as shown at the edges of the lens in <a href="#Fig_38">Fig.&nbsp;38</a>.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_45" id="Fig_45"></a>
+<img src="images/i162.png" width="500" height="290" alt="Fig. 45.&mdash;Resolution of light into its component colors." title="Fig. 45.&mdash;Resolution of light into its component colors." />
+<span class="caption"><span class="smcap">Fig. 45.</span>&mdash;Resolution of light into its component colors.</span>
+</div>
+
+<p>The course of a beam of light in passing through such
+a prism is shown in <a href="#Fig_45">Fig.&nbsp;45</a>. Note that the bending of the
+light from its original course into a new one, which is here
+shown as produced by the prism, is quite similar to the
+bending shown at the edges of a lens and comes from the<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span>
+same cause, the slower velocity of light in glass than in
+air. It takes the light-waves as long to move over the
+path <i>A&nbsp;B</i> in glass as over the longer path <i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, of
+which only the middle section lies in the glass.</p>
+
+<p>Not only does the prism bend the beam of light transmitted
+by it, but it bends in different degree light of different
+colors, as is shown in the figure, where the beam at the
+left of the prism is supposed to be made up of a mixture of
+blue and red light, while at the right of the prism the
+greater deviation imparted to the blue quite separates the
+colors, so that they fall at different places on the screen,
+<i>S&nbsp;S</i>. The compound light has been analyzed into its constituents,
+and in the same way every other color would be
+put down at its appropriate place on the screen, and a beam
+of white light falling upon the prism would be resolved by
+it into a sequence of colors, falling upon the screen in the
+order red, orange, yellow, green, blue, indigo, violet. The
+initial letters of these names make the word <i>Roygbiv</i>, and
+by means of it their order is easily remembered.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_46" id="Fig_46"></a>
+<img src="images/i164.png" width="500" height="230" alt="Fig. 46.&mdash;Principal parts of a spectroscope." title="Fig. 46.&mdash;Principal parts of a spectroscope." />
+<span class="caption"><span class="smcap">Fig. 46.</span>&mdash;Principal parts of a spectroscope.</span>
+</div>
+
+<p>If the light which is to be examined comes from a star
+the analysis made by the prism is complete, and when
+viewed through a telescope the image of the star is seen to
+be drawn out into a band of light, which is called a <i>spectrum</i>,
+and is red at one end and violet or blue at the other,
+with all the colors of the rainbow intervening in proper
+order between these extremes. Such a prism placed in
+front of the objective of a telescope is called an objective
+prism, and has been used for stellar work with marked
+success at the Harvard College Observatory. But if the
+light to be analyzed comes from an object having an appreciable
+extent of surface, such as the sun or a planet,
+the objective prism can not be successfully employed,
+since each point of the surface will produce its own spectrum,
+and these will appear in the <i>view telescope</i> superposed
+and confused one with another in a very objectionable
+manner. To avoid this difficulty there is placed<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>
+between the prism and the source of light an opaque
+screen, <i>S</i>, with a very narrow slit cut in it, through which all
+the light to be analyzed must pass and must also go through
+a lens, <i>A</i>, placed between the slit and the prism, as shown
+in <a href="#Fig_46">Fig.&nbsp;46</a>. The slit and lens, together with the tube in
+which they are usually supported, are called a <i>collimator</i>.
+By this device a very limited amount of light is permitted
+to pass from the object through the slit and lens to the
+prism and is there resolved into a spectrum, which is in
+effect a series of images of the slit in light of different
+colors, placed side by side so close as to make practically a
+continuous ribbon of light whose width is the length of
+each individual picture of the slit. The length of the ribbon
+(dispersion) depends mainly upon the shape of the prism
+and the kind of glass of which it is made, and it may be
+very greatly increased and the efficiency of the spectroscope
+enhanced by putting two, three, or more prisms in
+place of the single one above described. When the amount
+of light is very great, as in the case of the sun or an electric
+arc lamp, it is advantageous to alter slightly the arrangement
+of the spectroscope and to substitute in place
+of the prism a grating&mdash;i.&nbsp;e., a metallic mirror with a great
+number of fine parallel lines ruled upon its surface at equal
+intervals, one from another. It is by virtue of such a system
+of fine parallel grooves that mother-of-pearl displays<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>
+its beautiful color effects, and a brilliant spectrum of great
+purity and high dispersion is furnished by a grating ruled
+with from 10,000 to 20,000 lines to the inch. <a href="#Fig_47">Fig.&nbsp;47</a> represents,
+rather crudely, a part of the spectrum
+of an arc light furnished by such a
+grating, or rather it shows three different
+spectra arranged side by side, and looking
+something like a rude ladder. The sides
+of the ladder are the spectra furnished by
+the incandescent carbons of the lamp, and
+the cross pieces are the spectrum of the
+electric arc filling the space between the
+carbons. <a href="#Fig_48">Fig.&nbsp;48</a> shows a continuation of
+the same spectra into a region where the
+radiant energy is invisible to the eye, but
+is capable of being photographed.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_47" id="Fig_47"></a>
+<a href="images/i165.jpg"><img src="images/i165.jpg" width="600" height="96" alt="Fig. 47.&mdash;Green and blue part of the spectrum of an electric arc light." title="Fig. 47.&mdash;Green and blue part of the spectrum of an electric arc light." /></a>
+<span class="caption"><span class="smcap">Fig. 47.</span>&mdash;Green and blue part of the spectrum of an electric arc light.</span>
+</div>
+
+<p>It is only when a lens is placed between
+the lamp and the slit of the spectroscope
+that the three spectra are shown
+distinct from each other as in the figure.
+The purpose of the lens is to make a picture
+of the lamp upon the slit, so that
+all the radiant energy from any one point
+of the arc may be brought to one part of
+the slit, and thus appear in the resulting
+spectrum separated from the energy
+which comes from every other part of
+the arc. Such an instrument is called
+an <i>analyzing spectroscope</i> while one without
+the lens is called an <i>integrating spectroscope</i>,
+since it furnishes to each point
+of the slit a sample of the radiant energy
+coming from every part of the source of
+light, and thus produces only an average
+spectrum of that source without distinction of its parts.
+When a spectroscope is attached to a telescope, as is often<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span>
+done (see <a href="#Fig_49">Fig.&nbsp;49</a>), the eyepiece is removed to make way
+for it, and the telescope objective takes the part of the
+analyzing lens. A camera is frequently combined with
+such an apparatus to photograph the spectra it furnishes,
+and the whole instrument is then called a <i>spectrograph</i>.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_48" id="Fig_48"></a>
+<a href="images/i166.jpg"><img src="images/i166.jpg" width="500" height="93" alt="Fig. 48.&mdash;Violet and ultraviolet parts of spectrum of an arc lamp." title="Fig. 48.&mdash;Violet and ultraviolet parts of spectrum of an arc lamp." /></a>
+<span class="caption"><span class="smcap">Fig. 48.</span>&mdash;Violet and ultraviolet parts of spectrum of an arc lamp.</span>
+</div>
+
+<p><a name="S_85" id="S_85"></a>85. <b>Spectrum analysis.</b>&mdash;Having seen the mechanism of
+the spectroscope by which the light incident upon it is
+resolved into its constituent parts and drawn out into a
+series of colors arranged in the order of their wave lengths,
+we have now to consider the interpretation which is to be
+placed upon the various kinds of spectra which may be
+seen, and here we rely upon the experience of physicists
+and chemists, from whom we learn as follows:</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_49" id="Fig_49"></a>
+<a href="images/i167-full.jpg"><img src="images/i167.jpg" width="500" height="388" alt="Fig. 49.&mdash;A spectroscope attached to the Yerkes telescope." title="Fig. 49.&mdash;A spectroscope attached to the Yerkes telescope." /></a>
+<span class="caption"><span class="smcap">Fig. 49.</span>&mdash;A spectroscope attached to the Yerkes telescope.</span>
+</div>
+
+<p>The radiant energy which is analyzed by the spectroscope
+has its source in the atoms and molecules which make
+up the luminous body from which the energy is radiated,
+and these atoms and molecules are able to impress upon
+the ether their own peculiarities in the shape of waves of
+different length and amplitude. We have seen that by
+varying the conditions of the experiment different kinds of
+waves may be produced in a bucket of water; and as a
+study of these waves might furnish an index to the conditions
+which produced them, so the study of the waves
+peculiar to the light which comes from any source may be
+made to give information about the molecules which make
+up that source. Thus the molecules of iron produce a
+system of waves peculiar to themselves and which can be
+duplicated by nothing else, and every other substance
+gives off its own peculiar type of energy, presenting a<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span>
+limited and definite number of wave lengths dependent
+upon the nature and condition of its molecules. If these
+molecules are free to behave in their own characteristic
+fashion without disturbance or crowding, they emit light of
+these wave lengths only, and we find in the spectrum a
+series of bright lines, pictures of the slit produced by light
+of these particular wave lengths, while between these bright
+lines lie dark spaces showing the absence from the radiant
+energy of light of intermediate wave lengths. Such a
+spectrum is shown in the central portion of <a href="#Fig_47">Fig.&nbsp;47</a>, which,
+as we have already seen, is produced by the space between
+the carbons of the arc lamp. On the other hand, if the
+molecules are closely packed together under pressure they
+so interfere with each other as to give off a jumble of
+energy of all wave lengths, and this is translated by the
+spectroscope into a continuous ribbon of light with no dark
+spaces intervening, as in the upper and lower parts of Figs.&nbsp;<a href="#Fig_47">47</a><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>
+and&nbsp;<a href="#Fig_48">48</a>, produced by the incandescent solid carbons of
+the lamp. These two types are known as the continuous
+and discontinuous spectrum, and we may lay down the following
+principle regarding them:</p>
+
+<p>A discontinuous spectrum, or bright-line spectrum as
+it is familiarly called, indicates that the molecules of the
+source of light are not crowded together, and therefore the
+light must come from an incandescent gas. A continuous
+spectrum shows only that the molecules are crowded together,
+or are so numerous that the body to which they
+belong is not transparent and gives no further information.
+The body may be solid, liquid, or gaseous, but in
+the latter case the gas must be under considerable pressure
+or of great extent.</p>
+
+<p>A second principle is: The lines which appear in a spectrum
+are characteristic of the source from which the light
+came&mdash;e.&nbsp;g., the double line in the yellow part of the spectrum
+at the extreme left in <a href="#Fig_47">Fig.&nbsp;47</a> is produced by sodium
+vapor in and around the electric arc and is never produced
+by anything but sodium. When by laboratory experiments
+we have learned the particular set of lines
+corresponding to iron, we may treat the presence of these
+lines in another spectrum as proof that iron is present
+in the source from which the light came, whether that
+source be a white-hot poker in the next room or a star
+immeasurably distant. The evidence that iron is present
+lies in the nature of the light, and there is no reason
+to suppose that nature to be altered on the way from
+star to earth. It may, however, be altered by something
+happening to the source from which it comes&mdash;e.&nbsp;g., changing
+temperature or pressure may affect, and does affect, the
+spectrum which such a substance as iron emits, and we must
+be prepared to find the same substance presenting different
+spectra under different conditions, only these conditions
+must be greatly altered in order to produce radical changes
+in the spectrum.<span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_50" id="Fig_50"></a>
+<img src="images/i169.png" width="600" height="137" alt="Fig. 50.&mdash;The chief lines in the spectrum of sunlight.&mdash;Herschel." title="Fig. 50.&mdash;The chief lines in the spectrum of sunlight.&mdash;Herschel." />
+<span class="caption"><span class="smcap">Fig. 50.</span>&mdash;The chief lines in the spectrum of sunlight.&mdash;<span class="smcap">Herschel.</span></span>
+</div>
+
+<p><a name="S_86" id="S_86"></a>86. <b>Wave lengths.</b>&mdash;To identify
+a line as belonging to and produced
+by iron or any other substance,
+its position in the spectrum&mdash;i.&nbsp;e.,
+its wave length&mdash;must
+be very accurately determined,
+and for the identification of a substance
+by means of its spectrum it
+is often necessary to determine accurately
+the wave lengths of many
+lines. A complicated spectrum
+may consist of hundreds or thousands
+of lines, due to the presence
+of many different substances in
+the source of light, and unless
+great care is taken in assigning
+the exact position of these lines
+in the spectrum, confusion and
+wrong identifications are sure to
+result. For the measurement of
+the required wave length a tenth
+meter (<a href="#S_75">§&nbsp;75</a>) is the unit employed,
+and a scale of wave lengths expressed
+in this unit is presented
+in <a href="#Fig_50">Fig.&nbsp;50</a>. The accuracy with
+which some of these wave lengths
+are determined is truly astounding;
+a ten-billionth of an inch!
+These numerical wave lengths
+save all necessity for referring to
+the color of any part of the spectrum,
+and pictures of spectra for
+scientific use are not usually
+printed in colors.</p>
+
+<p><a name="S_87" id="S_87"></a>87. <b>Absorption spectra.</b>&mdash;There
+is another kind of spectrum, of<span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span>
+greater importance than either of those above considered,
+which is well illustrated by the spectrum of sunlight (<a href="#Fig_50">Fig.&nbsp;50</a>).
+This is a nearly continuous spectrum crossed by numerous
+<i>dark</i> lines due to absorption of radiant energy in a
+comparatively cool gas through which it passes on its way
+to the spectroscope. Fraunhofer, who made the first careful
+study of spectra, designated some of the more conspicuous
+of these lines by letters of the alphabet which are shown
+in the plate, and which are still in common use as names
+for the lines, not only in the spectrum of sunlight but
+wherever they occur in other spectra. Thus the double
+line marked <i>D</i>, wave length 5893, falls at precisely the same
+place in the spectrum as does the double (sodium) line
+which we have already seen in the yellow part of the arc-light
+spectrum, which line is also called <i>D</i> and bears a very
+intimate relation to the dark <i>D</i> line of the solar spectrum.</p>
+
+<p>The student who has access to colored crayons should
+color one edge of <a href="#Fig_50">Fig.&nbsp;50</a> in accordance with the lettering
+there given and, so far as possible, he should make the
+transition from one color to the next a gradual one, as it is
+in the rainbow.</p>
+
+<p><a href="#Fig_50">Fig.&nbsp;50</a> is far from being a complete representation of
+the spectrum of sunlight. Not only does this spectrum extend
+both to the right and to the left into regions invisible
+to the human eye, but within the limits of the figure, instead
+of the seventy-five lines there shown, there are literally
+thousands upon thousands of lines, of which only the
+most conspicuous can be shown in such a cut as this.</p>
+
+<p>The dark lines which appear in the spectrum of sunlight
+can, under proper conditions, be made to appear in
+the spectrum of an arc light, and <a href="#Fig_51">Fig.&nbsp;51</a> shows a magnified
+representation of a small part of such a spectrum adjacent
+to the <i>D</i> (sodium) lines. Down the middle of each of these
+lines runs a black streak whose position (wave length) is
+precisely that of the <i>D</i> lines in the spectrum of sunlight,
+and whose presence is explained as follows:<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span></p>
+
+<p>The very hot sodium vapor at the center of the arc gives
+off its characteristic light, which, shining through the outer
+and cooler layers of sodium vapor, is partially absorbed by
+these, resulting in a fine dark line corresponding exactly in
+position and wave length to the bright lines, and seen
+against these as a background, since the higher temperature
+at the center of the arc tends to broaden the bright
+lines and make them diffuse. Similarly the dark lines in
+the spectrum of the sun (<a href="#Fig_50">Fig.&nbsp;50</a>) point to the existence of
+a surrounding envelope of relatively cool gases, which absorb
+from the sunlight precisely those kinds of radiant energy
+which they would themselves emit if incandescent. The
+resulting dark lines in the spectrum are to be interpreted
+by the same set of principles which we have above applied
+to the bright lines of a discontinuous spectrum, and they
+may be used to determine the chemical composition of the
+sun, just as the bright lines serve to determine the chemical
+elements present in the electric arc. With reference to
+the mode of their formation, bright-line and dark-line spectra
+are sometimes called respectively <i>emission</i> and <i>absorption</i>
+spectra.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_51" id="Fig_51"></a>
+<img src="images/i171.jpg" width="500" height="266" alt="Fig. 51.&mdash;The lines reversed." title="Fig. 51.&mdash;The lines reversed." />
+<span class="caption"><span class="smcap">Fig. 51.</span>&mdash;The lines reversed.</span>
+</div>
+
+<p><a name="S_88" id="S_88"></a>88. <b>Types of spectrum.</b>&mdash;The sun presents by far the
+most complex spectrum known, and <a href="#Fig_50">Fig.&nbsp;50</a> shows only a
+small number of the more conspicuous lines which appear<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>
+in it. Spectra of stars, <i>per contra</i>, appear relatively simple,
+since their feeble light is insufficient to bring out faint
+details. In Chapters&nbsp;<a href="#CHAPTER_XIII">XIII</a> and&nbsp;<a href="#CHAPTER_XIV">XIV</a> there are shown types
+of the different kinds of spectra given by starlight, and
+these are to be interpreted by the principles above established.
+Thus the spectrum of the bright star &beta;&nbsp;Aurigę
+shows a continuous spectrum crossed by a few heavy absorption
+lines which are known from laboratory experiments
+to be produced only by hydrogen. There must
+therefore be an atmosphere of relatively cool hydrogen
+surrounding this star. The spectrum of Pollux is quite
+similar to that of the sun and is to be interpreted as showing
+a physical condition similar to that of the sun, while
+the spectrum of &alpha;&nbsp;Herculis is quite different from either of
+the others. In subsequent chapters we shall have occasion
+to consider more fully these different types of spectrum.</p>
+
+<p><a name="S_89" id="S_89"></a>89. <b>The Doppler principle.</b>&mdash;This important principle of
+the spectrum analysis is most readily appreciated through
+the following experiment:</p>
+
+<p>Listen to the whistle of a locomotive rapidly approaching,
+and observe how the pitch changes and the note becomes
+more grave as the locomotive passes by and commences
+to recede. During the approach of the whistle
+each successive sound wave has a shorter distance to travel
+in coming to the ear of the listener than had its predecessor,
+and in consequence the waves appear to come in
+quicker succession, producing a higher note with a correspondingly
+shorter wave length than would be heard if the
+same whistle were blown with the locomotive at rest. On
+the other hand, the wave length is increased and the pitch
+of the note lowered by the receding motion of the whistle.
+A similar effect is produced upon the wave length of light
+by a rapid change of distance between the source from
+which it comes and the instrument which receives it, so
+that a diminishing distance diminishes very slightly the
+wave length of every line in the spectrum produced by the<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span>
+light, and an increasing distance increases these wave
+lengths, and this holds true whether the change of distance
+is produced by motion of the source of light or by
+motion of the instrument which receives it.</p>
+
+<p>This change of wave length is sometimes described by
+saying that when a body is rapidly approaching, the lines
+of its spectrum are all displaced toward the violet end of
+the spectrum, and are correspondingly displaced toward the
+red end by a receding motion. The amount of this shifting,
+when it can be measured, measures the velocity of the
+body along the line of sight, but the observations are exceedingly
+delicate, and it is only in recent years that it has
+been found possible to make them with precision. For this
+purpose there is made to pass through the spectroscope
+light from an artificial source which contains one or more
+chemical elements known to be present in the star which
+is to be observed, and the corresponding lines in the
+spectrum of this light and in the spectrum of the star
+are examined to determine whether they exactly match
+in position, or show, as they sometimes do, a slight displacement,
+as if one spectrum had been slipped past
+the other. The difficulty of the observations lies in the
+extremely small amount of this slipping, which rarely if
+ever in the case of a moving star amounts to one sixth part
+of the interval between the close parallel lines marked <i>D</i>
+in <a href="#Fig_50">Fig.&nbsp;50</a>. The spectral lines furnished by the headlight
+of a locomotive running at the rate of a hundred miles
+per hour would be displaced by this motion less than one
+six-thousandth part of the space between the <i>D</i> lines,
+an amount absolutely imperceptible in the most powerful
+spectroscope yet constructed. But many of the celestial
+bodies have velocities so much greater than a hundred
+miles per hour that these may be detected and measured
+by means of the Doppler principle.</p>
+
+<p><a name="S_90" id="S_90"></a>90. <b>Other instruments.</b>&mdash;Other instruments of importance
+to the astronomer, but of which only casual mention<span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span>
+can here be made, are the meridian-circle; the transit, one
+form of which is shown in <a href="#Fig_52">Fig.&nbsp;52</a>, and the zenith telescope,
+which furnish refined methods for making observations
+similar in kind to those which the student has already
+learned to make with plumb line and protractor; the sextant,
+which is pre-eminently the sailor's instrument for
+finding the latitude and longitude at sea, by measuring the
+altitudes of sun and stars above the sea horizon; the heliometer,
+which serves for the very accurate measurement of
+small angles, such as the angular distance between two stars
+not more than one or two degrees apart; and the photometer,
+which is used for measuring the amount of light received
+from the celestial bodies.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_52" id="Fig_52"></a>
+<a href="images/i174-full.jpg"><img src="images/i174.jpg" width="500" height="375" alt="Fig. 52.&mdash;A combined transit instrument and zenith telescope." title="Fig. 52.&mdash;A combined transit instrument and zenith telescope." /></a>
+<span class="caption"><span class="smcap">Fig. 52.</span>&mdash;A combined transit instrument and zenith telescope.</span>
+</div>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span></p>
+<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX</h2>
+
+<h3>THE MOON</h3>
+
+
+<p><a name="S_91" id="S_91"></a>91. <b>Results of observation with the unaided eye.</b>&mdash;The
+student who has made the observations of the moon which
+are indicated in <a href="#CHAPTER_III">Chapter&nbsp;III</a> has in hand data from which
+much may be learned about the earth's satellite. Perhaps
+the most striking feature brought out by them is the motion
+of the moon among the stars, always from west toward
+east, accompanied by that endless series of changes in
+shape and brightness&mdash;new moon, first quarter, full moon,
+etc.&mdash;whose successive stages we represent by the words,
+the phase of the moon. From his own observation the
+student should be able to verify, at least approximately,
+the following statements, although the degree of numerical
+precision contained in some of them can be reached
+only by more elaborate apparatus and longer study than he
+has given to the subject:</p>
+
+<p>A. The phase of the moon depends upon the distance
+apart of sun and moon in the sky, new moon coming
+when they are together, and full moon when they are as
+far apart as possible.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="THE_MOON" id="THE_MOON"></a>
+<a href="images/i176-full.jpg"><img src="images/i176.jpg" width="500" height="756" alt="THE MOON, ONE DAY AFTER FIRST QUARTER.
+
+From a photograph made at the Paris Observatory." title="THE MOON, ONE DAY AFTER FIRST QUARTER.
+
+From a photograph made at the Paris Observatory." /></a>
+<span class="caption">THE MOON, ONE DAY AFTER FIRST QUARTER.
+
+From a photograph made at the Paris Observatory.</span>
+</div>
+
+<p>B. The moon is essentially a round, dark body, giving
+off no light of its own, but shining solely by reflected sunlight.
+The proof of this is that whenever we see a part of
+the moon which is turned away from the sun it looks dark&mdash;e.&nbsp;g.,
+at new moon, sun and moon are in nearly the same
+direction from us and we see little or nothing of the moon,
+since the side upon which the sun shines is turned away
+from us. At full moon the earth is in line between sun<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>
+and moon, and we see, round and bright, the face upon
+which the sun shines. At other phases, such as the quarters,
+the moon turns toward the earth a part of its night
+hemisphere and a part of its day hemisphere, but in general
+only that part which belongs to the day side of the
+moon is visible and the peculiar curved line which forms
+the boundary&mdash;the "ragged edge," or <i>terminator</i>, as it is
+called, is the dividing line between day and night upon
+the moon.</p>
+
+<p>A partial exception to what precedes is found for a few
+days after new moon when the moon and sun are not very
+far apart in the sky, for then the whole round disk of the
+moon may often be seen, a small part of it brightly illuminated
+by the sun and the larger part feebly illuminated
+by sunlight which fell first upon the earth and was by it
+reflected back to the moon, giving the pleasing effect which
+is sometimes called the old moon in the new moon's arms.
+The new moon&mdash;i.&nbsp;e., the part illumined by the sun&mdash;usually
+appears to belong to a sphere of larger radius than the
+old moon, but this is purely a trick played by the eyes of
+the observer, and the effect disappears altogether in a telescope.
+Is there any similar effect in the few days before
+new moon?</p>
+
+<p>C. The moon makes the circuit of the sky from a given
+star around to the same star again in a little more than
+27 days (27.32166), but the interval between successive new
+moons&mdash;i.&nbsp;e., from the sun around to the sun again&mdash;is
+more than 29 days (29.53059). This last interval, which is
+called a lunar month or <i>synodical</i> month, indicates what
+we have learned before&mdash;that the sun has changed its place
+among the stars during the month, so that it takes the
+moon an extra two days to overtake him after having
+made the circuit of the sky, just as it takes the minute
+hand of a clock an extra 5 minutes to catch up with
+the hour hand after having made a complete circuit of the
+dial.<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span></p>
+
+<p>D. Wherever the moon may be in the sky, it turns
+always the same face toward the earth, as is shown by the
+fact that the dark markings which appear on its surface
+stand always upon (nearly) the same part of its disk. It
+does not always turn the same face toward the sun, for
+the boundary line between the illumined and unillumined
+parts of the moon shifts from one side to the other as the
+phase changes, dividing at each moment day from night
+upon the moon and illustrating by its slow progress that
+upon the moon the day and the month are of equal length
+(29.5 terrestrial days), instead of being time units of different
+lengths as with us.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_53" id="Fig_53"></a>
+<img src="images/i180.png" width="500" height="777" alt="Fig. 53.&mdash;Motion of moon and earth relative to the sun." title="Fig. 53.&mdash;Motion of moon and earth relative to the sun." />
+<span class="caption"><span class="smcap">Fig. 53.</span>&mdash;Motion of moon and earth relative to the sun.</span>
+</div>
+
+<p><a name="S_92" id="S_92"></a>92. <b>The moon's motion.</b>&mdash;The student should compare the
+results of his own observations, as well as the preceding
+section, with <a href="#Fig_53">Fig.&nbsp;53</a>, in which the lines with dates printed
+on them are all supposed to radiate from the sun and to
+represent the direction from the sun of earth and moon
+upon the given dates which are arbitrarily assumed for
+the sake of illustration, any other set would do equally
+well. The black dots, small and large, represent the
+moon revolving about the earth, but having the circular
+path shown in <a href="#Fig_34">Fig.&nbsp;34</a> (ellipse) transformed by the earth's
+forward motion into the peculiar sinuous line here shown.
+With respect to both earth and sun, the moon's orbit
+deviates but little from a circle, since the sinuous curve
+of <a href="#Fig_53">Fig.&nbsp;53</a> follows very closely the earth's orbit around
+the sun and is almost identical with it. For clearness
+of representation the distance between earth and moon
+in the figure has been made ten times too great, and to
+get a proper idea of the moon's orbit with reference to
+the sun, we must suppose the moon moved up toward the
+earth until its distance from the line of the earth's orbit is
+only a tenth part of what it is in the figure. When this is
+done, the moon's path becomes almost indistinguishable
+from that of the earth, as may be seen in the figure, where
+the attempt has been made to show both lines, and it<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span>
+is to be especially noted that this real orbit of the moon is
+everywhere concave toward the sun.</p>
+
+<p>The phase presented by the moon at different parts of
+its path is indicated by the row of circles at the right, and
+the student should show why a new moon is associated
+with June 30th and a full moon with July 15th, etc. What
+was the date of first quarter? Third quarter?</p>
+
+<p>We may find in <a href="#Fig_53">Fig.&nbsp;53</a> another effect of the same
+kind as that noted above in&nbsp;C. Between noon, June 30th,
+and noon, July 3d, the earth makes upon its axis three complete
+revolutions with respect to the sun, but the meridian
+which points toward the moon at noon on June 30th will
+not point toward it at noon on July 3d, since the moon has
+moved into a new position and is now 37° away from the
+meridian. Verify this statement by measuring, in <a href="#Fig_53">Fig.&nbsp;53</a>,
+with the protractor, the moon's angular distance from the
+meridian at noon on July 3d. When will the meridian
+overtake the moon?</p>
+
+<p><a name="S_93" id="S_93"></a>93. <b>Harvest moon.</b>&mdash;The interval between two successive
+transits of the meridian past the moon is called a lunar
+day, and the student should show from the figure that on
+the average a lunar day is 51 minutes longer than a solar
+day&mdash;i.&nbsp;e., upon the average each day the moon comes to
+the meridian 51 minutes of solar time later than on the
+day before. It is also true that on the average the moon
+rises and sets 51 minutes later each day than on the day
+before. But there is a good deal of irregularity in the
+retardation of the time of moonrise and moonset, since
+the time of rising depends largely upon the particular
+point of the horizon at which the moon appears, and between
+two days this point may change so much on account
+of the moon's orbital motion as to make the retardation
+considerably greater or less than its average value. In
+northern latitudes this effect is particularly marked in the
+month of September, when the eastern horizon is nearly
+parallel with the moon's apparent path in the sky, and near<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span>
+the time of full moon in that month the moon rises on
+several successive nights at nearly the same hour, and in
+less degree the same is true for October. This highly
+convenient arrangement of moonlight has caused the full
+moons of these two months to be christened respectively
+the Harvest Moon and the Hunter's Moon.</p>
+
+<p><a name="S_94" id="S_94"></a>94. <b>Size and mass of the moon.</b>&mdash;It has been shown in
+<a href="#CHAPTER_I">Chapter&nbsp;I</a> how the distance of the moon from the earth
+may be measured and its diameter determined by means of
+angles, and without enlarging upon the details of these observations,
+we note as their result that the moon is a globe
+2,163 miles in diameter, and distant from the earth on the
+average about 240,000 miles. But, as we have seen in
+<a href="#CHAPTER_VII">Chapter&nbsp;VII</a>, this distance changes to the extent of a few
+thousand miles, sometimes less, sometimes greater, mainly
+on account of the elliptic shape of the moon's orbit about
+the earth, but also in part from the disturbing influence of
+other bodies, such as the sun, which pull the moon to and
+fro, backward and forward, to quite an appreciable extent.</p>
+
+<p>From the known diameter of the moon it is a matter of
+elementary geometry to derive in miles the area of its surface
+and its volume or solid contents. Leaving this as an
+exercise for the student, we adopt the earth as the standard
+of comparison and find that the diameter of the moon is
+rather more than a quarter, 4/15, that of the earth, the area
+of its surface is a trifle more than 1/14 that of the earth,
+and its volume a little more than 1/49 of the earth's. So
+much is pure geometry, but we may combine with it some
+mechanical principles which enable us to go a step farther
+and to "weigh" the moon&mdash;i.&nbsp;e., determine its mass and
+the average density of the material of which it is made.</p>
+
+<p>We have seen that the moon moves around the sun in a
+path differing but little from the smooth curve shown in
+<a href="#Fig_53">Fig.&nbsp;53</a>, with arrows indicating the direction of motion,
+and it would follow absolutely such a smooth path were
+it not for the attraction of the earth, and in less degree<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>
+of some of the other planets, which swing it about first
+to one side then to the other. But action and reaction
+are equal; the moon pulls as strongly upon the earth
+as does the earth upon the moon, and if earth and moon
+were of equal mass, the deviation of the earth from the
+smooth curve in the figure would be just as large as that
+of the moon. It is shown in the figure that the moon does
+displace the earth from this curve, and we have only to
+measure the amount of this displacement of the earth and
+compare it with the displacement suffered by the moon to
+find how much the mass of the one exceeds that of the
+other. It may be seen from the figure that at first quarter,
+about July 7th, the earth is thrust ahead in the direction
+of its orbital motion, while at the third quarter, July 22d, it
+is pulled back by the action of the moon, and at all times
+it is more or less displaced by this action, so that, in order
+to be strictly correct, we must amend our former statement
+about the moon moving around the earth and make it read,
+Both earth and moon revolve around a point on line between
+their centers. This point is called their <i>center of
+gravity</i>, and the earth and the moon both move in ellipses
+having this center of gravity at their common focus.
+Compare this with Kepler's First Law. These ellipses are
+similarly shaped, but of very different size, corresponding
+to Newton's third law of motion (<a href="#CHAPTER_IV">Chapter&nbsp;IV</a>), so that the
+action of the earth in causing the small moon to move
+around a large orbit is just equal to the reaction of the
+moon in causing the larger earth to move in the smaller
+orbit. This is equivalent to saying that the dimensions of
+the two orbits are inversely proportional to the masses of
+the earth and the moon.</p>
+
+<p>By observing throughout the month the direction from
+the earth to the sun or to a near planet, such as Mars or
+Venus, astronomers have determined that the diameter of
+the ellipse in which the earth moves is about 5,850 miles,
+so that the distance of the earth from the center of gravity<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>
+is 2,925 miles, and the distance of the moon from it is
+240,000&nbsp;-&nbsp;2,925 =&nbsp;237,075. We may now write in the form
+of a proportion&mdash;</p>
+
+<p class="center">Mass of earth : Mass of moon :: 237,075 : 2,925,</p>
+
+<p>and find from it that the mass of the earth is 81 times
+as great as the mass of the moon&mdash;i.&nbsp;e., leaving kind and
+quality out of account, there is enough material in the
+earth to make 81 moons. We may note in this connection
+that the diameter of the earth, 7,926 miles, is
+greater than the diameter of the monthly orbit in which
+the moon causes it to move, and therefore the center of
+gravity of earth and moon always lies inside the body of
+the earth, about 1,000 miles below the surface.</p>
+
+<p><a name="S_95" id="S_95"></a>95. <b>Density of the moon.</b>&mdash;It is believed that in a general
+way the moon is made of much the same kind of material
+which goes to make up the earth&mdash;metals, minerals, rocks,
+etc.&mdash;and a part of the evidence upon which this belief is
+based lies in the density of the moon. By density of a
+substance we mean the amount of it which is contained in
+a given volume&mdash;i.&nbsp;e., the weight of a bushel or a cubic
+centimeter of the stuff. The density of chalk is twice as
+great as the density of water, because a cubic centimeter
+of chalk weighs twice as much as an equal volume of
+water, and similarly in other cases the density is found by
+dividing the mass or weight of the body by the mass or
+weight of an equal volume of water.</p>
+
+<p>We know the mass of the earth (<a href="#S_45">§&nbsp;45</a>), and knowing
+the mass of a cubic foot of water, it is easy, although a
+trifle tedious, to compute what would be the mass of a volume
+of water equal in size to the earth. The quotient
+obtained by dividing one of these masses by the other (mass
+of earth&nbsp;÷&nbsp;mass of water) is the average density of the material
+composing the earth, and we find numerically that
+this is 5.6&mdash;i.&nbsp;e., it would take 5.6 water earths to attract as
+strongly as does the real one. From direct experiment we<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span>
+know that the average density of the principal rocks which
+make up the crust of the earth is only about half of this,
+showing that the deep-lying central parts of the earth are
+denser than the surface parts, as we should expect them to
+be, because they have to bear the weight of all that lies
+above them and are compressed by it.</p>
+
+<p>Turning now to the moon, we find in the same way as
+for the earth that its average density is 3.4 as great as that
+of water.</p>
+
+<p><a name="S_96" id="S_96"></a>96. <b>Force of gravity upon the moon.</b>&mdash;This number, 3.4,
+compared with the 5.6 which we found for the earth, shows
+that on the whole the moon is made of lighter stuff than is
+the body of the earth, and this again is much what we should
+expect to find, for weight, the force which tends to compress
+the substance of the moon, is less there than here.
+The weight of a cubic yard of rock at the surface of either
+earth or moon is the force with which the earth or moon
+attracts it, and this by the law of gravitation is for the
+earth&mdash;</p>
+
+<p class="center"><i>W</i> = <i>k</i> · (<i>m</i> <i>m'</i>)/(3963)<sup>2</sup>;</p>
+
+<p>and for the moon&mdash;</p>
+
+<p class="center"><i>w</i> = <i>k</i> · {<i>m</i> (<i>m'</i>/81)}/(1081)<sup>2</sup>;</p>
+
+<p>from which we find by division&mdash;</p>
+
+<p class="center"><i>w</i> = (<i>W</i>/81) (3963/1081)<sup>2</sup> = <i>W</i>/6 (approximately).</p>
+
+<p>The cubic yard of rock, which upon the earth weighs two
+tons, would, if transported to the moon, weigh only one
+third of a ton, and would have only one sixth as much
+influence in compressing the rocks below it as it had upon
+the earth. Note that this rock when transported to the
+moon would be still attracted by the earth and would have
+weight toward the earth, but it is not this of which we are<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>
+speaking; by its weight in the moon we mean the force
+with which the moon attracts it. Making due allowance
+for the difference in compression produced by weight, we
+may say that in general, so far as density goes, the moon is
+very like a piece of the earth of equal mass set off by itself
+alone.</p>
+
+<p><a name="S_97" id="S_97"></a>97. <b>Albedo.</b>&mdash;In another respect the lunar stuff is like
+that of which the earth is made: it reflects the sunlight in
+much the same way and to the same amount. The contrast
+of light and dark areas on the moon's surface shows,
+as we shall see in another section, the presence of different
+substances upon the moon which reflect the sunlight in
+different degrees. This capacity for reflecting a greater or
+less percentage of the incident sunlight is called <i>albedo</i>
+(Latin, whiteness), and the brilliancy of the full moon might
+lead one to suppose that its albedo is very great, like that
+of snow or those masses of summer cloud which we call
+thunderheads. But this is only an effect of contrast with
+the dark background of the sky. The same moon by day
+looks pale, and its albedo is, in fact, not very different
+from that of our common rocks&mdash;weather-beaten sandstone
+according to Sir John Herschel&mdash;so that it would be possible
+to build an artificial moon of rock or brick which
+would shine in the sunlight much as does the real moon.</p>
+
+<p>The effect produced by the differences of albedo upon
+the moon's face is commonly called the "man in the moon,"
+but, like the images presented by glowing coals, the face in
+the moon is anything which we choose to make it. Among
+the Chinese it is said to be a monkey pounding rice; in
+India, a rabbit; in Persia, the earth reflected as in a mirror,
+etc.</p>
+
+<p><a name="S_98" id="S_98"></a>98. <b>Librations.</b>&mdash;We have already learned that the moon
+turns always the same face toward the earth, and we have
+now to modify this statement and to find that here, as in
+so many other cases, the thing we learn first is only approximately
+true and needs to be limited or added to or<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span>
+modified in some way. In general, Nature is too complex
+to be completely understood at first sight or to be perfectly
+represented by a simple statement. In <a href="#Fig_55">Fig.&nbsp;55</a> we
+have two photographs of the moon, taken nearly three years
+apart, the right-hand one a little after first quarter and the
+left-hand one a little before third quarter. They therefore
+represent different parts of the moon's surface, but
+along the ragged edge the same region is shown on both
+photographs, and features common to both pictures may
+readily be found&mdash;e.&nbsp;g., the three rings which form a right-angled
+triangle about one third of the way down from the
+top of the cut, and the curved mountain chain just below
+these. If the moon turned exactly the same face toward
+us in the two pictures, the distance of any one of these
+markings from any part of the moon's edge must be the
+same in both pictures; but careful measurement will show
+that this is not the case, and that in the left-hand picture
+the upper edge of the moon is tipped toward us and
+the lower edge away from us, as if the whole moon had
+been rotated slightly about a horizontal line and must be
+turned back a little (about&nbsp;7°) in order to match perfectly
+the other part of the picture.</p>
+
+<p>This turning is called a <i>libration</i>, and it should be borne
+in mind that the moon librates not only in the direction
+above measured, north and south, but also at right angles
+to this, east and west, so that we are able to see a little
+farther around every part of the moon's edge than would
+be possible if it turned toward us at all times exactly the
+same face. But in spite of the librations there remains on
+the farther side of the moon an area of 6,000,000 square
+miles which is forever hidden from us, and of whose character
+we have no direct knowledge, although there is no
+reason to suppose it very different from that which is visible,
+despite the fact that some of the books contain quaint
+speculations to the contrary. The continent of South
+America is just about equal in extent to this unknown region,<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span>
+while North America is a fair equivalent for all the
+rest of the moon's surface, both those central parts which
+are constantly visible, and the zone around the edge whose
+parts sometimes come into sight and are sometimes hidden.</p>
+
+<p>An interesting consequence of the peculiar rotation of
+the moon is that from our side of it the earth is always
+visible. Sun, stars, and planets rise and set there as well
+as here, but to an observer on the moon the earth swings
+always overhead, shifting its position a few degrees one
+way or the other on account of the libration but running
+through its succession of phases, new earth, first quarter,
+etc., without ever going below the horizon, provided the
+observer is anywhere near the center of the moon's disk.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_54" id="Fig_54"></a>
+<img src="images/i188.png" width="350" height="366" alt="Fig. 54.&mdash;Illustrating the moon&#39;s
+rotation." title="Fig. 54.&mdash;Illustrating the moon&#39;s
+rotation." />
+<span class="caption"><span class="smcap">Fig. 54.</span>&mdash;Illustrating the moon&#39;s
+rotation.</span>
+</div>
+
+<p><a name="S_99" id="S_99"></a>99. <b>Cause of librations.</b>&mdash;That the moon should librate
+is by no means so remarkable a fact as that it should at all
+times turn very nearly the
+same face toward the earth.
+This latter fact can have but
+one meaning: the moon revolves
+about an axis as does
+the earth, but the time required
+for this revolution is
+just equal to the time required
+to make a revolution
+in its orbit. Place two coins
+upon a table with their heads
+turned toward the north, as
+in <a href="#Fig_54">Fig.&nbsp;54</a>, and move the
+smaller one around the larger
+in such a way that its face shall always look away from the
+larger one. In making one revolution in its orbit the head
+on this small coin will be successively directed toward every
+point of the compass, and when it returns to its initial
+position the small coin will have made just one revolution
+about an axis perpendicular to the plane of its orbit.
+In no other way can it be made to face always away<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>
+from the figure at the center of its orbit while moving
+around it.</p>
+
+<p>We are now in a position to understand the moon's
+librations, for, if the small coin at any time moves faster or
+slower in its orbit than it turns about its axis, a new side
+will be turned toward the center, and the same may happen
+if the central coin itself shifts into a new position. This is
+what happens to the moon, for its orbital motion, like that
+of Mercury (<a href="#Fig_17">Fig.&nbsp;17</a>), is alternately fast and slow, and in
+addition to this there are present other minor influences,
+such as the fact that its rotation axis is not exactly perpendicular
+to the plane of its orbit; in addition to this the
+observer upon the earth is daily carried by its rotation from
+one point of view to another, etc., so that it is only in a general
+way that the rotation upon the axis and motion in the
+orbit keep pace with each other. In a general way a cable
+keeps a ship anchored in the same place, although wind and
+waves may cause it to "librate" about the anchor.</p>
+
+<p>How the moon came to have this exact equality between
+its times of revolution and rotation constitutes a
+chapter of its history upon which we shall not now enter;
+but the equality having once been established, the mechanism
+by which it is preserved is simple enough.</p>
+
+<p>The attraction of the earth for the moon has very
+slightly pulled the latter out of shape (<a href="#S_42">§&nbsp;42</a>), so that the
+particular diameter, which points toward the earth, is a little
+longer than any other, and thus serves as a handle which
+the earth lays hold of and pulls down into its lowest possible
+position&mdash;i.&nbsp;e., the position in which it points toward the
+center of the earth. Just how long this handle is, remains
+unknown, but it may be shown from the law of gravitation
+that less than a hundred yards of elongation would suffice
+for the work it has to do.</p>
+
+<p><a name="S_100" id="S_100"></a>100. <b>The moon as a world.</b>&mdash;Thus far we have considered
+the moon as a satellite of the earth, dependent upon the
+earth, and interesting chiefly because of its relation to it.<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span>
+But the moon is something more than this; it is a world in
+itself, very different from the earth, although not wholly
+unlike it. The most characteristic feature of the earth's
+surface is its division into land and water, and nothing of
+this kind can be found upon the moon. It is true that the
+first generation of astronomers who studied the moon with
+telescopes fancied that the large dark patches shown in
+<a href="#Fig_55">Fig.&nbsp;55</a> were bodies of water, and named them oceans,
+seas, lakes, and ponds, and to the present day we keep
+those names, although it is long since recognized that these
+parts of the moon's surface are as dry as any other. Their
+dark appearance indicates a different kind of material from
+that composing the lighter parts of the moon, material
+with a different albedo, just as upon the earth we have
+light-colored and dark-colored rocks, marble and slate,
+which seen from the moon must present similar contrasts
+of brightness. Although these dark patches are almost
+the only features distinguishable with the unaided eye, it
+is far otherwise in the telescope or the photograph, especially
+along the ragged edge where great numbers of rings
+can be seen, which are apparently depressions in the moon
+and are called craters. These we find in great number
+all over the moon, but, as the figure shows, they are seen
+to the best advantage near the <i>terminator</i>&mdash;i.&nbsp;e., the dividing
+line between day and night, since the long shadows
+cast here by the rising or setting sun bring out the details
+of the surface better than elsewhere. Carefully examine
+<a href="#Fig_55">Fig.&nbsp;55</a> with reference to these features.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_55" id="Fig_55"></a>
+<a href="images/i191-full.jpg"><img src="images/i191.jpg" width="600" height="433" alt="Fig. 55.&mdash;The moon at first and last quarter. Lick Observatory photographs." title="Fig. 55.&mdash;The moon at first and last quarter. Lick Observatory photographs." /></a>
+<span class="caption"><span class="smcap">Fig. 55.</span>&mdash;The moon at first and last quarter. Lick Observatory photographs.</span>
+</div>
+
+<p>Another feature which exists upon both earth and
+moon, although far less common there than here, is illustrated
+in the chain of mountains visible near the terminator,
+a little above the center of the moon in both parts of
+<a href="#Fig_55">Fig.&nbsp;55</a>. This particular range of mountains, which is
+called the Lunar Apennines, is by far the most prominent
+one upon the moon, although others, the Alps and Caucasus,
+exist. But for the most part the lunar mountains<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span>
+stand alone, each by itself, instead of being grouped into
+ranges, as on the earth. Note in the figure that some of
+the lunar mountains stretch out into the night side of the
+moon, their peaks projecting up into the sunlight, and
+thus becoming visible, while the lowlands are buried in the
+shadow.</p>
+
+<p>A subordinate feature of the moon's surface is the system
+of <i>rays</i> which seem to radiate like spokes from some
+of the larger craters, extending over hill and valley sometimes
+for hundreds of miles. A suggestion of these rays
+may be seen in <a href="#Fig_55">Fig.&nbsp;55</a>, extending from the great crater
+Copernicus a little southwest of the end of the Apennines,
+but their most perfect development is to be seen at the
+time of full moon around the crater Tycho, which lies near
+the south pole of the moon. Look for them with an opera
+glass.</p>
+
+<p>Another and even less conspicuous feature is furnished
+by the rills, which, under favorable conditions of illumination,
+appear like long cracks on the moon's surface, perhaps
+analogous to the cańons of our Western country.</p>
+
+<p><a name="S_101" id="S_101"></a>101. <b>The map of the moon.</b>&mdash;<a href="#Fig_55">Fig.&nbsp;55</a> furnishes a fairly
+good map of a limited portion of the moon near the terminator,
+but at the edges little or no detail can be seen. This
+is always true; the whole of the moon can not be seen to
+advantage at any one time, and to remedy this we need to
+construct from many photographs or drawings a map which
+shall represent the several parts of the moon as they appear
+at their best. <a href="#Fig_56">Fig.&nbsp;56</a> shows such a map photographed from
+a relief model of the moon, and representing the principal
+features of the lunar surface in a way they can never be
+seen simultaneously. Perhaps its most striking feature is
+the shape of the craters, which are shown round in the central
+parts of the map and oval at the edges, with their long
+diameters parallel to the moon's edge. This is, of course,
+an effect of the curvature of the moon's surface, for we look
+very obliquely at the edge portions, and thus see their formations<span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span>
+much foreshortened in the direction of the moon's
+radius.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_56" id="Fig_56"></a>
+<a href="images/i193-full.jpg"><img src="images/i193.jpg" width="500" height="501" alt="Fig. 56.&mdash;Relief map of the moon&#39;s surface.&mdash;After Nasmyth and Carpenter." title="Fig. 56.&mdash;Relief map of the moon&#39;s surface.&mdash;After Nasmyth and Carpenter." /></a>
+<span class="caption"><span class="smcap">Fig. 56.</span>&mdash;Relief map of the moon&#39;s surface.&mdash;After <span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span>
+</div>
+
+<p>The north and south poles of the moon are at the top
+and bottom of the map respectively, and a mere inspection
+of the regions around them will show how much more
+rugged is the southern hemisphere of the moon than the
+northern. It furnishes, too, some indication of how numerous
+are the lunar craters, and how in crowded regions they
+overlap one another.</p>
+
+<p>The student should pick out upon the map those features
+which he has learned to know in the photograph (<a href="#Fig_55">Fig.&nbsp;55</a>)&mdash;the
+Apennines, Copernicus, and the continuation of the
+Apennines, extending into the dark part of the moon.<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span></p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_57" id="Fig_57"></a>
+<a href="images/i194-full.jpg"><img src="images/i194.jpg" width="500" height="476" alt="Fig. 57.&mdash;Mare Imbrium. Photographed by G. W. Ritchey." title="Fig. 57.&mdash;Mare Imbrium. Photographed by G. W. Ritchey." /></a>
+<span class="caption"><span class="smcap">Fig. 57.</span>&mdash;Mare Imbrium. Photographed by <span class="smcap">G.&nbsp;W. Ritchey.</span></span>
+</div>
+
+<p><a name="S_102" id="S_102"></a>102. <b>Size of the lunar features.</b>&mdash;We may measure distances
+here in the same way as upon a terrestrial map, remembering
+that near the edges the scale of the map is very
+much distorted parallel to the moon's diameter, and measurements
+must not be taken in this direction, but may be
+taken parallel to the edge. Measuring with a millimeter
+scale, we find on the map for the diameter of the crater
+Copernicus, 2.1 millimeters. To turn this into the diameter
+of the real Copernicus in miles, we measure upon the
+same map the diameter of the moon, 79.7 millimeters, and
+then have the proportion&mdash;</p>
+
+<p class="center">Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_58" id="Fig_58"></a>
+<a href="images/i195-full.jpg"><img src="images/i195.jpg" width="350" height="468" alt="Fig. 58.&mdash;Mare Crisium.
+Lick Observatory photographs." title="Fig. 58.&mdash;Mare Crisium.
+Lick Observatory photographs." /></a>
+<span class="caption"><span class="smcap">Fig. 58.</span>&mdash;Mare Crisium.
+Lick Observatory photographs.</span>
+</div>
+
+<p>which when solved gives 57 miles. The real diameter of
+Copernicus is a trifle over 56 miles. At the eastern edge
+of the moon, opposite the Apennines, is a large oval spot
+called the Mare Crisium (Latin, <i>ma-re</i> =&nbsp;sea). Measure its<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>
+length. The large crater to the northwest of the Apennines
+is called Archimedes. Measure its diameter both in
+the map and in the photograph (<a href="#Fig_55">Fig.&nbsp;55</a>), and see how the
+two results agree. The true diameter of this crater, east
+and west, is very approximately 50 miles. The great smooth
+surface to the west of Archimedes is the Mare Imbrium. Is
+it larger or smaller than
+Lake Superior? <a href="#Fig_57">Fig.&nbsp;57</a>
+is from a photograph
+of the Mare Imbrium,
+and the amount
+of detail here shown at
+the bottom of the sea
+is a sufficient indication
+that, in this case
+at least, the water has
+been drawn off, if indeed
+any was ever present.</p>
+
+<p><a href="#Fig_58">Fig.&nbsp;58</a> is a representation
+of the Mare
+Crisium at a time when
+night was beginning to
+encroach upon its eastern
+border, and it
+serves well to show the
+rugged character of the ring-shaped wall which incloses
+this area.</p>
+
+<p>With these pictures of the smoother parts of the moon's
+surface we may compare <a href="#Fig_59">Fig.&nbsp;59</a>, which shows a region
+near the north pole of the moon, and <a href="#Fig_60">Fig.&nbsp;60</a>, giving an
+early morning view of Archimedes and the Apennines.
+Note how long and sharp are the shadows.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_59" id="Fig_59"></a>
+<a href="images/i196-full.jpg"><img src="images/i196.jpg" width="350" height="447" alt="Fig. 59.&mdash;Illustrating the rugged character of the
+moon&#39;s surface.&mdash;Nasmyth and Carpenter." title="Fig. 59.&mdash;Illustrating the rugged character of the
+moon&#39;s surface.&mdash;Nasmyth and Carpenter." /></a>
+<span class="caption"><span class="smcap">Fig. 59.</span>&mdash;Illustrating the rugged character of the
+moon&#39;s surface.&mdash;<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span>
+</div>
+
+<p><a name="S_103" id="S_103"></a>103. <b>The moon's atmosphere.</b>&mdash;Upon the earth the sun
+casts no shadows so sharp and black as those of <a href="#Fig_60">Fig.&nbsp;60</a>,
+because his rays are here scattered and reflected in all directions<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span>
+by the dust and vapors of the atmosphere (<a href="#S_51">§&nbsp;51</a>),
+so that the place from which direct sunlight is cut off
+is at least partially illumined by this reflected light. The
+shadows of <a href="#Fig_60">Fig.&nbsp;60</a> show that upon the moon it must be
+otherwise, and suggest that if the moon has any atmosphere
+whatever, its density must be utterly insignificant in comparison
+with that of the earth. In its motion around the
+earth the moon frequently
+eclipses stars
+(<i>occults</i> is the technical
+word), and if the
+moon had an atmosphere
+such as is shown
+in <a href="#Fig_61">Fig.&nbsp;61</a>, the light
+from the star <i>A</i> must
+shine through this atmosphere
+just before
+the moon's advancing
+body cuts it off, and it
+must be refracted by
+the atmosphere so that
+the star would appear
+in a slightly different
+direction (nearer to
+<i>B</i>) than before. The
+earth's atmosphere refracts
+the starlight
+under such circumstances by more than a degree, but no
+one has been able to find in the case of the moon any effect
+of this kind amounting to even a fraction of a second of
+arc. While this hardly justifies the statement sometimes
+made that the moon has no atmosphere, we shall be entirely
+safe in saying that if it has one at all its density is less
+than a thousandth part of that of the earth's atmosphere.
+Quite in keeping with this absence of an atmosphere is the
+fact that clouds never float over the surface of the moon.<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>
+Its features always stand out hard and clear, without any
+of that haze and softness of outline which our atmosphere
+introduces into all terrestrial landscapes.</p>
+
+<div class="figleft" style="width: 375px;"><a name="Fig_60" id="Fig_60"></a>
+<a href="images/i197-full.jpg"><img src="images/i197.jpg" width="375" height="322" alt="Fig. 60.&mdash;Archimedes and Apennines.
+Nasmyth and Carpenter." title="Fig. 60.&mdash;Archimedes and Apennines.
+Nasmyth and Carpenter." /></a>
+<span class="caption"><span class="smcap">Fig. 60.</span>&mdash;Archimedes and Apennines.
+<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span>
+</div>
+
+<p><a name="S_104" id="S_104"></a>104. <b>Height of the lunar mountains.</b>&mdash;Attention has already
+been called to the detached mountain peaks, which
+in <a href="#Fig_55">Fig.&nbsp;55</a> prolong
+the range of
+Apennines into
+the lunar night.
+These are the beginnings
+of the
+Caucasus mountains,
+and from
+the photograph
+we may measure
+as follows the
+height to which
+they rise above
+the surrounding
+level of the moon:
+<a href="#Fig_62">Fig.&nbsp;62</a> represents
+a part of
+the lunar surface along the boundary line between night
+and day, the horizontal line at the top of the figure representing
+a level ray of sunlight which just touches the moon
+at <i>T</i> and barely illuminates the top of the mountain, <i>M</i>,
+whose height, <i>h</i>, is to be determined. If we let <i>R</i> stand for
+the radius of the moon and <i>s</i> for the distance, <i>T&nbsp;M</i>, we shall
+have in the right-angled triangle <i>M&nbsp;T&nbsp;C</i>,</p>
+
+<p class="center"><i>R</i><sup>2</sup> + <i>s</i><sup>2</sup> = (<i>R</i> + <i>h</i>)<sup>2</sup>,</p>
+
+<p>and we need only to measure <i>s</i>&mdash;that is, the distance from
+the terminator to the detached mountain peak&mdash;to make
+this equation determine <i>h</i>, since <i>R</i> is already known, being
+half the diameter of the moon&mdash;1,081 miles. Practically it
+is more convenient to use instead of this equation another<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span>
+form, which the student who is expert in algebra may show
+to be very nearly equivalent to it:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"><i>h</i> (miles)</td><td align="center">=</td><td align="left"><i>s</i><sup>2</sup> / 2163,</td></tr>
+<tr><td align="right">or <i>h</i> (feet)</td><td align="center">=</td><td align="left">2.44 <i>s</i><sup>2</sup>.</td></tr>
+</table></div>
+
+<div class="figright" style="width: 350px;"><a name="Fig_61" id="Fig_61"></a>
+<img src="images/i198a.png" width="350" height="217" alt="Fig. 61.&mdash;Occultations and the moon&#39;s
+atmosphere." title="Fig. 61.&mdash;Occultations and the moon&#39;s
+atmosphere." />
+<span class="caption"><span class="smcap">Fig. 61.</span>&mdash;Occultations and the moon&#39;s
+atmosphere.</span>
+</div>
+
+<p>The distance <i>s</i> must be expressed in miles in all of these
+equations. In <a href="#Fig_55">Fig.&nbsp;55</a> the distance from the terminator
+to the first detached peak
+of the Caucasus mountains
+is 1.7 millimeters =
+52 miles, from which we
+find the height of the
+mountain to be 1.25
+miles, or 6,600 feet.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_62" id="Fig_62"></a>
+<img src="images/i198b.png" width="350" height="269" alt="Fig. 62.&mdash;Determining the height of a lunar
+mountain." title="Fig. 62.&mdash;Determining the height of a lunar
+mountain." />
+<span class="caption"><span class="smcap">Fig. 62.</span>&mdash;Determining the height of a lunar
+mountain.</span>
+</div>
+
+<p>Two things, however,
+need to be borne in mind
+in this connection. On
+the earth we measure the
+heights of mountains <i>above sea level</i>, while on the moon
+there is no sea, and our 6,600 feet is simply the height of
+the mountain top above
+the level of that particular
+point in the
+terminator, from which
+we measure its distance.
+So too it is evident
+from the appearance of
+things, that the sunlight,
+instead of just
+touching the top of the
+particular mountain
+whose height we have
+measured, really extends
+some little distance down from its summit, and the 6,600
+feet is therefore the elevation of the lowest point on the
+mountains to which the sunlight reaches. The peak itself<span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span>
+may be several hundred feet higher, and our photograph
+must be taken at the exact moment when this peak appears
+in the lunar morning or disappears in the evening if we are
+to measure the altitude of the mountain's summit. Measure
+the height of the most northern visible mountain of
+the Caucasus range. This is one of the outlying spurs of
+the great mountain Calippus, whose principal peak, 19,000
+feet high, is shown in <a href="#Fig_55">Fig.&nbsp;55</a> as the brightest part of the
+Caucasus range.</p>
+
+<p>The highest peak of the lunar Apennines, Huyghens,
+has an altitude of 18,000 feet, and the Leibnitz and Doerfel
+Mountains, near the south pole of the moon, reach an altitude
+50 per cent greater than this, and are probably the
+highest peaks on the moon. This falls very little short of
+the highest mountain on the earth, although the moon is
+much smaller than the earth, and these mountains are considerably
+higher than anything on the western continent of
+the earth.</p>
+
+<p>The vagueness of outline of the terminator makes it
+difficult to measure from it with precision, and somewhat
+more accurate determinations of the heights of lunar
+mountains can be obtained by measuring the length of
+the shadows which they cast, and the depths of craters
+may also be measured by means of the shadows which fall
+into them.</p>
+
+<p><a name="S_105" id="S_105"></a>105. <b>Craters.</b>&mdash;<a href="#Fig_63">Fig.&nbsp;63</a> shows a typical lunar crater, and
+conveys a good idea of the ruggedness of the lunar landscape.
+Compare the appearance of this crater with the
+following generalizations, which are based upon the accurate
+measurement of many such:</p>
+
+<p>A. A crater is a real depression in the surface of the
+moon, surrounded usually by an elevated ring which rises
+above the general level of the region outside, while the bottom
+of the crater is about an equal distance below that
+level.</p>
+
+<p>B. Craters are shallow, their diameters ranging from<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span>
+five times to more than fifty times their depth. Archimedes,
+whose diameter we found to be 50 miles, has an
+average depth of about 4,000 feet below the crest of its
+surrounding wall, and is relatively a shallow crater.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_63" id="Fig_63"></a>
+<a href="images/i200-full.jpg"><img src="images/i200.jpg" width="500" height="363" alt="Fig. 63.&mdash;A typical lunar crater.&mdash;Nasmyth and Carpenter." title="Fig. 63.&mdash;A typical lunar crater.&mdash;Nasmyth and Carpenter." /></a>
+<span class="caption"><span class="smcap">Fig. 63.</span>&mdash;A typical lunar crater.&mdash;<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span>
+</div>
+
+<p>C. Craters frequently have one or more hills rising
+within them which, however, rarely, if ever, reach up to the
+level of the surrounding wall.</p>
+
+<p>D. Whatever may have been the mode of their formation,
+the craters can not have been produced by scooping
+out material from the center and piling it up to make the
+wall, for in three cases out of four the volume of the excavation
+is greater than the volume of material contained in
+the wall.</p>
+
+<p><a name="S_106" id="S_106"></a>106. <b>Moon and earth.</b>&mdash;We have gone far enough now
+to appreciate both the likeness and the unlikeness of the
+moon and earth. They may fairly enough be likened to
+offspring of the same parent who have followed very different
+careers, and in the fullness of time find themselves in
+very different circumstances. The most serious point of
+difference in these circumstances is the atmosphere, which
+gives to the earth a wealth of phenomena altogether lacking<span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span>
+in the moon. Clouds, wind, rain, snow, dew, frost, and
+hail are all dependent upon the atmosphere and can not be
+found where it is not. There can be nothing upon the
+moon at all like that great group of changes which we
+call weather, and the unruffled aspect of the moon's face
+contrasts sharply with the succession of cloud and sunshine
+which the earth would present if seen from the moon.</p>
+
+<p>The atmosphere is the chief agent in the propagation
+of sound, and without it the moon must be wrapped in
+silence more absolute than can be found upon the surface
+of the earth. So, too, the absence of an atmosphere shows
+that there can be no water or other liquid upon the moon,
+for if so it would immediately evaporate and produce a
+gaseous envelope which we have seen does not exist. With
+air and water absent there can be of course no vegetation
+or life of any kind upon the moon, and we are compelled
+to regard it as an arid desert, utterly waste.</p>
+
+<p><a name="S_107" id="S_107"></a>107. <b>Temperature of the moon.</b>&mdash;A characteristic feature
+of terrestrial deserts, which is possessed in exaggerated degree
+by the moon, is the great extremes of temperature to
+which they and it are subject. Owing to its slow rotation
+about its axis, a point on the moon receives the solar radiation
+uninterruptedly for more than a fortnight, and that
+too unmitigated by any cloud or vaporous covering. Then
+for a like period it is turned away from the sun and allowed
+to cool off, radiating into interplanetary space without hindrance
+its accumulated store of heat. It is easy to see that
+the range of temperature between day and night must be
+much greater under these circumstances than it is with us
+where shorter days and clouded skies render day and night
+more nearly alike, to say nothing of the ocean whose waters
+serve as a great balance wheel for equalizing temperatures.
+Just how hot or how cold the moon becomes is hard to
+determine, and very different estimates are to be found in
+the books. Perhaps the most reliable of these are furnished
+by the recent researches of Professor Very, whose<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span>
+experiments lead him to conclude that "its rocky surface at
+midday, in latitudes where the sun is high, is probably hotter
+than boiling water and only the most terrible of earth's deserts,
+where the burning sands blister the skin, and men,
+beasts, and birds drop dead, can approach a noontide on
+the cloudless surface of our satellite. Only the extreme
+polar latitudes of the moon can have an endurable temperature
+by day, to say nothing of the night, when we
+should have to become troglodytes to preserve ourselves
+from such intense cold."</p>
+
+<p>While the night temperature of the moon, even very
+soon after sunset, sinks to something like 200° below zero
+on the centigrade scale, or 320° below zero on the Fahrenheit
+scale, the lowest known temperature upon the earth,
+according to General Greely, is 90° Fahr. below zero, recorded
+in Siberia in January, 1885.</p>
+
+<p>Winter and summer are not markedly different upon
+the moon, since its rotation axis is nearly perpendicular to
+the plane of the earth's orbit about the sun, and the sun
+never goes far north or south of the moon's equator. The
+month is the one cycle within which all seasonal changes in
+its physical condition appear to run their complete course.</p>
+
+<p><a name="S_108" id="S_108"></a>108. <b>Changes in the moon.</b>&mdash;It is evidently idle to look
+for any such changes in the condition of the moon's surface
+as with us mark the progress of the seasons or
+the spread of civilization over the wilderness. But minor
+changes there may be, and it would seem that the violent
+oscillations of temperature from day to night ought to have
+some effect in breaking down and crumbling the sharp
+peaks and crags which are there so common and so pronounced.
+For a century past astronomers have searched
+carefully for changes of this kind&mdash;the filling up of some
+crater or the fall of a mountain peak; but while some
+things of this kind have been reported from time to time,
+the evidence in their behalf has not been altogether conclusive.
+At the present time it is an open question whether<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>
+changes of this sort large enough to be seen from the
+earth are in progress. A crater much less than a mile
+wide can be seen in the telescope, but it is not easy to
+tell whether so minute an object has changed in size or
+shape during a year or a decade, and even if changes are
+seen they may be apparent rather than real. <a href="#Fig_64">Fig.&nbsp;64</a> contains
+two views of the crater Archimedes, taken under a
+morning and an afternoon sun respectively, and shows a
+very pronounced difference between the two which proceeds
+solely from a difference of illumination. In the presence
+of such large fictitious changes astronomers are slow
+to accept smaller ones as real.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_64" id="Fig_64"></a>
+<a href="images/i203.jpg"><img src="images/i203.jpg" width="500" height="347" alt="Fig. 64.&mdash;Archimedes in the lunar morning and afternoon.&mdash;Weinek." title="Fig. 64.&mdash;Archimedes in the lunar morning and afternoon.&mdash;Weinek." /></a>
+<span class="caption"><span class="smcap">Fig. 64.</span>&mdash;Archimedes in the lunar morning and afternoon.&mdash;<span class="smcap">Weinek.</span></span>
+</div>
+
+<p>It is this absence of change that is responsible for the
+rugged and sharp-cut features of the moon which continue
+substantially as they were made, while upon the earth rain
+and frost are continually wearing down the mountains and
+spreading their substance upon the lowland in an unending
+process of smoothing off the roughnesses of its surface.
+Upon the moon this process is almost if not wholly wanting,
+and the moon abides to-day much more like its primitive
+condition than is the earth.</p>
+
+<p><a name="S_109" id="S_109"></a>109. <b>The moon's influence upon the earth.</b>&mdash;There is a
+widespread popular belief that in many ways the moon exercises<span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span>
+a considerable influence upon terrestrial affairs: that
+it affects the weather for good or ill, that crops must be
+planted and harvested, pigs must be killed, and timber cut
+at the right time of the moon, etc. Our common word
+lunatic means moonstruck&mdash;i.&nbsp;e., one upon whom the moon
+has shone while sleeping. There is not the slightest scientific
+basis for any of these beliefs, and astronomers everywhere
+class them with tales of witchcraft, magic, and popular
+delusion. For the most part the moon's influence
+upon the earth is limited to the light which it sends and
+the effect of its gravitation, chiefly exhibited in the ocean
+tides. We receive from the moon a very small amount of
+second-hand solar heat and there is also a trifling magnetic
+influence, but neither of these last effects comes within the
+range of ordinary observation, and we shall not go far wrong
+in saying that, save the moonlight and the tides, every supposed
+lunar influence upon the earth is either fictitious or
+too small to be readily detected.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span></p>
+<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X</h2>
+
+<h3>THE SUN</h3>
+
+
+<p><a name="S_110" id="S_110"></a>110. <b>Dependence of the earth upon the sun.</b>&mdash;There is no
+better introduction to the study of the sun than Byron's
+Ode to Darkness, beginning with the lines&mdash;</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"I dreamed a dream<br /></span>
+<span class="i0">That was not all a dream.<br /></span>
+<span class="i0">The bright sun was extinguished,"<br /></span>
+</div></div>
+
+<p>and proceeding to depict in vivid words the consequences
+of this extinction. The most matter-of-fact language of
+science agrees with the words of the poet in declaring the
+earth's dependence upon the sun for all those varied forms
+of energy which make it a fit abode for living beings. The
+winds blow and the rivers run; the crops grow, are gathered
+and consumed, by virtue of the solar energy. Factory,
+locomotive, beast, bird, and the human body furnish types
+of machines run by energy derived from the sun; and the
+student will find it an instructive exercise to search for
+kinds of terrestrial energy which are not derived either
+directly or indirectly from the sun. There are a few such,
+but they are neither numerous nor important.</p>
+
+<p><a name="S_111" id="S_111"></a>111. <b>The sun's distance from the earth.</b>&mdash;To the astronomer
+the sun presents problems of the highest consequence
+and apparently of very diverse character, but all tending
+toward the same goal: the framing of a mechanical explanation
+of the sun considered as a machine; what it is, and
+how it does its work. In the forefront of these problems
+stand those numerical determinations of distance, size,<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span>
+mass, density, etc., which we have already encountered in
+connection with the moon, but which must here be dealt
+with in a different manner, because the immensely greater
+distance of the sun makes impossible the resort to any such
+simple method as the triangle used for determining the
+moon's distance. It would be like determining the distance
+of a steeple a mile away by observing its direction first
+from one eye, then from the other; too short a base for the
+triangle. In one respect, however, we stand upon a better
+footing than in the case of the moon, for the mass of the
+earth has already been found (<a href="#CHAPTER_IV">Chapter&nbsp;IV</a>) as a fractional
+part of the sun's mass, and we have only to invert the
+fraction in order to find that the sun's mass is 329,000
+times that of the earth and moon combined, or 333,000
+times that of the earth alone.</p>
+
+<p>If we could rely implicitly upon this number we might
+make it determine for us the distance of the sun through
+the law of gravitation as follows: It was suggested in <a href="#S_38">§&nbsp;38</a>
+that Newton proved Kepler's three laws to be imperfect
+corollaries from the law of gravitation, requiring a little
+amendment to make them strictly correct, and below we
+give in the form of an equation Kepler's statement of the
+Third Law together with Newton's amendment of it. In
+these equations&mdash;</p>
+
+<p><i>T</i> = Periodic time of any planet;</p>
+
+<p><i>a</i> = One half the major axis of its orbit;</p>
+
+<p><i>m</i> = Its mass;</p>
+
+<p><i>M</i> = The mass of the sun;</p>
+
+<p><i>k</i> = The gravitation constant corresponding to the particular
+set of units in which <i>T</i>, <i>a</i>, <i>m</i>, and <i>M</i> are expressed.</p>
+
+<p class="center">(Kepler) <i>a</i><sup>3</sup>/<i>T</i><sup>2</sup> = <i>h</i>; (Newton) <i>a</i><sup>3</sup>/<i>T</i><sup>2</sup> = <i>k</i> (<i>M</i> + <i>m</i>).</p>
+
+<p>Kepler's idea was: For every planet which moves
+around the sun, <i>a</i><sup>3</sup> divided by <i>T</i><sup>2</sup> always gives the same
+quotient, <i>h</i>; and he did not concern himself with the significance<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span>
+of this quotient further than to note that if the
+particular <i>a</i> and <i>T</i> which belong to any planet&mdash;e.&nbsp;g., the
+earth&mdash;be taken as the units of length and time, then the
+quotient will be&nbsp;1. Newton, on the other hand, attached
+a meaning to the quotient, and showed that it is equal to
+the product obtained by multiplying the sum of the two
+masses, planet and sun, by a number which is always the
+same when we are dealing with the action of gravitation,
+whether it be between the sun and planet, or between
+moon and earth, or between the earth and a roast of beef
+in the butcher's scales, provided only that we use always
+the same units with which to measure times, distances,
+and masses.</p>
+
+<p>Numerically, Newton's correction to Kepler's Third
+Law does not amount to much in the motion of the
+planets. Jupiter, which shows the greatest effect, makes
+the circuit of his orbit in 4,333 days instead of 4,335, which
+it would require if Kepler's law were strictly true. But in
+another respect the change is of the utmost importance,
+since it enables us to extend Kepler's law, which relates
+solely to the sun and its planets, to other attracting bodies,
+such as the earth, moon, and stars. Thus for the moon's
+motion around the earth we write&mdash;</p>
+
+<p class="center">(240,000)<sup>3</sup>/(27.32)<sup>2</sup> = <i>k</i> (1 + 1/81),</p>
+
+<p>from which we may find that, with the units here employed,
+the earth's mass as the unit of mass, the mean solar day as
+the unit of time, and the mile as the unit of distance&mdash;</p>
+
+<p class="center"><i>k</i> = 1830 × 10<sup>10</sup>.</p>
+
+<p>If we introduce this value of <i>k</i> into the corresponding
+equation, which represents the motion of the earth around
+the sun, we shall have&mdash;</p>
+
+<p class="center"><i>a</i><sup>3</sup>/(365.25)<sup>2</sup> = 1830 × 10<sup>10</sup> (333,000 + 1),<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span></p>
+
+<p>where the large number in the parenthesis represents the
+number of times the mass of the sun is greater than the
+mass of the earth. We shall find by solving this equation
+that <i>a</i>, the mean distance of the sun from the earth, is
+very approximately 93,000,000 miles.</p>
+
+<p><a name="S_113" id="S_113"></a>113. <b>Another method of determining the sun's distance.</b>&mdash;This
+will be best appreciated by a reference to <a href="#Fig_17">Fig.&nbsp;17</a>. It
+appears here that the earth makes its nearest approach to the
+orbit of Mars in the month of August, and if in any August
+Mars happens to be in opposition, its distance from the earth
+will be very much less than the distance of the sun from
+the earth, and may be measured by methods not unlike
+those which served for the moon. If now the orbits of
+Mars and the earth were circles having their centers at the
+sun this distance between them, which we may represent by
+<i>D</i>, would be the difference of the radii of these orbits&mdash;</p>
+
+<p class="center"><i>D</i> = <i>a''</i> - <i>a'</i>,</p>
+
+<p>where the accents&nbsp;'',&nbsp;' represent Mars and the earth respectively.
+Kepler's Third Law furnishes the relation&mdash;</p>
+
+<p class="center">(<i>a''</i>)<sup>3</sup>/(<i>T''</i>)<sup>2</sup> = (<i>a'</i>)<sup>3</sup>/(<i>T'</i>)<sup>2</sup>;</p>
+
+<p>and since the periodic times of the earth and Mars, <i>T'</i>, <i>T''</i>,
+are known to a high degree of accuracy, these two equations
+are sufficient to determine the two unknown quantities,
+<i>a'</i>, <i>a''</i>&mdash;i.&nbsp;e., the distance of the sun from Mars as well
+as from the earth. The first of these equations is, of
+course, not strictly true, on account of the elliptical shape
+of the orbits, but this can be allowed for easily enough.</p>
+
+<p>In practice it is found better to apply this method of
+determining the sun's distance through observations of an
+asteroid rather than observations of Mars, and great interest
+has been aroused among astronomers by the discovery,
+in 1898, of an asteroid, or planet, Eros, which at times comes
+much closer to the earth than does Mars or any other heavenly<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span>
+body except the moon, and which will at future oppositions
+furnish a more accurate determination of the sun's
+distance than any hitherto available. Observations for this
+purpose are being made at the present time (October, 1900).</p>
+
+<p>Many other methods of measuring the sun's distance
+have been devised by astronomers, some of them extremely
+ingenious and interesting, but every one of them has its
+weak point&mdash;e.&nbsp;g., the determination of the mass of the
+earth in the first method given above and the measurement
+of <i>D</i> in the second method, so that even the best results at
+present are uncertain to the extent of 200,000 miles or more,
+and astronomers, instead of relying upon any one method,
+must use all of them, and take an average of their results.
+According to Professor Harkness, this average value is 92,796,950
+miles, and it seems certain that a line of this length
+drawn from the earth toward the sun would end somewhere
+within the body of the sun, but whether on the nearer or
+the farther side of the center, or exactly at it, no man
+knows.</p>
+
+<p><a name="S_114" id="S_114"></a>114. <b>Parallax and distance.</b>&mdash;It is quite customary among
+astronomers to speak of the sun's parallax, instead of its
+distance from the earth, meaning by parallax its difference
+of direction as seen from the center and surface of the
+earth&mdash;i.&nbsp;e., the angle subtended at the sun by a radius of
+the earth placed at right angles to the line of sight. The
+greater the sun's distance the smaller will this angle be,
+and it therefore makes a substitute for the distance which
+has the advantage of being represented by a small number,
+8".8, instead of a large one.</p>
+
+<p>The books abound with illustrations intended to help
+the reader comprehend how great is a distance of 93,000,000
+miles, but a single one of these must suffice here. To ride
+100 miles a day 365 days in the year would be counted a
+good bicycling record, but the rider who started at the beginning
+of the Christian era and rode at that rate toward
+the sun from the year 1 <span class="smcap">A.&nbsp;D.</span> down to the present moment<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span>
+would not yet have reached his destination, although his
+journey would be about three quarters done. He would
+have crossed the orbit of Venus about the time of Charlemagne,
+and that of
+Mercury soon after
+the discovery of
+America.</p>
+
+<p><a name="S_115" id="S_115"></a>115. <b>Size and
+density of the sun.</b>&mdash;Knowing
+the distance
+of the sun,
+it is easy to find
+from the angle subtended
+by its diameter
+(32 minutes
+of arc) that the
+length of that diameter
+is 865,000
+miles. We recall
+in this connection
+that the diameter
+of the moon's <i>orbit</i>
+is only 480,000
+miles, but little
+more than half the
+diameter of the
+sun, thus affording
+abundant room inside
+the sun, and
+to spare, for the moon to perform the monthly revolution
+about its orbit, as shown in <a href="#Fig_65">Fig.&nbsp;65</a>.</p>
+
+<div class="figright" style="width: 375px;"><a name="Fig_65" id="Fig_65"></a>
+<a href="images/i210-full.jpg"><img src="images/i210.jpg" width="375" height="619" alt="Fig. 65.&mdash;The sun&#39;s size.&mdash;Young." title="Fig. 65.&mdash;The sun&#39;s size.&mdash;Young." /></a>
+<span class="caption"><span class="smcap">Fig. 65.</span>&mdash;The sun&#39;s size.&mdash;<span class="smcap">Young.</span></span>
+</div>
+
+<p>In the same manner in which the density of the moon
+was found from its mass and diameter, the student may
+find from the mass and diameter of the sun given above
+that its mean density is 1.4 times that of water. This is
+about the same as the density of gravel or soft coal, and<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span>
+is just about one quarter of the average density of the
+earth.</p>
+
+<p>We recall that the small density of the moon was accounted
+for by the diminished weight of objects upon it,
+but this explanation can not hold in the case of the sun,
+for not only is the density less but the force of gravity
+(weight) is there 28 times as great as upon the earth. The
+athlete who here weighs 175 pounds, if transported to the
+surface of the sun would weigh more than an elephant does
+here, and would find his bones break under his own weight
+if his muscles were strong enough to hold him upright.
+The tremendous pressure exerted by gravity at the surface
+of the sun must be surpassed below the surface, and as it
+does not pack the material together and make it dense, we
+are driven to one of two conclusions: Either the stuff of
+which the sun is made is altogether unlike that of the
+earth, not so readily compressed by pressure, or there is
+some opposing influence at work which more than balances
+the effect of gravity and makes the solar stuff much lighter
+than the terrestrial.</p>
+
+<p><a name="S_116" id="S_116"></a>116. <b>Material of which the sun is made.</b>&mdash;As to the first
+of these alternatives, the spectroscope comes to our aid and
+shows in the sun's spectrum (<a href="#Fig_50">Fig.&nbsp;50</a>) the characteristic
+line marked <i>D</i>, which we know always indicates the presence
+of sodium and identifies at least one terrestrial substance
+as present in the sun in considerable quantity. The
+lines marked <i>C</i> and <i>F</i> are produced by hydrogen, which is
+one of the constituents of water, <i>E</i> shows calcium to be
+present in the sun, <i>b</i> magnesium, etc. In this way it has
+been shown that about one half of our terrestrial elements,
+mainly the metallic ones, are present as gases on or near the
+sun's surface, but it must not be inferred that elements not
+found in this way are absent from the sun. They may be
+there, probably are there, but the spectroscopic proof of
+their presence is more difficult to obtain. Professor Rowland,
+who has been prominent in the study of the solar<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span>
+spectrum, says: "Were the whole earth heated to the temperature
+of the sun, its spectrum would probably resemble
+that of the sun very closely."</p>
+
+<p>Some of the common terrestrial elements found in the
+sun are:</p>
+
+<div class="center">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">Aluminium.</td></tr>
+<tr><td align="left">Calcium.</td></tr>
+<tr><td align="left">Carbon.</td></tr>
+<tr><td align="left">Copper.</td></tr>
+<tr><td align="left">Hydrogen.</td></tr>
+<tr><td align="left">Iron.</td></tr>
+<tr><td align="left">Lead.</td></tr>
+<tr><td align="left">Nickel.</td></tr>
+<tr><td align="left">Potassium.</td></tr>
+<tr><td align="left">Silicon.</td></tr>
+<tr><td align="left">Silver.</td></tr>
+<tr><td align="left">Sodium.</td></tr>
+<tr><td align="left">Tin.</td></tr>
+<tr><td align="left">Zinc.</td></tr>
+<tr><td align="left">Oxygen (?)</td></tr>
+</table></div>
+
+<p>Whatever differences of chemical structure may exist
+between the sun and the earth, it seems that we must regard
+these bodies as more like than unlike to each other in
+substance, and we are brought back to the second of our
+alternatives: there must be some influence opposing the
+force of gravity and making the substance of the sun light
+instead of heavy, and we need not seek far to find it in&mdash;</p>
+
+<p><a name="S_117" id="S_117"></a>117. <b>The heat of the sun.</b>&mdash;That the sun is hot is too
+evident to require proof, and it is a familiar fact that heat
+expands most substances and makes them less dense. The
+sun's heat falling upon the earth expands it and diminishes
+its density in some small degree, and we have only to imagine
+this process of expansion continued until the earth's
+diameter becomes 58 per cent larger than it now is, to find
+the earth's density reduced to a level with that of the sun.
+Just how much the temperature of the earth must be raised
+to produce this amount of expansion we do not know,
+neither do we know accurately the temperature of the sun,
+but there can be no doubt that heat is the cause of the
+sun's low density and that the corresponding temperature
+is very high.</p>
+
+<p>Before we inquire more closely into the sun's temperature,<span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span>
+it will be well to draw a sharp distinction between the
+two terms heat and temperature, which are often used as if
+they meant the same thing. Heat is a form of energy
+which may be found in varying degree in every substance,
+whether warm or cold&mdash;a block of ice contains a considerable
+amount of heat&mdash;while temperature corresponds to our
+sensations of warm and cold, and measures the extent to
+which heat is concentrated in the body. It is the amount
+of heat per molecule of the body. A barrel of warm water
+contains more heat than the flame of a match, but its temperature
+is not so high. Bearing in mind this distinction,
+we seek to determine not the amount of heat contained in
+the sun but the sun's temperature, and this involves the
+same difficulty as does the question, What is the temperature
+of a locomotive? It is one thing in the fire box and
+another thing in the driving wheels, and still another at
+the headlight; and so with the sun, its temperature is certainly
+different in different parts&mdash;one thing at the center
+and another at the surface. Even those parts which we
+see are covered by a veil of gases which produce by absorption
+the dark lines of the solar spectrum, and seriously
+interfere both with the emission of energy from the sun
+and with our attempts at measuring the temperature of
+those parts of the surface from which that energy streams.</p>
+
+<p>In view of these and other difficulties we need not be
+surprised that the wildest discordance has been found in
+estimates of the solar temperature made by different investigators,
+who have assigned to it values ranging from 1,400° C.
+to more than 5,000,000° C. Quite recently, however, improved
+methods and a better understanding of the problem
+have brought about a better agreement of results, and it
+now seems probable that the temperature of the visible
+surface of the sun lies somewhere between 5,000° and
+10,000° C., say 15,000° of the Fahrenheit scale.</p>
+
+<p><a name="S_118" id="S_118"></a>118. <b>Determining the sun's temperature.</b>&mdash;One ingenious
+method which has been used for determining this temperature<span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span>
+is based upon the principle stated above, that every
+object, whether warm or cold, contains heat and gives it
+off in the form of radiant energy. The radiation from a
+body whose temperature is lower than 500° C. is made up
+exclusively of energy whose wave length is greater than
+7,600 tenth meters, and is therefore invisible to the eye, although
+a thermometer or even the human hand can often
+detect it as radiant heat. A brick wall in the summer sunshine
+gives off energy which can be felt as heat but can
+not be seen. When such a body is further heated it continues
+to send off the same kinds (wave lengths) of energy
+as before, but new and shorter waves are added to its radiation,
+and when it begins to emit energy of wave length 7,500
+or 7,600 tenth meters, it also begins to shine with a dull-red
+light, which presently becomes brighter and less ruddy
+and changes to white as the temperature rises, and waves
+of still shorter length are thereby added to the radiation.
+We say, in common speech, the body becomes first red hot
+and then white hot, and we thus recognize in a general
+way that the kind or color of the radiation which a body
+gives off is an index to its temperature. The greater the
+proportion of energy of short wave lengths the higher is
+the temperature of the radiating body. In sunlight the
+maximum of brilliancy to the eye lies at or near the wave
+length, 5,600 tenth meters, but the greatest intensity of
+radiation of all kinds (light included) is estimated to fall
+somewhere between green and blue in the spectrum at or
+near the wave length 5,000 tenth meters, and if we can apply
+to this wave length Paschen's law&mdash;temperature reckoned
+in degrees centigrade from the absolute zero is always
+equal to the quotient obtained by dividing the number
+27,000,000 by the wave length corresponding to maximum
+radiation&mdash;we shall find at once for the absolute temperature
+of the sun's surface 5,400° C.</p>
+
+<p>Paschen's law has been shown to hold true, at least
+approximately, for lower temperatures and longer wave<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span>
+lengths than are here involved, but as it is not yet certain
+that it is strictly true and holds for all temperatures, too
+great reliance must not be attached to the numerical result
+furnished by it.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_66" id="Fig_66"></a>
+<a href="images/i215-full.jpg"><img src="images/i215.jpg" width="500" height="498" alt="Fig. 66.&mdash;The sun, August 11, 1894. Photographed at the Goodsell Observatory." title="Fig. 66.&mdash;The sun, August 11, 1894. Photographed at the Goodsell Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 66.</span>&mdash;The sun, August 11, 1894. Photographed at the Goodsell Observatory.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_67" id="Fig_67"></a>
+<a href="images/i216.jpg"><img src="images/i216.jpg" width="500" height="498" alt="Fig. 67.&mdash;The sun, August 14, 1894. Photographed at the Goodsell Observatory." title="Fig. 67.&mdash;The sun, August 14, 1894. Photographed at the Goodsell Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 67.</span>&mdash;The sun, August 14, 1894. Photographed at the Goodsell Observatory.</span>
+</div>
+
+<p><a name="S_119" id="S_119"></a>119. <b>The sun's surface.</b>&mdash;A marked contrast exists between
+the faces of sun and moon in respect of the amount
+of detail to be seen upon them, the sun showing nothing
+whatever to correspond with the mountains, craters, and
+seas of the moon. The unaided eye in general finds in the
+sun only a blank bright circle as smooth and unmarked as
+the surface of still water, and even the telescope at first
+sight seems to show but little more. There may usually be
+found upon the sun's face a certain number of black patches
+called <i>sun spots</i>, such as are shown in Figs.&nbsp;<a href="#Fig_66">66</a> to&nbsp;<a href="#Fig_69">69</a>, and<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>
+occasionally these are large enough to be seen through a
+smoked glass without the aid of a telescope. When seen
+near the edge of the sun they are quite frequently accompanied,
+as in <a href="#Fig_69">Fig.&nbsp;69</a>, by vague patches called <i>faculę</i> (Latin,
+<i>facula</i> =&nbsp;a little torch), which look a little brighter than
+the surrounding parts of the sun. So, too, a good photograph
+of the sun usually shows that the central parts of
+the disk are rather brighter than the edge, as indeed we
+should expect them to be, since the absorption lines in the
+sun's spectrum have already taught us that the visible surface
+of the sun is enveloped by invisible vapors which in
+some measure absorb the emitted light and render it feebler
+at the edge where it passes through a greater thickness of
+this envelope than at the center. See <a href="#Fig_70">Fig.&nbsp;70</a>, where it is<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>
+shown that the energy coming from the edge of the sun to
+the earth has to traverse a much longer path inside the
+vapors than does that coming from the center.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_68" id="Fig_68"></a>
+<a href="images/i217.jpg"><img src="images/i217.jpg" width="500" height="499" alt="Fig. 68.&mdash;The sun, August 18, 1894. Photographed at the Goodsell Observatory." title="Fig. 68.&mdash;The sun, August 18, 1894. Photographed at the Goodsell Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 68.</span>&mdash;The sun, August 18, 1894. Photographed at the Goodsell Observatory.</span>
+</div>
+
+<p>Examine the sun spots in the four photographs, Figs.&nbsp;<a href="#Fig_66">66</a>
+to&nbsp;<a href="#Fig_69">69</a>, and note that the two spots which appear at the
+extreme left of the first photograph, very much distorted
+and foreshortened by the curvature of the sun's surface, are
+seen in a different part of the second picture, and are not
+only more conspicuous but show better their true shape.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="PLATE_II" id="PLATE_II"></a>
+<a href="images/i219-full.jpg"><img src="images/i219.jpg" width="600" height="421" alt="PLATE II.
+
+THE EQUATORIAL CONSTELLATIONS" title="PLATE II.
+
+THE EQUATORIAL CONSTELLATIONS" /></a>
+<span class="caption">PLATE II.
+
+THE EQUATORIAL CONSTELLATIONS</span>
+</div>
+
+<p><a name="S_120" id="S_120"></a>120. <b>The sun's rotation.</b>&mdash;The changed position of these
+spots shows that the sun rotates about an axis at right
+angles to the direction of the spot's motion, and the position
+of this axis is shown in the figure by a faint line ruled
+obliquely across the face of the sun nearly north and south<span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span>
+in each of the four photographs. This rotation in the
+space of three days has carried the spots from the edge
+halfway to the center of the disk, and the student should
+note the progress of the spots in the two later photographs,
+that of August 21st showing them just ready to disappear
+around the farther edge of the sun.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_69" id="Fig_69"></a>
+<a href="images/i221-full.jpg"><img src="images/i221.jpg" width="500" height="546" alt="Fig. 69.&mdash;The sun, August 21, 1894. Photographed at the Goodsell Observatory." title="Fig. 69.&mdash;The sun, August 21, 1894. Photographed at the Goodsell Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 69.</span>&mdash;The sun, August 21, 1894. Photographed at the Goodsell Observatory.</span>
+</div>
+
+<p>Plot accurately in one of these figures the positions of
+the spots as shown in the other three, and observe whether
+the path of the spots across the sun's face is a straight line.
+Is there any reason why it should not be straight?</p>
+
+<p>These four pictures may be made to illustrate many
+things about the sun. Thus the sun's axis is not parallel
+to that of the earth, for the letters <i>N&nbsp;S</i> mark the direction
+of a north and south line across the face of the sun, and<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>
+this line, of course, is parallel to the earth's axis, while it is
+evidently not parallel to the sun's axis. The group of
+spots took more than
+ten days to move
+across the sun's face,
+and as at least an
+equal time must be
+required to move
+around the opposite
+side of the sun, it is
+evident that the period
+of the sun's rotation
+is something more than 20 days. It is, in fact,
+rather more than 25 days, for this same group of spots reappeared
+again on the left-hand edge of the sun on September
+5th.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_70" id="Fig_70"></a>
+<img src="images/i222.png" width="350" height="198" alt="Fig. 70.&mdash;Absorption at the sun&#39;s edge." title="Fig. 70.&mdash;Absorption at the sun&#39;s edge." />
+<span class="caption"><span class="smcap">Fig. 70.</span>&mdash;Absorption at the sun&#39;s edge.</span>
+</div>
+
+<p><a name="S_121" id="S_121"></a>121. <b>Sun spots.</b>&mdash;Another significant fact comes out
+plainly from the photographs. The spots are not permanent
+features of the sun's face, since they changed their
+size and shape very appreciably in the few days covered by
+the pictures. Compare particularly the photographs of
+August 14th and August 18th, where the spots are least
+distorted by the curvature of the sun's surface. By September
+16th this group of spots had disappeared absolutely
+from the sun's face, although when at its largest the group
+extended more than 80,000 miles in length, and several of
+the individual spots were large enough to contain the
+earth if it had been dropped upon them. From <a href="#Fig_67">Fig.&nbsp;67</a>
+determine in miles the length of the group on August
+14th. <a href="#Fig_71">Fig.&nbsp;71</a> shows an enlarged view of these spots as
+they appeared on August 17th, and in this we find some
+details not so well shown in the preceding pictures. The
+larger spots consist of a black part called the <i>nucleus</i> or
+<i>umbra</i> (Latin, shadow), which is surrounded by an irregular
+border called the <i>penumbra</i> (partial shadow), which is
+intermediate in brightness between the nucleus and the<span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span>
+surrounding parts of the sun. It should not be inferred
+from the picture that the nucleus is really black or even
+dark. It shines, in
+fact, with a brilliancy
+greater than that of
+an electric lamp, but
+the background furnished
+by the sun's
+surface is so much
+brighter that by contrast
+with it the nucleus
+and penumbra
+appear relatively dark.</p>
+
+<div class="figcenter" style="width: 350px;"><a name="Fig_71" id="Fig_71"></a>
+<a href="images/i223a.jpg"><img src="images/i223a.jpg" width="350" height="350" alt="Fig. 71.&mdash;Sun spots, August 17, 1894.
+Goodsell Observatory." title="Fig. 71.&mdash;Sun spots, August 17, 1894.
+Goodsell Observatory." /></a>
+<span class="caption"><span class="smcap">Fig. 71.</span>&mdash;Sun spots, August 17, 1894.
+Goodsell Observatory.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_72" id="Fig_72"></a>
+<a href="images/i223b-full.jpg"><img src="images/i223b.jpg" width="500" height="335" alt="Fig. 72.&mdash;Sun spot of March 5, 1873.&mdash;From Langley, The New Astronomy.
+By permission of the publishers." title="Fig. 72.&mdash;Sun spot of March 5, 1873.&mdash;From Langley, The New Astronomy.
+By permission of the publishers." /></a>
+<span class="caption"><span class="smcap">Fig. 72.</span>&mdash;Sun spot of March 5, 1873.&mdash;From <span class="smcap">Langley</span>, The New Astronomy.
+By permission of the publishers.</span>
+</div>
+
+<p>The bright shining
+surface of the sun, the
+background for the
+spots, is called the
+<i>photosphere</i> (Greek,
+light sphere), and, as <a href="#Fig_71">Fig.&nbsp;71</a> shows, it assumes under a
+suitable magnifying power a mottled aspect quite different
+from the featureless expanse shown in the earlier pictures.
+The photosphere is, in fact, a layer of little clouds with<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span>
+darker spaces between them, and the fine detail of these
+clouds, their complicated structure, and the way in which,
+when projected against the background of a sun spot, they
+produce its penumbra, are all brought out in <a href="#Fig_72">Fig.&nbsp;72</a>.
+Note that the little patch in one corner of this picture
+represents North and South America drawn to the same
+scale as the sun spots.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_73" id="Fig_73"></a>
+<a href="images/i224.jpg"><img src="images/i224.jpg" width="350" height="343" alt="Fig. 73.&mdash;Spectroheliograph, showing distribution
+of faculę upon the sun.&mdash;Hale." title="Fig. 73.&mdash;Spectroheliograph, showing distribution
+of faculę upon the sun.&mdash;Hale." /></a>
+<span class="caption"><span class="smcap">Fig. 73.</span>&mdash;Spectroheliograph, showing distribution
+of faculę upon the sun.&mdash;<span class="smcap">Hale.</span></span>
+</div>
+
+<p><a name="S_122" id="S_122"></a>122. <b>Faculę.</b>&mdash;We have seen in <a href="#Fig_69">Fig.&nbsp;69</a> a few of the
+bright spots called faculę. At the telescope or in the
+ordinary photograph these can be seen only at the edge of
+the sun, because elsewhere
+the background
+furnished by the photosphere
+is so bright
+that they are lost in it.
+It is possible, however,
+by an ingenious application
+of the spectroscope
+to break up the
+sunlight into a spectrum
+in such a way as
+to diminish the brightness
+of this background,
+much more
+than the brightness of
+the faculę is diminished,
+and in this way to obtain a photograph of the sun's
+surface which shall show them wherever they occur, and
+such a photograph, showing faintly the spectral lines, is
+reproduced in <a href="#Fig_73">Fig.&nbsp;73</a>. The faculę are the bright patches
+which stretch inconspicuously across the face of the sun,
+in two rather irregular belts with a comparatively empty
+lane between them. This lane lies along the sun's equator,
+and it is upon either side of it between latitudes 5°
+and 40° that faculę seem to be produced. It is significant
+of their connection with sun spots that the spots occur<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span>
+in these particular zones and are rarely found outside
+them.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_74" id="Fig_74"></a>
+<a href="images/i225-full.jpg"><img src="images/i225.jpg" width="600" height="431" alt="Fig. 74.&mdash;Eclipse of July 20, 1878.&mdash;Trouvelot." title="Fig. 74.&mdash;Eclipse of July 20, 1878.&mdash;Trouvelot." /></a>
+<span class="caption"><span class="smcap">Fig. 74.</span>&mdash;Eclipse of July 20, 1878.&mdash;<span class="smcap">Trouvelot.</span></span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_75" id="Fig_75"></a>
+<a href="images/i226-full.jpg"><img src="images/i226.jpg" width="500" height="494" alt="Fig. 75.&mdash;Eclipse of April 16, 1893.&mdash;Schaeberle." title="Fig. 75.&mdash;Eclipse of April 16, 1893.&mdash;Schaeberle." /></a>
+<span class="caption"><span class="smcap">Fig. 75.</span>&mdash;Eclipse of April 16, 1893.&mdash;<span class="smcap">Schaeberle.</span></span>
+</div>
+
+<p><a name="S_123" id="S_123"></a>123. <b>Invisible parts of the sun. The Corona.</b>&mdash;Thus far
+we have been dealing with parts of the sun that may be
+seen and photographed under all ordinary conditions.
+But outside of and surrounding these parts is an envelope,
+or rather several envelopes, of much greater extent than
+the visible sun. These envelopes are for the most part
+invisible save at those times when the brighter central
+portions of the sun are hidden in a total eclipse.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_76" id="Fig_76"></a>
+<a href="images/i227-full.jpg"><img src="images/i227.jpg" width="500" height="498" alt="Fig. 76.&mdash;Eclipse of January 21, 1898.&mdash;Campbell." title="Fig. 76.&mdash;Eclipse of January 21, 1898.&mdash;Campbell." /></a>
+<span class="caption"><span class="smcap">Fig. 76.</span>&mdash;Eclipse of January 21, 1898.&mdash;<span class="smcap">Campbell.</span></span>
+</div>
+
+<p><a href="#Fig_74">Fig.&nbsp;74</a> is from a drawing, and Figs.&nbsp;<a href="#Fig_75">75</a> and&nbsp;<a href="#Fig_76">76</a> are from
+eclipse photographs showing this region, in which the most<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span>
+conspicuous object is the halo of soft light called the <i>corona</i>,
+that completely surrounds the sun but is seen to be of differing
+shapes and differing extent at the several eclipses
+here shown, although a large part of these apparent differences
+is due to technical difficulties in photographing, and
+reproducing an object with outlines so vague as those of
+the corona. The outline of the corona is so indefinite and
+its outer portions so faint that it is impossible to assign to
+it precise dimensions, but at its greatest extent it reaches
+out for several millions of miles and fills a space more than
+twenty times as large as the visible part of the sun. Despite
+its huge bulk, it is of most unsubstantial character,<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>
+an airy nothing through which comets have been known
+to force their way around the sun from one side to the
+other, literally for millions of miles, without having their
+course influenced or their
+velocity checked to any
+appreciable extent. This
+would hardly be possible
+if the density even at the
+bottom of the corona were
+greater than that of the
+best vacuum which we
+are able to produce in laboratory
+experiments. It
+seems odd that a vacuum
+should give off so bright
+a light as the coronal pictures
+show, and the exact character of that light and the
+nature of the corona are still subjects of dispute among
+astronomers, although it is generally agreed that, in part
+at least, its light is ordinary sunlight faintly reflected
+from the widely scattered molecules composing the substance
+of the corona. It is also probable that in part the
+light has its origin in the corona itself. A curious and at
+present unconfirmed result announced by one of the observers
+of the eclipse of May 28, 1900, is that <i>the corona is
+not hot</i>, its effective temperature being lower than that of
+the instrument used for the observation.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_77" id="Fig_77"></a>
+<a href="images/i228.jpg"><img src="images/i228.jpg" width="350" height="289" alt="Fig. 77.&mdash;Solar prominence of March 25,
+1895.&mdash;Hale." title="Fig. 77.&mdash;Solar prominence of March 25,
+1895.&mdash;Hale." /></a>
+<span class="caption"><span class="smcap">Fig. 77.</span>&mdash;Solar prominence of March 25,
+1895.&mdash;<span class="smcap">Hale.</span></span>
+</div>
+
+<div class="figright" style="width: 375px;"><a name="Fig_78" id="Fig_78"></a>
+<a href="images/i229-full.jpg"><img src="images/i229.jpg" width="375" height="437" alt="Fig. 78.&mdash;A solar prominence.&mdash;Hale." title="Fig. 78.&mdash;A solar prominence.&mdash;Hale." /></a>
+<span class="caption"><span class="smcap">Fig. 78.</span>&mdash;A solar prominence.&mdash;<span class="smcap">Hale.</span></span>
+</div>
+
+
+<p><a name="S_124" id="S_124"></a>124. <b>The chromosphere.</b>&mdash;Between the corona and the
+photosphere there is a thin separating layer called the
+<i>chromosphere</i> (Greek, color sphere), because when seen at
+an eclipse it shines with a brilliant red light quite unlike
+anything else upon the sun save the <i>prominences</i> which are
+themselves only parts of the chromosphere temporarily
+thrown above its surface, as in a fountain a jet of water is
+thrown up from the basin and remains for a few moments
+suspended in mid-air. Not infrequently in such a fountain
+<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span>
+foreign matter is swept up by the rush of the water&mdash;dirt,
+twigs, small fish, etc.&mdash;and in like manner the prominences
+often carry along with them parts of the underlying
+layers of the sun, photosphere, faculę, etc., which
+reveal their presence in the prominence by adding their
+characteristic lines to the spectrum, like that of the chromosphere,
+which the prominence presents when they are
+absent. None of the eclipse photographs (Figs.&nbsp;<a href="#Fig_74">74</a> to&nbsp;<a href="#Fig_76">76</a>)
+show the chromosphere, because the color effect is lacking
+in them, but a great curving prominence may be seen near
+the bottom of <a href="#Fig_75">Fig.&nbsp;75</a>, and smaller ones at other parts of
+the sun's edge.</p>
+
+<p><a name="S_125" id="S_125"></a>125. <b>Prominences.</b>&mdash;<a href="#Fig_77">Fig.&nbsp;77</a> shows upon a larger scale one
+of these prominences rising to a height of 160,000 miles
+above the photosphere;
+and another
+photograph,
+taken 18 minutes
+later, but not reproduced
+here,
+showed the same
+prominence grown
+in this brief interval
+to a stature
+of 280,000 miles.
+These pictures
+were not taken
+during an eclipse,
+but in full sunlight,
+using the
+same spectroscopic
+apparatus which
+was employed in
+connection with
+the faculę to diminish the brightness of the background
+without much enfeebling the brilliancy of the prominence<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>
+itself. The dark base from which the prominence seems
+to spring is not the sun's edge, but a part of the apparatus
+used to cut off the direct sunlight.</p>
+
+<p><a href="#Fig_78">Fig.&nbsp;78</a> contains a series of photographs of another
+prominence taken within an interval of 1 hour 47 minutes
+and showing changes in size and shape which are much
+more nearly typical of the ordinary prominence than was
+the very unusual change in the case of <a href="#Fig_77">Fig.&nbsp;77</a>.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_79" id="Fig_79"></a>
+<a href="images/i230-full.jpg"><img src="images/i230.jpg" width="500" height="375" alt="Fig. 79.&mdash;Contrasted forms of solar prominences.&mdash;Zoellner." title="Fig. 79.&mdash;Contrasted forms of solar prominences.&mdash;Zoellner." /></a>
+<span class="caption"><span class="smcap">Fig. 79.</span>&mdash;Contrasted forms of solar prominences.&mdash;<span class="smcap">Zoellner.</span></span>
+</div>
+
+<p>The preceding pictures are from photographs, and with
+them the student may compare <a href="#Fig_79">Fig.&nbsp;79</a>, which is constructed
+from drawings made at the spectroscope by the
+German astronomer Zoellner. The changes here shown
+are most marked in the prominence at the left, which is
+shaped like a broken tree trunk, and which appears to be
+vibrating from one side to the other like a reed shaken
+in the wind. Such a prominence is frequently called an
+<i>eruptive</i> one, a name suggested by its appearance of having
+been blown out from the sun by something like an
+explosion, while the prominence at the right in this series
+of drawings, which appears much less agitated, is called by
+contrast with the other a <i>quiescent</i> prominence. These
+quiescent prominences are, as a rule, much longer-lived<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span>
+than the eruptive ones. One more picture of prominences
+(<a href="#Fig_80">Fig.&nbsp;80</a>) is introduced to show the continuous stretch of
+chromosphere out of which they spring.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_80" id="Fig_80"></a>
+<a href="images/i231-full.jpg"><img src="images/i231.jpg" width="500" height="414" alt="Fig. 80.&mdash;Prominences and chromosphere.&mdash;Hale." title="Fig. 80.&mdash;Prominences and chromosphere.&mdash;Hale." /></a>
+<span class="caption"><span class="smcap">Fig. 80.</span>&mdash;Prominences and chromosphere.&mdash;<span class="smcap">Hale.</span></span>
+</div>
+
+<p>Prominences are seen only at the edge of the sun, because
+it is there alone that the necessary background can
+be obtained, but they must occur at the center of the sun
+and elsewhere quite as well as at the edge, and it is probable
+that quiescent prominences are distributed over all
+parts of the sun's surface, but eruptive prominences show
+a strong tendency toward the regions of sun spots and
+faculę as if all three were intimately related phenomena.</p>
+
+<p><a name="S_126" id="S_126"></a>126. <b>The sun as a machine.</b>&mdash;Thus far we have considered
+the anatomy of the sun, dissecting it into its several
+parts, and our next step should be a consideration of its
+physiology, the relation of the parts to each other, and
+their function in carrying on the work of the solar organism,
+but this step, unfortunately, must be a lame one.
+The science of astronomy to-day possesses no comprehensive
+and well-established theory of this kind, but looks to
+the future for the solution of this the greatest pending<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span>
+problem of solar physics. Progress has been made toward
+its solution, and among the steps of this progress that we
+shall have to consider, the first and most important is the
+conception of the sun as a kind of heat engine.</p>
+
+<p>In a steam engine coal is burned under the boiler, and
+its chemical energy, transformed into heat, is taken up by
+the water and delivered, through steam as a medium, to
+the engine, which again transforms and gives it out as
+mechanical work in the turning of shafts, the driving of
+machinery, etc. Now, the function of the sun is exactly
+opposite to that of the engine and boiler: it gives out,
+instead of receiving, radiant energy; but, like the engine,
+it must be fed from some source; it can not be run upon
+nothing at all any more than the engine can run day after
+day without fresh supplies of fuel under its boiler. We
+know that for some thousands of years the sun has been
+furnishing light and heat to the earth in practically unvarying
+amount, and not to the earth alone, but it has
+been pouring forth these forms of energy in every direction,
+without apparent regard to either use or economy.
+Of all the radiant energy given off by the sun, only two
+parts out of every thousand million fall upon any planet
+of the solar system, and of this small fraction the earth
+takes about one tenth for the maintenance of its varied
+forms of life and action. Astronomers and physicists have
+sought on every hand for an explanation of the means by
+which this tremendous output of energy is maintained
+century after century without sensible diminution, and
+have come with almost one mind to the conclusion that
+the gravitative forces which reside in the sun's own mass
+furnish the only adequate explanation for it, although
+they may be in some small measure re-enforced by minor
+influences, such as the fall of meteoric dust and stones
+into the sun.</p>
+
+<p>Every boy who has inflated a bicycle tire with a hand
+pump knows that the pump grows warm during the operation,<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>
+on account of the compression of the air within the
+cylinder. A part of the muscular force (energy) expended
+in working the pump reappears in the heat which warms
+both air and pump, and a similar process is forever going on
+in the sun, only in place of muscular force we must there substitute
+the tremendous attraction of gravitation, 28 times
+as great as upon the earth. "The matter in the interior
+of the sun must be as a shuttlecock between the stupendous
+pressure and the enormously high temperature," the
+one tending to compress and the other to expand it, but
+with this important difference between them: the temperature
+steadily tends to fall as the heat energy is wasted
+away, while the gravitative force suffers no corresponding
+diminution, and in the long run must gain the upper
+hand, causing the sun to shrink and become more dense.
+It is this progressive shrinking and compression of its
+molecules into a smaller space which supplies the energy
+contained in the sun's output of light and heat. According
+to Lord Kelvin, each centimeter of shrinkage in the
+sun's diameter furnishes the energy required to keep up
+its radiation for something more than an hour, and, on
+account of the sun's great distance, the shrinkage might
+go on at this rate for many centuries without producing
+any measurable effect in the sun's appearance.</p>
+
+<p><a name="S_127" id="S_127"></a>127. <b>Gaseous constitution of the sun.</b>&mdash;But Helmholtz's dynamical
+theory of the maintenance of the sun's heat, which
+we are here considering, includes one essential feature
+that is not sufficiently stated above. In order that the
+explanation may hold true, it is necessary that the sun
+should be in the main a gaseous body, composed from center
+to circumference of gases instead of solid or liquid
+parts. Pumping air warms the bicycle pump in a way
+that pumping water or oil will not.</p>
+
+<p>The high temperature of the sun itself furnishes sufficient
+reason for supposing the solar material to be in the
+gaseous state, but the gas composing those parts of the<span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span>
+sun below the photosphere must be very different in some
+of its characteristics from the air or other gases with which
+we are familiar at the earth, since its average density is
+1,000 times as great as that of air, and its consistence and
+mechanical behavior must be more like that of honey or tar
+than that of any gas with which we are familiar. It is
+worth noting, however, that if a hole were dug into the
+crust of the earth to a depth of 15 or 20 miles the air at
+the bottom of the hole would be compressed by that above
+it to a density comparable with that of the solar gases.</p>
+
+<p><a name="S_128" id="S_128"></a>128. <b>The sun's circulation.</b>&mdash;It is plain that under the
+conditions which exist in the sun the outer portions, which
+can radiate their heat freely into space, must be cooler than
+the inner central parts, and this difference of temperature
+must set up currents of hot matter drifting upward and outward
+from within the sun and counter currents of cooler
+matter settling down to take its place. So, too, there must
+be some level at which the free radiation into outer space
+chills the hot matter sufficiently to condense its less refractory
+gases into clouds made up of liquid drops, just as on a
+cloudy day there is a level in our own atmosphere at which
+the vapor of water condenses into liquid drops which form
+the thin shell of clouds that hovers above the earth's surface,
+while above and below is the gaseous atmosphere. In the
+case of the sun this cloud layer is always present and is that
+part which we have learned to call the photosphere. Above
+the photosphere lies the chromosphere, composed of gases
+less easily liquefied, hydrogen is the chief one, while between
+photosphere and chromosphere is a thin layer of metallic
+vapors, perhaps indistinguishable from the top crust
+of the photosphere itself, which by absorbing the light
+given off from the liquid photosphere produces the greater
+part of the Fraunhofer lines in the solar spectrum.</p>
+
+<p>From time to time the hot matter struggling up from
+below breaks through the photosphere and, carrying with
+it a certain amount of the metallic vapors, is launched into<span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span>
+the upper and cooler regions of the sun, where, parting
+with its heat, it falls back again upon the photosphere and
+is absorbed into it. It is altogether probable that the
+corona is chiefly composed of fine particles ejected from
+the sun with velocities sufficient to carry them to a height
+of millions of miles, or even sufficient to carry them off
+never to return. The matter of the corona must certainly
+be in a state of the most lively agitation, its particles being
+alternately hurled up from the photosphere and falling
+back again like fireworks, the particles which make up the
+corona of to-day being quite a different set from those of
+yesterday or last week. It seems beyond question that
+the prominences and faculę too are produced in some
+way by this up-and-down circulation of the sun's matter,
+and that any mechanical explanation of the sun must be
+worked out along these lines; but the problem is an exceedingly
+difficult one, and must include and explain many other
+features of the sun's activity of which only a few can be considered
+here.</p>
+
+<p><a name="S_129" id="S_129"></a>129. <b>The sun-spot period.</b>&mdash;Sun spots come and go, and
+at best any particular spot is but short-lived, rarely lasting
+more than a month or two, and more often its duration is
+a matter of only a few days. They are not equally numerous
+at all times, but, like swarms of locusts, they seem to
+come and abound for a season and then almost to disappear,
+as if the forces which produced them were of a periodic
+character alternately active and quiet. The effect of
+this periodic activity since 1870 is shown in <a href="#Fig_81">Fig.&nbsp;81</a>, where
+the horizontal line is a scale of times, and the distance of
+the curve above this line for any year shows the relative
+number of spots which appeared upon the sun in that
+year. This indicates very plainly that 1870, 1883, and
+1893 were years of great sun-spot activity, while 1879 and
+1889 were years in which few spots appeared. The older
+records, covering a period of two centuries, show the same
+fluctuations in the frequency of sun spots and from these<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span>
+records curves (which may be found in Young's, The Sun)
+have been plotted, showing a succession of waves extending
+back for many years.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_81" id="Fig_81"></a>
+<img src="images/i236.png" width="500" height="197" alt="Fig. 81.&mdash;The curve of sun-spot frequency." title="Fig. 81.&mdash;The curve of sun-spot frequency." />
+<span class="caption"><span class="smcap">Fig. 81.</span>&mdash;The curve of sun-spot frequency.</span>
+</div>
+
+<p>The sun-spot period is the interval of time from the
+crest or hollow of one wave to the corresponding part of
+the next one, and on the average this appears to be a little
+more than eleven years, but is subject to considerable variation.
+In accordance with this period there is drawn in
+broken lines at the right of <a href="#Fig_81">Fig.&nbsp;81</a> a predicted continuation
+of the sun-spot curve for the first decade of the twentieth
+century. The irregularity shown by the three preceding
+waves is such that we must not expect the actual
+course of future sun spots to correspond very closely to
+the prediction here made; but in a general way 1901 and
+1911 will probably be years of few sun spots, while they
+will be numerous in 1905, but whether more or less numerous
+than at preceding epochs of greatest frequency can not
+be foretold with any approach to certainty so long as we
+remain in our present ignorance of the causes which make
+the sun-spot period.</p>
+
+<p>Determine from <a href="#Fig_81">Fig.&nbsp;81</a> as accurately as possible the
+length of the sun-spot period. It is hard to tell the exact
+position of a crest or hollow of the curve. Would it
+do to draw a horizontal line midway between top and bottom
+of the curve and determine the length of the period<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span>
+from its intersections with the curve&mdash;e.&nbsp;g., in 1874 and
+1885?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_82" id="Fig_82"></a>
+<img src="images/i237.png" width="500" height="506" alt="Fig. 82.&mdash;Illustrating change of the sun-spot zones." title="Fig. 82.&mdash;Illustrating change of the sun-spot zones." />
+<span class="caption"><span class="smcap">Fig. 82.</span>&mdash;Illustrating change of the sun-spot zones.</span>
+</div>
+
+<p><a name="S_130" id="S_130"></a>130. <b>The sun-spot zones.</b>&mdash;It has been already noted that
+sun spots are found only in certain zones of latitude upon
+the sun, and that faculę and eruptive prominences abound
+in these zones more than elsewhere, although not strictly
+confined to them. We have now to note a peculiarity of
+these zones which ought to furnish a clew to the sun's
+mechanism, although up to the present time it has not
+been successfully traced out. Just before a sun-spot minimum
+the few spots which appear are for the most part
+clustered near the sun's equator. As these spots die out<span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>
+two new groups appear, one north the other south of the
+sun's equator and about 25° or 30° distant from it, and as
+the period advances toward a maximum these groups shift
+their positions more and more toward the equator, thus approaching
+each other but leaving between them a vacant
+lane, which becomes steadily narrower until at the close
+of the period, when the next minimum is at hand, it
+reaches its narrowest dimensions, but does not altogether
+close up even then. In <a href="#Fig_82">Fig.&nbsp;82</a> these relations are shown
+for the period falling between 1879 and 1890, by means of
+the horizontal lines; for each year one line in the northern
+and one in the southern hemisphere of the sun, their
+lengths being proportional to the number of spots which
+appeared in the corresponding hemisphere during the year,
+and their positions on the sun's disk showing the average
+latitude of the spots in question. It is very apparent from
+the figure that during this decade the sun's southern hemisphere
+was much more active than the northern one in the
+production of spots, and this appears to be generally the
+case, although the difference is not usually as great as in
+this particular decade.</p>
+
+<p><a name="S_131" id="S_131"></a>131. <b>Influence of the sun-spot period.</b>&mdash;Sun spots are certainly
+less hot than the surrounding parts of the sun's surface,
+and, in view of the intimate dependence of the earth
+upon the solar radiation, it would be in no way surprising
+if their presence or absence from the sun's face should
+make itself felt in some degree upon the earth, raising and
+lowering its temperature and quite possibly affecting it in
+other ways. Ingenious men have suggested many such
+kinds of influence, which, according to their investigations,
+appear to run in cycles of eleven years. Abundant and
+scanty harvests, cyclones, tornadoes, epidemics, rainfall,
+etc., are among these alleged effects, and it is possible that
+there may be a real connection between any or all of them
+and the sun-spot period, but for the most part astronomers
+are inclined to hold that there is only one case in which<span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span>
+the evidence is strong enough to really establish a connection
+of this kind. The magnetic condition of the earth
+and its disturbances, which are called magnetic storms, do
+certainly follow in a very marked manner the course of
+sun-spot activity, and perhaps there should be added to
+this the statement that auroras (northern lights) stand in
+close relation to these magnetic disturbances and are most
+frequent at the times of sun-spot maxima.</p>
+
+<p>Upon the sun, however, the influence of the spot period
+is not limited to things in and near the photosphere, but
+extends to the outermost limits of the corona. Determine
+from <a href="#Fig_81">Fig.&nbsp;81</a> the particular part of the sun-spot period
+corresponding to the date of each picture of the corona
+and note how the pictures which were taken near times of
+sun-spot minima present a general agreement in the shape
+and extent of the corona, while the pictures taken at a time
+of maximum activity of the sun spots show a very differently
+shaped and much smaller corona.</p>
+
+<p><a name="S_132" id="S_132"></a>132. <b>The law of the sun's rotation.</b>&mdash;We have seen in a
+previous part of the chapter how the time required by the
+sun to make a complete rotation upon its axis may be determined
+from photographs showing the progress of a spot
+or group of spots across its disk, and we have now to add
+that when this is done systematically by means of many
+spots situated in different solar latitudes it leads to a
+very peculiar and extraordinary result. Each particular
+parallel of latitude has its own period of rotation different
+from that of its neighbors on either side, so that there can
+be no such thing as a fixed geography of the sun's surface.
+Every part of it is constantly taking up a new position
+with respect to every other part, much as if the Gulf of
+Mexico should be south of the United States this year,
+southeast of it next year, and at the end of a decade should
+have shifted around to the opposite side of the earth from
+us. A meridian of longitude drawn down the Mississippi
+Valley remains always a straight line, or, rather, great<span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span>
+circle, upon the surface of the earth, while <a href="#Fig_83">Fig.&nbsp;83</a> shows
+what would become of such a meridian drawn through
+the equatorial parts of the sun's disk. In the first diagram
+it appears as a straight line running down the middle
+of the sun's disk. Twenty-five days later, when the
+same face of the sun comes back into view again, after
+making a complete revolution about the axis, the equatorial
+parts will have moved so much faster and farther
+than those in higher latitudes that the meridian
+will be warped as in the second diagram, and still more
+warped after another and another revolution, as shown in
+the figure.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_83" id="Fig_83"></a>
+<img src="images/i240.png" width="500" height="140" alt="Fig. 83.&mdash;Effect of the sun&#39;s peculiar rotation in warping a meridian, originally
+straight." title="Fig. 83.&mdash;Effect of the sun&#39;s peculiar rotation in warping a meridian, originally
+straight." />
+<span class="caption"><span class="smcap">Fig. 83.</span>&mdash;Effect of the sun&#39;s peculiar rotation in warping a meridian, originally
+straight.</span>
+</div>
+
+<p>At least such is the case if the spots truly represent the
+way in which the sun turns round. There is, however, a
+possibility that the spots themselves drift with varying
+speeds across the face of the sun, and that the differences
+which we find in their rates of motion belong to them
+rather than to the photosphere. Just what happens in the
+regions near the poles is hard to say, for the sun spots only
+extend about halfway from the equator to the poles, and
+the spectroscope, which may be made to furnish a certain
+amount of information bearing upon the case, is not as yet
+altogether conclusive, nor are the faculę which have also
+been observed for this purpose.</p>
+
+<p>The simple theory that the solar phenomena are caused
+by an interchange of hotter and cooler matter between the
+photosphere and the lower strata of the sun furnishes in<span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span>
+its present shape little or no explanation of such features
+as the sun-spot period, the variations in the corona, the
+peculiar character of the sun's rotation, etc., and we have
+still unsolved in the mechanical theory of the sun one of
+the noblest problems of astronomy, and one upon which
+both observers and theoretical astronomers are assiduously
+working at the present time. A close watch is kept upon
+sun spots and prominences, the corona is observed at every
+total eclipse, and numerous are the ingenious methods
+which are being suggested and tried for observing it without
+an eclipse in ordinary daylight. Attempts, more or
+less plausible, have been made and are now pending to
+explain photosphere, spots and the reversing layer by means
+of the refraction of light within the sun's outer envelope
+of gases, and it seems altogether probable, in view of these
+combined activities, that a considerable addition to our
+store of knowledge concerning the sun may be expected in
+the not distant future.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span></p>
+<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI</h2>
+
+<h3>THE PLANETS</h3>
+
+
+<p><a name="S_133" id="S_133"></a>133. <b>Planets.</b>&mdash;Circling about the sun, under the influence
+of his attraction, is a family of planets each member
+of which is, like the moon, a dark body shining by reflected
+sunlight, and therefore presenting phases; although only
+two of them, Mercury and Venus, run through the complete
+series&mdash;new, first quarter, full, last quarter&mdash;which
+the moon presents. The way in which their orbits are
+grouped about the sun has been considered in <a href="#CHAPTER_III">Chapter&nbsp;III</a>,
+and Figs.&nbsp;<a href="#Fig_16">16</a> and&nbsp;<a href="#Fig_17">17</a> of that chapter may be completed
+so as to represent all of the planets by drawing in <a href="#Fig_16">Fig.&nbsp;16</a>
+two circles with radii of 7.9 and 12.4 centimeters respectively,
+to represent the orbits of the planets Uranus and
+Neptune, which are more remote from the sun than Saturn,
+and by introducing a little inside the orbit of Jupiter
+about 500 ellipses of different sizes, shapes, and positions to
+represent a group of minor planets or asteroids as they are
+often called. It is convenient to regard these asteroids as
+composing by themselves a class of very small planets, while
+the remaining 8 larger planets fall naturally into two other
+classes, a group of medium-sized ones&mdash;Mercury, Venus,
+Earth, and Mars&mdash;called inner planets by reason of their
+nearness to the sun; and the outer planets&mdash;Jupiter, Saturn,
+Uranus, Neptune&mdash;each of which is much larger and
+more massive than any planet of the inner group. Compare
+in Figs.&nbsp;<a href="#Fig_84">84</a> and&nbsp;<a href="#Fig_85">85</a> their relative sizes. The earth, <i>E</i>, is
+introduced into <a href="#Fig_85">Fig.&nbsp;85</a> as a connecting link between the
+two figures.</p>
+
+<p>Some of these planets, like the earth, are attended by<span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span>
+one or more moons, technically called satellites, which also
+shine by reflected sunlight and which move about their
+respective planets in accordance with the law of gravitation,
+much as the moon moves around the earth.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_84" id="Fig_84"></a>
+<img src="images/i243a.png" width="500" height="191" alt="Fig. 84.&mdash;The inner planets and the moon." title="Fig. 84.&mdash;The inner planets and the moon." />
+<span class="caption"><span class="smcap">Fig. 84.</span>&mdash;The inner planets and the moon.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_85" id="Fig_85"></a>
+<img src="images/i243b.png" width="500" height="188" alt="Fig. 85.&mdash;The outer planets." title="Fig. 85.&mdash;The outer planets." />
+<span class="caption"><span class="smcap">Fig. 85.</span>&mdash;The outer planets.</span>
+</div>
+
+<p><a name="S_134" id="S_134"></a>134. <b>Distances of the planets from the sun.</b>&mdash;It is a comparatively
+simple matter to observe these planets year after
+year as they move among the stars, and to find from these
+observations how long each one of them requires to make
+its circuit around the sun&mdash;that is, its periodic time, <i>T</i>,
+which figures in Kepler's Third Law, and when these periodic
+times have been ascertained, to use them in connection
+with that law to determine the mean distance of each
+planet from the sun. Thus, Jupiter requires 4,333 days to
+move completely around its orbit; and comparing this with
+the periodic time and mean distance of the earth we find&mdash;</p>
+
+<p class="center"><i>a</i><sup>3</sup> / (4333)<sup>2</sup> = (93,000,000)<sup>3</sup> / (365.25)<sup>2</sup>,<span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span></p>
+
+<p>which when solved gives as the mean distance of Jupiter
+from the sun, 483,730,000 miles, or 5.20 times as distant as
+the earth. If we make a similar computation for each
+planet, we shall find that their distances from the sun show
+a remarkable agreement with an artificial series of numbers
+called Bode's law. We write down the numbers contained
+in the first line of figures below, each of which, after the
+second, is obtained by doubling the preceding one, add 4
+to each number and point off one place of decimals; the
+resulting number is (approximately) the distance of the
+corresponding planet from the sun.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void">
+<tfoot>
+<tr><td align="right">0.4</td><td align="right">0.7</td><td align="right">1.0</td><td align="right">1.6</td><td align="right">2.8</td><td align="right">5.2</td><td align="right">10.0</td><td align="right">19.6</td><td align="right">38.8</td></tr>
+<tr><td align="right">0.4</td><td align="right">0.7</td><td align="right">1.0</td><td align="right">1.5</td><td align="right">2.8</td><td align="right">5.2</td><td align="right">9.5</td><td align="right">19.2</td><td align="right">30.1</td></tr>
+</tfoot>
+<tbody>
+<tr><td align="right">Mercury.</td><td align="right">Venus.</td><td align="right">Earth.</td><td align="right">Mars.</td><td align="right"></td><td align="right">Jupiter.</td><td align="right">Saturn.</td><td align="right">Uranus.</td><td align="right">Neptune.</td></tr>
+<tr><td align="right">0</td><td align="right">3</td><td align="right">6</td><td align="right">12</td><td align="right">24</td><td align="right">48</td><td align="right">96</td><td align="right">192</td><td align="right">384</td></tr>
+<tr><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td></tr>
+</tbody>
+</table></div>
+
+<p>The last line of figures shows the real distance of the
+planet as determined from Kepler's law, the earth's mean
+distance from the sun being taken as the unit for this purpose.
+With exception of Neptune, the agreement between
+Bode's law and the true distances is very striking, but most
+remarkable is the presence in the series of a number, 2.8,
+with no planet corresponding to it. This led astronomers
+at the time Bode published the law, something more than
+a century ago, to give new heed to a suggestion made long
+before by Kepler, that there might be an unknown planet
+moving between the orbits of Mars and Jupiter, and a number
+of them agreed to search for such a planet, each in a
+part of the sky assigned him for that purpose. But they
+were anticipated by Piazzi, an Italian, who found the new
+planet, by accident, on the first day of the nineteenth century,
+moving at a distance from the sun represented by the
+number 2.77.<span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span></p>
+
+<p>This planet was the first of the asteroids, and in the
+century that has elapsed hundreds of them have been discovered,
+while at the present time no year passes by without
+several more being added to the number. While some
+of these are nearer to the sun than is the first one discovered,
+and others are farther from it, their average distance
+is fairly represented by the number 2.8.</p>
+
+<p>Why Bode's law should hold true, or even so nearly
+true as it does, is an unexplained riddle, and many astronomers
+are inclined to call it no law at all, but only a chance
+coincidence&mdash;an illustration of the "inherent capacity of
+figures to be juggled with"; but if so, it is passing strange
+that it should represent the distance of the asteroids and
+of Uranus, which was also an undiscovered planet at the
+time the law was published.</p>
+
+<p><a name="S_135" id="S_135"></a>135. <b>The planets compared with each other.</b>&mdash;When we
+pass from general considerations to a study of the individual
+peculiarities of the planets, we find great differences
+in the extent of knowledge concerning them, and the reason
+for this is not far to seek. Neptune and Uranus, at the
+outskirts of the solar system, are so remote from us and so
+feebly illumined by the sun that any detailed study of them
+can go but little beyond determining the numbers which
+represent their size, mass, density, the character of their
+orbits, etc. The asteroids are so small that in the telescope
+they look like mere points of light, absolutely indistinguishable
+in appearance from the fainter stars. Mercury, although
+closer at hand and presenting a disk of considerable
+size, always stands so near the sun that its observation is
+difficult on this account. Something of the same kind is
+true for Venus, although in much less degree; while Mars,
+Jupiter, and Saturn are comparatively easy objects for telescopic
+study, and our knowledge of them, while far from
+complete, is considerably greater than for the other planets.</p>
+
+<p>Figs.&nbsp;<a href="#Fig_84">84</a> and&nbsp;<a href="#Fig_85">85</a> show the relative sizes of the planets
+composing the inner and outer groups respectively, and furnish
+<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span>
+the numerical data concerning their diameters, masses,
+densities, etc., which are of most importance in judging of
+their physical condition. Each planet, save Saturn, is
+represented by two circles, of which the outer is drawn
+proportional to the size of the planet, and the inner shows
+the amount of material that must be subtracted from the
+interior in order that the remaining shell shall just float in
+water. Note the great difference in thickness of shell
+between the two groups. Saturn, having a mean density
+less than that of water, must have something loaded upon
+it, instead of removed, in order that it should float just
+submerged.</p>
+
+
+<h3><span class="smcap">Jupiter</span></h3>
+
+<p><a name="S_136" id="S_136"></a>136. <b>Appearance.</b>&mdash;Commencing our consideration of the
+individual planets with Jupiter, which is by far the largest
+of them, exceeding both in bulk and mass all the others
+combined, we have in <a href="#Fig_86">Fig.&nbsp;86</a> four representations of
+Jupiter and his family of satellites as they may be seen in
+a very small telescope&mdash;e. g., an opera glass&mdash;save that the
+little dots which here represent the satellites are numbered
+<i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, in order to preserve their identity in the successive
+pictures.</p>
+
+<p>The chief interest of these pictures lies in the satellites,
+but, reserving them for future consideration, we note that
+the planet itself resembles in shape the full moon, although
+in respect of brightness it sends to us less than 1/6000 part
+as much light as the moon. From a consideration of the
+motion of Jupiter and the earth in <a href="#Fig_16">Fig.&nbsp;16</a>, show that
+Jupiter can not present any such phases as does the moon,
+but that its disk must be at all times nearly full. As seen
+from Saturn, what kind of phases would Jupiter present?</p>
+
+<p><a name="S_137" id="S_137"></a>137. <b>The belts.</b>&mdash;Even upon the small scale of <a href="#Fig_86">Fig.&nbsp;86</a>
+we detect the most characteristic feature of Jupiter's appearance
+in the telescope, the two bands extending across
+his face parallel to the line of the satellites, and in <a href="#Fig_87">Fig.&nbsp;87</a>
+these same dark bands may be recognized amid the abundance<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span>
+of detail which is here brought out by a large telescope.
+Photography does not succeed as a means of reproducing
+this detail, and for it we have to rely upon the skill
+of the artist astronomer. The lettering shows the Pacific
+Standard time at which the sketches were made, and also
+the longitude of the meridian of Jupiter passing down the
+center of the planet's disk.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_86" id="Fig_86"></a>
+<a href="images/i247-full.jpg"><img src="images/i247.jpg" width="500" height="353" alt="Fig. 86.&mdash;Jupiter and his satellites." title="Fig. 86.&mdash;Jupiter and his satellites." /></a>
+<span class="caption"><span class="smcap">Fig. 86.</span>&mdash;Jupiter and his satellites.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_87" id="Fig_87"></a>
+<a href="images/i248.jpg"><img src="images/i248.jpg" width="500" height="826" alt="Fig. 87.&mdash;Drawings of Jupiter made at the 36-inch telescope of the Lick
+Observatory.&mdash;Keeler." title="Fig. 87.&mdash;Drawings of Jupiter made at the 36-inch telescope of the Lick
+Observatory.&mdash;Keeler." /></a>
+<span class="caption"><span class="smcap">Fig. 87.</span>&mdash;Drawings of Jupiter made at the 36-inch telescope of the Lick
+Observatory.&mdash;<span class="smcap">Keeler.</span></span>
+</div>
+
+<p>The dark bands are called technically the belts of Jupiter;
+and a comparison of these belts in the second and third
+pictures of the group, in which nearly the same face of the
+planet is turned toward us, will show that they are subject
+to considerable changes of form and position even within
+the space of a few days. So, too, by a comparison of such
+markings as the round white spots in the upper parts of
+the disks, and the indentations in the edges of the belts,
+we may recognize that the planet is in the act of turning
+round, and must therefore have an axis about which it
+turns, and poles, an equator, etc. The belts are in fact
+parallel to the planet's equator; and generalizing from what
+appears in the pictures, we may say that there is always a
+strongly marked belt on each side of the equator with a<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span><span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>
+lighter colored streak between them, and that farther from
+the equator are other belts variable in number, less conspicuous,
+and less permanent than the two first seen. Compare
+the position of the principal belts with the position of
+the zones of sun-spot activity in the sun. A feature of
+the planet's surface, which can not be here reproduced, is
+the rich color effect to be found upon it. The principal
+belts are a brick-red or salmon color, the intervening spaces
+in general white but richly mottled, and streaked with
+purples, browns, and greens.</p>
+
+<p>The drawings show the planet as it appeared in the
+telescope, inverted, and they must be turned upside down
+if we wish the points of the compass to appear as upon a
+terrestrial map. Bearing this in mind, note in the last
+picture the great oval spot in the southern hemisphere of
+Jupiter. This is a famous marking, known from its color
+as the <i>great red spot</i>, which appeared first in 1878 and has
+persisted to the present day (1900), sometimes the most
+conspicuous marking on the planet, at others reduced to a
+mere ghost of itself, almost invisible save for the indentation
+which it makes in the southern edge of the belt
+near it.</p>
+
+<p><a name="S_138" id="S_138"></a>138. <b>Rotation and flattening at the poles.</b>&mdash;One further
+significant fact with respect to Jupiter may be obtained
+from a careful measurement of the drawings; the planet is
+flattened at the poles, so that its polar diameter is about
+one sixteenth part shorter than the equatorial diameter.
+The flattening of the earth amounts to only one three-hundredth
+part, and the marked difference between these
+two numbers finds its explanation in the greater swiftness
+of Jupiter's rotation about its axis, since in both cases it is
+this rotation which makes the flattening.</p>
+
+<p>It is not easy to determine the precise dimensions of the
+planet, since this involves a knowledge both of its distance
+from us and of the angle subtended by its diameter, but
+the most recent determinations of this kind assign as the<span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span>
+equatorial diameter 90,200 miles, and for the polar diameter
+84,400 miles. Determine from either of these numbers
+the size of the great red spot.</p>
+
+<p>The earth turns on its axis once in 24 hours but no
+such definite time can be assigned to Jupiter, which, like
+the sun, seems to have different rotation periods in different
+latitudes&mdash;9h. 50m. in the equatorial belt and 9h. 56m.
+in the dark belts and higher latitudes. There is some indication
+that the larger part of the visible surface rotates in
+9h. 55.6m., while a broad stream along the equator flows
+eastward some 270 miles per hour, and thus comes back to
+the center of the planet, as seen from the earth, five or six
+minutes earlier than the parts which do not share in this
+motion. Judged by terrestrial standards, 270 miles per
+hour is a great velocity, but Jupiter is constructed on a
+colossal scale, and, too, we have to compare this movement,
+not to a current flowing in the ocean, but to a wind blowing
+in the upper regions of the earth's atmosphere. The
+visible surface of Jupiter is only the top of a cloud formation,
+and contains nothing solid or permanent, if indeed
+there is anything solid even at the core of the planet. The
+great red spot during the first dozen years of its existence,
+instead of remaining fixed relative to the surrounding formations,
+drifted two thirds of the way around the planet,
+and having come to a standstill about 1891, it is now slowly
+retracing its path.</p>
+
+<p><a name="S_139" id="S_139"></a>139. <b>Physical condition.</b>&mdash;For a better understanding of
+the physical condition of Jupiter, we have now to consider
+some independent lines of evidence which agree in pointing
+to the conclusion that Jupiter, although classed with
+the earth as a planet, is in its essential character much
+more like the sun.</p>
+
+<p><i>Appearance.</i>&mdash;The formations which we see in <a href="#Fig_87">Fig.&nbsp;87</a>
+look like clouds. They gather and disappear, and the only
+element of permanence about them is their tendency to
+group themselves along zones of latitude. If we measure<span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span>
+the light reflected from the planet we find that its albedo
+is very high, like that of snow or our own cumulus clouds,
+and it is of course greater from the light parts of the disk
+than from the darker bands. The spectroscope shows that
+the sunlight reflected from these darker belts is like that
+reflected from the lighter parts, save that a larger portion of
+the blue and violet rays has been absorbed out of it, thus
+producing the ruddy tint of the belts, as sunset colors are
+produced on the earth, and showing that here the light has
+penetrated farther into the planet's atmosphere before
+being thrown back by reflection from lower-lying cloud surfaces.
+The dark bands are therefore to be regarded as rifts
+in the clouds, reaching down to some considerable distance
+and indicating an atmosphere of great depth. The great
+red spot, 28,000 miles long, and obviously thrusting back
+the white clouds on every side of it, year after year, can
+hardly be a mere patch on the face of the planet, but indicates
+some considerable depth of atmosphere.</p>
+
+<p><i>Density.</i>&mdash;So, too, the small mean density of the planet,
+only 1.3 times that of water and actually less than the density
+of the sun, suggests that the larger part of the planet's
+bulk may be made of gases and clouds, with very little solid
+matter even at the center; but here we get into a difficulty
+from which there seems but one escape. The force of
+gravity at the visible surface of Jupiter may be found
+from its mass and dimensions to be 2.6 times as great as
+at the surface of the earth, and the pressure exerted upon
+its atmosphere by this force ought to compress the lower
+strata into something more dense than we find in the
+planet. Some idea of this compression may be obtained
+from <a href="#Fig_88">Fig.&nbsp;88</a>, where the line marked <i>E</i> shows approximately
+how the density of the air increases as we move from its
+upper strata down toward the surface of the earth through
+a distance of 16 miles, the density at any level being proportional
+to the distance of the curved line from the straight
+one near it. The line marked <i>J</i> in the same figure shows<span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span>
+how the density would increase if the force of gravity were
+as great here as it is in Jupiter, and indicates a much
+greater rate of increase. Starting from the upper surface
+of the cloud in Jupiter's atmosphere, if we descend,
+not 16 miles, but 1,600 or 16,000, what must the density
+of the atmosphere become and how is this to be
+reconciled with what we know to be the very small
+mean density of the planet?</p>
+
+<p>We are here in a dilemma between density on the
+one hand and the effects of gravity on the other, and
+the only escape from it lies in the assumption that
+the interior of Jupiter is tremendously hot, and that
+this heat expands the substance of the planet in spite
+of the pressure to which it is subject, making a large
+planet with a low density, possibly gaseous at
+the very center, but in its outer part surrounded
+by a shell of clouds condensed
+from the gases by
+radiating their heat into
+the cold of outer space.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_88" id="Fig_88"></a>
+<img src="images/i252.png" width="350" height="477" alt="Fig. 88.&mdash;Increase of density in the atmospheres
+of Jupiter and the earth." title="Fig. 88.&mdash;Increase of density in the atmospheres
+of Jupiter and the earth." />
+<span class="caption"><span class="smcap">Fig. 88.</span>&mdash;Increase of density in the atmospheres
+of Jupiter and the earth.</span>
+</div>
+
+<p>This is essentially the
+same physical condition
+that we found for the sun, and we may add, as further
+points of resemblance between it and Jupiter, that there
+seems to be a circulation of matter from the hot interior of
+the planet to its cooler surface that is more pronounced in
+the southern hemisphere than in the northern, and that has
+its periods of maximum and minimum activity, which, curiously
+enough, seem to coincide with periods of maximum
+and minimum sun-spot development. Of this, however, we
+can not be entirely sure, since it is only in recent years that
+it has been studied with sufficient care, and further observations
+are required to show whether the agreement is
+something more than an accidental and short-lived coincidence.</p>
+
+<p><i>Temperature.</i>&mdash;The temperature of Jupiter must, of<span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span>
+course, be much lower than that of the sun, since the surface
+which we see is not luminous like the sun's; but below
+the clouds it is not improbable that Jupiter may be incandescent,
+white hot, and it is surmised with some show of
+probability that a little of its light escapes through the
+clouds from time to time, and helps to produce the striking
+brilliancy with which this planet shines.</p>
+
+<p><a name="S_140" id="S_140"></a>140. <b>The satellites of Jupiter.</b>&mdash;The satellites bear much
+the same relation to Jupiter that the moon bears to the
+earth, revolving about the planet in accordance with the
+law of gravitation, and conforming to Kepler's three laws,
+as do the planets in their courses about the sun. Observe in
+<a href="#Fig_86">Fig.&nbsp;86</a> the position of satellite No.&nbsp;<i>1</i> on the four dates, and
+note how it oscillates back and forth from left to right of
+Jupiter, apparently making a complete revolution in about
+two days, while No.&nbsp;<i>4</i> moves steadily from left to right during
+the entire period, and has evidently made only a fraction
+of a revolution in the time covered by the pictures.
+This quicker motion, of course, means that No.&nbsp;<i>1</i> is nearer
+to Jupiter than No.&nbsp;<i>4</i>, and the numbers given to the satellites
+show the order of their distances from the planet.
+The peculiar way in which the satellites are grouped, always
+standing nearly in a straight line, shows that their orbits
+must lie nearly in the same plane, and that this plane, which
+is also the plane of the planets' equator, is turned edgewise
+toward the earth.</p>
+
+<p>These satellites enjoy the distinction of being the first
+objects ever discovered with the telescope, having been
+found by Galileo almost immediately after its invention,
+<span class="smcap">A.&nbsp;D.</span> 1610. It is quite possible that before this time they
+may have been seen with the naked eye, for in more recent
+years reports are current that they have been seen under
+favorable circumstances by sharp-eyed persons, and very
+little telescopic aid is required to show them. Look for
+them with an opera or field glass. They bear the names
+Io, Europa, Ganymede, Callisto, which, however, are rarely<span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span>
+used, and, following the custom of astronomers, we shall
+designate them by the Roman numerals I, II, III, IV.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_89" id="Fig_89"></a>
+<img src="images/i254.png" width="500" height="392" alt="Fig. 89.&mdash;Orbits of Jupiter&#39;s satellites." title="Fig. 89.&mdash;Orbits of Jupiter&#39;s satellites." />
+<span class="caption"><span class="smcap">Fig. 89.</span>&mdash;Orbits of Jupiter&#39;s satellites.</span>
+</div>
+
+<p>For nearly three centuries (1610 to 1892) astronomers
+spoke of the four satellites of Jupiter; but in September,
+1892, a fifth one was added to the number by Professor Barnard,
+who, observing with the largest telescope then extant,
+found very close to Jupiter a tiny object only 1/600 part as
+bright as the other satellites, but, like them, revolving around
+Jupiter, a permanent member of his system. This is called
+the fifth satellite, and <a href="#Fig_89">Fig.&nbsp;89</a> shows the orbits of these satellites
+around Jupiter, which is here represented on the same
+scale as the orbits themselves. The broken line just inside
+the orbit of I represents the size of the moon's orbit. The
+cut shows also the periodic times of the satellites expressed
+in days, and furnishes in this respect a striking illustration
+of the great mass of Jupiter. Satellite&nbsp;I is a little<span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span>
+farther from Jupiter than is the moon from the earth, but
+under the influence of a greater attraction it makes the circuit
+of its orbit in 1.77 days, instead of taking 29.53 days,
+as does the moon. Determine from the figure by the method
+employed in <a href="#S_111">§&nbsp;111</a> how much more massive is Jupiter than
+the earth.</p>
+
+<p>Small as these satellites seem in <a href="#Fig_86">Fig.&nbsp;86</a>, they are really
+bodies of considerable size, as appears from <a href="#Fig_90">Fig.&nbsp;90</a>, where
+their dimensions are compared with those of the earth
+and moon, save that the fifth satellite is not included.
+This one is so small as to escape all attempts at measuring
+its diameter, but, judging from the amount of light it reflects,
+the period printed with the legend of the figure
+represents a gross exaggeration of this satellite's size.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_90" id="Fig_90"></a>
+<img src="images/i255.png" width="500" height="165" alt="Fig. 90.&mdash;Jupiter&#39;s satellites compared with the earth and moon." title="Fig. 90.&mdash;Jupiter&#39;s satellites compared with the earth and moon." />
+<span class="caption"><span class="smcap">Fig. 90.</span>&mdash;Jupiter&#39;s satellites compared with the earth and moon.</span>
+</div>
+
+<p>Like the moon, each of these satellites may fairly be
+considered a world in itself, and as such a fitting object of
+detailed study, but, unfortunately, their great distance from
+us makes it impossible, even with the most powerful telescope,
+to see more upon their surfaces than occasional vague
+markings, which hardly suffice to show the rotations of the
+satellites upon their axes.</p>
+
+<p>One striking feature, however, comes out from a study
+of their influence in disturbing each other's motion about
+Jupiter. Their masses and the resulting densities of the
+satellites are smaller than we should have expected to find,
+the density being less than that of the moon, and averaging
+only a little greater than the density of Jupiter<span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span>
+itself. At the surface of the third satellite the force of
+gravity is but little less than on the moon, although the
+moon's density is nearly twice as great as that of III, and
+there can be no question here of accounting for the low
+density through expansion by great heat, as in the case of
+the sun and Jupiter. It has been surmised that these satellites
+are not solid bodies, like the earth and moon, but only
+shoals of rock and stone, loosely piled together and kept
+from packing into a solid mass by the action of Jupiter in
+raising tides within them. But the explanation can hardly
+be regarded as an accepted article of astronomical belief,
+although it is supported by some observations which tend
+to show that the apparent shapes of the satellites change under
+the influence of the tidal forces impressed upon them.</p>
+
+<p><a name="S_141" id="S_141"></a>141. <b>Eclipses of the satellites.</b>&mdash;It may be seen from <a href="#Fig_89">Fig.&nbsp;89</a>
+that in their motion around the planet Jupiter's satellites
+must from time to time pass through his shadow and be
+eclipsed, and that the shadows of the satellites will occasionally
+fall upon the planet, producing to an observer upon
+Jupiter an eclipse of the sun, but to an observer on the earth
+presenting only the appearance of a round black spot moving
+slowly across the face of the planet. Occasionally also
+a satellite will pass exactly between the earth and Jupiter,
+and may be seen projected against the planet as a background.
+All of these phenomena are duly predicted and
+observed by astronomers, but the eclipses are the only ones
+we need consider here. The importance of these eclipses
+was early recognized, and astronomers endeavored to construct
+a theory of their recurrence which would permit
+accurate predictions of them to be made. But in this they
+met with no great success, for while it was easy enough
+to foretell on what night an eclipse of a given satellite
+would occur, and even to assign the hour of the night, it
+was not possible to make the predicted minute agree with
+the actual time of eclipse until after Roemer, a Danish
+astronomer of the seventeenth century, found where lay the<span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span>
+trouble. His discovery was, that whenever the earth was
+on the side of its orbit toward Jupiter the eclipses really
+occurred before the predicted time, and when the earth
+was on the far side of its orbit they came a few minutes
+later than the predicted time. He correctly inferred that
+this was to be explained, not by any influence which the
+earth exerted upon Jupiter and his satellites, but through
+the fact that the light by which we see the satellite and its
+eclipse requires an appreciable time to cross the intervening
+space, and a longer time when the earth is far from
+Jupiter than when it is near.</p>
+
+<p>For half a century Roemer's views found little credence,
+but we know now that he was right, and that on the
+average the eclipses come 8m. 18s. early when the earth is
+nearest to Jupiter, and 8m. 18s. late when it is on the opposite
+side of its orbit. This is equivalent to saying that
+light takes 8m. 18s. to cover the distance from the sun to
+the earth, so that at any moment we see the sun not as it
+then is, but as it was 8 minutes earlier. It has been found
+possible in recent years to measure by direct experiment
+the velocity with which light travels&mdash;186,337 miles per
+second&mdash;and multiplying this number by the 498s. (= 8m.
+18s.) we obtain a new determination of the sun's distance
+from the earth. The product of the two numbers is
+92,795,826, in very fair agreement with the 93,000,000
+miles found in <a href="#CHAPTER_X">Chapter&nbsp;X</a>; but, as noted there, this method,
+like every other, has its weak side, and the result may be a
+good many thousands of miles in error.</p>
+
+<p>It is worthy of note in this connection that both methods
+of obtaining the sun's distance which were given in
+<a href="#CHAPTER_X">Chapter&nbsp;X</a> involve Kepler's Third Law, while the result
+obtained from Jupiter's satellites is entirely independent
+of this law, and the agreement of the several results is
+therefore good evidence both for the truth of Kepler's laws
+and for the soundness of Roemer's explanation of the
+eclipses. This mode of proof, by comparing the numerical<span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span>
+results furnished by two or more different principles, and
+showing that they agree or disagree, is of wide application
+and great importance in physical science.</p>
+
+
+<h3><span class="smcap">Saturn</span></h3>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_91" id="FIg_91"></a>
+<a href="images/i258-full.jpg"><img src="images/i258.jpg" width="350" height="492" alt="Fig. 91.&mdash;Aspects of Saturn&#39;s rings." title="Fig. 91.&mdash;Aspects of Saturn&#39;s rings." /></a>
+<span class="caption"><span class="smcap">Fig. 91.</span>&mdash;Aspects of Saturn&#39;s rings.</span>
+</div>
+
+<p><a name="S_142" id="S_142"></a>142. <b>The ring of Saturn.</b>&mdash;In respect of size and mass
+Saturn stands next to Jupiter, and although far inferior to
+him in these respects, it contains more material than all
+the remaining planets combined. But the unique feature
+of Saturn which distinguishes it from every other known
+body in the heavens is
+its ring, which was long
+a puzzle to the astronomers
+who first studied
+the planet with a telescope
+(one of them called
+Saturn a planet with
+ears), but, was after
+nearly half a century
+correctly understood and
+described by Huyghens,
+whose Latin text we
+translate into&mdash;"It is
+surrounded by a ring,
+thin, flat, nowhere touching
+it, and making quite
+an angle with the ecliptic."</p>
+
+<p>Compare with this
+description <a href="#Fig_91">Fig.&nbsp;91</a>, which shows some of the appearances
+presented by the ring at different positions of Saturn in
+its orbit. It was their varying aspects that led Huyghens
+to insert the last words of his description, for, if the plane
+of the ring coincided with the plane of the earth's orbit,
+then at all times the ring must be turned edgewise toward
+the earth, as shown in the middle picture of the group.<span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span>
+<a href="#Fig_92">Fig.&nbsp;92</a> shows the sun and the orbit of the earth placed
+near the center of Saturn's orbit, across whose circumference
+are ruled some oblique lines representing the plane
+of the ring, the right end always tilted up, no matter where
+the planet is in its orbit. It is evident that an observer
+upon the earth will see the <i>N</i> side of the ring when the
+planet is at <i>N</i> and the <i>S</i> side when it is at <i>S</i>, as is shown
+in the first and third pictures of <a href="#Fig_91">Fig.&nbsp;91</a>, while midway between
+these positions the edge of the ring will be presented
+to the earth.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_92" id="Fig_92"></a>
+<img src="images/i259.png" width="500" height="503" alt="Fig. 92.&mdash;Aspects of the ring in their relation to Saturn&#39;s orbital motion." title="Fig. 92.&mdash;Aspects of the ring in their relation to Saturn&#39;s orbital motion." />
+<span class="caption"><span class="smcap">Fig. 92.</span>&mdash;Aspects of the ring in their relation to Saturn&#39;s orbital motion.</span>
+</div>
+
+<p>The last occasion of this kind was in October, 1891, and
+with the large telescope of the Washburn Observatory the<span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span>
+writer at that time saw Saturn without a trace of a ring
+surrounding it. The ring is so thin that it disappears
+altogether when turned edgewise. The names of the zodiacal
+constellations are inserted in <a href="#Fig_92">Fig.&nbsp;92</a> in their proper
+direction from the sun, and from these we learn that the
+ring will disappear, or be exceedingly narrow, whenever
+Saturn is in the constellation Pisces or near the boundary
+line between Leo and Virgo. It will be broad and show its
+northern side when Saturn is in Scorpius or Sagittarius, and
+its southern face when the planet is in Gemini. What will
+be its appearance in 1907 at the date marked in the figure?</p>
+
+<p><a name="S_143" id="S_143"></a>143. <b>Nature of the ring.</b>&mdash;It is apparent from Figs.&nbsp;<a href="#Fig_91">91</a>
+and&nbsp;<a href="#Fig_93">93</a> that Saturn's ring is really made up of two or more
+rings lying one inside of the other and completely separated
+by a dark space which, though narrow, is as clean and
+sharp as if cut with a knife. Also, the inner edge of the
+ring fades off into an obscure border called the <i>dusky ring</i>
+or <i>crape ring</i>. This requires a pretty good telescope to
+show it, as may be inferred from the fact that it escaped
+notice for more than two centuries during which the planet
+was assiduously studied with telescopes, and was discovered
+at the Harvard College Observatory as recently as 1850.</p>
+
+<p>Although the rings appear oval in all of the pictures,
+this is mainly an effect of perspective, and they are in fact
+nearly circular with the planet at their center. The extreme
+diameter of the ring is 172,000 miles, and from this
+number, by methods already explained (<a href="#CHAPTER_IX">Chapter&nbsp;IX</a>), the
+student should obtain the width of the rings, their distance
+from the ball of the planet, and the diameter of the ball.
+As to thickness, it is evident, from the disappearance of the
+ring when its edge is turned toward the earth, that it is
+very thin in comparison with its diameter, probably not
+more than 100 miles thick, although no exact measurement
+of this can be made.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_93" id="Fig_93"></a>
+<a href="images/i261-full.jpg"><img src="images/i261.jpg" width="500" height="619" alt="Fig. 93.&mdash;Saturn." title="Fig. 93.&mdash;Saturn." /></a>
+<span class="caption"><span class="smcap">Fig. 93.</span>&mdash;Saturn.</span>
+</div>
+
+<p>From theoretical reasons based upon the law of gravitation
+astronomers have held that the rings of Saturn could<span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span>
+not possibly be solid or liquid bodies. The strains impressed
+upon them by the planet's attraction would tear
+into fragments steel rings made after their size and shape.
+Quite recently Professor Keeler has shown, by applying the
+spectroscope (Doppler's principle) to determine the velocity
+of the ring's rotation about Saturn, that the inner parts of
+the ring move, as Kepler's Third Law requires, more rapidly
+than do the outer parts, thus furnishing a direct proof that
+they are not solid, and leaving no doubt that they are made
+up of separate fragments, each moving about the planet in
+its own orbit, like an independent satellite, but standing so
+close to its neighbors that the whole space reflects the sunlight
+as completely as if it were solid. With this understanding
+of the rings it is easy to see why they are so thin.
+Like Jupiter, Saturn is greatly flattened at the poles, and
+this flattening, or rather the protuberant mass about the
+equator, lays hold of every satellite near the planet and
+exerts upon it a direct force tending to thrust it down
+into the plane of the planet's equator and hold it there.
+The ring lies in the plane of Saturn's equator because each
+particle is constrained to move there.</p>
+
+<p>The division of the ring into two parts, an outer and an
+inner ring, is usually explained as follows: Saturn is surrounded
+by a numerous brood of satellites, which by their
+attractions produce perturbations in the material composing
+the rings, and the dividing line between the outer and
+inner rings falls at the place where by the law of gravitation
+the perturbations would have their greatest effect.
+The dividing line between the rings is therefore a narrow
+lane, 2,400 miles wide, from which the fragments have been
+swept clean away by the perturbing action of the satellites.
+Less conspicuous divisions are seen from time to time in
+other parts of the ring, where the perturbations, though
+less, are still appreciable. But it is open to some question
+whether this explanation is sufficient.</p>
+
+<p>The curious darkness of the inner or crape ring is easily<span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span>
+explained. The particles composing it are not packed together
+so closely as in the outer ring, and therefore reflect
+less sunlight. Indeed, so sparsely strewn are the particles
+in this ring that it is in great measure transparent to the
+sunlight, as is shown by a recorded observation of one of the
+satellites which was distinctly although faintly seen while
+moving through the shadow of the dark ring, but disappeared
+in total eclipse when it entered the shadow cast by
+the bright ring.</p>
+
+<p><a name="S_144" id="S_144"></a>144. <b>The ball of Saturn.</b>&mdash;The ball of the planet is in
+most respects a smaller copy of Jupiter. With an equatorial
+diameter of 76,000 miles, a polar diameter of 69,000
+miles, and a mass 95 times that of the earth, its density
+is found to be the least of any planet in the solar system,
+only 0.70 of the density of water, and about one half as
+great as is the density of Jupiter. The force of gravity at
+its surface is only a little greater (1.18) than on the earth;
+and this, in connection with the low density, leads, as in the
+case of Jupiter, to the conclusion that the planet must be
+mainly composed of gases and vapors, very hot within, but
+inclosed by a shell of clouds which cuts off their glow from
+our eyes.</p>
+
+<p>Like Jupiter in another respect, the planet turns very
+swiftly upon its axis, making a revolution in 10 hours 14
+minutes, but up to the present it remains unknown whether
+different parts of the surface have different rotation times.</p>
+
+<p><a name="S_145" id="S_145"></a>145. <b>The satellites.</b>&mdash;Saturn is attended by a family of
+nine satellites, a larger number than belongs to any other
+planet, but with one exception they are exceedingly small
+and difficult to observe save with a very large telescope.
+Indeed, the latest one is said to have been discovered in
+1898 by means of the image which it impressed upon a
+photographic plate, and it has never been <i>seen</i>.</p>
+
+<p>Titan, the largest of them, is distant 771,000 miles from
+the planet and bears much the same relation to Saturn that
+Satellite&nbsp;III bears to Jupiter, the similarity in distance, size<span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span>
+and mass being rather striking, although, of course, the
+smaller mass of Saturn as compared with Jupiter makes the
+periodic time of Titan&mdash;15 days 23 hours&mdash;much greater
+than that of III. Can you apply Kepler's Third Law to
+the motion of Titan so as to determine from the data given
+above, the time required for a particle at the outer or inner
+edge of the ring to revolve once around Saturn?</p>
+
+<p>Japetus, the second satellite in point of size, whose distance
+from Saturn is about ten times as great as the moon's
+distance from the earth, presents the remarkable peculiarity
+of being always brighter in one part of its orbit than
+in another, three or four times as bright when west of
+Saturn as when east of it. This probably indicates that,
+like our own moon, the satellite turns always the same face
+toward its planet, and further, that one side of the satellite
+reflects the sunlight much better than the other side&mdash;i.&nbsp;e.,
+has a higher albedo. With these two assumptions it
+is easily seen that the satellite will always turn toward
+the earth one face when west, and the other face when
+east of Saturn, and thus give the observed difference of
+brightness.</p>
+
+
+<h3><span class="smcap">Uranus and Neptune</span></h3>
+
+<p><a name="S_146" id="S_146"></a>146. <b>Chief characteristics.</b>&mdash;The two remaining large
+planets are interesting chiefly as modern additions to the
+known members of the sun's family. The circumstances
+leading to the discovery of Neptune have been touched
+upon in <a href="#CHAPTER_IV">Chapter&nbsp;IV</a>, and for Uranus we need only note
+that it was found by accident in the year 1781 by William
+Herschel, who for some time after the discovery considered
+it to be only a comet. It was the first planet ever discovered,
+all of its predecessors having been known from prehistoric
+times.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="WILLIAM_HERSCHEL" id="WILLIAM_HERSCHEL"></a>
+<a href="images/i265-full.jpg"><img src="images/i265.jpg" width="500" height="693" alt="WILLIAM HERSCHEL (1738-1822)." title="WILLIAM HERSCHEL (1738-1822)." /></a>
+<span class="caption">WILLIAM HERSCHEL (1738-1822).</span>
+</div>
+
+<p>Uranus has four satellites, all of them very faint, which
+present only one feature of special importance. Instead of
+moving in orbits which are approximately parallel to the<span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span>
+plane of the ecliptic, as do the satellites of the inner planets,
+their orbit planes are tipped up nearly perpendicular to the
+planes of the orbits of both Uranus and the earth. The
+one satellite which Neptune possesses has the same peculiarity
+in even greater degree, for its motion around the
+planet takes place in the direction opposite to that in
+which all the planets move around the sun, much as if the
+orbit of the satellite had been tipped over through an angle
+of 150°. Turn a watch face down and note how the hands
+go round in the direction opposite to that in which they
+moved before the face was turned through 180°.</p>
+
+<p>Both Uranus and Neptune are too distant to allow
+much detail to be seen upon their surfaces, but the presence
+of broad absorption bands in their spectra shows that
+they must possess dense atmospheres quite different in constitution
+from the atmosphere of the earth. In respect of
+density and the force of gravity at their surfaces, they are
+not very unlike Saturn, although their density is greater
+and gravity less than his, leading to the supposition that
+they are for the most part gaseous bodies, but cooler and
+probably more nearly solid than either Jupiter or Saturn.</p>
+
+<p>Under favorable circumstances Uranus may be seen
+with the naked eye by one who knows just where to look
+for it. Neptune is never visible save in a telescope.</p>
+
+<p><a name="S_147" id="S_147"></a>147. <b>The inner planets.</b>&mdash;In sharp contrast with the giant
+planets which we have been considering stands the group
+of four inner planets, or five if we count the moon as an
+independent body, which resemble each other in being all
+small, dense, and solid bodies, which by comparison with
+the great distances separating the outer planets may fairly
+be described as huddled together close to the sun. Their
+relative sizes are shown in <a href="#Fig_84">Fig.&nbsp;84</a>, together with the numerical
+data concerning size, mass, density, etc., which we
+have already found important for the understanding of a
+planet's physical condition.<span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span></p>
+
+
+<h3><span class="smcap">Venus</span></h3>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_94" id="Fig_94"></a>
+<a href="images/i268-full.jpg"><img src="images/i268.jpg" width="500" height="345" alt="Fig. 94.&mdash;The phases of Venus.&mdash;Antoniadi." title="Fig. 94.&mdash;The phases of Venus.&mdash;Antoniadi." /></a>
+<span class="caption"><span class="smcap">Fig. 94.</span>&mdash;The phases of Venus.&mdash;<span class="smcap">Antoniadi.</span></span>
+</div>
+
+<p><a name="S_148" id="S_148"></a>148. <b>Appearance.</b>&mdash;Omitting the earth, Venus is by far
+the most conspicuous member of this group, and when at its
+brightest is, with exception of the sun and moon, the most
+brilliant object in the sky, and may be seen with the naked
+eye in broad daylight if the observer knows just where to
+look for it. But its brilliancy is subject to considerable
+variations on account of its changing distance from the
+earth, and the apparent size of its disk varies for the same
+reason, as may be seen from <a href="#Fig_94">Fig.&nbsp;94</a>. These drawings bring
+out well the phases of the planet, and the student should
+determine from <a href="#Fig_17">Fig.&nbsp;17</a> what are the relative positions in
+their orbits of the earth and Venus at which the planet
+would present each of these phases. As a guide to this,
+observe that the dark part of Venus's earthward side is
+always proportional in area to the angle at Venus between
+the earth and sun. In the first picture of <a href="#Fig_94">Fig.&nbsp;94</a> about<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span>
+two thirds of the surface corresponding to the full hemisphere
+of the planet is dark, and the angle at Venus
+between earth and sun is therefore two thirds of 180°&mdash;i.&nbsp;e.,
+120°. In <a href="#Fig_17">Fig.&nbsp;17</a> find a place on the orbit of Venus from
+which if lines be drawn to the sun and earth, as there
+shown, the angle between them will be 120°. Make a similar
+construction for the fourth picture in <a href="#Fig_94">Fig.&nbsp;94</a>. Which
+of these two positions is farther from the earth? How do
+the distances compare with the apparent size of Venus in
+the two pictures? What is the phase of Venus to-day?</p>
+
+<p>The irregularities in the shading of the illuminated
+parts of the disk are too conspicuous in <a href="#Fig_94">Fig.&nbsp;94</a>, on account
+of difficulties of reproduction; these shadings are at the
+best hard to see in the telescope, and distinct permanent
+markings upon the planet are wholly lacking. This absence
+of markings makes almost impossible a determination of
+the planet's time of rotation about its axis, and astronomers
+are divided in this respect into two parties, one of
+which maintains that Venus, like the earth, turns upon its
+axis in some period not very different from 24 hours, while
+the other contends that, like the moon, it turns always the
+same face toward the center of its orbit, making a rotation
+upon its axis in the same period in which it makes a revolution
+about the sun. The reason why no permanent markings
+are to be seen on this planet is easily found. Like
+Jupiter and Saturn, its atmosphere is at all times heavily
+cloud-laden, so that we seldom, if ever, see down to the
+level of its solid parts. There is, however, no reason here
+to suppose the interior parts hot and gaseous. It is much
+more probable that Venus, like the earth, possesses a solid
+crust whose temperature we should expect to be considerably
+higher than that of the earth, because Venus is nearer
+the sun. But the cloud layer in its atmosphere must modify
+the temperature in some degree, and we have practically
+no knowledge of the real temperature conditions at the
+surface of the planet.<span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span></p>
+
+<p>It is the clouds of Venus which in great measure are
+responsible for its marked brilliancy, since they are an excellent
+medium for reflecting the sunlight, and give to its
+surface an albedo greater than that of any other planet,
+although Saturn is nearly equal to it.</p>
+
+<p>Of course, the presence of such cloud formations indicates
+that Venus is surrounded by a dense atmosphere, and
+we have independent evidence of this in the shape of its
+disk when the planet is very nearly between the earth and
+sun. The illuminated part, from tip to tip of the horns,
+then stretches more than halfway around the planet's circumference,
+and shows that a certain amount of light must
+have been refracted through its atmosphere, thus making
+the horns of the crescent appear unduly prolonged. This
+atmosphere is shown by the spectroscope to be not unlike
+that of the earth, although, possibly, more dense.</p>
+
+
+<h3><span class="smcap">Mercury</span></h3>
+
+<p><a name="S_149" id="S_149"></a>149. <b>Chief characteristics.</b>&mdash;Mercury, on account of its
+nearness to the sun, is at all times a difficult object to observe,
+and Copernicus, who spent most of his life in Poland,
+is said, despite all his efforts, to have gone to his grave without
+ever seeing it. In our more southern latitude it can
+usually be seen for about a fortnight at the time of each
+elongation&mdash;i.&nbsp;e., when at its greatest angular distance from
+the sun&mdash;and the student should find from <a href="#Fig_16">Fig.&nbsp;16</a> the time
+at which the next elongation occurs and look for the planet,
+shining like a star of the first magnitude, low down in the
+sky just after sunset or before sunrise, according as the
+elongation is to the east or west of the sun. When seen in
+the morning sky the planet grows brighter day after day
+until it disappears in the sun's rays, while in the evening
+sky its brilliancy as steadily diminishes until the planet is
+lost. It should therefore be looked for in the evening as
+soon as possible after it emerges from the sun's rays.</p>
+
+<p>Mercury, as the smallest of the planets, is best compared<span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span>
+with the moon, which it does not greatly surpass in size
+and which it strongly resembles in other respects. Careful
+comparisons of the amount of light reflected by the planet
+in different parts of its orbit show not only that its albedo
+agrees very closely with that of the moon, but also that its
+light changes with the varying phase of the planet in almost
+exactly the same way as the amount of moonlight
+changes. We may therefore infer that its surface is like
+that of the moon, a rough and solid one, with few or no
+clouds hanging over it, and most probably covered with
+very little or no atmosphere. Like Venus, its rotation period
+is uncertain, with the balance of probability favoring
+the view that it rotates upon its axis once in 88 days, and
+therefore always turns the same face toward the sun.</p>
+
+<p>If such is the case, its climate must be very peculiar:
+one side roasted in a perpetual day, where the direct heating
+power of the sun's rays, when the planet is at perihelion,
+is ten times as great as on the moon, and which six weeks
+later, when the planet is at its farthest from the sun, has
+fallen off to less than half of this. On the opposite side of
+the planet there must reign perpetual night and perpetual
+cold, mitigated by some slight access of warmth from the
+day side, and perhaps feebly imitating the rapid change of
+season which takes place on the day side of the planet.
+This view, however, takes no account of a possible deviation
+of the planet's axis from being perpendicular to the
+plane of its orbit, or of the librations which must be produced
+by the great eccentricity of the orbit, either of which
+would complicate without entirely destroying the ideal
+conditions outlined above.</p>
+
+
+<h3><span class="smcap">Mars</span></h3>
+
+<p><a name="S_150" id="S_150"></a>150. <b>Appearance.</b>&mdash;The one remaining member of the
+inner group, Mars, has in recent years received more attention
+than any other planet, and the newspapers and magazines
+have announced marvelous things concerning it: that<span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span>
+it is inhabited by a race of beings superior in intelligence
+to men; that the work of their hands may be seen upon
+the face of the planet; that we should endeavor to communicate
+with them, if indeed they are not already sending
+messages to us, etc.&mdash;all of which is certainly important,
+if true, but it rests upon a very slender foundation of evidence,
+a part of which we shall have to consider.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_95" id="Fig_95"></a>
+<a href="images/i272.jpg"><img src="images/i272.jpg" width="350" height="440" alt="Fig. 95.&mdash;Mars.&mdash;Schaeberle." title="Fig. 95.&mdash;Mars.&mdash;Schaeberle." /></a>
+<span class="caption"><span class="smcap">Fig. 95.</span>&mdash;Mars.&mdash;<span class="smcap">Schaeberle.</span></span>
+</div>
+
+<p>Beginning with facts of which there is no doubt, this
+ruddy-colored planet, which usually shines about as brightly
+as a star of the first magnitude,
+sometimes displays
+more than tenfold
+this brilliancy, surpassing
+every other planet
+save Venus and presenting
+at these times especially
+favorable opportunities
+for the study of
+its surface. The explanation
+of this increase
+of brilliancy is, of course,
+that the planet approaches
+unusually near to the
+earth, and we have already
+seen from a consideration
+of <a href="#Fig_17">Fig.&nbsp;17</a>
+that this can only happen
+in the months of August and September. The last
+favorable epoch of this kind was in 1894. From <a href="#Fig_17">Fig.&nbsp;17</a>
+the student should determine when the next one will
+come.</p>
+
+<p><a href="#Fig_95">Fig.&nbsp;95</a> presents nine drawings of the planet made at
+one of the epochs of close approach to the earth, and shows
+that its face bears certain faint markings which, though
+inconspicuous, are fixed and permanent features of the
+planet. The dark triangular projection in the lower half<span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span>
+of the second drawing was seen and sketched by Huyghens,
+1659 <span class="smcap">A.&nbsp;D.</span> In <a href="#Fig_96">Fig.&nbsp;96</a> some of these markings are shown
+much more plainly, but <a href="#Fig_95">Fig.&nbsp;95</a> gives a better idea of their
+usual appearance in the telescope.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_96" id="Fig_96"></a>
+<a href="images/i273.jpg"><img src="images/i273.jpg" width="350" height="385" alt="Fig. 96.&mdash;Four views of Mars differing 90° in
+longitude.&mdash;Barnard." title="Fig. 96.&mdash;Four views of Mars differing 90° in
+longitude.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 96.</span>&mdash;Four views of Mars differing 90° in
+longitude.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_151" id="S_151"></a>151. <b>Rotation.</b>&mdash;It may be seen readily enough, from a
+comparison of the first two sketches of <a href="#Fig_95">Fig.&nbsp;95</a>, that the
+planet rotates about an
+axis, and from a more
+extensive study it is
+found to be very like
+the earth in this respect,
+turning once in
+24h. 37m. around an
+axis tipped from being
+perpendicular to the
+plane of its orbit about
+a degree and a half
+more than is the earth's
+axis. Since it is this
+inclination of the axis
+which is the cause of
+changing seasons upon
+the earth, there must
+be similar changes,
+winter and summer, as well as day and night, upon Mars,
+only each season is longer there than here in the same proportion
+that its year is longer than ours&mdash;i&nbsp; e., nearly two
+to one. It is summer in the northern hemisphere of Mars
+whenever the sun, as seen from Mars, stands in that constellation
+which is nearest the point of the sky toward
+which the planet's axis points. But this axis points toward
+the constellation Cygnus, and Alpha Cygni is the bright
+star nearest the north pole of Mars. As Pisces is the
+zodiacal constellation nearest to Cygnus, it must be summer
+in the northern hemisphere of Mars when the sun is in
+Pisces, or, turning the proposition about, it must be summer<span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span>
+in the <i>southern</i> hemisphere of Mars when the planet, as
+seen from the sun, lies in the direction of Pisces.</p>
+
+<p><a name="S_152" id="S_152"></a>152. <b>The polar caps.</b>&mdash;One effect of the changing seasons
+upon Mars is shown in <a href="#Fig_97">Fig.&nbsp;97</a>, where we have a series of
+drawings of the region about its south pole made in 1894,
+on dates between May 21st and December 10th. Show
+from <a href="#Fig_17">Fig.&nbsp;17</a> that during this time it was summer in the
+region here shown. Mars crossed the prime radius in 1894
+on September 5th. The striking thing in these pictures is
+the white spot surrounding the pole, which shrinks in size
+from the beginning to
+near the end of the series,
+and then disappears
+altogether. The spot
+came back again a year
+later, and like a similar
+spot at the north pole of
+the planet it waxes in the
+winter and wanes during
+the summer of Mars in
+endless succession.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_97" id="Fig_97"></a>
+<a href="images/i274-full.jpg"><img src="images/i274.jpg" width="350" height="418" alt="Fig. 97.&mdash;The south polar cap of Mars in
+1894.&mdash;Barnard." title="Fig. 97.&mdash;The south polar cap of Mars in
+1894.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 97.</span>&mdash;The south polar cap of Mars in
+1894.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p>Sir W.&nbsp;Herschel, who
+studied these appearances
+a century ago, compared
+them with the snow
+fields which every winter
+spread out from the region
+around the terrestrial
+pole, and in the summer melt and shrink, although
+with us they do not entirely disappear. This explanation of
+the polar caps of Mars has been generally accepted among
+astronomers, and from it we may draw one interesting conclusion:
+the temperature upon Mars between summer and
+winter oscillates above and below the freezing point of
+water, as it does in the temperate zones of the earth. But
+this conclusion plunges us into a serious difficulty. The<span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span>
+temperature of the earth is made by the sun, and at the
+distance of Mars from the sun the heating effect of the
+latter is reduced to less than half what it is at the earth,
+so that, if Mars is to be kept at the same temperature as
+the earth, there must be some peculiar means for storing
+the solar heat and using it more economically than is done
+here. Possibly there is some such mechanism, although
+no one has yet found it, and some astronomers are very
+confident that it does not exist, and assert that the comparison
+of the polar caps with snow fields is misleading,
+and that the temperature upon Mars must be at least 100°,
+and perhaps 200° or more, below zero.</p>
+
+<p><a name="S_153" id="S_153"></a>153. <b>Atmosphere and climate.</b>&mdash;In this connection one
+feature of Mars is of importance. The markings upon its
+surface are always visible when turned toward the earth,
+thus showing that the atmosphere contains no such amount
+of cloud as does our own, but on the whole is decidedly
+clear and sunny, and presumably much less dense than
+ours. We have seen in comparing the earth and the moon
+how important is the service which the earth's atmosphere
+renders in storing the sun's heat and checking those great
+vicissitudes of temperature to which the moon is subject;
+and with this in mind we must regard the smaller density
+and cloudless character of the atmosphere of Mars as unfavorable
+to the maintenance there of a temperature like
+that of the earth. Indeed, this cloudlessness must mean
+one of two things: either the temperature is so low that
+vapors can not exist in any considerable quantity, or the
+surface of Mars is so dry that there is little water or other
+liquid to be evaporated. The latter alternative is adopted
+by those astronomers who look upon the polar caps as true
+snow fields, which serve as the chief reservoir of the planet's
+water supply, and who find in <a href="#Fig_98">Fig.&nbsp;98</a> evidence that as the
+snow melts and the water flows away over the flat, dry surface
+of the planet, vegetation springs up, as shown by the
+dark markings on the disk, and gradually dies out with<span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span>
+the advancing season. Note that in the first of these pictures
+the season upon Mars corresponds to the end of May
+with us, and in the last picture to the beginning of August,
+a period during which in much of our western country the
+luxuriant vegetation of spring is burned out by the scorching
+sun. From this point of view the permanent dark
+spots are the low-lying parts of the planet's surface, in
+which at all times there is a sufficient accumulation of
+water to support vegetable life.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_98" id="Fig_98"></a>
+<a href="images/i276.jpg"><img src="images/i276.jpg" width="500" height="253" alt="Fig. 98.&mdash;The same face of Mars at three different seasons.&mdash;Lowell." title="Fig. 98.&mdash;The same face of Mars at three different seasons.&mdash;Lowell." /></a>
+<span class="caption"><span class="smcap">Fig. 98.</span>&mdash;The same face of Mars at three different seasons.&mdash;<span class="smcap">Lowell.</span></span>
+</div>
+
+<p><a name="S_154" id="S_154"></a>154. <b>The canals.</b>&mdash;In <a href="#Fig_98">Fig.&nbsp;98</a> the lower part of the disk
+of Mars shows certain faint dark lines which are generally
+called canals, and in <a href="#PLATE_III">Plate&nbsp;III</a> there is given a map of Mars
+showing many of these canals running in narrow, dusky
+streaks across the face of the planet according to a pattern
+almost as geometrical as that of a spider's web. This must
+not be taken for a picture of the planet's appearance in a
+telescope. No man ever saw Mars look like this, but the
+map is useful as a plain representation of things dimly
+seen. Some of the regions of this map are marked Mare
+(sea), in accordance with the older view which regarded
+the darker parts of the planet&mdash;and of the moon&mdash;as bodies
+of water, but this is now known to be an error in both
+cases. The curved surface of a planet can not be accurately
+reproduced upon the flat surface of paper, but is always
+more or less distorted by the various methods of "projecting"
+it which are in use. Compare the map of Mars in<span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span>
+<a href="#PLATE_III">Plate&nbsp;III</a> with <a href="#Fig_99">Fig.&nbsp;99</a>, in which the projection represents
+very well the equatorial parts of the planet, but enormously
+exaggerates the region around the poles.</p>
+
+<p>It is a remarkable feature of the canals that they all
+begin and end in one of these dark parts of the planet's
+surface; they show no loose ends lying on the bright parts
+of the planet. Another even more remarkable feature is
+that while the larger canals are permanent features of the
+planet's surface, they at times appear "doubled"&mdash;i.&nbsp;e., in
+place of one canal two parallel ones side by side, lasting
+for a time and then giving place again to a single canal.</p>
+
+<p>It is exceedingly difficult to frame any reasonable explanation
+of these canals and the varied appearances which
+they present. The source of the wild speculations about
+Mars, to which reference is made above, is to be found in
+the suggestion frequently made, half in jest and half in
+earnest, that the canals are artificial water courses constructed
+upon a scale vastly exceeding any public works
+upon the earth, and testifying to the presence in Mars of
+an advanced civilization. The distinguished Italian astronomer,
+Schiaparelli, who has studied these formations
+longer than any one else, seems inclined to regard them as
+water courses lined on either side by vegetation, which
+flourishes as far back from the central channel as water
+can be supplied from it&mdash;a plausible enough explanation if
+the fundamental difficulty about temperature can be overcome.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_99" id="Fig_99"></a>
+<img src="images/i278.jpg" width="600" height="308" alt="Fig. 99.&mdash;A chart of Mars, 1898-&#39;99.&mdash;Cerulli." title="Fig. 99.&mdash;A chart of Mars, 1898-&#39;99.&mdash;Cerulli." />
+<span class="caption"><span class="smcap">Fig. 99.</span>&mdash;A chart of Mars, 1898-&#39;99.&mdash;<span class="smcap">Cerulli.</span></span>
+</div>
+
+<div class="figcenter" style="width: 600px;"><a name="PLATE_III" id="PLATE_III"></a>
+<a href="images/i279-full.jpg"><img src="images/i279.jpg" width="600" height="328" alt="PLATE III.
+
+MAP OF MARS
+
+(AFTER SCHIAPARELLI)" title="PLATE III.
+
+MAP OF MARS
+
+(AFTER SCHIAPARELLI)" /></a>
+<span class="caption">PLATE III.
+
+MAP OF MARS
+
+(AFTER SCHIAPARELLI)</span>
+</div>
+
+<p><a name="S_155" id="S_155"></a>155. <b>Satellites.</b>&mdash;In 1877, one of the times of near approach,
+Professor Hall, of Washington, discovered two tiny
+satellites revolving about Mars in orbits so small that the
+nearer one, Phobos, presents the remarkable anomaly of
+completing the circuit of its orbit in less time than the
+planet takes for a rotation about its axis. This satellite, in
+fact, makes three revolutions in its orbit while the planet
+turns once upon its axis, and it therefore rises in the west
+and sets in the east, as seen from Mars, going from one<span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a><a name="Page_246" id="Page_246"></a></span>
+horizon to the other in a little less than 6 hours. The
+other satellite, Deimos, takes a few hours more than a day
+to make the circuit of its orbit, but the difference is so
+small that it remains continuously above the horizon of
+any given place upon Mars for more than 60 hours at a
+time, and during this period runs twice through its complete
+set of phases&mdash;new, first quarter, full, etc. In ordinary
+telescopes these satellites can be seen only under especially
+favorable circumstances, and are far too small to
+permit of any direct measurement of their size. The
+amount of light which they reflect has been compared
+with that of Mars and found to be as much inferior to it
+as is Polaris to two full moons, and, judging from this comparison,
+their diameters can not much exceed a half dozen
+miles, unless their albedo is far less than that of Mars,
+which does not seem probable.</p>
+
+
+<h3><span class="smcap">The Asteroids</span></h3>
+
+<p><a name="S_156" id="S_156"></a>156. <b>Minor planets.</b>&mdash;These may be dismissed with few
+words. There are about 500 of them known, all discovered
+since the beginning of the nineteenth century, and new
+ones are still found every year. No one pretends to
+remember the names which have been assigned them, and
+they are commonly represented by a number inclosed in a
+circle, showing the order in which they were discovered&mdash;e.&nbsp;g.,
+&#10112;&nbsp;= Ceres, [circle 433]&nbsp;= Eros, etc. For the most part they
+are little more than chips, world fragments, adrift in space,
+and naturally it was the larger and brighter of them that
+were first discovered. The size of the first four of them&mdash;Ceres,
+Pallas, Juno, and Vesta&mdash;compared with the size of
+the moon, according to Professor Barnard, is shown in <a href="#Fig_100">Fig.&nbsp;100</a>.
+The great majority of them must be much smaller
+than the smallest of these, perhaps not more than a score
+of miles in diameter.</p>
+
+<p>A few of the asteroids present problems of special interest,
+such as Eros, on account of its close approach to the<span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span>
+earth; Polyhymnia, whose very eccentric orbit makes it a
+valuable means for determining the mass of Jupiter, etc.;
+but these are special cases and the average asteroid now
+receives scant attention, although half a century ago, when
+only a few of them were known, they were regarded with
+much interest, and the discovery of a new one was an event
+of some consequence.</p>
+
+<p>It was then a favorite speculation that they were in fact
+fragments of an ill-fated planet which once filled the gap
+between the orbits of Mars
+and Jupiter, but which, by
+some mischance, had been
+blown into pieces. This is
+now known to be well-nigh
+impossible, for every fragment
+which after the explosion
+moved in an elliptical
+orbit, as all the asteroids do
+move, would be brought
+back once in every revolution
+to the place of the explosion,
+and all the asteroid
+orbits must therefore intersect
+at this place. But there is no such common point of
+intersection.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_100" id="Fig_100"></a>
+<img src="images/i282.png" width="350" height="343" alt="Fig. 100.&mdash;The size of the first four
+asteroids.&mdash;Barnard." title="Fig. 100.&mdash;The size of the first four
+asteroids.&mdash;Barnard." />
+<span class="caption"><span class="smcap">Fig. 100.</span>&mdash;The size of the first four
+asteroids.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_157" id="S_157"></a>157. <b>Life on the planets.</b>&mdash;There is a belief firmly
+grounded in the popular mind, and not without its advocates
+among professional astronomers, that the planets
+are inhabited by living and intelligent beings, and it seems
+proper at the close of this chapter to inquire briefly how
+far the facts and principles here developed are consistent
+with this belief, and what support, if any, they lend to it.</p>
+
+<p>At the outset we must observe that the word life is an
+elastic term, hard to define in any satisfactory way, and yet
+standing for something which we know here upon the
+earth. It is this idea, our familiar though crude knowledge<span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span>
+of life, which lies at the root of the matter. Life, if
+it exists in another planet, must be in its essential character
+like life upon the earth, and must at least possess
+those features which are common to all forms of terrestrial
+life. It is an abuse of language to say that life in Mars
+may be utterly unlike life in the earth; if it is absolutely
+unlike, it is not life, whatever else it may be. Now, every
+form of life found upon the earth has for its physical basis
+a certain chemical compound, called protoplasm, which
+can exist and perpetuate itself only within a narrow range
+of temperature, roughly speaking, between 0° and 100°
+centigrade, although these limits can be considerably overstepped
+for short periods of time. Moreover, this protoplasm
+can be active only in the presence of water, or water
+vapor, and we may therefore establish as the necessary conditions
+for the continued existence and reproduction of
+life in any place that its temperature must not be permanently
+above 100° or below 0°, C., and water must be present
+in that place in some form.</p>
+
+<p>With these conditions before us it is plain that life can
+not exist in the sun on account of its high temperature.
+It is conceivable that active and intelligent beings, salamanders,
+might exist there, but they could not properly be said
+to live. In Jupiter and Saturn the same condition of high
+temperature prevails, and probably also in Uranus and
+Neptune, so that it seems highly improbable that any of
+these planets should be the home of life.</p>
+
+<p>Of the inner planets, Mercury and the moon seem destitute
+of any considerable atmospheres, and are therefore
+lacking in the supply of water necessary for life, and the
+same is almost certainly true of all the asteroids. There
+remain Venus, Mars, and the satellites of the outer planets,
+which latter, however, we must drop from consideration as
+being too little known. On Venus there is an atmosphere
+probably containing vapor of water, and it is well within
+the range of possibility that liquid water should exist upon<span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span>
+the surface of this planet and that its temperature should
+fall within the prescribed limits. It would, however, be
+straining our actual knowledge to affirm that such is the
+case, or to insist that if such were the case, life would necessarily
+exist upon the planet.</p>
+
+<p>On Mars we encounter the fundamental difficulty of
+temperature already noted in <a href="#S_152">§&nbsp;152</a>. If in some unknown
+way the temperature is maintained sufficiently high for the
+polar caps to be real snow, thawing and forming again with
+the progress of the seasons, the necessary conditions of life
+would seem to be fulfilled here and life if once introduced
+upon the planet might abide and flourish. But of positive
+proof that such is the case we have none.</p>
+
+<p>On the whole, our survey lends little encouragement to
+the belief in planetary life, for aside from the earth, of all
+the hundreds of bodies in the solar system, not one is found
+in which the necessary conditions of life are certainly fulfilled,
+and only two exist in which there is a reasonable
+probability that these conditions may be satisfied.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p>
+<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII</h2>
+
+<h3>COMETS AND METEORS</h3>
+
+
+<p><a name="S_158" id="S_158"></a>158. <b>Visitors in the solar system.</b>&mdash;All of the objects&mdash;sun,
+moon, planets, stars&mdash;which we have thus far had to
+consider, are permanent citizens of the sky, and we have no
+reason to suppose that their present appearance differs appreciably
+from what it was 1,000 years or 10,000 years ago.
+But there is another class of objects&mdash;comets, meteors&mdash;which
+appear unexpectedly, are visible for a time, and then
+vanish and are seen no more. On account of this temporary
+character the astronomers of ancient and medięval times
+for the most part refused to regard them as celestial bodies
+but classed them along with clouds, fogs, Jack-o'-lanterns,
+and fireflies, as exhalations from the swamps or the volcano;
+admitting them to be indeed important as harbingers
+of evil to mankind, but having no especial significance for
+the astronomer.</p>
+
+<p>The comet of 1618 <span class="smcap">A.&nbsp;D.</span> inspired the lines&mdash;</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Eight things there be a Comet brings,<br /></span>
+<span class="i1">When it on high doth horrid range:<br /></span>
+<span class="i0">Wind, Famine, Plague, and Death to Kings,<br /></span>
+<span class="i1">War, Earthquakes, Floods, and Direful Change,"<br /></span>
+</div></div>
+
+<p>which, according to White (History of the Doctrine of
+Comets), were to be taught in all seriousness to peasants
+and school children.</p>
+
+<p>It was by slow degrees, and only after direct measurements
+of parallax had shown some of them to be more distant
+than the moon, that the tide of old opinion was turned
+and comets were transferred from the sublunary to the<span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span>
+celestial sphere, and in more recent times meteors also
+have been recognized as coming to us from outside the
+earth. A meteor, or shooting star as it is often called, is
+one of the commonest of phenomena, and one can hardly
+watch the sky for an hour on any clear and moonless night
+without seeing several of those quick flashes of light which
+look as if some star had suddenly left its place, dashed
+swiftly across a portion of the sky and then vanished. It
+is this misleading appearance that probably is responsible
+for the name shooting star.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_101" id="Fig_101"></a>
+<a href="images/i286.jpg"><img src="images/i286.jpg" width="500" height="362" alt="Fig. 101.&mdash;Donati&#39;s comet.&mdash;Bond." title="Fig. 101.&mdash;Donati&#39;s comet.&mdash;Bond." /></a>
+<span class="caption"><span class="smcap">Fig. 101.</span>&mdash;Donati&#39;s comet.&mdash;<span class="smcap">Bond.</span></span>
+</div>
+
+<p><a name="S_159" id="S_159"></a>159. <b>Comets.</b>&mdash;Comets are less common and much longer-lived
+than meteors, lasting usually for several weeks, and
+may be visible night after night for many months, but
+never for many years, at a time. During the last decade
+there is no year in which less than three comets have
+appeared, and 1898 is distinguished by the discovery of
+ten of these bodies, the largest number ever found in
+one year. On the average, we may expect a new comet to<span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span>
+be found about once in every ten weeks, but for the most
+part they are small affairs, visible only in the telescope, and
+a fine large one, like Donati's comet of 1858 (<a href="#Fig_101">Fig.&nbsp;101</a>), or
+the Great Comet of September,
+1882, which was visible in
+broad daylight close beside the
+sun, is a rare spectacle, and as
+striking and impressive as it
+is rare.</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_102" id="Fig_102"></a>
+<a href="images/i287.jpg"><img src="images/i287.jpg" width="300" height="455" alt="Fig. 102.&mdash;Some famous comets." title="Fig. 102.&mdash;Some famous comets." /></a>
+<span class="caption"><span class="smcap">Fig. 102.</span>&mdash;Some famous comets.</span>
+</div>
+
+<p>Note in <a href="#Fig_102">Fig.&nbsp;102</a> the great
+variety of aspect presented
+by some of the more famous
+comets, which are here represented
+upon a very small scale.</p>
+
+<p><a href="#Fig_103">Fig.&nbsp;103</a> is from a photograph
+of one of the faint
+comets of the year 1893, which
+appears here as a rather feeble
+streak of light amid the stars
+which are scattered over the
+background of the picture.
+An apparently detached portion of this comet is shown at
+the extreme left of the picture, looking almost like another
+independent comet. The clean, straight line running diagonally
+across the picture is the flash of a bright meteor
+that chanced to pass within the range of the camera while
+the comet was being photographed.</p>
+
+
+<div class="figleft" style="width: 350px;"><a name="Fig_103" id="Fig_103"></a>
+<a href="images/i288-full.jpg"><img src="images/i288.jpg" width="350" height="397" alt="Fig. 103.&mdash;Brooks&#39;s comet, November 13, 1893.
+Barnard." title="Fig. 103.&mdash;Brooks&#39;s comet, November 13, 1893. Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 103.</span>&mdash;Brooks&#39;s comet, November 13, 1893.
+<span class="smcap">Barnard.</span></span>
+</div>
+
+
+<p>A more striking representation of a moderately bright
+telescopic comet is contained in Figs.&nbsp;<a href="#Fig_104">104</a> and&nbsp;<a href="#Fig_105">105</a>, which
+present two different views of the same comet, showing a
+considerable change in its appearance. A striking feature
+of <a href="#Fig_105">Fig.&nbsp;105</a> is the star images, which are here drawn out into
+short lines all parallel with each other. During the exposure
+of 2h. 20m. required to imprint this picture upon the
+photographic plate, the comet was continually changing its
+position among the stars on account of its orbital motion,<span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span>
+and the plate was therefore moved from time to time, so as
+to follow the comet and make its image always fall at the
+same place. Hence the plate was continually shifted relative
+to the stars whose images, drawn out into lines, show
+the direction in which the plate was moved&mdash;i.&nbsp;e., the direction
+in which the comet was moving across the sky. The
+same effect is shown in the other photographs, but less
+conspicuously than here on account of their shorter exposure
+times.</p>
+
+<p>These pictures all show that one end of the comet is
+brighter and apparently more dense than the other, and it
+is customary to call
+this bright part the
+<i>head</i> of the comet,
+while the brushlike
+appendage that
+streams away from
+it is called the
+comet's <i>tail</i>.</p>
+
+<p><a name="S_160" id="S_160"></a>160. <b>The parts
+of a comet.</b>&mdash;It is
+not every comet
+that has a tail,
+though all the
+large ones do, and
+in <a href="#Fig_103">Fig.&nbsp;103</a> the detached
+piece of
+cometary matter at
+the left of the
+picture represents
+very well the appearance of a tailless comet, a rather large
+but not very bright star of a fuzzy or hairy appearance.
+The word comet means long-haired or hairy star. Something
+of this vagueness of outline is found in all comets,
+whose exact boundaries are hard to define, instead of being
+sharp and clean-cut like those of a planet or satellite.
+<span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span>
+Often, however, there is found in the head of a comet a
+much more solid appearing part, like the round white ball
+at the center of <a href="#Fig_106">Fig.&nbsp;106</a>, which is called the nucleus of
+the comet, and appears to be in some sort the center from
+which its activities radiate. As shown in Figs.&nbsp;<a href="#Fig_106">106</a> and&nbsp;<a href="#Fig_107">107</a>,
+the nucleus is sometimes surrounded by what are
+called envelopes, which have the appearance of successive
+wrappings or halos placed about it, and odd, spurlike projections,
+called jets, are sometimes found in connection
+with the envelopes or in place of them. These figures also
+show what is quite a common characteristic of large
+comets, a dark streak running down the axis of the tail,
+showing that the tail is hollow, a mere shell surrounding
+empty space.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_104" id="Fig_104"></a>
+<a href="images/i289-full.jpg"><img src="images/i289.jpg" width="500" height="520" alt="Fig. 104.&mdash;Swift&#39;s comet, April 17, 1892.&mdash;Barnard." title="Fig. 104.&mdash;Swift&#39;s comet, April 17, 1892.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 104.</span>&mdash;Swift&#39;s comet, April 17, 1892.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p>The amount of detail shown in Figs.&nbsp;<a href="#Fig_106">106</a> and&nbsp;<a href="#Fig_107">107</a> is,
+however, quite exceptional, and the ordinary comet is much
+more like Fig.&nbsp;<a href="#Fig_103">103</a> or&nbsp;<a href="#Fig_104">104</a>. Even a great comet when it<span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span>
+first appears is not unlike the detached fragment in <a href="#Fig_103">Fig.&nbsp;103</a>,
+a faint and roundish patch of foggy light which grows
+through successive stages to its maximum estate, developing
+a tail, nucleus, envelopes, etc., only to lose them again
+as it shrinks and finally disappears.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_105" id="Fig_105"></a>
+<a href="images/i290-full.jpg"><img src="images/i290.jpg" width="500" height="445" alt="Fig. 105.&mdash;Swift&#39;s comet, April 24, 1892.&mdash;Barnard." title="Fig. 105.&mdash;Swift&#39;s comet, April 24, 1892.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 105.</span>&mdash;Swift&#39;s comet, April 24, 1892.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_161" id="S_161"></a>161. <b>The orbits of comets.</b>&mdash;It will be remembered that
+Newton found, as a theoretical consequence of the law of
+gravitation, that a body moving under the influence of the
+sun's attraction might have as its orbit any one of the
+conic sections, ellipse, parabola, or hyperbola, and among
+the 400 and more comet orbits which have been determined
+every one of these orbit forms appears, but curiously
+enough there is not a hyperbola among them which, if
+drawn upon paper, could be distinguished by the unaided
+eye from a parabola, and the ellipses are all so long and
+narrow, not one of them being so nearly round as is the
+most eccentric planet orbit, that astronomers are accustomed
+to look upon the parabola as being the normal type<span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span>
+of comet orbit, and to regard a comet whose motion differs
+much from a parabola as being abnormal and calling for
+some special explanation.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_106" id="Fig_106"></a>
+<a href="images/i291-full.jpg"><img src="images/i291.jpg" width="350" height="504" alt="Fig. 106.&mdash;Head of Coggia&#39;s comet,
+July 13, 1874.&mdash;Trouvelot." title="Fig. 106.&mdash;Head of Coggia&#39;s comet,
+July 13, 1874.&mdash;Trouvelot." /></a>
+<span class="caption"><span class="smcap">Fig. 106.</span>&mdash;Head of Coggia&#39;s comet,
+July 13, 1874.&mdash;<span class="smcap">Trouvelot.</span></span>
+</div>
+
+<p>The fact that comet orbits are parabolas, or differ but
+little from them, explains at once the temporary character
+and speedy disappearance
+of these bodies. They
+are visitors to the solar
+system and visible for
+only a short time, because
+the parabola in which
+they travel is not a closed
+curve, and the comet, having
+passed once along
+that portion of it near the
+earth and the sun, moves
+off along a path which
+ever thereafter takes it
+farther and farther away,
+beyond the limit of visibility.
+The development
+of the comet during the
+time it is visible, the
+growth and disappearance
+of tail, nucleus, etc., depend upon its changing distance
+from the sun, the highest development and most complex
+structure being presented when it is nearest to the sun.</p>
+
+<p><a href="#Fig_108">Fig.&nbsp;108</a> shows the path of the Great Comet of 1882
+during the period in which it was seen, from September 3,
+1882, to May 26, 1883. These dates&mdash;IX, 3, and V, 26&mdash;are
+marked in the figure opposite the parts of the orbit in
+which the comet stood at those times. Similarly, the positions
+of the earth in its orbit at the beginning of September,
+October, November, etc., are marked by the Roman
+numerals IX, X, XI, etc. The line <i>S&nbsp;V</i> shows the direction
+from the sun to the vernal equinox, and <i>S</i>&nbsp;&Omega; is the line<span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span>
+along which the plane of the comet's orbit intersects the
+plane of the earth's orbit&mdash;i.&nbsp;e., it is the line of nodes of the
+comet orbit. Since the comet approached the sun from
+the south side of the ecliptic, all of its orbit, save the little
+segment which falls to the left of <i>S</i>&nbsp;&Omega;, lies below (south) of
+the plane of the earth's orbit, and the part which would
+be hidden if this plane were opaque is represented by a
+broken line.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_107" id="Fig_107"></a>
+<a href="images/i292-full.jpg"><img src="images/i292.jpg" width="350" height="496" alt="Fig. 107.&mdash;Head of Donati&#39;s comet, September
+30, October 2, 1858.&mdash;Bond." title="Fig. 107.&mdash;Head of Donati&#39;s comet, September
+30, October 2, 1858.&mdash;Bond." /></a>
+<span class="caption"><span class="smcap">Fig. 107.</span>&mdash;Head of Donati&#39;s comet, September
+30, October 2, 1858.&mdash;<span class="smcap">Bond.</span></span>
+</div>
+
+<p><a name="S_162" id="S_162"></a>162. <b>Elements of a comet's orbit.</b>&mdash;There is a theorem of
+geometry to the effect that through any three points not
+in the same straight line one circle, and only one, can be
+drawn. Corresponding to this there is a theorem of celestial
+mechanics, that through any three positions of a comet
+one conic section, and
+only one, can be passed
+along which the comet
+can move in accordance
+with the law of gravitation.
+This conic section
+is, of course, its orbit, and
+at the discovery of a comet
+astronomers always
+hasten to observe its position
+in the sky on different
+nights in order to
+obtain the three positions
+(right ascensions and declinations)
+necessary for
+determining the particular
+orbit in which it
+moves. The circle, to
+which reference was made
+above, is completely ascertained
+and defined when we know its radius and the
+position of its center. A parabola is not so simply defined,
+and five numbers, called the <i>elements</i> of its orbit, are<span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span>
+required to fix accurately a comet's path around the sun.
+Two of these relate to the position of the line of nodes and
+the angle which the orbit plane makes with the plane of the
+ecliptic; a third fixes the direction of the axis of the orbit
+in its plane, and the remaining two, which are of more
+interest to us, are the date at which the comet makes its
+nearest approach to the sun (<i>perihelion passage</i>) and its
+distance from the sun at that date (<i>perihelion distance</i>).
+The date, September 17th, placed near the center of <a href="#Fig_108">Fig.&nbsp;108</a>,
+is the former of these elements, while the latter, which
+is too small to be accurately measured here, may be found
+from <a href="#Fig_109">Fig.&nbsp;109</a> to be 0.82 of the sun's diameter, or, in terms
+of the earth's distance from the sun, 0.008.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_108" id="Fig_108"></a>
+<img src="images/i293.png" width="500" height="402" alt="Fig. 108.&mdash;Orbits of the earth and the
+Great Comet of 1882." title="Fig. 108.&mdash;Orbits of the earth and the
+Great Comet of 1882." />
+<span class="caption"><span class="smcap">Fig. 108.</span>&mdash;Orbits of the earth and the
+Great Comet of 1882.</span>
+</div>
+
+<p><a href="#Fig_109">Fig.&nbsp;109</a> shows on a large scale the shape of that part of
+the orbit near the sun and gives the successive positions of
+the comet, at intervals of 2/10 of a day, on September 16th
+and 17th, showing that in less than 10 hours&mdash;17.0 to 17.4&mdash;the
+comet swung around the sun through an angle of<span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span>
+more than 240°. When at its perihelion it was moving
+with a velocity of 300 miles per second! This very unusual
+velocity was due to the comet's extraordinarily close approach
+to the sun. The earth's velocity in its orbit is only
+19 miles per second, and the velocity of any comet at any
+distance from the sun, provided its orbit is a parabola, may
+be found by dividing this number by the square root of
+half the comet's distance&mdash;e.&nbsp;g., 300 miles per second equals
+19&nbsp;÷&nbsp;&#8730;&nbsp;0.004.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_109" id="Fig_109"></a>
+<img src="images/i294.png" width="500" height="390" alt="Fig. 109.&mdash;Motion of the Great Comet of 1883 in passing around the sun." title="Fig. 109.&mdash;Motion of the Great Comet of 1883 in passing around the sun." />
+<span class="caption"><span class="smcap">Fig. 109.</span>&mdash;Motion of the Great Comet of 1883 in passing around the sun.</span>
+</div>
+
+<p>Most of the visible comets have their perihelion distances
+included between 1/3 and 4/3 of the earth's distance
+from the sun, but occasionally one is found, like the
+second comet of 1885, whose nearest approach to the sun
+lies far outside the earth's orbit, in this case half-way
+out to the orbit of Jupiter; but such a comet must be a
+very large one in order to be seen at all from the earth.<span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span>
+There is, however, some reason for believing that the number
+of comets which move around the sun without ever
+coming inside the orbit of Jupiter, or even that of Saturn,
+is much larger than the number of those which come close
+enough to be discovered from the earth. In any case we
+are reminded of Kepler's saying, that comets in the sky are
+as plentiful as fishes in the sea, which seems to be very little
+exaggerated when we consider that, according to Kleiber,
+out of all the comets which enter the solar system probably
+not more than 2 or 3 per cent are ever discovered.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_110" id="Fig_110"></a>
+<a href="images/i295-full.jpg"><img src="images/i295.jpg" width="500" height="393" alt="Fig. 110.&mdash;The Great Comet of 1843." title="Fig. 110.&mdash;The Great Comet of 1843." /></a>
+<span class="caption"><span class="smcap">Fig. 110.</span>&mdash;The Great Comet of 1843.</span>
+</div>
+
+<p><a name="S_163" id="S_163"></a>163. <b>Dimensions of comets.</b>&mdash;The comet whose orbit is
+shown in Figs.&nbsp;<a href="#Fig_108">108</a> and&nbsp;<a href="#Fig_109">109</a> is the finest and largest that
+has appeared in recent years. Its tail, which at its maximum
+extent would have more than bridged the space between
+sun and earth (100,000,000 miles), is made very much
+too short in <a href="#Fig_109">Fig.&nbsp;109</a>, but when at its best was probably not
+inferior to that of the Great Comet of 1843, shown in <a href="#Fig_110">Fig.&nbsp;110</a>.<span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span>
+As we shall see later, there is a peculiar and special
+relationship between these two comets.</p>
+
+<p>The head of the comet of 1882 was not especially large&mdash;about
+twice the diameter of the ball of Saturn&mdash;but its
+nucleus, according to an estimate made by Dr. Elkin when
+it was very near perihelion, was as large as the moon. The
+head of the comet shown in <a href="#Fig_107">Fig.&nbsp;107</a> was too large to be
+put in the space between the earth and the moon, and the
+Great Comet of 1811 had a head considerably larger than
+the sun itself. From these colossal sizes down to the
+smallest shred just visible in the telescope, comets of all
+dimensions may be found, but the smaller the comet the
+less the chance of its being discovered, and a comet as small
+as the earth would probably go unobserved unless it approached
+very close to us.</p>
+
+<p><a name="S_164" id="S_164"></a>164. <b>The mass of a comet.</b>&mdash;There is no known case in
+which the mass of a comet has ever been measured, yet
+nothing about them is more sure than that they are bodies
+with mass which is attracted by the sun and the planets,
+and which in its turn attracts both sun and planets and
+produces perturbations in their motion. These perturbations
+are, however, too small to be measured, although the
+corresponding perturbations in the comet's motion are
+sometimes enormous, and since these mutual perturbations
+are proportional to the masses of comet and planet, we are
+forced to say that, by comparison with even such small
+bodies as the moon or Mercury, the mass of a comet is
+utterly insignificant, certainly not as great as a ten-thousandth
+part of the mass of the earth. In the case of the
+Great Comet of 1882, if we leave its hundred million miles
+of tail out of account and suppose the entire mass condensed
+into its head, we find by a little computation that the average
+density of the head under these circumstances must
+have been less than 1/1500 of the density of air. In
+ordinary laboratory practice this would be called a pretty
+good vacuum.<span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span>
+
+A striking observation made on September 17, 1882,
+goes to confirm the very small density of this comet. It
+is shown in <a href="#Fig_109">Fig.&nbsp;109</a> that early on that day the comet
+crossed the line joining earth and sun, and therefore passed
+in transit over the sun's disk. Two observers at the Cape
+of Good Hope saw the comet approach the sun, and followed
+it with their telescopes until the nucleus actually
+reached the edge of the sun and disappeared, behind it as
+they supposed, for no trace of the comet, not even its
+nucleus, could be seen against the sun, although it was carefully
+looked for. Now, the figure shows that the comet
+passed between the earth and sun, and its densest parts
+were therefore too attenuated to cut off any perceptible
+fraction of the sun's rays. In other cases stars have been
+seen through the head of a comet, shining apparently with
+undimmed luster, although in some cases they seem to
+have been slightly refracted out of their true positions.</p>
+
+<p><a name="S_165" id="S_165"></a>165. <b>Meteors.</b>&mdash;Before proceeding further with the study
+of comets it is well to turn aside and consider their humbler
+relatives, the shooting stars. On some clear evening,
+when the moon is absent from the sky, watch the heavens
+for an hour and count the meteors visible during that time.
+Note their paths, the part of the sky where they appear
+and where they disappear, their brightness, and whether
+they all move with equal swiftness. Out of such simple
+observations with the unaided eye there has grown a large
+and important branch of astronomical science, some parts
+of which we shall briefly summarize here.</p>
+
+<p>A particular meteor is a local phenomenon seen over
+only a small part of the earth's surface, although occasionally
+a very big and bright one may travel and be visible
+over a considerable territory. Such a one in December,
+1876, swept over the United States from Kansas to Pennsylvania,
+and was seen from eleven different States. But the
+ordinary shooting star is much less conspicuous, and, as we
+know from simultaneous observations made at neighboring<span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span>
+places, it makes its appearance at a height of some 75 miles
+above the earth's surface, occupies something like a second
+in moving over its path, and then disappears at a height
+of about 50 miles or more, although occasionally a big one
+comes down to the very surface of the earth with force
+sufficient to bury itself in the ground, from which it may
+be dug up, handled, weighed, and turned over to the chemist
+to be analyzed. The pieces thus found show that the
+big meteors, at least, are masses of stone or mineral; iron
+is quite commonly found in them, as are a considerable
+number of other terrestrial substances combined in rather
+peculiar ways. But no chemical element not found on the
+earth has ever been discovered in a meteor.</p>
+
+<p><a name="S_166" id="S_166"></a>166. <b>Nature of meteors.</b>&mdash;The swiftness with which the
+meteors sweep down shows that they must come from outside
+the earth, for even half their velocity, if given to them
+by some terrestrial volcano or other explosive agent, would
+send them completely away from the earth never to return.
+We must therefore look upon them as so many projectiles,
+bullets, fired against the earth from some outside source
+and arrested in their motion by the earth's atmosphere,
+which serves as a cushion to protect the ground from the
+bombardment which would otherwise prove in the highest
+degree dangerous to both property and life. The speed of
+the meteor is checked by the resistance which the atmosphere
+offers to its motion, and the energy represented by
+that speed is transformed into heat, which in less than a
+second raises the meteor and the surrounding air to incandescence,
+melts the meteor either wholly or in part, and
+usually destroys its identity, leaving only an impalpable
+dust, which cools off as it settles slowly through the lower
+atmosphere to the ground. The heating effect of the air's
+resistance is proportional to the square of the meteor's
+velocity, and even at such a moderate speed as 1 mile per
+second the effect upon the meteor is the same as if it stood
+still in a bath of red-hot air. Now, the actual velocity of<span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span>
+meteors through the air is often 30 or 40 times as great as
+this, and the corresponding effect of the air in raising its
+temperature is more than 1,000 times that of red heat.
+Small wonder that the meteor is brought to lively incandescence
+and consumed even in a fraction of a second.</p>
+
+<p><a name="S_167" id="S_167"></a>167. <b>The number of meteors.</b>&mdash;A single observer may
+expect to see in the evening hours about one meteor every
+10 minutes on the average, although, of course, in this
+respect much irregularity may occur. Later in the night
+they become more frequent, and after 2 <span class="smcap">A.&nbsp;M.</span> there are
+about three times as many to be seen as in the evening
+hours. But no one person can keep a watch upon the
+whole sky, high and low, in front and behind, and experience
+shows that by increasing the number of observers and
+assigning to each a particular part of the sky, the total
+number of meteors counted may be increased about five-fold.
+So, too, the observers at any one place can keep an
+effective watch upon only those meteors which come into the
+earth's atmosphere within some moderate distance of their
+station, say 50 or 100 miles, and to watch every part of that
+atmosphere would require a large number of stations, estimated
+at something more than 10,000, scattered systematically
+over the whole face of the earth. If we piece together
+the several numbers above considered, taking 14 as
+a fair average of the hourly number of meteors to be seen
+by a single observer at all hours of the night, we shall find
+for the total number of meteors encountered by the earth
+in 24 hours, 14&nbsp;×&nbsp;5 ×&nbsp;10,000 ×&nbsp;24 =&nbsp;16,800,000. Without
+laying too much stress upon this particular number, we
+may fairly say that the meteors picked up by the earth
+every day are to be reckoned by millions, and since they
+come at all seasons of the year, we shall have to admit that
+the region through which the earth moves, instead of being
+empty space, is really a dust cloud, each individual particle
+of dust being a prospective meteor.</p>
+
+<p>On the average these individual particles are very small<span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span>
+and very far apart; a cloud of silver dimes each about 250
+miles from its nearest neighbor is perhaps a fair representation
+of their average mass and distance from each other,
+but, of course, great variations are to be expected both in the
+size and in the frequency of the particles. There must be
+great numbers of them that are too small to make shooting
+stars visible to the naked eye, and such are occasionally
+seen darting by chance across the field of view of a telescope.</p>
+
+<p><a name="S_168" id="S_168"></a>168. <b>The zodiacal light</b> is an effect probably due to the
+reflection of sunlight from the myriads of these tiny meteors
+which occupy the space inside the earth's orbit. It is a
+faint and diffuse stream of light, something like the Milky
+Way, which may be seen in the early evening or morning
+stretching up from the sunrise or sunset point of the
+horizon along the ecliptic and following its course for
+many degrees, possibly around the entire circumference of
+the sky. It may be seen at any season of the year, although
+it shows to the best advantage in spring evenings and
+autumn mornings. Look for it.</p>
+
+<p><a name="S_169" id="S_169"></a>169. <b>Great meteors.</b>&mdash;But there are other meteors, veritable
+fireballs in appearance, far more conspicuous and imposing
+than the ordinary shooting star. Such a one exploded
+over the city of Madrid, Spain, on the morning of
+February 10, 1896, giving in broad sunlight "a brilliant
+flash which was followed ninety seconds later by a succession
+of terrific noises like the discharge of a battery of
+artillery." <a href="#Fig_111">Fig.&nbsp;111</a> shows a large meteor which was seen
+in California in the early evening of July 27, 1894, and
+which left behind it a luminous trail or cloud visible for
+more than half an hour.</p>
+
+<p>Not infrequently large meteors are found traveling
+together, two or three or more in company, making their
+appearance simultaneously as did the California meteor of
+October 22, 1896, which is described as triple, the trio following
+one another like a train of cars, and Arago cites an<span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span>
+instance, from the year 1830, where within a short space of
+time some forty brilliant meteors crossed the sky, all moving
+in the same direction with a whistling noise and displaying
+in their flight all the colors of the rainbow.</p>
+
+<p>The mass of great meteors such as these must be measured
+in hundreds if not thousands of pounds, and stories
+are current, although not
+very well authenticated, of
+even larger ones, many tons
+in weight, having been found
+partially buried in the ground.
+Of meteors which have been
+actually seen to fall from the
+sky, the largest single fragment
+recovered weighs about
+500 pounds, but it is only a
+fragment of the original meteor,
+which must have been
+much more massive before it
+was broken up by collision
+with the atmosphere.</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_111" id="Fig_111"></a>
+<a href="images/i301-full.jpg"><img src="images/i301.jpg" width="300" height="562" alt="Fig. 111.&mdash;The California meteor of
+July 27, 1894." title="Fig. 111.&mdash;The California meteor of
+July 27, 1894." /></a>
+<span class="caption"><span class="smcap">Fig. 111.</span>&mdash;The California meteor of
+July 27, 1894.</span>
+</div>
+
+<p><a name="S_170" id="S_170"></a>170. <b>The velocity of meteors.</b>&mdash;Every
+meteor, big or
+little, is subject to the law of
+gravitation, and before it encounters
+the earth must be
+moving in some kind of orbit
+having the sun at its focus,
+the particular species of orbit&mdash;ellipse, parabola, hyperbola&mdash;depending
+upon the velocity and direction of its motion.
+Now, the direction in which a meteor is moving can be
+determined without serious difficulty from observations of
+its apparent path across the sky made by two or more observers,
+but the velocity can not be so readily found, since
+the meteors go too fast for any ordinary process of timing.
+But by photographing one of them two or three times on<span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span>
+the same plate, with an interval of only a tenth of a second
+between exposures, Dr. Elkin has succeeded in showing, in
+a few cases, that their velocities varied from 20 to 25 miles
+per second, and must have been considerably greater than
+this before the meteors encountered the earth's atmosphere.
+This is a greater velocity than that of the earth in its orbit,
+19 miles per second, as might have been anticipated, since
+the mere fact that meteors can be seen at all in the evening
+hours shows that some of them at least must travel considerably
+faster than the earth, for, counting in the direction
+of the earth's motion, the region of sunset and evening is
+always on the rear side of the earth, and meteors in order
+to strike this region must overtake it by their swifter
+motion. We have here, in fact, the reason why meteors
+are especially abundant in the morning hours; at this time
+the observer is on the front side of the earth which catches
+swift and slow meteors alike, while the rear is pelted only
+by the swifter ones which follow it.</p>
+
+<p>A comparison of the relative number of morning and
+evening meteors makes it probable that the average meteor
+moves, relative to the sun, with a velocity of about 26 miles
+per second, which is very approximately the average velocity
+of comets when they are at the earth's distance from the
+sun. Astronomers, therefore, consider meteors as well as
+comets to have the parabola and the elongated ellipse as
+their characteristic orbits.</p>
+
+<p><a name="S_171" id="S_171"></a>171. <b>Meteor showers</b>&mdash;<b>The radiant.</b>&mdash;There is evident
+among meteors a distinct tendency for individuals, to the
+number of hundreds or even hundreds of millions, to
+travel together in flocks or swarms, all going the same way
+in orbits almost exactly alike. This gregarious tendency is
+made manifest not only by the fact that from time to time
+there are unusually abundant meteoric displays, but also
+by a striking peculiarity of their behavior at such times.
+The meteors all seem to come from a particular part of the
+heavens, as if here were a hole in the sky through which<span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span>
+they were introduced, and from which they flow away in
+every direction, even those which do not visibly start from
+this place having paths among the stars which, if prolonged
+backward, would pass through it. The cause of this appearance
+may be understood from <a href="#Fig_112">Fig.&nbsp;112</a>, which represents
+a group of meteors moving together along parallel
+paths toward an observer at <i>D</i>. Traveling unseen above
+the earth until they encounter the upper strata of its atmosphere,
+they here become incandescent and speed on in
+parallel paths, <i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, <i>5</i>, <i>6</i>, which, as seen by the observer,
+are projected back against the sky into luminous streaks
+that, as is shown by the arrowheads, <i>b</i>, <i>c</i>, <i>d</i>, all seem to
+radiate from the point <i>a</i>&mdash;i.&nbsp;e., from the point in the sky
+whose direction from the observer is parallel to the paths
+of the meteors.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_112" id="Fig_112"></a>
+<img src="images/i303.jpg" width="500" height="304" alt="Fig. 112.&mdash;Explanation of the radiant of a meteoric shower.&mdash;Denning." title="Fig. 112.&mdash;Explanation of the radiant of a meteoric shower.&mdash;Denning." />
+<span class="caption"><span class="smcap">Fig. 112.</span>&mdash;Explanation of the radiant of a meteoric shower.&mdash;<span class="smcap">Denning.</span></span>
+</div>
+
+<p>Such a display is called a meteor shower, and the point
+<i>a</i> is called its radiant. Note how those meteors which
+appear near the radiant all have short paths, while those
+remote from it in the sky have longer ones. Query: As
+the night wears on and the stars shift toward the west, will<span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span>
+the radiant share in their motion or will it be left behind?
+Would the luminous part of the path of any of these meteors
+pass across the radiant from one side to the other?
+Is such a crossing of the radiant possible under any circumstances?
+<a href="#Fig_113">Fig.&nbsp;113</a> shows how the meteor paths are grouped
+around the radiant of a strongly marked shower. Select
+from it the meteors which do not belong to this shower.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_113" id="Fig_113"></a>
+<img src="images/i304.jpg" width="500" height="429" alt="Fig. 113.&mdash;The radiant of a meteoric shower, showing also the paths of three meteors
+which do not belong to this shower.&mdash;Denning." title="Fig. 113.&mdash;The radiant of a meteoric shower, showing also the paths of three meteors
+which do not belong to this shower.&mdash;Denning." />
+<span class="caption"><span class="smcap">Fig. 113.</span>&mdash;The radiant of a meteoric shower, showing also the paths of three meteors
+which do not belong to this shower.&mdash;<span class="smcap">Denning.</span></span>
+</div>
+
+<p>Many hundreds of these radiants have been observed in
+the sky, each of which represents an orbit along which a
+group of meteors moves, and the relation of one of these<span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span>
+orbits to that of the earth is shown in <a href="#Fig_114">Fig.&nbsp;114</a>. The orbit
+of the meteors is an ellipse extending out beyond the orbit
+of Uranus, but so eccentric that a part of it comes inside
+the orbit of the earth, and the figure shows only that part
+of it which lies nearest the sun. The Roman numerals
+which are placed along the earth's orbit show the position
+of the earth at the beginning of the tenth month, eleventh
+month, etc. The meteors flow along their orbit in a long
+procession, whose direction of motion is indicated by the
+arrow heads, and the earth, coming in the opposite direction,
+plunges into this stream and receives the meteor
+shower when it reaches the intersection of the two orbits.
+The long arrow at the left of the figure represents the
+direction of motion of another meteor shower which
+encounters the earth at this point.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_114" id="Fig_114"></a>
+<img src="images/i305.jpg" width="500" height="449" alt="Fig. 114.&mdash;The orbits of the earth and the November meteors." title="Fig. 114.&mdash;The orbits of the earth and the November meteors." />
+<span class="caption"><span class="smcap">Fig. 114.</span>&mdash;The orbits of the earth and the November meteors.</span>
+</div>
+
+<p>Can you determine from the figure answers to the following
+questions? On what day of the year will the earth
+meet each of these showers? Will the radiant points of
+the showers lie above or below the plane of the earth's<span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span>
+orbit? Will these meteors strike the front or the rear of
+the earth? Can they be seen in the evening hours?</p>
+
+<p>From many of the radiants year after year, upon the
+same day or week in each year, there comes a swarm of
+shooting stars, showing that there must be a continuous
+procession of meteors moving along this orbit, so that some
+are always ready to strike the earth whenever it reaches
+the intersection of its orbit with theirs. Such is the explanation
+of the shower which appears each year in the first
+half of August, and whose meteors are sometimes called
+Perseids, because their radiant lies in the constellation
+Perseus, and a similar explanation holds for all the star
+showers which are repeated year after year.</p>
+
+<p><a name="S_172" id="S_172"></a>172. <b>The Leonids.</b>&mdash;There is, however, a kind of star
+shower, of which the Leonids (radiant in Leo) is the most
+conspicuous type, in which the shower, although repeated
+from year to year, is much more striking in some years
+than in others. Thus, to quote from the historian: "In
+1833 the shower was well observed along the whole eastern
+coast of North America from the Gulf of Mexico to Halifax.
+The meteors were most numerous at about 5 <span class="smcap">A.&nbsp;M.</span> on
+November 13th, and the rising sun could not blot out all
+traces of the phenomena, for large meteors were seen now and
+then in full daylight. Within the scope that the eye could
+contain, more than twenty could be seen at a time shooting
+in every direction. Not a cloud obscured the broad expanse,
+and millions of meteors sped their way across in every
+point of the compass. Their coruscations were bright,
+gleaming, and incessant, and they fell thick as the flakes in
+the early snows of December." But, so far as is known, none
+of them reached the ground. An illiterate man on the following
+day remarked: "The stars continued to fall until
+none were left. I am anxious to see how the heavens will
+appear this evening, for I believe we shall see no more stars."</p>
+
+<p>An eyewitness in the Southern States thus describes
+the effect of this shower upon the plantation negroes:<span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span>
+"Upward of a hundred lay prostrate upon the ground,
+some speechless and some with the bitterest cries, but with
+their hands upraised, imploring God to save the world and
+them. The scene was truly awful, for never did rain fall
+much thicker than the meteors fell toward the earth&mdash;east,
+west, north, and south it was the same." In the preceding
+year a similar but feebler shower from the same radiant
+created much alarm in France, and through the old historic
+records its repetitions may be traced back at intervals of 33
+or 34 years, although with many interruptions, to October
+12, 902, O.&nbsp;S., when "an immense number of falling stars
+were seen to spread themselves over the face of the sky
+like rain."</p>
+
+<p>Such a star shower differs from the one repeated every
+year chiefly in the fact that its meteors, instead of being
+drawn out into a long procession, are mainly clustered in a
+single flock which may be long enough to require two or
+three or four years to pass a given point of its orbit, but
+which is far from extending entirely around it, so that meteors
+from this source are abundant only in those years in
+which the flock is at or near the intersection of its orbit
+with that of the earth. The fact that the Leonid shower is
+repeated at intervals of 33 or 34 years (it appeared in 1799,
+1832-'33, 1866-'67) shows that this is the "periodic time"
+in its orbit, which latter must of course be an ellipse, and
+presumably a long and narrow one. It is this orbit which
+is shown in <a href="#Fig_114">Fig.&nbsp;114</a>, and the student should note in this
+figure that if the meteor stream at the point where it cuts
+through the plane of the earth's orbit were either nearer to
+or farther from the sun than is the earth there could be no
+shower; the earth and the meteors would pass by without a
+collision. Now, the meteors in their motion are subject to
+perturbations, particularly by the large planets Jupiter,
+Saturn, and Uranus, which slightly change the meteor orbit,
+and it seems certain that the changes thus produced will
+sometimes thrust the swarm inside or outside the orbit of<span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span>
+the earth, and thus cause a failure of the shower at times
+when it is expected. The meteors were due at the crossing
+of the orbits in November, 1899 and 1900, and, although a
+few were then seen, the shower was far from being a brilliant
+one, and its failure was doubtless caused by the outer
+planets, which switched the meteors aside from the path in
+which they had been moving for a century. Whether they
+will be again switched back so as to produce future showers
+is at the present time uncertain.</p>
+
+<p><a name="S_173" id="S_173"></a>173. <b>Capture of the Leonids.</b>&mdash;But a far more striking
+effect of perturbations is to be found in <a href="#Fig_115">Fig.&nbsp;115</a>, which
+shows the relation of the Leonid orbit to those of the principal
+planets, and illustrates a curious chapter in the history
+of the meteor swarm that has been worked out by
+mathematical analysis, and is probably a pretty good account
+of what actually befell them. Early in the second
+century of the Christian era this flock of meteors came
+down toward the sun from outer space, moving along a
+parabolic orbit which would have carried it just inside the
+orbit of Jupiter, and then have sent it off to return no
+more. But such was not to be its fate. As it approached
+the orbit of Uranus, in the year 126 <span class="smcap">A.&nbsp;D.</span>, that planet
+chanced to be very near at hand and perturbed the motion
+of the meteors to such an extent that the character of their
+orbit was completely changed into the ellipse shown in the
+figure, and in this new orbit they have moved from that
+time to this, permanent instead of transient members of
+the solar system. The perturbations, however, did not end
+with the year in which the meteors were captured and annexed
+to the solar system, but ever since that time Jupiter,
+Saturn, and Uranus have been pulling together upon the
+orbit, and have gradually turned it around into its present
+position as shown in the figure, and it is chiefly this shifting
+of the orbit's position in the thousand years that have
+elapsed since 902 <span class="smcap">A.&nbsp;D.</span> that makes the meteor shower now
+come in November instead of in October as it did then.<span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span></p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_115" id="Fig_115"></a>
+<a href="images/i309.png"><img src="images/i309.png" width="600" height="363" alt="Fig. 115.&mdash;Supposed capture of the November meteors by Uranus." title="Fig. 115.&mdash;Supposed capture of the November meteors by Uranus." /></a>
+<span class="caption"><span class="smcap">Fig. 115.</span>&mdash;Supposed capture of the November meteors by Uranus.</span>
+</div><p><span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span></p>
+
+<p><a name="S_174" id="S_174"></a>174. <b>Breaking up a meteor swarm.</b>&mdash;How closely packed
+together these meteors were at the time of their annexation
+to the solar system is unknown, but it is certain that ever
+since that time the sun has been exerting upon them a
+tidal influence tending to break up the swarm and distribute
+its particles around the orbit, as the Perseids are distributed,
+and, given sufficient time, it will accomplish this, but
+up to the present the work is only partly done. A certain
+number of the meteors have gained so much over the slower
+moving ones as to have made an extra circuit of the orbit
+and overtaken the rear of the procession, so that there is a
+thin stream of them extending entirely around the orbit
+and furnishing in every November a Leonid shower; but by
+far the larger part of the meteors still cling together, although
+drawn out into a stream or ribbon, which, though
+very thin, is so long that it takes some three years to pass
+through the perihelion of its orbit. It is only when the
+earth plunges through this ribbon, as it should in 1899,
+1900, 1901, that brilliant Leonid showers can be expected.</p>
+
+<p><a name="S_175" id="S_175"></a>175. <b>Relation of comets and meteors.</b>&mdash;It appears from
+the foregoing that meteors and comets move in similar orbits,
+and we have now to push the analogy a little further
+and note that in some instances at least they move in identically
+the same orbit, or at least in orbits so like that an
+appreciable difference between them is hardly to be found.
+Thus a comet which was discovered and observed early in
+the year 1866, moves in the same orbit with the Leonid
+meteors, passing its perihelion about ten months ahead of
+the main body of the meteors. If it were set back in its
+orbit by ten months' motion, <i>it would be a part of the meteor
+swarm</i>. Similarly, the Perseid meteors have a comet moving
+in their orbit actually immersed in the stream of meteor
+particles, and several other of the more conspicuous star
+showers have comets attending them.</p>
+
+<p>Perhaps the most remarkable case of this character is
+that of a shower which comes in the latter part of November<span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span>
+from the constellation Andromeda, and which from its
+association with the comet called Biela (after the name of
+its discoverer) is frequently referred to as the Bielid shower.
+This comet, an inconspicuous one moving in an unusually
+small elliptical orbit, had been observed at various times
+from 1772 down to 1846 without presenting anything remarkable
+in its appearance; but about the beginning of the
+latter year, with very little warning, it broke in two, and
+for three months the pieces were watched by astronomers
+moving off, side by side, something more than half as far
+apart as are the earth and moon. It disappeared, made the
+circuit of its orbit, and six years later came back, with the
+fragments nearly ten times as far apart as before, and after
+a short stay near the earth once more disappeared in the distance,
+never to be seen again, although the fragments should
+have returned to perihelion at least half a dozen times since
+then. In one respect the orbit of the comet was remarkable:
+it passed through the place in which the earth stands
+on November 27th of each year, so that if the comet were at
+that particular part of its orbit on any November 27th, a
+collision between it and the earth would be inevitable. So
+far as is known, no such collision with the comet has ever
+occurred, but the Bielid meteors which are strung along
+its orbit do encounter the earth on that date, in greater or
+less abundance in different years, and are watched with
+much interest by the astronomers who look upon them as
+the final appearance of the <i>débris</i> of a worn-out comet.</p>
+
+<p><a name="S_176" id="S_176"></a>176. <b>Periodic comets.</b>&mdash;The Biela comet is a specimen of
+the type which astronomers call periodic comets&mdash;i.&nbsp;e.,
+those which move in small ellipses and have correspondingly
+short periodic times, so that they return frequently
+and regularly to perihelion. The comets which accompany
+the other meteor swarms&mdash;Leonids, Perseids, etc.&mdash;also belong
+to this class as do some 30 or 40 others which have
+periodic times less than a century. As has been already
+indicated, these deviations from the normal parabolic orbit<span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span>
+call for some special explanation, and the substance of that
+explanation is contained in the account of the Leonid
+meteors and their capture by Uranus. Any comet may be
+thus captured by the attraction of a planet near which it
+passes. It is only necessary that the perturbing action
+of the planet should result in a diminution of the comet's
+velocity, for we have already learned that it is this velocity
+which determines the character of the orbit, and anything
+less than the velocity appropriate to a parabola must produce
+an ellipse&mdash;i.&nbsp;e., a closed orbit around which the body
+will revolve time after time in endless succession. We
+note in <a href="#Fig_115">Fig.&nbsp;115</a> that when the Leonid swarm encountered
+Uranus it passed <i>in front of</i> the planet and had its velocity
+diminished and its orbit changed into an ellipse thereby.
+It might have passed behind Uranus, it would have passed
+behind had it come a little later, and the effect would then
+have been just the opposite. Its velocity would have been
+increased, its orbit changed to a hyperbola, and it would
+have left the solar system more rapidly than it came into
+it, thrust out instead of held in by the disturbing planet.
+Of such cases we can expect no record to remain, but the
+captured comet is its own witness to what has happened,
+and bears imprinted upon its orbit the brand of the planet
+which slowed down its motion. Thus in <a href="#Fig_115">Fig.&nbsp;115</a> the changed
+orbit of the meteors has its <i>aphelion</i> (part remotest from
+the sun) quite close to the orbit of Uranus, and one of its
+nodes, &#8487;, the point in which it cuts through the plane of
+the ecliptic from north to south side, is also very near to
+the same orbit. It is these two marks, aphelion and node,
+which by their position identify Uranus as the planet instrumental
+in capturing the meteor swarm, and the date of
+the capture is found by working back with their respective
+periodic times to an epoch at which planet and comet were
+simultaneously near this node.</p>
+
+<p>Jupiter, by reason of his great mass, is an especially efficient
+capturer of comets, and <a href="#Fig_116">Fig.&nbsp;116</a> shows his group of<span class="pagenum"><a name="Page_279" id="Page_279">[Pg 279]</a></span>
+captives, his family of comets as they are sometimes called.
+The several orbits are marked with the names commonly
+given to the comets. Frequently this is the name of their
+discoverer, but often a different system is followed&mdash;e.&nbsp;g.,
+the name 1886, IV, means the fourth comet to pass through
+perihelion in the year 1886. The other great planets&mdash;Saturn,
+Uranus, Neptune&mdash;have also their families of captured
+comets, and according to Schulhof, who does not
+entirely agree with the common opinion about captured
+comets, the earth has caught no less than nine of these
+bodies.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_116" id="Fig_116"></a>
+<a href="images/i313-full.jpg"><img src="images/i313.jpg" width="500" height="469" alt="Fig. 116.&mdash;Jupiter&#39;s family of comets." title="Fig. 116.&mdash;Jupiter&#39;s family of comets." /></a>
+<span class="caption"><span class="smcap">Fig. 116.</span>&mdash;Jupiter&#39;s family of comets.</span>
+</div>
+
+<p><a name="S_177" id="S_177"></a>177. <b>Comet groups.</b>&mdash;But there is another kind of comet
+family, or comet group as it is called, which deserves some
+notice, and which is best exemplified by the Great Comet of
+1882 and its relatives. No less than four other comets are
+known to be traveling in substantially the same orbit with<span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span>
+this one, the group consisting of comets 1668, I; 1843, I;
+1880, I; 1882, II; 1887, I. The orbit itself is not quite a
+parabola, but a very elongated ellipse, whose major axis
+and corresponding periodic time can not be very accurately
+determined from the available data, but it certainly
+extends far beyond the orbit of Neptune, and requires not
+less than 500 years for the comet to complete a revolution
+in it. It was for a time supposed that some one of the
+recent comets of this group of five might be a return of
+the comet of 1668 brought back ahead of time by unknown
+perturbations. There is still a possibility of this, but it is
+quite out of the question to suppose that the last four
+members of the group are anything other than separate
+and distinct comets moving in practically the same orbit.
+This common orbit suggests a common origin for the
+comets, but leaves us to conjecture how they became separated.</p>
+
+<p>The observed orbits of these five comets present some
+slight discordances among themselves, but if we suppose
+each comet to move in the average of the observed paths it
+is a simple matter to fix their several positions at the present
+time. They have all receded from the sun nearly on
+line toward the bright star Sirius, and were all of them, at
+the beginning of the year 1900, standing nearly motionless
+inside of a space not bigger than the sun and distant from
+the sun about 150 radii of the earth's orbit. The great
+rapidity with which they swept through that part of their
+orbit near the sun (see <a href="#S_162">§&nbsp;162</a>) is being compensated by
+the present extreme slowness of their motions, so that
+the comets of 1668 and 1882, whose passages through the
+solar system were separated by an interval of more than
+two centuries, now stand together near the aphelion of their
+orbits, separated by a distance only 50 per cent greater than
+the diameter of the moon's orbit, and they will continue
+substantially in this position for some two or three centuries
+to come.<span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span></p>
+
+<p>The slowness with which these bodies move when far
+from the sun is strikingly illustrated by an equation of
+celestial mechanics which for parabolic orbits takes the
+place of Kepler's Third Law&mdash;viz.:</p>
+
+<p class="center"><i>r</i><sup>3</sup> / <i>T</i><sup>2</sup> = 178,</p>
+
+<p>where <i>T</i> is the time, in years, required for the comet to
+move from its perihelion to any remote part of the orbit,
+whose distance from the sun is represented, in radii of the
+earth's orbit, by <i>r</i>. If the comet of 1668 had moved in a
+parabola instead of the ellipse supposed above, how many
+years would have been required to reach its present distance
+from the sun?</p>
+
+<p><a name="S_178" id="S_178"></a>178. <b>Relation of comets to the solar system.</b>&mdash;The orbits
+of these comets illustrate a tendency which is becoming
+ever more strongly marked. Because comet orbits are
+nearly parabolas, it used to be assumed that they were
+exactly parabolic, and this carried with it the conclusion
+that comets have their origin outside the solar system. It
+may be so, and this view is in some degree supported by
+the fact that these nearly parabolic orbits of both comets
+and meteors are tipped at all possible angles to the plane
+of the ecliptic instead of lying near it as do the orbits of
+the planets; and by the further fact that, unlike the planets,
+the comets show no marked tendency to move around their
+orbits in the direction in which the sun rotates upon his
+axis. There is, in fact, the utmost confusion among them
+in this respect, some going one way and some another.
+The law of the solar system (gravitation) is impressed upon
+their movements, but its order is not.</p>
+
+<p>But as observations grow more numerous and more
+precise, and comet orbits are determined with increasing
+accuracy, there is a steady gain in the number of elliptic
+orbits at the expense of the parabolic ones, and if comets
+are of extraneous origin we must admit that a very considerable<span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span>
+percentage of them have their velocities slowed
+down within the solar system, perhaps not so much by the
+attraction of the planets as by the resistance offered to their
+motion by meteor particles and swarms along their paths.
+A striking instance of what may befall a comet in this way
+is shown in <a href="#Fig_117">Fig.&nbsp;117</a>, where the tail of a comet appears
+sadly distorted and broken by what is presumed to have
+been a collision with a meteor swarm. A more famous case
+of impeded motion is offered by the comet which bears the
+name of Encke. This has a periodic time less than that of
+any other known comet, and at intervals of forty months
+comes back to perihelion, each time moving in a little
+smaller orbit than before, unquestionably on account of
+some resistance which it has suffered.</p>
+
+<div class="figcenter" style="width: 400px;"><a name="Fig_117" id="Fig_117"></a>
+<a href="images/i316-full.jpg"><img src="images/i316.jpg" width="400" height="421" alt="Fig. 117.&mdash;Brooks&#39;s comet, October 21, 1893.&mdash;Barnard." title="Fig. 117.&mdash;Brooks&#39;s comet, October 21, 1893.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 117.</span>&mdash;Brooks&#39;s comet, October 21, 1893.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_179" id="S_179"></a>179. <b>The development of a comet.</b>&mdash;We saw in <a href="#S_174">§&nbsp;174</a>
+that the sun's action upon a meteor swarm tends to
+break it up into a long stream, and the same tendency to<span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span>
+break up is true of comets whose attenuated substance presents
+scant resistance to this force. According to the
+mathematical analysis of Roche, if the comet stood still
+the sun's tidal force would tend first to draw it out on line
+with the sun, just as the earth's tidal force pulled the
+moon out of shape (<a href="#S_42">§&nbsp;42</a>), and then it would cause the
+lighter part of the comet's substance to flow away from
+both ends of this long diameter. This destructive action
+of the sun is not limited to comets and meteor streams,
+for it tends to tear the earth and moon to pieces as well;
+but the densities and the resulting mutual attractions of
+their parts are far too great to permit this to be accomplished.</p>
+
+<p>As a curiosity of mathematical analysis we may note
+that a spherical cloud of meteors, or dust particles weighing
+a gramme each, and placed at the earth's distance from
+the sun, will be broken up and dissipated by the sun's tidal
+action if the average distance between the particles exceeds
+two yards. Now, the earth is far more dense than such a
+cloud, whose extreme tenuity, however, suggests what we
+have already learned of the small density of comets, and
+prepares us in their case for an outflow of particles at both
+ends of the diameter directed toward the sun. Something
+of this kind actually occurs, for the tail of a comet
+streams out on the side opposite to the sun, and in general
+points away from the sun, as is shown in <a href="#Fig_109">Fig.&nbsp;109</a>, and the
+envelopes and jets rise up toward the sun; but an inspection
+of <a href="#Fig_106">Fig.&nbsp;106</a> will show that the tail and the envelope
+are too unlike to be produced by one and the same set of
+forces.</p>
+
+<p>It was long ago suggested that the sun possibly exerts
+upon a comet's substance a repelling force in addition to
+the attracting force which we call gravity. We think naturally
+in this connection of the repelling force which a
+charge of electricity exerts upon a similar charge placed
+on a neighboring body, and we note that if both sun and<span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span>
+comet carried a considerable store of electricity upon their
+surfaces this would furnish just such a repelling force as
+seems indicated by the phenomena of comets' tails; for the
+force of gravity would operate between the substance of
+sun and comet, and on the whole would be the controlling
+force, while the electric charges would produce a repulsion,
+relatively feeble for the big particles and strong for the
+little ones, since an electric charge lies wholly on the surface,
+while gravity permeates the whole mass of a body,
+and the ratio of volume (gravity) to surface (electric
+charge) increases rapidly with increasing size. The repelling
+force would thrust back toward the comet those particles
+which flowed out toward the sun, while it would urge
+forward those which flowed away from it, thus producing
+the difference in appearance between tail and envelopes,
+the latter being regarded from this standpoint as stunted
+tails strongly curved backward. In recent years the Russian
+astronomer Bredichin has made a careful study of the
+shape and positions of comets' tails and finds that they fit
+with mathematical precision to the theories of electric
+repulsion.</p>
+
+<p><a name="S_180" id="S_180"></a>180. <b>Comet tails.</b>&mdash;According to Bredichin, a comet's
+tail is formed by something like the following process: In
+the head of the comet itself a certain part of its matter is
+broken up into fine bits, single molecules perhaps, which,
+as they no longer cling together, may be described as in
+the condition of vapor. By the repellent action of both
+sun and comet these molecules are cast out from the head
+of the comet and stream away in the direction opposite to
+the sun with different velocities, the heavy ones slowly and
+the light ones faster, much as particles of smoke stream
+away from a smokestack, making for the comet a tail
+which like a trail of smoke is composed of constantly
+changing particles. The result of this process is shown
+in <a href="#Fig_118">Fig.&nbsp;118</a>, where the positions of the comet in its orbit
+on successive days are marked by the Roman numerals, and<span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span>
+the broken lines represent the paths of molecules <i>m<sup>I</sup></i>, <i>m<sup>II</sup></i>,
+<i>m<sup>III</sup></i>, etc., expelled from it on their several dates and traveling
+thereafter in
+orbits determined
+by the combined
+effect of the sun's
+attraction, the
+sun's repulsion,
+and the comet's
+repulsion. The
+comet's attraction
+(gravity) is
+too small to be
+taken into account.
+The line
+drawn upward
+from <i>VI</i> represents
+the positions
+of these
+molecules on the
+sixth day, and
+shows that all of
+them are arranged
+in a tail pointing
+nearly away from the sun. A similar construction for the
+other dates gives the corresponding positions of the tail,
+always pointing away from the sun.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_118" id="Fig_118"></a>
+<img src="images/i319.png" width="350" height="462" alt="Fig. 118.&mdash;Formation of a comet&#39;s tail." title="Fig. 118.&mdash;Formation of a comet&#39;s tail." />
+<span class="caption"><span class="smcap">Fig. 118.</span>&mdash;Formation of a comet&#39;s tail.</span>
+</div>
+
+<p>Only the lightest kind of molecules&mdash;e.&nbsp;g., hydrogen&mdash;could
+drift away from the comet so rapidly as is here shown.
+The heavier ones, such as carbon and iron, would be repelled
+as strongly by the electric forces, but they would be
+more strongly pulled back by the gravitative forces, thus
+producing a much slower separation between them and the
+head of the comet. Construct a figure such as the above,
+in which the molecules shall recede from the comet only
+one eighth as fast as in <a href="#Fig_118">Fig.&nbsp;118</a>, and note what a different<span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span>
+position it gives to the comet's tail. Instead of pointing
+directly away from the sun, it will be bent strongly to one
+side, as is the large plume-shaped tail of the Donati comet
+shown in <a href="#Fig_101">Fig.&nbsp;101</a>. But observe that this comet has also a
+nearly straight tail, like the theoretical one of <a href="#Fig_118">Fig.&nbsp;118</a>.
+We have here two distinct types of comet tails, and according
+to Bredichin there is still another but unusual type,
+even more strongly bent to one side of the line joining
+comet and sun, and appearing quite short and stubby.
+The existence of these three types, and their peculiarities
+of shape and position, are all satisfactorily accounted for
+by the supposition that they are made of different materials.
+The relative molecular weights of hydrogen, some of
+the hydrocarbons, and iron, are such that tails composed
+of these molecules would behave just as do the actual tails
+observed and classified into these three types. The spectroscope
+shows that these materials&mdash;hydrogen, hydrocarbons,
+and iron&mdash;are present in comets, and leaves little
+room for doubt of the essential soundness of Bredichin's
+theory.</p>
+
+<p><a name="S_181" id="S_181"></a>181. <b>Disintegration of comets.</b>&mdash;We must regard the tail
+as waste matter cast off from the comet's head, and although
+the amount of this matter is very small, it must in some
+measure diminish the comet's mass. This process is, of
+course, most active at the time of perihelion passage, and
+if the comet returns to perihelion time after time, as the
+periodic ones which move in elliptic orbits must do, this
+waste of material may become a serious matter, leading
+ultimately to the comet's destruction. It is significant in
+this connection that the periodic comets are all small and
+inconspicuous, not one of them showing a tail of any considerable
+dimensions, and it appears probable that they are
+far advanced along the road which, in the case of Biela's
+comet, led to its disintegration. Their fragments are in
+part strewn through the solar system, making some small
+fraction of its cloud of cosmic dust, and in part they have<span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span>
+been carried away from the sun and scattered throughout
+the universe along hyperbolic orbits impressed upon them
+at the time they left the comet.</p>
+
+<p>But it is not through the tail only that the disintegrating
+process is worked out. While Biela's comet is perhaps
+the most striking instance in which the head has
+broken up, it is by no means the only one. The Great
+Comet of 1882 cast off a considerable number of fragments
+which moved away as independent though small comets
+and other more recent comets have been seen to do the
+same. An even more striking phenomenon was the gradual
+breaking up of the nucleus of the same comet, 1882,
+II, into a half dozen nuclei arranged in line like beads
+upon a string, and pointing along the axis of the tail. See
+<a href="#Fig_119">Fig.&nbsp;119</a>, which shows the series of changes observed in
+the head of this comet.</p>
+
+<p><a name="S_182" id="S_182"></a>182. <b>Comets and the spectroscope.</b>&mdash;The spectrum presented
+by comets was long a puzzle, and still retains something
+of that character, although much progress has been
+made toward an understanding of it. In general it consists
+of two quite distinct parts&mdash;first, a faint background
+of continuous spectrum due to ordinary sunlight reflected
+from the comet; and, second, superposed upon this, three
+bright bands like the carbon band shown at the middle of
+<a href="#Fig_48">Fig.&nbsp;48</a>, only not so sharply defined. These bands make a
+discontinuous spectrum quite similar to that given off by
+compounds of hydrogen and carbon, and of course indicate
+that a part of the comet's light originates in the body
+itself, which must therefore be incandescent, or at least
+must contain some incandescent portions.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_119" id="Fig_119"></a>
+<a href="images/i322-full.jpg"><img src="images/i322.jpg" width="500" height="787" alt="October 9, 1882.
+
+November 21, 1882.
+
+February 1, 1883.
+
+March 3, 1883.
+
+Fig. 119.&mdash;The head of the Great Comet of 1882.&mdash;Winlock." title="October 9, 1882.
+
+November 21, 1882.
+
+February 1, 1883.
+
+March 3, 1883.
+
+Fig. 119.&mdash;The head of the Great Comet of 1882.&mdash;Winlock." /></a>
+<span class="caption"><span class="smcap">Fig. 119.</span>&mdash;The head of the Great Comet of 1882.&mdash;<span class="smcap">Winlock.</span></span>
+</div>
+
+<p>By heating hydrocarbons in our laboratories until they
+become incandescent, something like the comet spectrum
+may be artificially produced, but the best approximation
+to it is obtained by passing a disruptive electrical discharge
+through a tube in which fragments of meteors
+have been placed. A flash of lightning is a disruptive<span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span>
+electrical discharge upon a grand scale. Now, meteors
+and electric phenomena have been independently brought
+to our notice in connection with comets, and with this
+suggestion it is easy to frame a general idea of the physical
+condition of these objects&mdash;for example, a cloud of
+meteors of different sizes so loosely clustered that the
+average density of the swarm is very low indeed; the several
+particles in motion relative to each other, as well as to
+the sun, and disturbed in that motion by the sun's tidal
+action. Each particle carries its own electric charge,
+which may be of higher or lower tension than that of its
+neighbor, and is ready to leap across the intervening gap
+whenever two particles approach each other. To these
+conditions add the inductive effect of the sun's electric
+charge, which tends to produce a particular and artificial
+distribution of electricity among the comet's particles, and
+we may expect to find an endless succession of sparks, tiny
+lightning flashes, springing from one particle to another,
+most frequent and most vivid when the comet is near the
+sun, but never strong enough to be separately visible.
+Their number is, however, great enough to make the comet
+in part self-luminous with three kinds of light&mdash;i.&nbsp;e., the three
+bright bands of its spectrum, whose wave lengths show in
+the comet the same elements and compounds of the elements&mdash;carbon,
+hydrogen, and oxygen&mdash;which chemical
+analysis finds in the fallen meteor. It is not to be supposed
+that these are the only chemical elements in the
+comet, as they certainly are not the only ones in the meteor.
+They are the easy ones to detect under ordinary circumstances,
+but in special cases, like that of the Great
+Comet of 1882, whose near approach to the sun rendered
+its whole substance incandescent, the spectrum glows with
+additional bright lines of sodium, iron, etc.</p>
+
+<p><a name="S_183" id="S_183"></a>183. <b>Collisions.</b>&mdash;A question sometimes asked, What
+would be the effect of a collision between the earth and a
+comet? finds its answer in the results reached in the preceding<span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span>
+sections. There would be a star shower, more or
+less brilliant according to the number and size of the pieces
+which made up the comet's head. If these were like the
+remains of the Biela comet, the shower might even be a
+very tame one; but a collision with a great comet would
+certainly produce a brilliant meteoric display if its head
+came in contact with the earth. If the comet were built of
+small pieces whose individual weights did not exceed a few
+ounces or pounds, the earth's atmosphere would prove a
+perfect shield against their attacks, reducing the pieces to
+harmless dust before they could reach the ground, and
+leaving the earth uninjured by the encounter, although the
+comet might suffer sadly from it. But big stones in the
+comet, meteors too massive to be consumed in their flight
+through the air, might work a very different effect, and by
+their bombardment play sad havoc with parts of the earth's
+surface, although any such result as the wrecking of the
+earth, or the destruction of all life upon it, does not seem
+probable. The 40 meteors of <a href="#S_169">§&nbsp;169</a> may stand for a collision
+with a small comet. Consult the Bible (Joshua&nbsp;x, 11)
+for an example of what might happen with a larger one.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span></p>
+<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII</h2>
+
+<h3>THE FIXED STARS</h3>
+
+
+<p><a name="S_184" id="S_184"></a>184. <b>The constellations.</b>&mdash;In the earlier chapters the student
+has learned to distinguish between wandering stars
+(planets) and those fixed luminaries which remain year after
+year in the same constellation, shining for the most part
+with unvarying brilliancy, and presenting the most perfect
+known image of immutability. Homer and Job and prehistoric
+man saw Orion and the Pleiades much as we see
+them to-day, although the precession, by changing their
+relation to the pole of the heavens, has altered their risings
+and settings, and it may be that their luster has changed
+in some degree as they grew old with the passing centuries.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="Fig_120" id="Fig_120"></a>
+<a href="images/i326-full.jpg"><img src="images/i326.jpg" width="600" height="414" alt="Fig. 120.&mdash;Illustrating the division of the sky into constellations." title="Fig. 120.&mdash;Illustrating the division of the sky into constellations." /></a>
+<span class="caption"><span class="smcap">Fig. 120.</span>&mdash;Illustrating the division of the sky into constellations.</span>
+</div>
+
+<p>The division of the sky into constellations dates back to
+the most primitive times, long before the Christian era,
+and the crooked and irregular boundaries of these constellations,
+shown by the dotted lines in <a href="#Fig_120">Fig.&nbsp;120</a>, such
+as no modern astronomer would devise, are an inheritance
+from antiquity, confounded and made worse in its
+descent to our day. The boundaries assigned to constellations
+near the south pole are much more smooth and regular,
+since this part of the sky, invisible to the peoples from
+whom we inherit, was not studied and mapped until more
+modern times. The old traditions associated with each
+constellation a figure, often drawn from classical mythology,
+which was supposed to be suggested by the grouping
+of the stars: thus Ursa Major is a great bear, stalking across
+the sky, with the handle of the Dipper for his tail; Leo is a
+lion; Cassiopeia, a lady in a chair; Andromeda, a maiden<span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span>
+chained to a rock, etc.; but for the most part the resemblances
+are far-fetched and quite too fanciful to be followed
+by the ordinary eye.</p>
+
+<p><a name="S_185" id="S_185"></a>185. <b>The number of stars.</b>&mdash;"As numerous as the stars
+of heaven" is a familiar figure of speech for expressing the
+idea of countless number, but as applied to the visible
+stars of the sky the words convey quite a wrong impression,
+for, under ordinary circumstances, in a clear sky every star
+to be seen may be counted in the course of a few hours,
+since they do not exceed 3,000 or 4,000, the exact number
+depending upon atmospheric conditions and the keenness
+of the individual eye. Test your own vision by counting
+the stars of the Pleiades. Six are easily seen, and you may
+possibly find as many as ten or twelve; but however many
+are seen, there will be a vague impression of more just beyond
+the limit of visibility, and doubtless this impression is
+partly responsible for the popular exaggeration of the number
+of the stars. In fact, much more than half of what we
+call starlight comes from stars which are separately too
+small to be seen, but whose number is so great as to more
+than make up for their individual faintness.</p>
+
+<p>The Milky Way is just such a cloud of faint stars, and
+the student who can obtain access to a small telescope, or
+even an opera glass, should not fail to turn it toward the
+Milky Way and see for himself how that vague stream of
+light breaks up into shining points, each an independent
+star. These faint stars, which are found in every part of
+the sky as well as in the Milky Way, are usually called
+<i>telescopic</i>, in recognition of the fact that they can be seen
+only in the telescope, while the other brighter ones are
+known as <i>lucid stars</i>.</p>
+
+<p><a name="S_186" id="S_186"></a>186. <b>Magnitudes.</b>&mdash;The telescopic stars show among themselves
+an even greater range of brightness than do the lucid
+ones, and the system of magnitudes (<a href="#S_9">§&nbsp;9</a>) has accordingly
+been extended to include them, the faintest star visible in
+the greatest telescope of the present time being of the sixteenth<span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span>
+or seventeenth magnitude, while, as we have already
+learned, stars on the dividing line between the telescopic and
+the lucid ones are of the sixth magnitude. To compare the
+amount of light received from the stars with that from the
+planets, and particularly from the sun and moon, it has
+been found necessary to prolong the scale of magnitudes
+backward into the negative numbers, and we speak of the
+sun as having a stellar magnitude represented by the number
+-26.5. The full moon's stellar magnitude is -12, and
+the planets range from&nbsp;-3 (Venus) to&nbsp;+8 (Neptune).
+Even a very few of the stars are so bright that negative
+magnitudes must be used to represent their true relation
+to the fainter ones. Sirius, for example, the brightest of
+the fixed stars, is of the -1 magnitude, and such stars as
+Arcturus and Vega are of the 0 magnitude.</p>
+
+<p>The relation of these magnitudes to each other has been
+so chosen that a star of any one magnitude is very approximately
+2.5 times as bright as one of the next fainter magnitude,
+and this ratio furnishes a convenient method of
+comparing the amount of light received from different stars.
+Thus the brightness of Venus is 2.5&nbsp;×&nbsp;2.5 times that of
+Sirius. The full moon is (2.5)<sup>9</sup> times as bright as Venus,
+etc.; only it should be observed that the number 2.5 is not
+exactly the value of the <i>light ratio</i> between two consecutive
+magnitudes. Strictly this ratio is the <sup>5</sup>&#8730;&nbsp;100&nbsp;=&nbsp;2.5119+,
+so that to be entirely accurate we must say that a difference
+of five magnitudes gives a hundredfold difference of brightness.
+In mathematical symbols, if <i>B</i> represents the ratio of
+brightness (quantity of light) of two stars whose magnitudes
+are <i>m</i> and <i>n</i>, then</p>
+
+<p class="center"><i>B</i> = (100)<sup>(<i>m</i>-<i>n</i>)/5</sup></p>
+
+<p>How much brighter is an ordinary first-magnitude star,
+such as Aldebaran or Spica, than a star just visible to the
+naked eye? How many of the faintest stars visible in a
+great telescope would be required to make one star just<span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span>
+visible to the unaided eye? How many full moons must
+be put in the sky in order to give an illumination as bright
+as daylight? How large a part of the visible hemisphere
+would they occupy?</p>
+
+<p><a name="S_187" id="S_187"></a>187. <b>Classification by magnitudes.</b>&mdash;The brightness of all
+the lucid stars has been carefully measured with an instrument
+(photometer) designed for that special purpose, and
+the following table shows, according to the Harvard Photometry,
+the number of stars in the whole sky, from pole to
+pole, which are brighter than the several magnitudes
+named in the table:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">The number</td><td align="center">of stars</td><td align="center">brighter</td><td align="center">than</td><td align="center">magnitude</td><td align="right">1.0</td><td align="center">is</td><td align="right">11</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">2.0</td><td align="center">"</td><td align="right">39</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">3.0</td><td align="center">"</td><td align="right">142</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">4.0</td><td align="center">"</td><td align="right">463</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">5.0</td><td align="center">"</td><td align="right">1,483</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">6.0</td><td align="center">"</td><td align="right">4,326</td></tr>
+</table></div>
+
+<p>It must not be inferred from this table that there are
+in the whole sky only 4,326 stars visible to the naked eye.
+The actual number is probably 50 or 60 per cent greater
+than this, and the normal human eye sees stars as faint as
+the magnitude 6.4 or 6.5, the discordance between this number
+and the previous statement, that the sixth magnitude is
+the limit of the naked-eye vision, having been introduced
+in the attempt to make precise and accurate a classification
+into magnitudes which was at first only rough and approximate.
+This same striving after accuracy leads to the introduction
+of fractional numbers to represent gradations of
+brightness intermediate between whole magnitudes. Thus
+of the 2,843 stars included between the fifth and sixth
+magnitudes a certain proportion are said to be of the 5.1
+magnitude, 5.2 magnitude, and so on to the 5.9 magnitude,
+even hundredths of a magnitude being sometimes employed.</p>
+
+<p>We have found the number of stars included between
+the fifth and sixth magnitudes by subtracting from the
+last number of the preceding table the number immediately<span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span>
+preceding it, and similarly we may find the number
+included between each other pair of consecutive magnitudes,
+as follows:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">Magnitude</td><td align="center">0</td><td align="right">&nbsp;</td><td align="center">1</td><td align="right">&nbsp;</td><td align="center">2</td><td align="right">&nbsp;</td><td align="center">3</td><td align="right">&nbsp;</td><td align="center">4</td><td align="right">&nbsp;</td><td align="center">5</td><td align="right">&nbsp;</td><td align="center">6</td></tr>
+<tr><td align="left">Number of stars</td><td align="center">&nbsp;</td><td align="right">11</td><td align="center">&nbsp;</td><td align="right">28</td><td align="center">&nbsp;</td><td align="right">103</td><td align="center">&nbsp;</td><td align="right">321</td><td align="center">&nbsp;</td><td align="right">1,020</td><td align="center">&nbsp;</td><td align="right">2,843</td></tr>
+<tr><td align="left">4 × 3<sup>m</sup></td><td align="center">&nbsp;</td><td align="right">12</td><td align="center">&nbsp;</td><td align="right">36</td><td align="center">&nbsp;</td><td align="right">108</td><td align="center">&nbsp;</td><td align="right">324</td><td align="center">&nbsp;</td><td align="right">972</td><td align="center">&nbsp;</td><td align="right">2,916</td></tr>
+</table></div>
+
+<p>In the last line each number after the first is found by
+multiplying the preceding one by 3, and the approximate
+agreement of each such number with that printed above it
+shows that on the whole, as far as the table goes, the fainter
+stars are approximately three times as numerous as those
+a magnitude brighter.</p>
+
+<p>The magnitudes of the telescopic stars have not yet
+been measured completely, and their exact number is unknown;
+but if we apply our principle of a threefold increase
+for each successive magnitude, we shall find for the fainter
+stars&mdash;those of the tenth and twelfth magnitudes&mdash;prodigious
+numbers which run up into the millions, and even these
+are probably too small, since down to the ninth or tenth
+magnitude it is certain that the number of the telescopic
+stars increases from magnitude to magnitude in more than
+a threefold ratio. This is balanced in some degree by the
+less rapid increase which is known to exist in magnitudes
+still fainter; and applying our formula without regard to
+these variations in the rate of increase, we obtain as a rude
+approximation to the total number of stars down to the
+fifteenth magnitude, 86,000,000. The Herschels, father
+and son, actually counted the number of stars visible in
+nearly 8,000 sample regions of the sky, and, inferring the
+character of the whole sky from these samples, we find it
+to contain 58,500,000 stars; but the magnitude of the faintest
+star visible in their telescope, and included in their
+count, is rather uncertain.</p>
+
+<p>How many first-magnitude stars would be needed to
+give as much light as do the 2,843 stars of magnitude 5.0<span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span>
+to 6.0? How many tenth-magnitude stars are required to
+give the same amount of light?</p>
+
+<p>To the modern man it seems natural to ascribe the different
+brilliancies of the stars to their different distances
+from us; but such was not the case 2,000 years ago, when
+each fixed star was commonly thought to be fastened to
+a "crystal sphere," which carried them with it, all at the
+same distance from us, as it turned about the earth. In
+breaking away from this erroneous idea and learning to
+think of the sky itself as only an atmospheric illusion
+through which we look to stars at very different distances
+beyond, it was easy to fall into the opposite error and to
+think of the stars as being much alike one with another,
+and, like pebbles on the beach, scattered throughout space
+with some rough degree of uniformity, so that in every
+direction there should be found in equal measure stars
+near at hand and stars far off, each shining with a luster
+proportioned to its remoteness.</p>
+
+<p><a name="S_188" id="S_188"></a>188. <b>Distances of the stars.</b>&mdash;Now, in order to separate
+the true from the false in this last mode of thinking about
+the stars, we need some knowledge of their real distances
+from the earth, and in seeking it we encounter what is
+perhaps the most delicate and difficult problem in the
+whole range of observational astronomy. As shown in
+<a href="#Fig_121">Fig.&nbsp;121</a>, the principles involved in determining these distances
+are not fundamentally different from those employed
+in determining the moon's distance from the earth.
+Thus, the ellipse at the left of the figure represents the
+earth's orbit and the position of the earth at different
+times of the year. The direction of the star <i>A</i> at these
+several times is shown by lines drawn through <i>A</i> and prolonged
+to the background apparently furnished by the sky.
+A similar construction is made for the star <i>B</i>, and it is
+readily seen that owing to the changing position of the
+observer as he moves around the earth's orbit, both <i>A</i> and
+<i>B</i> will appear to move upon the background in orbits<span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span>
+shaped like that of the earth as seen from the star, but
+having their size dependent upon the star's distance, the
+apparent orbit of <i>A</i> being larger than that of <i>B</i>, because <i>A</i>
+is nearer the earth. By measuring the angular distance
+between <i>A</i> and <i>B</i> at opposite seasons of the year (e.&nbsp;g., the
+angles <i>A&mdash;Jan.&mdash;B</i>, and <i>A&mdash;July&mdash;B</i>) the astronomer
+determines from the change in this angle how much larger
+is the one path than the other, and thus concludes how
+much nearer is <i>A</i> than <i>B</i>. Strictly, the difference between
+the January and July angles is equal to the difference between
+the angles subtended at <i>A</i> and <i>B</i> by the diameter of
+the earth's orbit, and if <i>B</i> were so far away that the angle
+<i>Jan.&mdash;B&mdash;July</i> were nothing at all we should get immediately
+from the observations the angle <i>Jan.&mdash;A&mdash;July</i>,
+which would suffice to determine the stars' distance. Supposing
+the diameter of the earth's orbit and the angle at <i>A</i>
+to be known, can you make a graphical construction that
+will determine the distance of <i>A</i> from the earth?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_121" id="Fig_121"></a>
+<img src="images/i332.png" width="500" height="287" alt="Fig. 121.&mdash;Determining a star&#39;s parallax." title="Fig. 121.&mdash;Determining a star&#39;s parallax." />
+<span class="caption"><span class="smcap">Fig. 121.</span>&mdash;Determining a star&#39;s parallax.</span>
+</div>
+
+<p>The angle subtended at <i>A</i> by the radius of the earth's
+orbit&mdash;i.&nbsp;e., 1/2&nbsp;(<i>Jan.&mdash;A&mdash;July</i>)&mdash;is called the star's parallax,
+and this is commonly used by astronomers as a measure
+of the star's distance instead of expressing it in linear
+units such as miles or radii of the earth's orbit. The distance<span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span>
+of a star is equal to the radius of the earth's orbit
+divided by the parallax, in seconds of arc, and multiplied
+by the number 206265.</p>
+
+<p>A weak point of this method of measuring stellar distances
+is that it always gives what is called a relative parallax&mdash;i.&nbsp;e.,
+the difference between the parallaxes of <i>A</i> and
+<i>B</i>; and while it is customary to select for <i>B</i> a star or stars
+supposed to be much farther off than <i>A</i>, it may happen,
+and sometimes does happen, that these comparison stars
+as they are called are as near or nearer than <i>A</i>, and give
+a negative parallax&mdash;i.&nbsp;e., the difference between the angles
+at <i>A</i> and <i>B</i> proves to be negative, as it must whenever the
+star <i>B</i> is nearer than <i>A</i>.</p>
+
+<p>The first really successful determinations of stellar
+parallax were made by Struve and Bessel a little prior to
+1840, and since that time the distances of perhaps 100 stars
+have been measured with some degree of reliability, although
+the parallaxes themselves are so small&mdash;never as
+great as 1''&mdash;that it is extremely difficult to avoid falling
+into error, since even for the nearest star the problem of
+its distance is equivalent to finding the distance of an object
+more than 5 miles away by looking at it first with one
+eye and then with the other. Too short a base line.</p>
+
+<p><a name="S_189" id="S_189"></a>189. <b>The sun and his neighbors.</b>&mdash;The distances of the
+sun's nearer neighbors among the stars are shown in <a href="#Fig_122">Fig.&nbsp;122</a>,
+where the two circles having the sun at their center
+represent distances from it equal respectively to 1,000,000
+and 2,000,000 times the distance between earth and sun.
+In the figure the direction of each star from the sun corresponds
+to its right ascension, as shown by the Roman
+numerals about the outer circle; the true direction of the
+star from the sun can not, of course, be shown upon the
+flat surface of the paper, but it may be found by elevating
+or depressing the star from the surface of the paper
+through an angle, as seen from the sun, equal to its declination,
+as shown in the fifth column of the following table,<span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span></p>
+
+<h4><i>The Sun's Nearest Neighbors</i></h4>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides">
+<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup>
+<thead>
+<tr><th align="center">No.</th><th align="center"><span class="smcap">Star.</span></th><th align="center">Magnitude.</th><th align="center">R.&nbsp;A.</th><th align="center">Dec.</th><th align="center">Parallax.</th><th align="center">Distance.</th></tr>
+</thead>
+<tbody>
+<tr><td align="right">1</td><td align="left">&alpha; Centauri</td><td align="right">0.7</td><td align="right">14.5h.</td><td align="right">-60°</td><td align="right">0.75"</td><td align="right">0.27</td></tr>
+<tr><td align="right">2</td><td align="left">Ll. 21,185</td><td align="right">6.8</td><td align="right">11.0</td><td align="right">+37</td><td align="right">0.45</td><td align="right">0.46</td></tr>
+<tr><td align="right">3</td><td align="left">61 Cygni</td><td align="right">5.0</td><td align="right">21.0</td><td align="right">+38</td><td align="right">0.40</td><td align="right">0.51</td></tr>
+<tr><td align="right">4</td><td align="left">&eta; Herculis</td><td align="right">3.6</td><td align="right">16.7</td><td align="right">+39</td><td align="right">0.40</td><td align="right">0.51</td></tr>
+<tr><td align="right">5</td><td align="left">Sirius</td><td align="right">-1.4</td><td align="right">6.7</td><td align="right">-17</td><td align="right">0.37</td><td align="right">0.56</td></tr>
+<tr><td align="right">6</td><td align="left">&Sigma; 2,398</td><td align="right">8.2</td><td align="right">18.7</td><td align="right">+59</td><td align="right">0.35</td><td align="right">0.58</td></tr>
+<tr><td align="right">7</td><td align="left">Procyon</td><td align="right">0.5</td><td align="right">7.6</td><td align="right">+5</td><td align="right">0.34</td><td align="right">0.60</td></tr>
+<tr><td align="right">8</td><td align="left">&gamma; Draconis</td><td align="right">4.8</td><td align="right">17.5</td><td align="right">+55</td><td align="right">0.30</td><td align="right">0.68</td></tr>
+<tr><td align="right">9</td><td align="left">Gr. 34</td><td align="right">7.9</td><td align="right">0.2</td><td align="right">+43</td><td align="right">0.29</td><td align="right">0.71</td></tr>
+<tr><td align="right">10</td><td align="left">Lac. 9,352</td><td align="right">7.5</td><td align="right">23.0</td><td align="right">-36</td><td align="right">0.28</td><td align="right">0.74</td></tr>
+<tr><td align="right">11</td><td align="left">&sigma; Draconis</td><td align="right">4.8</td><td align="right">19.5</td><td align="right">+69</td><td align="right">0.25</td><td align="right">0.82</td></tr>
+<tr><td align="right">12</td><td align="left">A. O. 17,415-6</td><td align="right">9.0</td><td align="right">17.6</td><td align="right">+68</td><td align="right">0.25</td><td align="right">0.82</td></tr>
+<tr><td align="right">13</td><td align="left">&eta; Cassiopeię</td><td align="right">3.4</td><td align="right">0.7</td><td align="right">+57</td><td align="right">0.25</td><td align="right">0.82</td></tr>
+<tr><td align="right">14</td><td align="left">Altair</td><td align="right">1.0</td><td align="right">19.8</td><td align="right">+9</td><td align="right">0.21</td><td align="right">0.97</td></tr>
+<tr><td align="right">15</td><td align="left">&#1013; Indi</td><td align="right">5.2</td><td align="right">21.9</td><td align="right">-57</td><td align="right">0.20</td><td align="right">1.03</td></tr>
+<tr><td align="right">16</td><td align="left">Gr. 1,618</td><td align="right">6.7</td><td align="right">10.1</td><td align="right">+50</td><td align="right">0.20</td><td align="right">1.03</td></tr>
+<tr><td align="right">17</td><td align="left">10 Ursę Majoris</td><td align="right">4.2</td><td align="right">8.9</td><td align="right">+42</td><td align="right">0.20</td><td align="right">1.03</td></tr>
+<tr><td align="right">18</td><td align="left">Castor</td><td align="right">1.5</td><td align="right">7.5</td><td align="right">+32</td><td align="right">0.20</td><td align="right">1.03</td></tr>
+<tr><td align="right">19</td><td align="left">Ll. 21,258</td><td align="right">8.5</td><td align="right">11.0</td><td align="right">+44</td><td align="right">0.20</td><td align="right">1.03</td></tr>
+<tr><td align="right">20</td><td align="left">&omicron;<sup>2</sup> Eridani</td><td align="right">4.5</td><td align="right">4.2</td><td align="right">-8</td><td align="right">0.19</td><td align="right">1.08</td></tr>
+<tr><td align="right">21</td><td align="left">A. O. 11,677</td><td align="right">9.0</td><td align="right">11.2</td><td align="right">+66</td><td align="right">0.19</td><td align="right">1.08</td></tr>
+<tr><td align="right">22</td><td align="left">Ll. 18,115</td><td align="right">8.0</td><td align="right">9.1</td><td align="right">+53</td><td align="right">0.18</td><td align="right">1.14</td></tr>
+<tr><td align="right">23</td><td align="left">B. D. 36°, 3,883</td><td align="right">7.1</td><td align="right">20.0</td><td align="right">+36</td><td align="right">0.18</td><td align="right">1.14</td></tr>
+<tr><td align="right">24</td><td align="left">Gr. 1,618</td><td align="right">6.5</td><td align="right">10.1</td><td align="right">+50</td><td align="right">0.17</td><td align="right">1.21</td></tr>
+<tr><td align="right">25</td><td align="left">&beta; Cassiopeię</td><td align="right">2.3</td><td align="right">0.1</td><td align="right">+59</td><td align="right">0.16</td><td align="right">1.28</td></tr>
+<tr><td align="right">26</td><td align="left">70 Ophiuchi</td><td align="right">4.4</td><td align="right">18.0</td><td align="right">+2</td><td align="right">0.16</td><td align="right">1.28</td></tr>
+<tr><td align="right">27</td><td align="left">&Sigma; 1,516</td><td align="right">6.5</td><td align="right">11.2</td><td align="right">+74</td><td align="right">0.15</td><td align="right">1.38</td></tr>
+<tr><td align="right">28</td><td align="left">Gr. 1,830</td><td align="right">6.6</td><td align="right">11.8</td><td align="right">+39</td><td align="right">0.15</td><td align="right">1.38</td></tr>
+<tr><td align="right">29</td><td align="left">&mu; Cassiopeię</td><td align="right">5.4</td><td align="right">1.0</td><td align="right">+54</td><td align="right">0.14</td><td align="right">1.47</td></tr>
+<tr><td align="right">30</td><td align="left">&#977; Eridani</td><td align="right">4.4</td><td align="right">3.5</td><td align="right">-10</td><td align="right">0.14</td><td align="right">1.47</td></tr>
+<tr><td align="right">31</td><td align="left">&iota; Ursę Majoris</td><td align="right">3.2</td><td align="right">8.9</td><td align="right">+48</td><td align="right">0.13</td><td align="right">1.58</td></tr>
+<tr><td align="right">32</td><td align="left">&beta; Hydri</td><td align="right">2.9</td><td align="right">0.3</td><td align="right">-78</td><td align="right">0.1</td><td align="right">1.58</td></tr>
+<tr><td align="right">33</td><td align="left">Fomalhaut</td><td align="right">1.0</td><td align="right">22.9</td><td align="right">-30</td><td align="right">0.13</td><td align="right">1.58</td></tr>
+<tr><td align="right">34</td><td align="left">Br. 3,077</td><td align="right">6.0</td><td align="right">23.1</td><td align="right">+57</td><td align="right">0.13</td><td align="right">1.58</td></tr>
+<tr><td align="right">35</td><td align="left">&#977; Cygni</td><td align="right">2.5</td><td align="right">20.8</td><td align="right">+33</td><td align="right">0.12</td><td align="right">1.71</td></tr>
+<tr><td align="right">36</td><td align="left">&beta; Comę</td><td align="right">4.5</td><td align="right">13.1</td><td align="right">+28</td><td align="right">0.11</td><td align="right">1.87</td></tr>
+<tr><td align="right">37</td><td align="left">&psi;<sup>5</sup> Aurigę</td><td align="right">8.8</td><td align="right">6.6</td><td align="right">+44</td><td align="right">0.11</td><td align="right">1.87</td></tr>
+<tr><td align="right">38</td><td align="left">&pi; Herculis</td><td align="right">3.3</td><td align="right">17.2</td><td align="right">+37</td><td align="right">0.11</td><td align="right">1.87</td></tr>
+<tr><td align="right">39</td><td align="left">Aldebaran</td><td align="right">1.1</td><td align="right">4.5</td><td align="right">+16</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">40</td><td align="left">Capella</td><td align="right">0.1</td><td align="right">5.1</td><td align="right">+46</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">41</td><td align="left">B. D. 35°, 4,003</td><td align="right">9.2</td><td align="right">20.1</td><td align="right">+35</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">42</td><td align="left">Gr. 1,646</td><td align="right">6.3</td><td align="right">10.3</td><td align="right">+49</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">43</td><td align="left">&gamma; Cygni</td><td align="right">2.3</td><td align="right">20.3</td><td align="right">+40</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">44</td><td align="left">Regulus</td><td align="right">1.2</td><td align="right">10.0</td><td align="right">+12</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+<tr><td align="right">45</td><td align="left">Vega</td><td align="right">0.2</td><td align="right">18.6</td><td align="right">+39</td><td align="right">0.10</td><td align="right">2.06</td></tr>
+</tbody>
+</table><span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span></div>
+
+<p>in which the numbers in the first column are those placed
+adjacent to the stars in the diagram to identify them.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_122" id="Fig_122"></a>
+<img src="images/i335.png" width="500" height="506" alt="Fig. 122.&mdash;Stellar neighbors of the sun." title="Fig. 122.&mdash;Stellar neighbors of the sun." />
+<span class="caption"><span class="smcap">Fig. 122.</span>&mdash;Stellar neighbors of the sun.</span>
+</div>
+
+<p><a name="S_190" id="S_190"></a>190. <b>Light years.</b>&mdash;The radius of the inner circle in <a href="#Fig_122">Fig.&nbsp;122</a>,
+1,000,000 times the earth's distance from the sun, is a
+convenient unit in which to express the stellar distances,
+and in the preceding table the distances of the stars from
+the sun are expressed in terms of this unit. To express
+them in miles the numbers in the table must be multiplied
+by 93,000,000,000,000. The nearest star, &alpha;&nbsp;Centauri,
+is 25,000,000,000,000 miles away. But there is another
+unit in more common use&mdash;i.&nbsp;e., the distance traveled over<span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span>
+by light in the period of one year. We have already found
+(<a href="#S_141">§&nbsp;141</a>) that it requires light 8m. 18s. to come from the sun
+to the earth, and it is a simple matter to find from this
+datum that in a year light moves over a space equal to
+63,368 radii of the earth's orbit. This distance is called a
+<i>light year</i>, and the distance of the same star, &alpha;&nbsp;Centauri,
+expressed in terms of this unit, is 4.26 years&mdash;i.&nbsp;e., it takes
+light that long to come from the star to the earth.</p>
+
+<p>In <a href="#Fig_122">Fig.&nbsp;122</a> the stellar magnitudes of the stars are indicated
+by the size of the dots&mdash;the bigger the dot the brighter
+the star&mdash;and a mere inspection of the figure will serve to
+show that within a radius of 30 light years from the sun
+bright stars and faint ones are mixed up together, and that,
+so far as distance is concerned, the sun is only a member
+of this swarm of stars, whose distances apart, each from its
+nearest neighbor, are of the same order of magnitude as
+those which separate the sun from the three or four stars
+nearest it.</p>
+
+<p><a href="#Fig_122">Fig.&nbsp;122</a> is not to be supposed complete. Doubtless
+other stars will be found whose distance from the sun is less
+than 2,000,000 radii of the earth's orbit, but it is not probable
+that they will ever suffice to more than double or perhaps
+treble the number here shown. The vast majority of
+the stars lie far beyond the limits of the figure.</p>
+
+<p><a name="S_191" id="S_191"></a>191. <b>Proper motions.</b>&mdash;It is evident that these stars are too
+far apart for their mutual attractions to have much influence
+one upon another, and that we have here a case in which,
+according to <a href="#S_34">§&nbsp;34</a>, each star is free to keep unchanged its
+state of rest or motion with unvarying velocity along a
+straight line. Their very name, <i>fixed stars</i>, implies that
+they are at rest, and so astronomers long believed. Hipparchus
+(125 <span class="smcap">B.&nbsp;C.</span>) and Ptolemy (130 <span class="smcap">A.&nbsp;D.</span>) observed and recorded
+many allineations among the stars, in order to give
+to future generations a means of settling this very question
+of a possible motion of the stars and a resulting change in
+their relative positions upon the sky. For example, they<span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span>
+found at the beginning of the Christian era that the four
+stars, Capella, &#977;&nbsp;Persei, &alpha;&nbsp;and &beta;&nbsp;Arietis, stood in a straight
+line&mdash;i.&nbsp;e., upon a great circle of the sky. Verify this by
+direct reference to the sky, and see how nearly these stars
+have kept the same position for nearly twenty centuries.
+Three of them may be identified from the star maps, and the
+fourth, &#977;&nbsp;Persei, is a third-magnitude star between Capella
+and the other two.</p>
+
+<p>Other allineations given by Ptolemy are: Spica, Arcturus
+and &beta;&nbsp;Bootis; Spica, &delta;&nbsp;Corvi and &gamma;&nbsp;Corvi; &alpha;&nbsp;Librę,
+Arcturus and &zeta;&nbsp;Ursę Majoris. Arcturus does not now fit
+very well to these alignments, and nearly two centuries
+ago it, together with Aldebaran and Sirius, was on other
+grounds suspected to have changed its place in the sky
+since the days of Ptolemy. This discovery, long since
+fully confirmed, gave a great impetus to observing with all
+possible accuracy the right ascensions and declinations of the
+stars, with a view to finding other cases of what was called
+<i>proper motion</i>&mdash;i.&nbsp;e., a motion peculiar to the individual
+star as contrasted with the change of right ascension and
+declination produced for all stars by the precession.</p>
+
+<p>Since the middle of the eighteenth century there have
+been made many thousands of observations of this kind,
+whose results have gone into star charts and star catalogues,
+and which are now being supplemented by a photographic
+survey of the sky that is intended to record permanently
+upon photographic plates the position and magnitude
+of every star in the heavens down to the fourteenth
+magnitude, with a view to ultimately determining all their
+proper motions.</p>
+
+<p>The complete achievement of this result is, of course, a
+thing of the remote future, but sufficient progress in determining
+these motions has been made during the past century
+and a half to show that nearly every lucid star possesses
+some proper motion, although in most cases it is very
+small, there being less than 100 known stars in which it<span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span>
+amounts to so much as 1" per annum&mdash;i.&nbsp;e., a rate of motion
+across the sky which would require nearly the whole
+Christian era to alter a star's direction from us by so much
+as the moon's angular diameter. The most rapid known
+proper motion is that of a telescopic star midway between
+the equator and the south pole, which changes its position
+at the rate of nearly 9" per annum, and the next greatest is
+that of another telescopic star, in the northern sky, No.&nbsp;28
+of <a href="#Fig_122">Fig.&nbsp;122</a>. It is not until we reach the tenth place in a
+list of large proper motions that we find a bright lucid
+star, No.&nbsp;1 of <a href="#Fig_122">Fig.&nbsp;122</a>. It is a significant fact that for the
+most part the stars with large proper motions are precisely
+the ones shown in <a href="#Fig_122">Fig.&nbsp;122</a>, which is designed to show stars
+near the earth. This connection between nearness and
+rapidity of proper motions is indeed what we should expect
+to find, since a given amount of real motion of the star
+along its orbit will produce a larger angular displacement,
+proper motion, the nearer the star is to the earth, and this
+fact has guided astronomers in selecting the stars to be
+observed for parallax, the proper motion being determined
+first and the parallax afterward.</p>
+
+<p><a name="S_192" id="S_192"></a>192. <b>The paths of the stars.</b>&mdash;We have already seen reason
+for thinking that the orbit along which a star moves is
+practically a straight line, and from a study of proper motions,
+particularly their directions across the sky, it appears
+that these orbits point in all possible ways&mdash;north, south,
+east, and west&mdash;so that some of them are doubtless directed
+nearly toward or from the sun; others are square to the
+line joining sun and star; while the vast majority occupy
+some position intermediate between these two. Now, our
+relation to these real motions of the stars is well illustrated
+in <a href="#Fig_112">Fig.&nbsp;112</a>, where the observer finds in some of the
+shooting stars a tremendous proper motion across the sky,
+but sees nothing of their rapid approach to him, while
+others appear to stand motionless, although, in fact, they
+are moving quite as rapidly as are their fellows. The fixed<span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span>
+star resembles the shooting star in this respect, that its
+proper motion is only that part of its real motion which
+lies at right angles to the line of sight, and this needs to
+be supplemented by that other part of the motion which
+lies parallel to the line of sight, in order to give us any
+knowledge of the star's real orbit.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_123" id="Fig_123"></a>
+<a href="images/i339.jpg"><img src="images/i339.jpg" width="500" height="106" alt="Fig. 123.&mdash;Motion of Polaris in the line of sight as determined by the spectroscope.
+Frost." title="Fig. 123.&mdash;Motion of Polaris in the line of sight as determined by the spectroscope.
+Frost." /></a>
+<span class="caption"><span class="smcap">Fig. 123.</span>&mdash;Motion of Polaris in the line of sight as determined by the spectroscope.
+<span class="smcap">Frost.</span></span>
+</div>
+
+<p><a name="S_193" id="S_193"></a>193. <b>Motion in the line of sight.</b>&mdash;It is only within the
+last 25 years that anything whatever has been accomplished
+in determining these stellar motions of approach or recession,
+but within that time much progress has been made by
+applying the Doppler principle (<a href="#S_89">§&nbsp;89</a>) to the study of stellar
+spectra, and at the present time nearly every great telescope
+in the world is engaged upon work of this kind. The
+shifting of the lines of the spectrum toward the violet or
+toward the red end of the spectrum indicates with certainty
+the approach or recession of the star, but this shifting,
+which must be determined by comparing the star's
+spectrum with that of some artificial light showing corresponding
+lines, is so small in amount that its accurate measurement
+is a matter of extreme difficulty, as may be seen
+from <a href="#Fig_123">Fig.&nbsp;123</a>. This cut shows along its central line a part
+of the spectrum of Polaris, between wave lengths 4,450 and
+4,600 tenth meters, while above and below are the corresponding
+parts of the spectrum of an electric spark whose
+light passed through the same spectroscope and was photographed
+upon the same plate with that of Polaris. This
+comparison spectrum is, as it should be, a discontinuous or
+bright-line one, while the spectrum of the star is a continuous<span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span>
+one, broken only by dark gaps or lines, many of
+which have no corresponding lines in the comparison spectrum.
+But a certain number of lines in the two spectra
+do correspond, save that the dark line is always pushed a
+very little toward the direction of shorter wave lengths,
+showing that this star is approaching the earth. This spectrum
+was photographed for the express purpose of determining
+the star's motion in the line of sight, and with it
+there should be compared Figs.&nbsp;<a href="#Fig_124">124</a> and&nbsp;<a href="#Fig_125">125</a>, which show
+in the upper part of each a photograph obtained without
+comparison spectra by allowing the star's light to pass
+through some prisms placed just in front of the telescope.
+The lower section of each figure shows an enlargement of
+the original photograph, bringing out its details in a way
+not visible to the unaided eye. In the enlarged spectrum
+of &beta;&nbsp;Aurigę a rate of motion equal to that of the earth in
+its orbit would be represented by a shifting of 0.03 of a
+millimeter in the position of the broad, hazy lines.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_124" id="Fig_124"></a>
+<a href="images/i340.jpg"><img src="images/i340.jpg" width="500" height="168" alt="Fig. 124.&mdash;Spectrum of &beta;&nbsp;Aurigę.&mdash;Pickering." title="Fig. 124.&mdash;Spectrum of &beta;&nbsp;Aurigę.&mdash;Pickering." /></a>
+<span class="caption"><span class="smcap">Fig. 124.</span>&mdash;Spectrum of &beta;&nbsp;Aurigę.&mdash;<span class="smcap">Pickering.</span></span>
+</div>
+
+<p>Despite the difficulty of dealing with such small quantities
+as the above, very satisfactory results are now obtained,
+and from them it is known that the velocities of stars in
+the line of sight are of the same order of magnitude as the
+velocities of the planets in their orbits, ranging all the way
+from 0 to 60 miles per second&mdash;more than 200,000 miles per
+hour&mdash;which latter velocity, according to Campbell, is the
+rate at which &mu;&nbsp;Cassiopeię is approaching the sun.<span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span></p>
+
+<p>The student should not fail to note one important
+difference between proper motions and the motions determined
+spectroscopically: the latter are given directly in
+miles per second, or per hour, while the former are expressed
+in angular measure, seconds of arc, and there can
+be no direct comparison between the two until by means
+of the known distances of the stars their proper motions
+are converted from angular into linear measure. We are
+brought thus to the very heart of the matter; parallax,
+proper motion, and motion in the line of sight are intimately
+related quantities, all of which are essential to a
+knowledge of the real motions of the stars.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_125" id="Fig_125"></a>
+<a href="images/i341.jpg"><img src="images/i341.jpg" width="500" height="168" alt="Fig. 125.&mdash;Spectrum of Pollux.&mdash;Pickering." title="Fig. 125.&mdash;Spectrum of Pollux.&mdash;Pickering." /></a>
+<span class="caption"><span class="smcap">Fig. 125.</span>&mdash;Spectrum of Pollux.&mdash;<span class="smcap">Pickering.</span></span>
+</div>
+
+<p><a name="S_194" id="S_194"></a>194. <b>Star drift.</b>&mdash;An illustration of how they may be
+made to work together is furnished by some of the stars&mdash;which
+make up the Great Dipper&mdash;&beta;, &gamma;, &#977;, and &zeta;&nbsp;Ursę Majoris,
+whose proper motions have long been known to point
+in nearly the same direction across the sky and to be nearly
+equal in amount. More recently it has been found that
+these stars are all moving toward the sun with approximately
+the same velocity&mdash;18 miles per second. One other
+star of the Dipper, &delta;&nbsp;Ursę Majoris, shares in the common
+proper motion, but its velocity in the line of sight has not
+yet been determined with the spectroscope. These similar
+motions make it probable that the stars are really traveling
+together through space along parallel lines; and on the<span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span>
+supposition that such is the case it is quite possible to
+write out a set of equations which shall involve their
+known proper motions and motions in the line of sight,
+together with their unknown distances and the unknown
+direction and velocity of their real motion along their
+orbits. Solving these equations for the values of the unknown
+quantities, it is found that the five stars probably
+lie in a plane which is turned nearly edgewise toward us,
+and that in this plane they are moving about twice as fast
+as the earth moves around the sun, and are at a distance
+from us represented by a parallax of less than 0.02"&mdash;i.&nbsp;e.,
+six times as great as the outermost circle in <a href="#Fig_122">Fig.&nbsp;122</a>. A
+most extraordinary system of stars which, although separated
+from each other
+by distances as
+great as the whole
+breadth of <a href="#Fig_122">Fig.&nbsp;122</a>,
+yet move along in
+parallel paths which
+it is difficult to regard
+as the result
+of chance, and for
+which it is equally
+difficult to frame an
+explanation.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_126" id="Fig_126"></a>
+<a href="images/i342-full.jpg"><img src="images/i342.jpg" width="350" height="435" alt="Fig. 126.&mdash;The Great Dipper, past, present, and
+future." title="Fig. 126.&mdash;The Great Dipper, past, present, and
+future." /></a>
+<span class="caption"><span class="smcap">Fig. 126.</span>&mdash;The Great Dipper, past, present, and
+future.</span>
+</div>
+
+<p>The stars &alpha;&nbsp;and
+&eta;&nbsp;of the Great Dipper
+do not share
+in this motion, and
+must ultimately part
+company with the
+other five, to the
+complete destruction
+of the Dipper's shape. <a href="#Fig_126">Fig.&nbsp;126</a> illustrates this change of
+shape, the upper part of the figure&nbsp;(<i>a</i>) showing these seven
+stars as they were grouped at a remote epoch in the past,<span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span>
+while the lower section&nbsp;(<i>c</i>) shows their position for an
+equally remote epoch in the future. There is no resemblance
+to a dipper in either of these configurations, but it
+should be observed that in each of them the stars &alpha;&nbsp;and&nbsp;&eta;
+keep their relative position unaltered, and the other five
+stars also keep together, the entire change of appearance
+being due to the changing positions of these two groups
+with respect to each other.</p>
+
+<p>This phenomenon of groups of stars moving together is
+called <i>star drift</i>, and quite a number of cases of it are
+found in different parts of the sky. The Pleiades are perhaps
+the most conspicuous one, for here some sixty or
+more stars are found traveling together along similar paths.
+Repeated careful measurements of the relative positions of
+stars in this cluster show that one of the lucid stars and
+four or five of the telescopic ones do not share in this
+motion, and therefore are not to be considered as members
+of the group, but rather as isolated stars which, for a time,
+chance to be nearly on line with the Pleiades, and probably
+farther off, since their proper motions are smaller.</p>
+
+<p>To rightly appreciate the extreme slowness with which
+proper motions alter the constellations, the student should
+bear in mind that the changes shown in passing from one
+section of <a href="#Fig_126">Fig.&nbsp;126</a> to the next represent the effect of the
+present proper motions of the stars accumulated for a period
+of 200,000 years. Will the stars continue to move in
+straight paths for so long a time?</p>
+
+<p><a name="S_195" id="S_195"></a>195. <b>The sun's way.</b>&mdash;Another and even more interesting
+application of proper motions and motions in the line
+of sight is the determination from them of the sun's orbit
+among the stars. The principle involved is simple enough.
+If the sun moves with respect to the stars and carries the
+earth and the other planets year after year into new regions
+of space, our changing point of view must displace in some
+measure every star in the sky save those which happen to
+be exactly on the line of the sun's motion, and even these<span class="pagenum"><a name="Page_310" id="Page_310">[Pg 310]</a></span>
+will show its effect by their apparent motion of approach
+or recession along the line of sight. So far as their own
+orbital motions are concerned, there is no reason to suppose
+that more stars move north than south, or that more
+go east than west; and when we find in their proper motions
+a distinct tendency to radiate from a point somewhere
+near the bright star Vega and to converge toward
+a point on the opposite side of the sky, we infer that this
+does not come from any general drift of the stars in that
+direction, but that it marks the course of the sun among
+them. That it is moving along a straight line pointing
+toward Vega, and that at least a part of the velocities
+which the spectroscope shows in the line of sight, comes
+from the motion of the sun and earth. Working along
+these lines, Kapteyn finds that the sun is moving through
+space with a velocity of 11 miles per second, which is decidedly
+below the average rate of stellar motion&mdash;19 miles
+per second.</p>
+
+<p><a name="S_196" id="S_196"></a>196. <b>Distance of Sirian and solar stars.</b>&mdash;By combining
+this rate of motion of the sun with the average proper motions
+of the stars of different magnitudes, it is possible to
+obtain some idea of the average distance from us of a first-magnitude
+star or a sixth-magnitude star, which, while it
+gives no information about the actual distance of any particular
+star, does show that on the whole the fainter stars
+are more remote. But here a broad distinction must be
+drawn. By far the larger part of the stars belong to one of
+two well-marked classes, called respectively Sirian and solar
+stars, which are readily distinguished from each other by
+the kind of spectrum they furnish. Thus &beta;&nbsp;Aurigę belongs
+to the Sirian class, as does every other star which has a spectrum
+like that of <a href="#Fig_124">Fig.&nbsp;124</a>, while Pollux is a solar star presenting
+in <a href="#Fig_125">Fig.&nbsp;125</a> a spectrum like that of the sun, as do
+the other stars of this class.</p>
+
+<p>Two thirds of the sun's near neighbors, shown in <a href="#Fig_122">Fig.&nbsp;122</a>,
+have spectra of the solar type, and in general stars of<span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span>
+this class are nearer to us than are the stars with spectra
+unlike that of the sun. The average distance of a solar
+star of the first magnitude is very approximately represented
+by the outer circle in <a href="#Fig_122">Fig.&nbsp;122</a>, 2,000,000 times the
+distance of the sun from the earth; while the corresponding
+distance for a Sirian star of the first magnitude is represented
+by the number 4,600,000.</p>
+
+<p>A third-magnitude star is on the average twice as far
+away as one of the first magnitude, a fifth-magnitude star
+four times as far off, etc., each additional two magnitudes
+doubling the average distance of the stars, at least down to
+the eighth magnitude and possibly farther, although beyond
+this limit we have no certain knowledge. Put in
+another way, the naked eye sees many Sirian stars which
+<i>may</i> have "gone out" and ceased to shine centuries ago,
+for the light by which we now see them left those stars
+before the discovery of America by Columbus. For the
+student of mathematical tastes we note that the results of
+Kapteyn's investigation of the mean distances&nbsp;(<i>D</i>) of the
+stars of magnitude&nbsp;(<i>m</i>) may be put into two equations:</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">For Solar Stars,</td><td align="left"><i>D</i> = 23 × 2<sup><i>m</i>/2</sup></td></tr>
+<tr><td align="left">For Sirian Stars,</td><td align="left"><i>D</i> = 52 × 2<sup><i>m</i>/2</sup></td></tr>
+</table></div>
+
+<p>where the coefficients 23 and 52 are expressed in light
+years. How long a time is required for light to come from
+an average solar star of the sixth magnitude?</p>
+
+<p><a name="S_197" id="S_197"></a>197. <b>Consequences of stellar distance.</b>&mdash;The amount of
+light which comes to us from any luminous body varies
+inversely as the square of its distance, and since many of
+the stars are changing their distance from us quite rapidly,
+it must be that with the lapse of time they will grow
+brighter or fainter by reason of this altered distance.
+But the distances themselves are so great that the most
+rapid known motion in the line of sight would require
+more than 1,000 years (probably several thousand) to produce
+any perceptible change in brilliancy.<span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span></p>
+
+<p>The law in accordance with which this change of brilliancy
+takes place is that the distance must be increased or
+diminished tenfold in order to produce a change of five
+magnitudes in the brightness of the object, and we may
+apply this law to determine the sun's rank among the stars.
+If it were removed to the distance of an average first-, or
+second-, or third-magnitude star, how would its light compare
+with that of the stars? The average distance of a
+third-magnitude star of the solar type is, as we have seen
+above, 4,000,000 times the sun's distance from the earth,
+and since 4,000,000 =&nbsp;10<sup>6.6</sup>, we find that at this distance the
+sun's stellar magnitude would be altered by 6.6&nbsp;×&nbsp;5 magnitudes,
+and would therefore be -26.5&nbsp;+&nbsp;33.0 =&nbsp;6.5&mdash;i.&nbsp;e., the
+sun if removed to the average distance of the third-magnitude
+stars of its type would be reduced to the very limit
+of naked-eye visibility. It must therefore be relatively
+small and feeble as compared with the brightness of the
+average star. It is only its close proximity to us that
+makes the sun look brighter than the stars.</p>
+
+<p>The fixed stars may have planets circling around them,
+but an application of the same principles will show how
+hopeless is the prospect of ever seeing them in a telescope.
+If the sun's nearest neighbor, &alpha;&nbsp;Centauri, were attended by
+a planet like Jupiter, this planet would furnish to us no
+more light than does a star of the twenty-second magnitude&mdash;i.&nbsp;e.,
+it would be absolutely invisible, and would remain
+invisible in the most powerful telescope yet built,
+even though its bulk were increased to equal that of the
+sun. Let the student make the computation leading to
+this result, assuming the stellar magnitude of Jupiter to
+be&nbsp;-1.7.</p>
+
+<p><a name="S_198" id="S_198"></a>198. <b>Double stars.</b>&mdash;In the constellation Taurus, not far
+from Aldebaran, is the fourth-magnitude star &theta;&nbsp;Tauri,
+which can readily be seen to consist of two stars close
+together. The star &alpha;&nbsp;Capricorni is plainly double, and a
+sharp eye can detect that one of the faint stars which with<span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span>
+Vega make a small equilateral triangle, is also a double
+star. Look for them in the sky.</p>
+
+<p>In the strict language of astronomy the term double
+star would not be applied to the first two of these objects,
+since it is usually restricted to those stars whose angular
+distance from each other is so small that in the telescope
+they appear much as do the stars named above to the naked
+eye&mdash;i.&nbsp;e., their angular separation is measured by a few
+seconds or fractions of a single second, instead of the six
+minutes which separate the component stars of &theta;&nbsp;Tauri or
+&alpha;&nbsp;Capricorni. There are found in the sky many thousands
+of these close double stars, of which some are only optically
+double&mdash;i.&nbsp;e., two stars nearly on line with the earth
+but at very different distances from it&mdash;while more of them
+are really what they seem, stars near each other, and in
+many cases near enough to influence each other's motion.
+These are called <i>binary</i> systems, and in cases of this kind
+the principles of celestial mechanics set forth in <a href="#CHAPTER_IV">Chapter&nbsp;IV</a>
+hold true, and we may expect to find each component
+of a double star moving in a conic section of some kind,
+having its focus at the common center of gravity of the
+two stars. We are thus presented with problems of orbital
+motion quite similar to those which occur in the solar system,
+and careful telescopic observations are required year
+after year to fix the relative positions of the two stars&mdash;i.&nbsp;e.,
+their angular separation, which it is customary to call their
+<i>distance</i>, and their direction one from the other, which is
+called <i>position angle</i>.</p>
+
+<p><a name="S_199" id="S_199"></a>199. <b>Orbits of double stars.</b>&mdash;The sun's nearest neighbor,
+&alpha;&nbsp;Centauri, is such a double star, whose position angle and
+distance have been measured by successive generations of
+astronomers for more than a century, and <a href="#Fig_127">Fig.&nbsp;127</a> shows
+the result of plotting their observations. Each black dot
+that lies on or near the circumference of the long ellipse
+stands for an observed direction and distance of the fainter
+of the two stars from the brighter one, which is represented<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span>
+by the small circle at the intersection of the lines inside
+the ellipse. It appears from the figure that during this
+time the one star has
+gone completely around
+the other, as a planet
+goes around the sun,
+and the true orbit must
+therefore be an ellipse
+having one of its foci
+at the center of gravity
+of the two stars. The
+other star moves in an
+ellipse of precisely similar
+shape, but probably
+smaller size, since the
+dimensions of the two
+orbits are inversely proportional
+to the masses
+of the two bodies, but it is customary to neglect this motion
+of the larger star and to give to the smaller one an orbit
+whose diameter is equal to the sum of the diameters of the
+two real orbits. This practice, which has been followed in
+<a href="#Fig_127">Fig.&nbsp;127</a>, gives correctly the relative positions of the two
+stars, and makes one orbit do the work of two.</p>
+
+<div class="figleft" style="width: 350px;"><a name="Fig_127" id="Fig_127"></a>
+<a href="images/i348-full.jpg"><img src="images/i348.jpg" width="350" height="360" alt="Fig. 127.&mdash;The orbit of &alpha;&nbsp;Centauri.&mdash;See." title="Fig. 127.&mdash;The orbit of &alpha;&nbsp;Centauri.&mdash;See." /></a>
+<span class="caption"><span class="smcap">Fig. 127.</span>&mdash;The orbit of &alpha;&nbsp;Centauri.&mdash;<span class="smcap">See.</span></span>
+</div>
+
+<p>In <a href="#Fig_127">Fig.&nbsp;127</a> the bright star does not fall anywhere near
+the focus of the ellipse marked out by the smaller one, and
+from this we infer that the figure does not show the true
+shape of the orbit, which is certainly distorted, foreshortened,
+by the fact that we look obliquely down upon its
+plane. It is possible, however, by mathematical analysis,
+to find just how much and in what direction that plane
+should be turned in order to bring the focus of the
+ellipse up to the position of the principal star, and thus
+give the true shape and size of the orbit. See <a href="#Fig_128">Fig.&nbsp;128</a>
+for a case in which the true orbit is turned exactly edgewise
+toward the earth, and the small star, which really<span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span>
+moves in an ellipse like that shown in the figure, appears
+to oscillate to and fro along a straight line drawn through
+the principal star, as shown at the left of the figure.</p>
+
+<p>In the case of &alpha;&nbsp;Centauri
+the true orbit
+proves to have a major
+axis 47 times, and a
+minor axis 40 times,
+as great as the distance
+of the earth from the
+sun. The orbit, in
+fact, is intermediate
+in size between the
+orbits of Uranus and
+Neptune, and the periodic
+time of the star
+in this orbit is 81
+years, a little less than
+the period of Uranus.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_128" id="Fig_128"></a>
+<a href="images/i349-full.jpg"><img src="images/i349.jpg" width="350" height="341" alt="Fig. 128.&mdash;Apparent orbit and real orbit of the
+double star 42 Comę Berenicis.&mdash;See." title="Fig. 128.&mdash;Apparent orbit and real orbit of the
+double star 42 Comę Berenicis.&mdash;See." /></a>
+<span class="caption"><span class="smcap">Fig. 128.</span>&mdash;Apparent orbit and real orbit of the
+double star 42 Comę Berenicis.&mdash;<span class="smcap">See.</span></span>
+</div>
+
+<p><a name="S_200" id="S_200"></a>200. <b>Masses of double stars.</b>&mdash;If we apply to this orbit
+Kepler's Third Law in the form given it at <a href="#Page_179">page&nbsp;179</a>, we
+shall find&mdash;</p>
+
+<p class="center"><i>a</i><sup>3</sup> / <i>T</i><sup>2</sup> = (23.5)<sup>3</sup> / (81)<sup>2</sup> = <i>k</i> (<i>M</i> + <i>m</i>),</p>
+
+<p>where <i>M</i> and <i>m</i> represent the masses of the two stars. We
+have already seen that <i>k</i>, the gravitation constant, is equal
+to&nbsp;1 when the masses are measured in terms of the sun's
+mass taken as unity, and when <i>T</i> and <i>a</i> are expressed in
+years and radii of the earth's orbit respectively, and with
+this value of <i>k</i> we may readily find from the above equation,
+<i>M</i>&nbsp;+&nbsp;<i>m</i>&nbsp;=&nbsp;2.5&mdash;i.&nbsp;e., the combined mass of the two components
+of &alpha;&nbsp;Centauri is equal to rather more than twice
+the mass of the sun. It is not every double star to which
+this process of weighing can be applied. The major axis
+of the orbit, <i>a</i>, is found from the observations in angular
+measure, 35" in this case, and it is only when the parallax<span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span>
+of the star is known that this can be converted into the
+required linear units, radii of the earth's orbit, by dividing
+the angular major axis by the parallax; 47&nbsp;=&nbsp;35"&nbsp;÷&nbsp;0.75".</p>
+
+<p>Our list of distances (<a href="#S_189">§&nbsp;189</a>) contains four double stars
+whose periodic times and major axes have been fairly well
+determined, and we find in the accompanying table the information
+which they give about the masses of double stars
+and the size of the orbits in which they move:</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides">
+<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup>
+<thead>
+<tr><th align="center"><span class="smcap">Star.</span></th><th align="center">Major axis.</th><th align="center">Minor axis.</th><th align="center">Periodic<br />time.</th><th align="center">Mass.</th></tr>
+</thead>
+<tbody>
+<tr><td align="left">&alpha; Centauri</td><td align="center">47</td><td align="center">40</td><td align="center">81 y.</td><td align="center">2</td></tr>
+<tr><td align="left">70 Ophiuchi</td><td align="center">56</td><td align="center">48</td><td align="center">88</td><td align="center">3</td></tr>
+<tr><td align="left">Procyon</td><td align="center">34</td><td align="center">31</td><td align="center">40</td><td align="center">3</td></tr>
+<tr><td align="left">Sirius</td><td align="center">43</td><td align="center">34</td><td align="center">52</td><td align="center">4</td></tr>
+</tbody>
+</table></div>
+
+<p>The orbit of Uranus, diameter =&nbsp;38, and Neptune, diameter
+=&nbsp;60, are of much the same size as these double-star
+orbits; but the planetary orbits are nearly circular, while
+in every case the double stars show a substantial difference
+between the long and short diameters of their orbits. This
+is a characteristic feature of most double-star orbits, and
+seems to stand in some relation to their periodic times, for,
+on the average, the longer the time required by a star to
+make its orbital revolution the more eccentric is its orbit
+likely to prove.</p>
+
+<p>Another element of the orbits of double stars, which
+stands in even closer relation to the periodic time, is the
+major axis; the smaller the long diameter of the orbit the
+more rapid is the motion and the shorter the periodic time,
+so that astronomers in search of interesting double-star
+orbits devote themselves by preference to those stars whose
+distance apart is so small that they can barely be distinguished
+one from the other in the telescope.</p>
+
+<p>Although the half-dozen stars contained in the table
+all have orbits of much the same size and with much the<span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span>
+same periodic time as those in which Uranus and Neptune
+move, this is by no means true of all the double stars, many
+of which have periods running up into the hundreds if not
+thousands of years, while a few complete their orbital revolutions
+in periods comparable with, or even shorter than,
+that of Jupiter.</p>
+
+<p><a name="S_201" id="S_201"></a>201. <b>Dark stars.</b>&mdash;Procyon, the next to the last star of
+the preceding table, calls for some special mention, as the
+determination of its mass and orbit stands upon a rather
+different basis from that of the other stars. More than
+half a century ago it was discovered that its proper motion
+was not straight and uniform after the fashion of ordinary
+stars, but presented a series of loops like those marked out
+by a bright point on the rim of a swiftly running bicycle
+wheel. The hub may move straight forward with uniform
+velocity, but the point near the tire goes up and down, and,
+while sharing in the forward motion of the hub, runs sometimes
+ahead of it, sometimes behind, and such seemed to
+be the motion of Procyon and of Sirius as well. Bessel,
+who discovered it, did not hesitate to apply the laws of motion,
+and to affirm that this visible change of the star's
+motion pointed to the presence of an unseen companion,
+which produced upon the motions of Sirius and Procyon
+just such effects as the visible companions produce in the
+motions of double stars. A new kind of star, dark instead
+of bright, was added to the astronomer's domain, and its
+discoverer boldly suggested the possible existence of many
+more. "That countless stars are visible is clearly no argument
+against the existence of as many more invisible ones."
+"There is no reason to think radiance a necessary property
+of celestial bodies." But most astronomers were incredulous,
+and it was not until 1862 that, in the testing of a new
+and powerful telescope just built, a dark star was brought
+to light and the companion of Sirius actually seen. The
+visual discovery of the dark companion of Procyon is
+of still more recent date (November, 1896), when it was<span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span>
+detected with the great telescope of the Lick Observatory.
+This discovery is so recent that the orbit is still very uncertain,
+being based almost wholly upon the variations in the
+proper motion of the star, and while the periodic time must
+be very nearly correct, the mass of the stars and dimensions
+of the orbit may require considerable correction.</p>
+
+<p>The companion of Sirius is about ten magnitudes and
+that of Procyon about twelve magnitudes fainter than the
+star itself. How much more light does the bright star give
+than its faint companion? Despite the tremendous difference
+of brightness represented by the answer to this question,
+the mass of Sirius is only about twice as great as
+that of its companion, and for Procyon the ratio does not
+exceed five or six.</p>
+
+<p>The visual discovery of the companions to Sirius and
+Procyon removes them from the list of dark stars, but
+others still remain unseen, although their existence is indicated
+by variable proper motions or by variable orbital
+motion, as in the case of &zeta;&nbsp;Cancri, where one of the components
+of a triple star moves around the other two in a series
+of loops whose presence indicates a disturbing body which
+has never yet been seen.</p>
+
+<p><a name="S_202" id="S_202"></a>202. <b>Multiple stars.</b>&mdash;Combinations of three, four, or
+more stars close to each other, like &zeta;&nbsp;Cancri, are called multiple
+stars, and while they are far from being as common as
+are double stars, there is a considerable number of them in
+the sky, 100 or more as against the more than 10,000 double
+stars that are known. That their relative motions are
+subject to the law of gravitation admits of no serious doubt,
+but mathematical analysis breaks down in face of the difficulties
+here presented, and no astronomer has ever been
+able to determine what will be the general character of
+the motions in such a system.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_129" id="Fig_129"></a>
+<img src="images/i353.png" width="500" height="267" alt="Fig. 129.&mdash;Illustrating the motion of a spectroscopic binary." title="Fig. 129.&mdash;Illustrating the motion of a spectroscopic binary." />
+<span class="caption"><span class="smcap">Fig. 129.</span>&mdash;Illustrating the motion of a spectroscopic binary.</span>
+</div>
+
+<p><a name="S_203" id="S_203"></a>203. <b>Spectroscopic binaries.</b>&mdash;In the year 1890 Professor
+Pickering, of the Harvard Observatory, announced the discovery
+of a new class of double stars, invisible as such in<span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span>
+even the most powerful telescope, and producing no perturbations
+such as have been considered above, but showing
+in their spectrum that two or more bodies must be
+present in the source of light which to the eye is indistinguishable
+from a single star. In <a href="#Fig_129">Fig.&nbsp;129</a> we suppose&nbsp;<i>A</i>
+and&nbsp;<i>B</i> to be the two components of a double star, each
+moving in its own orbit about their common center of
+gravity, <i>C</i>, whose distance from the earth is several million
+times greater than the distance between the stars themselves.
+Under such circumstances no telescope could distinguish
+between the two stars, which would appear fused
+into one; but the smaller the orbit the more rapid would
+be their motion in it, and if this orbit were turned edgewise
+toward the earth, as is supposed in the figure, whenever
+the stars were in the relative position there shown, <i>A</i>&nbsp;would
+be rapidly approaching the earth by reason of its orbital
+motion, while <i>B</i>&nbsp;would move away from it, so that in
+accordance with the Doppler principle the lines composing
+their respective spectra would be shifted in opposite directions,
+thus producing a doubling of the lines, each single
+line breaking up into two, like the double-sodium line&nbsp;<i>D</i>,
+only not spaced so far apart. When the stars have moved
+a quarter way round their orbit to the points&nbsp;<i>A'</i>, <i>B'</i>, their
+velocities are turned at right angles to the line of sight<span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span>
+and the spectrum returns to the normal type with single
+lines, only to break up again when after another quarter
+revolution their velocities are again parallel with the line
+of sight. The interval of time between consecutive doublings
+of the lines in the spectrum thus furnishes half
+the time of a revolution in the orbit. The distance between
+the components of a double line shows by means of
+the Doppler principle how fast the stars are traveling, and
+this in connection with the periodic times fixes the size
+of the orbit, provided we assume that it is turned exactly
+edgewise to the earth. This assumption may not be quite
+true, but even though the orbit should deviate considerably
+from this position, it will still present the phenomenon
+of the double lines whose displacement will now show something
+less than the true velocities of the stars in their orbits,
+since the spectroscope measures only that component
+of the whole velocity which is directed toward the earth,
+and it is important to note that the real orbits and masses
+of these <i>spectroscopic binaries</i>, as they are called, will usually
+be somewhat larger than those indicated by the spectroscope,
+since it is only in exceptional cases that the orbit
+will be turned exactly edgewise to us.</p>
+
+<p>The bright star Capella is an excellent illustration of
+these spectroscopic binaries. At intervals of a little less
+than a month the lines of its spectrum are alternately
+single and double, their maximum separation corresponding
+to a velocity in the line of sight amounting to 37 miles
+per second. Each component of a doubled line appears to
+be shifted an equal amount from the position occupied by
+the line when it is single, thus indicating equal velocities
+and equal masses for the two component stars whose periodic
+time in their orbit is 104 days. From this periodic
+time, together with the velocity of the star's motion, let the
+student show that the diameter of the orbit&mdash;i.&nbsp;e., the distance
+of the stars from each other&mdash;is approximately 53,000,000
+miles, and that their combined mass is a little less than<span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span>
+that of &alpha;&nbsp;Centauri, provided that their orbit plane is turned
+exactly edgewise toward the earth.</p>
+
+<p>There are at the present time (1901) 34 spectroscopic
+binaries known, including among them such stars as Polaris,
+Capella, Algol, Spica, &beta;&nbsp;Aurigę, &zeta;&nbsp;Ursę Majoris, etc.,
+and their number is rapidly increasing, about one star out of
+every seven whose motion in the line of sight is determined
+proving to be a binary or, as in the case of Polaris, possibly
+triple. On account of smaller distance apart their periodic
+times are much shorter than those of the ordinary double
+stars, and range from a few days up to several months&mdash;more
+than two years in the case of &eta;&nbsp;Pegasi, which has the
+longest known period of any star of this class.</p>
+
+<p>Spectroscopic binaries agree with ordinary double stars
+in having masses rather greater than that of the sun, but
+there is as yet no assured case of a mass ten times as great
+as that of the sun.</p>
+
+<p><a name="S_204" id="S_204"></a>204. <b>Variable stars.</b>&mdash;Attention has already been drawn
+(<a href="#S_23">§&nbsp;23</a>) to the fact that some stars shine with a changing
+brightness&mdash;e.&nbsp;g., Algol, the most famous of these <i>variable
+stars</i>, at its maximum of brightness furnishes three times
+as much light as when at its minimum, and other variable
+stars show an even greater range. The star &omicron;&nbsp;Ceti has been
+named Mira (Latin, <i>the wonderful</i>), from its extraordinary
+range of brightness, more than six-hundred-fold. For the
+greater part of the time this star is invisible to the naked
+eye, but during some three months in every year it brightens
+up sufficiently to be seen, rising quite rapidly to its
+maximum brilliancy, which is sometimes that of a second-magnitude
+star, but more frequently only third or even
+fourth magnitude, and, after shining for a few weeks with
+nearly maximum brilliancy, falling off to become invisible
+for a time and then return to its maximum brightness
+after an interval of eleven months from the preceding
+maximum. In 1901 it should reach its greatest brilliancy
+about midsummer, and a month earlier than this for each<span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span>
+succeeding year. Find it by means of the star map, and
+by comparing its brightness from night to night with
+neighboring stars of about the same magnitude see how it
+changes with respect to them.</p>
+
+<p>The interval of time from maximum to maximum of
+brightness&mdash;331.6 days for Mira&mdash;is called the star's period,
+and within its period a star regularly variable runs
+through all its changes of brilliancy, much as the weather
+runs through its cycle of changes in the period of a year.
+But, as there are wet years and dry ones, hot years and cold,
+so also with variable stars, many of them show differences
+more or less pronounced between different periods, and
+one such difference has already been noted in the case of
+Mira; its maximum brilliancy is different in different years.
+So, too, the length of the period fluctuates in many cases,
+as does every other circumstance connected with it, and
+predictions of what such a variable star will do are notoriously
+unreliable.</p>
+
+<p><a name="S_205" id="S_205"></a>205. <b>The Algol variables.</b>&mdash;On the other hand, some variable
+stars present an almost perfect regularity, repeating
+their changes time after time with a precision like that of
+clockwork. Algol is one type of these regular variables,
+having a period of 68.8154 hours, during six sevenths of
+which time it shines with unchanging luster as a star of
+the 2.3 magnitude, but during the remaining 9 hours of
+each period it runs down to the 3.5 magnitude, and comes
+back again, as is shown by a curve in <a href="#Fig_130">Fig.&nbsp;130</a>. The horizontal
+scale here represents hours, reckoned from the time of
+the star's minimum brightness, and the vertical scale shows
+stellar magnitudes. Such a diagram is called the star's
+light curve, and we may read from it that at any time between
+5h. and 32h. after the time of minimum the star's
+magnitude is 2.32; at 2h. after a minimum the magnitude
+is 2.88, etc. What is the magnitude an hour and a
+half before the time of minimum? What is the magnitude
+43 days after a minimum?<span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span></p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_130" id="Fig_130"></a>
+<img src="images/i357.png" width="500" height="239" alt="Fig. 130.&mdash;The light curve of Algol." title="Fig. 130.&mdash;The light curve of Algol." />
+<span class="caption"><span class="smcap">Fig. 130.</span>&mdash;The light curve of Algol.</span>
+</div>
+
+<p>The arrows shown in <a href="#Fig_130">Fig.&nbsp;130</a> are a feature not usually
+found with light curves, but in this case each one represents
+a spectroscopic determination of the motion of Algol
+in the line of sight. These observations extended over a
+period of more than two years, but they are plotted in the
+figure with reference to the number of hours each one preceded
+or followed a minimum of the star's light, and each
+arrow shows not only the direction of the star's motion
+along the line of sight, the arrows pointing down denoting
+approach of the star toward the earth, but also its velocity,
+each square of the ruling corresponding to 10 kilometers
+(6.2 miles per second). The differences of velocity shown
+by adjacent arrows come mainly from errors of observation
+and furnish some idea of how consistent among themselves
+such observations are, but there can be no doubt that before
+minimum the star is moving away from the earth, and after
+minimum is approaching it. It is evident from these observations
+that in Algol we have to do with a spectroscopic
+binary, one of whose components is a dark star which, once
+in each revolution, partially eclipses the bright star and
+produces thus the variations in its light. By combining
+the spectroscopic observations with the variations in the
+star's light, Vogel finds that the bright star, Algol, itself
+has a diameter somewhat greater than that of the sun, but<span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span>
+is of low density, so that its mass is less than half that of
+the sun, while the dark star is a very little smaller than the
+sun and has about a quarter of its mass. The distance between
+the two stars, dark and bright, is 3,200,000 miles.
+<a href="#Fig_129">Fig.&nbsp;129</a>, which is drawn to scale, shows the relative positions
+and sizes of these stars as well as the orbits in which
+they move.</p>
+
+<p>The mere fact already noted that close binary systems
+exist in considerable numbers is sufficient to make it
+probable that a certain proportion of these stars would
+have their orbit planes turned so nearly edgewise toward
+the earth as to produce eclipses, and corresponding to this
+probability there are already known no less than 15 stars of
+the Algol type of eclipse variables, and only a beginning
+has been made in the search for them.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_131" id="Fig_131"></a>
+<img src="images/i358.png" width="500" height="252" alt="Fig. 131.&mdash;The light curve of &beta;&nbsp;Lyrę." title="Fig. 131.&mdash;The light curve of &beta;&nbsp;Lyrę." />
+<span class="caption"><span class="smcap">Fig. 131.</span>&mdash;The light curve of &beta;&nbsp;Lyrę.</span>
+</div>
+
+<p><a name="S_206" id="S_206"></a>206. <b>Variables of the &beta;&nbsp;Lyrę type.</b>&mdash;In addition to these
+there is a certain further number of binary variables in
+which both components are bright and where the variation
+of brightness follows a very different course. Capella
+would be such a variable if its orbit plane were directed
+exactly toward the earth, and the fact that its light is not
+variable shows conclusively that such is not the position of
+the orbit. <a href="#Fig_131">Fig.&nbsp;131</a> represents the light curve of one of the<span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span>
+best-known variable systems of this second type, that of
+&beta;&nbsp;Lyrę, whose period is 12 days 21.8 hours, and the student
+should read from the curve the magnitude of the star for
+different times during this interval. According to Myers,
+this light curve and the spectroscopic observations of the
+star point to the existence of a binary star of very remarkable
+character, such as is shown, together with its orbit and
+a scale of miles, in <a href="#Fig_132">Fig.&nbsp;132</a>. Note the tide which each of
+these stars raises in the other, thus changing their shapes
+from spheres into ellipsoids. The astonishing dimensions
+of these stars are in part compensated by their very low
+density, which is less than that of air, so that their masses
+are respectively only 10 times and 21 times that of the
+sun! But these dimensions and masses perhaps require
+confirmation, since they depend upon spectroscopic observations
+of doubtful interpretation. In <a href="#Fig_132">Fig.&nbsp;132</a> what relative
+positions must the stars occupy in their orbit in order
+that their combined light should give &beta;&nbsp;Lyrę its maximum
+brightness? What position will furnish a minimum
+brightness?</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_132" id="Fig_132"></a>
+<img src="images/i359.png" width="500" height="246" alt="Fig. 132.&mdash;The system of &beta;&nbsp;Lyrę.&mdash;Myers." title="Fig. 132.&mdash;The system of &beta;&nbsp;Lyrę.&mdash;Myers." />
+<span class="caption"><span class="smcap">Fig. 132.</span>&mdash;The system of &beta;&nbsp;Lyrę.&mdash;<span class="smcap">Myers.</span></span>
+</div>
+
+<p><a name="S_207" id="S_207"></a>207. <b>Variables of long and short periods.</b>&mdash;It must not be
+supposed that all variable stars are binaries which eclipse
+each other. By far the larger part of them, like Mira, are
+not to be accounted for in this way, and a distinction which<span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span>
+is pretty well marked in the length of their periods is significant
+in this connection. There is a considerable number
+of variable stars with periods shorter than a month, and
+there are many having periods longer than 6 months, but
+there are very few having periods longer than 18 months,
+or intermediate between 1 month and 6 months, so that it
+is quite customary to divide variable stars into two classes&mdash;those
+of long period, 6 months or more, and those of
+short period less than 6 months, and that this distinction
+corresponds to some real difference in the stars themselves
+is further marked by the fact that the long-period variables
+are prevailingly red in color, while the short-period stars
+are almost without exception white or very pale yellow.
+In fact, the longer the period the redder the star, although
+it is not to be inferred that all red stars are variable; a
+considerable percentage of them shine with constant light.
+The eclipse explanation of variability holds good only for
+short-period variables, and possibly not for all of them,
+while for the long-period variables there is no explanation
+which commands the general assent of astronomers, although
+unverified hypotheses are plenty.</p>
+
+<p>The number of stars known to be variable is about 400,
+while a considerable number of others are "suspected,"
+and it would not be surprising if a large fraction of all the
+stars should be found to fluctuate a little in brightness.
+The sun's spots may suffice to make it a variable star with
+a period of 11 years.</p>
+
+<p>The discovery of new variables is of frequent occurrence,
+and may be expected to become more frequent when
+the sky is systematically explored for them by the ingenious
+device suggested by Pickering and illustrated in <a href="#Fig_133">Fig.&nbsp;133</a>.
+A given region of the sky&mdash;e.&nbsp;g., the Northern Crown&mdash;is
+photographed repeatedly upon the same plate, which is
+shifted a little at each new exposure, so that the stars shall
+fall at new places upon it. The finally developed plate
+shows a row of images corresponding to each star, and if<span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span>
+the star's light is constant the images in any given row will
+all be of the same size, as are most of those in <a href="#Fig_133">Fig.&nbsp;133</a>;
+but a variable star such as is shown by the arrowhead
+reveals its presence by the broken aspect of its row of
+dots, a minimum brilliancy being shown by smaller and a
+maximum by larger ones. In this particular case, at two
+exposures the star was too faint to print its image upon
+the plate.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_133" id="Fig_133"></a>
+<img src="images/i361.jpg" width="500" height="501" alt="Fig. 133.&mdash;Discovery of a variable star by means of photography.&mdash;Pickering." title="Fig. 133.&mdash;Discovery of a variable star by means of photography.&mdash;Pickering." />
+<span class="caption"><span class="smcap">Fig. 133.</span>&mdash;Discovery of a variable star by means of photography.&mdash;<span class="smcap">Pickering.</span></span>
+</div>
+
+<p><a name="S_208" id="S_208"></a>208. <b>New stars.</b>&mdash;Next to the variable stars of very long
+or very irregular period stand the so-called <i>new</i> or <i>temporary
+stars</i>, which appear for the most part suddenly, and
+after a brief time either vanish altogether or sink to comparative
+insignificance. These were formerly thought to
+be very remarkable and unusual occurrences&mdash;"the birth
+of a new world"&mdash;and it is noteworthy that no new star
+is recorded to have been seen from 1670 to 1848 <span class="smcap">A.&nbsp;D.</span>, for
+since that time there have been no less than five of them<span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span>
+visible to the naked eye and others telescopic. In so far
+as these new stars are not ordinary variables (Mira, first
+seen in 1596, was long counted as a new star), they are commonly
+supposed due to chance encounters between stars
+or other cosmic bodies moving with considerable velocities
+along orbits which approach very close to each other. The
+actual collision of two dark bodies moving with high velocities
+is clearly sufficient to produce a luminous star&mdash;e.&nbsp;g.,
+meteors&mdash;and even the close approach of two cooled-off
+stars, might result in tidal actions which would rend
+open their crusts and pour out the glowing matter from
+within so as to produce temporarily a very great accession
+of brightness.</p>
+
+<p>The most famous of all new stars is that which, according
+to Tycho Brahe's report, appeared in the year 1572, and
+was so bright when at its best as to be seen with the naked
+eye in broad daylight. It continued visible, though with
+fading light, for about 16 months, and finally disappeared
+to the naked eye, although there is some reason to suppose
+that it can be identified with a ruddy star of the eleventh
+magnitude in the constellation Cassiopeia, whose light still
+shows traces of variability.</p>
+
+<p>No modern temporary star approaches that of Tycho
+in splendor, but in some respects the recent ones surpass
+it in interest, since it has been possible to apply the spectroscope
+to the analysis of their light and to find thereby
+a much more complex set of conditions in the star than
+would have been suspected from its light changes alone.</p>
+
+<p>One of the most extraordinary of new stars, and the
+most brilliant one since that of Tycho, appeared suddenly
+in the constellation Perseus in February, 1901, and for a
+short time equaled Capella in brightness. But its light
+rapidly waned, with periodic fluctuations of brightness like
+those of a variable star, and at the present time (September,
+1902) it is lost to the naked eye, although in the telescope
+it still shines like a star of the ninth or tenth magnitude.<span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span></p>
+
+<p>By the aid of powerful photographic apparatus, during
+the period of its waning brilliancy a ring of faint nebulous
+matter was detected surrounding the star and drifting
+around and away from it much as if a series of nebulę had
+been thrown off by the star at the time of its sudden outburst
+of light. But the extraordinary velocity of this nebular
+motion, nearly a billion miles per hour, makes such an
+explanation almost incredible, and astronomers are more inclined
+to believe that the ring was merely a reflection of the
+star's own light from a cloud of meteoric matter, into which
+a rapidly moving dark star plunged and, after the fashion of
+terrestrial meteors, was raised to brilliant incandescence by
+the collision. If we assume this to be the true explanation
+of these extraordinary phenomena, it is possible to show
+from the known velocity with which light travels through
+space and from the rate at which the nebula spread, that
+the distance of Nova Persei, as the new star is called, corresponds
+to a parallax of about one one-hundredth of a second,
+a result that is, in substance, confirmed by direct telescopic
+measurements of its parallax.</p>
+
+<p>Another modern temporary star is Nova Aurigę, which
+appeared suddenly in December, 1891, waned, and in the
+following April vanished, only to reappear three months
+later for another season of renewed brightness. The spectra
+of both these modern Novę contain both dark and
+bright lines displaced toward opposite ends of the spectrum,
+and suggesting the Doppler effect that would be
+produced by two or more glowing bodies having rapid and
+opposite motions in the line of sight. But the most recent
+investigations cast discredit on this explanation and leave
+the spectra of temporary stars still a subject of debate
+among astronomers, with respect both to the motion they
+indicate and the intrinsic nature of the stars themselves.
+The varying aspect of the spectra suggested at one time
+the sun's chromosphere, at another time the conditions that
+are present in nebulę, etc.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span></p>
+<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV</h2>
+
+<h3>STARS AND NEBULĘ</h3>
+
+
+<p><a name="S_209" id="S_209"></a>209. <b>Stellar colors.</b>&mdash;We have already seen that one star
+differs from another in respect of color as well as brightness,
+and the diligent student of the sky will not fail to
+observe for himself how the luster of Sirius and Rigel is
+more nearly a pure white than is that of any other stars in
+the heavens, while at the other end of the scale &alpha;&nbsp;Orionis
+and Aldebaran are strongly ruddy, and Antares presents an
+even deeper tone of red. Between these extremes the
+light of every star shows a mixture of the rainbow hues, in
+which a very pale yellow is the predominant color, shading
+off, as we have seen, to white at one end of the scale and
+red at the other. There are no green stars, or blue stars,
+or violet stars, save in one exceptional class of cases&mdash;viz.,
+where the two components of a double star are of very different
+brightness, it is quite the usual thing for them to
+have different colors, and then, almost without exception,
+the color of the fainter star lies nearer to the violet end
+of the spectrum than does the color of the bright one,
+and sometimes shows a distinctly blue or green hue. A
+fine type of such double star is &beta;&nbsp;Cygni, in which the
+components are respectively yellow and blue, and the yellow
+star furnishes eight times as much light as the blue
+one.</p>
+
+<p>The exception which double stars thus make to the general
+rule of stellar colors, yellow and red, but no color of
+shorter wave length, has never been satisfactorily explained,<span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span>
+but the rule itself presents no difficulties. Each star is an
+incandescent body, giving off radiant energy of every wave
+length within the limits of the visible spectrum, and, indeed,
+far beyond these limits. If this radiant energy could
+come unhindered to our eyes every star would appear white,
+but they are all surrounded by atmospheres&mdash;analogous to
+the chromosphere and reversing layer of the sun&mdash;which
+absorb a portion of their radiant energy and, like the earth's
+atmosphere, take a heavier toll from the violet than from
+the red end of the spectrum. The greater the absorption
+in the star's atmosphere, therefore, the feebler and the ruddier
+will be its light, and corresponding to this the red stars
+are as a class fainter than the white ones.</p>
+
+<p><a name="S_210" id="S_210"></a>210. <b>Chemistry of the stars.</b>&mdash;The spectroscope is pre-eminently
+the instrument to deal with this absorption of light
+in the stellar atmospheres, just as it deals with that absorption
+in the sun's atmosphere to which are due the dark lines
+of the solar spectrum, although the faintness of starlight,
+compared with that of the sun, presents a serious obstacle
+to its use. Despite this difficulty most of the lucid stars
+and many of the telescopic ones have been studied with
+the spectroscope and found to be similar to the sun and
+the earth as respects the material of which they are made.
+Such familiar chemical elements as hydrogen and iron, carbon,
+sodium, and calcium are scattered broadcast throughout
+the visible universe, and while it would be unwarranted
+by the present state of knowledge to say that the stars contain
+nothing not found in the earth and the sun, it is evident
+that in a broad way their substance is like rather than
+unlike that composing the solar system, and is subject to
+the same physical and chemical laws which obtain here.
+Galileo and Newton extended to the heavens the terrestrial
+sciences of mathematics and mechanics, but it remained to
+the nineteenth century to show that the physics and chemistry
+of the sky are like the physics and chemistry of the
+earth.<span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span></p>
+
+<p><a name="S_211" id="S_211"></a>211. <b>Stellar spectra.</b>&mdash;When the spectra of great numbers
+of stars are compared one with another, it is found that
+they bear some relation to the colors of the stars, as, indeed,
+we should expect, since spectrum and color are both produced
+by the stellar atmospheres, and it is found useful to
+classify these spectra into three types, as follows:</p>
+
+<p><i>Type I. Sirian stars.</i>&mdash;Speaking generally, the stars
+which are white or very faintly tinged with yellow, furnish
+spectra like that of Sirius, from which they take their
+name, or that of &beta;&nbsp;Aurigę (<a href="#Fig_124">Fig.&nbsp;124</a>), which is a continuous
+spectrum, especially rich in energy of short wave length&mdash;i.&nbsp;e.,
+violet and ultra-violet light, and is crossed by a relatively
+small number of heavy dark lines corresponding to
+the spectrum of hydrogen. Sometimes, however, these lines
+are much fainter than is here shown, and we find associated
+with them still other faint ones pointing to the presence of
+other metallic substances in the star's atmosphere. These
+metallic lines are not always present, and sometimes even
+the hydrogen lines themselves are lacking, but the spectrum
+is always rich in violet and ultra-violet light.</p>
+
+<p>Since with increasing temperature a body emits a continually
+increasing proportion of energy of short wave
+length (<a href="#S_118">§&nbsp;118</a>), the richness of these spectra in such energy
+points to a very high temperature in these stars, probably
+surpassing in some considerable measure that of the sun.
+Stars with this type of spectrum are more numerous than
+all others combined, but next to them in point of numbers
+stands&mdash;</p>
+
+<p><i>Type II. Solar stars.</i>&mdash;To this type of spectrum belong
+the yellow stars, which show spectra like that of the sun,
+or of Pollux (<a href="#Fig_125">Fig.&nbsp;125</a>). These are not so rich in violet
+light as are those of Type&nbsp;I, but in complexity of spectrum
+and in the number of their absorption lines they far surpass
+the Sirian stars. They are supposed to be at a lower
+temperature than the Sirian stars, and a much larger number
+of chemical elements seems present and active in the<span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span>
+reversing layer of their atmospheres. The strong resemblance
+which these spectra bear to that of the sun, together
+with the fact that most of the sun's stellar neighbors have
+spectra of this type, justify us in ranking both them and it
+as members of one class, called <i>solar stars</i>.</p>
+
+<p><i>Type III. Red stars.</i>&mdash;A small number of stars show
+spectra comparable with that of &alpha;&nbsp;Herculis (<a href="#Fig_134">Fig.&nbsp;134</a>), in
+which the blue and the violet part of the spectrum is almost
+obliterated, and the remaining yellow and red parts
+show not only dark lines, but also numerous broad dark
+bands, sharp at one edge, and gradually fading out at the
+other. It is this <i>selective absorption</i>, extinguishing the blue
+and leaving the red end of the spectrum, which produces
+the ruddy color of these stars, while the bands in their
+spectra "are characteristic of chemical combinations, and
+their presence ... proves that at certain elevations in the
+atmospheres of these stars the temperature has sunk so low
+that chemical combinations can be formed and maintained"
+(Scheiner-Frost). One of the chemical compounds here indicated
+is a hydrocarbon similar to that found in comets.
+In the white and yellow stars the temperatures are so high
+that the same chemical elements, although present, can not
+unite one with another to form compound substances.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_134" id="Fig_134"></a>
+<a href="images/i367.jpg"><img src="images/i367.jpg" width="500" height="70" alt="Fig. 134.&mdash;The spectrum of &alpha;&nbsp;Herculis.&mdash;Espin." title="Fig. 134.&mdash;The spectrum of &alpha;&nbsp;Herculis.&mdash;Espin." /></a>
+<span class="caption"><span class="smcap">Fig. 134.</span>&mdash;The spectrum of &alpha;&nbsp;Herculis.&mdash;<span class="smcap">Espin.</span></span>
+</div>
+
+<p>Most of the variable stars are red and have spectra of
+the third type; but this does not hold true for the eclipse
+variables like Algol, all of which are white stars with spectra
+of the first type. The ordinary variable star is therefore
+one with a dense atmosphere of relatively low temperature
+and complex structure, which produces the prevailing
+red color of these stars by absorbing the major part of<span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span>
+their radiant energy of short wave length while allowing
+the longer, red waves to escape. Although their exact
+nature is not understood, there can be little doubt that the
+fluctuation in the light of these stars is due to processes
+taking place within the star itself, but whether above or
+below its photosphere is still uncertain.</p>
+
+<p><a name="S_212" id="S_212"></a>212. <b>Classes of stars.</b>&mdash;There is no hard-and-fast dividing
+line between these types of stellar spectra, but the change
+from one to another is by insensible gradations, like the
+transition from youth to manhood and from manhood to
+old age, and along the line of transition are to be found
+numberless peculiarities and varieties of spectra not enumerated
+above&mdash;e.&nbsp;g., a few stars show not only dark absorption
+lines in their spectra but bright lines as well, which,
+like those in <a href="#Fig_48">Fig.&nbsp;48</a>, point to the presence of incandescent
+vapors, even in the outer parts of their atmospheres. Among
+the lucid stars about 75 per cent have spectra of the first
+type, 23 per cent are of the second type, 1&nbsp;per cent of the
+third type, and the remaining 1 per cent are peculiar or of
+doubtful classification. Among the telescopic stars it is
+probable that much the same distribution holds, but in the
+present state of knowledge it is not prudent to speak with
+entire confidence upon this point.</p>
+
+<p>That the great number of stars whose spectra have been
+studied should admit of a classification so simple as the
+above, is an impressive fact which, when supplemented by
+the further fact of a gradual transition from one type of
+spectrum to the next, leaves little room for doubt that in
+the stars we have an innumerable throng of individuals belonging
+to the same species but in different stages of development,
+and that the sun is only one of these individuals,
+of something less than medium size and in a stage of development
+which is not at all peculiar, since it is shared by
+nearly a fourth of all the stars.</p>
+
+<div class="figright" style="width: 350px;"><a name="Fig_135" id="Fig_135"></a>
+<a href="images/i369.jpg"><img src="images/i369.jpg" width="350" height="288" alt="Fig 135.&mdash;Star cluster in Hercules." title="Fig 135.&mdash;Star cluster in Hercules." /></a>
+<span class="caption"><span class="smcap">Fig 135.</span>&mdash;Star cluster in Hercules.</span>
+</div>
+
+
+<p><a name="S_213" id="S_213"></a>213. <b>Star clusters.</b>&mdash;In previous chapters we have noted
+the Pleiades and Pręsepe as star clusters visible to the
+<span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span>
+naked eye, and to them we may add the Hyades, near Aldebaran,
+and the little constellation Coma Berenices. But
+more impressive than any of these, although visible only
+in a telescope, is the splendid cluster in Hercules, whose
+appearance in a telescope
+of moderate size
+is shown in <a href="#Fig_135">Fig.&nbsp;135</a>,
+while <a href="#Fig_136">Fig.&nbsp;136</a> is a photograph
+of the same
+cluster taken with a
+very large reflecting
+telescope. This is only
+a type of many telescopic
+clusters which
+are scattered over the
+sky, and which are made
+up of stars packed so
+closely together as to become indistinguishable, one from
+another, at the center of the cluster. Within an area
+which could be covered by a third of the full moon's face
+are crowded in this cluster more than five thousand stars
+which are unquestionably close neighbors, but whose apparent
+nearness to each other is doubtless due to their
+great distance from us. It is quite probable that even at
+the center of this cluster, where more than a thousand stars
+are included within a radius of 160", the actual distances
+separating adjoining stars are much greater than that separating
+earth and sun, but far less than that separating the
+sun from its nearest stellar neighbor.</p>
+
+<p>An interesting discovery of recent date, made by Professor
+Bailey in photographing star clusters, is that some
+few of them, which are especially rich in stars, contain an
+extraordinary number of variable stars, mostly very faint
+and of short period. Two clusters, one in the northern and
+one in the southern hemisphere, contain each more than a
+hundred variables, and an even more extraordinary case is<span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span>
+presented by a cluster, called Messier&nbsp;5, not far from the
+star &alpha;&nbsp;Serpentis, which contains no less than sixty-three
+variables, all about of the fourteenth magnitude, all having
+light periods which differ but little from half a day, all
+having light curves of about the same shape, and all having
+a range of brightness from maximum to minimum of about
+one magnitude. An extraordinary set of coincidences
+which "points unmistakably to a common origin and cause
+of variability."</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_136" id="Fig_136"></a>
+<a href="images/i370-full.jpg"><img src="images/i370.jpg" width="500" height="542" alt="Fig. 136.&mdash;Star cluster in Hercules.&mdash;Keeler." title="Fig. 136.&mdash;Star cluster in Hercules.&mdash;Keeler." /></a>
+<span class="caption"><span class="smcap">Fig. 136.</span>&mdash;Star cluster in Hercules.&mdash;<span class="smcap">Keeler.</span></span>
+</div><p><span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span></p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_137" id="Fig_137"></a>
+<a href="images/i371a-full.jpg"><img src="images/i371a.jpg" width="500" height="330" alt="Fig. 137.&mdash;The Andromeda nebula as seen in a very small telescope." title="Fig. 137.&mdash;The Andromeda nebula as seen in a very small telescope." /></a>
+<span class="caption"><span class="smcap">Fig. 137.</span>&mdash;The Andromeda nebula as seen in a very small telescope.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_138" id="Fig_138"></a>
+<a href="images/i371b-full.jpg"><img src="images/i371b.jpg" width="500" height="508" alt="Fig. 138.&mdash;The Andromeda nebula and Holmes&#39;s comet.
+Photographed by Barnard." title="Fig. 138.&mdash;The Andromeda nebula and Holmes&#39;s comet.
+Photographed by Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 138.</span>&mdash;The Andromeda nebula and Holmes&#39;s comet.
+Photographed by <span class="smcap">Barnard</span>.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_139" id="Fig_139"></a>
+<a href="images/i372a-full.jpg"><img src="images/i372a.jpg" width="500" height="385" alt="Fig. 139.&mdash;A drawing of the Andromeda nebula." title="Fig. 139.&mdash;A drawing of the Andromeda nebula." /></a>
+<span class="caption"><span class="smcap">Fig. 139.</span>&mdash;A drawing of the Andromeda nebula.</span>
+</div>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_140" id="Fig_140"></a>
+<a href="images/i372b-full.jpg"><img src="images/i372b.jpg" width="500" height="445" alt="Fig. 140.&mdash;A photograph of the Andromeda nebula.&mdash;Roberts." title="Fig. 140.&mdash;A photograph of the Andromeda nebula.&mdash;Roberts." /></a>
+<span class="caption"><span class="smcap">Fig. 140.</span>&mdash;A photograph of the Andromeda nebula.&mdash;<span class="smcap">Roberts.</span></span>
+</div>
+
+<div class="figright" style="width: 300px;"><a name="Fig_141" id="Fig_141"></a>
+<a href="images/i373-full.jpg"><img src="images/i373.jpg" width="300" height="456" alt="Fig. 141.&mdash;Types of nebulę." title="Fig. 141.&mdash;Types of nebulę." /></a>
+<span class="caption"><span class="smcap">Fig. 141.</span>&mdash;Types of nebulę.</span>
+</div>
+
+<p><a name="S_214" id="S_214"></a>214. <b>Nebulę.</b>&mdash;Returning to <a href="#Fig_136">Fig.&nbsp;136</a>, we note that its
+background has a hazy appearance, and that at its center
+the stars can no longer be distinguished, but blend one
+with another so as to appear like a bright cloud. The<span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span>
+outer part of the cluster is <i>resolved</i> into stars, while in the
+picture the inner portion is not so resolved, although in
+the original photographic plate the individual stars can be
+distinguished to the very center of the cluster. In many<span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span>
+cases, however, this is not possible, and we have an <i>irresolvable
+cluster</i> which it is customary to call a <i>nebula</i>
+(Latin, <i>little cloud</i>).</p>
+
+<p>The most conspicuous example of this in the northern
+heavens is the great nebula in Andromeda (R.&nbsp;A. 0<sup>h</sup> 37<sup>m</sup>,
+Dec.&nbsp;+41°), which may be seen with the naked eye as a
+faint patch of foggy light. Look for it. This appears in
+an opera glass or very small telescope not unlike <a href="#Fig_137">Fig.&nbsp;137</a>,
+which is reproduced from a sketch. <a href="#Fig_138">Fig.&nbsp;138</a> is from a
+photograph of the same object showing essentially the same
+shape as in the preceding figure, but bringing out more
+detail. Note the two small nebulę adjoining the large
+one, and at the bottom of the picture an object which might
+easily be taken for another nebula but which is in fact
+a tailless comet that chanced to be passing that part of
+the sky when the picture was taken. <a href="#Fig_139">Fig.&nbsp;139</a> is from another
+drawing of this nebula,
+although it is hardly to be
+recognized as a representation
+of the same thing; but
+its characteristic feature, the
+two dark streaks near the center
+of the picture, is justified
+in part by <a href="#Fig_140">Fig.&nbsp;140</a>, which is
+from a photograph made with
+a large reflecting telescope.</p>
+
+<p>A comparison of these several
+representations of the
+same thing will serve to illustrate
+the vagueness of its outlines,
+and how much the impressions
+to be derived from
+nebulę depend upon the telescopes
+employed and upon the
+observer's own prepossessions. The differences among the
+pictures can not be due to any change in the nebula itself,<span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span>
+for half a century ago it was sketched much as shown in
+the latest of them (<a href="#Fig_140">Fig.&nbsp;140</a>).</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_142" id="Fig_142"></a>
+<a href="images/i374-full.jpg"><img src="images/i374.jpg" width="500" height="550" alt="Fig. 142.&mdash;The Trifid nebula.&mdash;Keeler." title="Fig. 142.&mdash;The Trifid nebula.&mdash;Keeler." /></a>
+<span class="caption"><span class="smcap">Fig. 142.</span>&mdash;The Trifid nebula.&mdash;<span class="smcap">Keeler.</span></span>
+</div>
+
+<p><a name="S_215" id="S_215"></a>215. <b>Typical nebulę.</b>&mdash;Some of the fantastic forms which
+nebulę present in the telescope are shown on a small scale
+in <a href="#Fig_141">Fig.&nbsp;141</a>, but in recent years astronomers have learned to
+place little reliance upon drawings such as these, which are
+now almost entirely supplanted by photographs made with
+long exposures in powerful telescopes. One of the most
+exquisite of these modern photographs is that of the Trifid<span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span>
+nebula in Sagittarius (<a href="#Fig_142">Fig.&nbsp;142</a>). Note especially the dark
+lanes that give to this nebula its name, Trifid, and which run
+through its brightest parts, breaking it into seemingly independent
+sections. The area of the sky shown in this cut is
+about 15 per cent less than that covered by the full moon.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_143" id="Fig_143"></a>
+<a href="images/i375-full.jpg"><img src="images/i375.jpg" width="500" height="546" alt="Fig. 143.&mdash;A nebula in Cygnus.&mdash;Keeler." title="Fig. 143.&mdash;A nebula in Cygnus.&mdash;Keeler." /></a>
+<span class="caption"><span class="smcap">Fig. 143.</span>&mdash;A nebula in Cygnus.&mdash;<span class="smcap">Keeler.</span></span>
+</div>
+
+<p><a href="#Fig_143">Fig.&nbsp;143</a> shows a very different type of nebula, found in
+the constellation Cygnus, which appears made up of filaments
+closely intertwined, and stretches across the sky for
+a distance considerably greater than the moon's diameter.<span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span></p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_144" id="Fig_144"></a>
+<a href="images/i376-full.jpg"><img src="images/i376.jpg" width="500" height="536" alt="Fig. 144.&mdash;Spiral nebula in Canes Venatici.&mdash;Keeler." title="Fig. 144.&mdash;Spiral nebula in Canes Venatici.&mdash;Keeler." /></a>
+<span class="caption"><span class="smcap">Fig. 144.</span>&mdash;Spiral nebula in Canes Venatici.&mdash;<span class="smcap">Keeler.</span></span>
+</div>
+
+<p>A much smaller but equally striking nebula is that in
+the constellation Canes Venatici (<a href="#Fig_144">Fig.&nbsp;144</a>), which shows a
+most extraordinary spiral structure, as if the stars composing
+it were flowing in along curved lines toward a center of
+condensation. The diameter of the circular part of this
+nebula, omitting the projection toward the bottom of the
+picture, is about five minutes of arc, a sixth part of the
+diameter of the moon, and its thickness is probably very
+small compared with its breadth, perhaps not much exceeding<span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span>
+the width of the spiral streams which compose it. Note
+how the bright stars that appear within the area of this
+nebula fall on the streams of nebulous matter as if they
+were part of them. This characteristic grouping of the
+stars, which is followed in many other nebulę, shows that
+they are really part and parcel of the nebula and not merely
+on line with it. <a href="#Fig_145">Fig.&nbsp;145</a> shows how a great nebula is associated
+with the star &rho;&nbsp;Ophiuchi.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_145" id="Fig_145"></a>
+<a href="images/i377-full.jpg"><img src="images/i377.jpg" width="500" height="483" alt="Fig. 145.&mdash;Great nebula about the star &rho;&nbsp;Ophiuchi.&mdash;Barnard." title="Fig. 145.&mdash;Great nebula about the star &rho;&nbsp;Ophiuchi.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 145.</span>&mdash;Great nebula about the star &rho;&nbsp;Ophiuchi.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p>Probably the most impressive of all nebulę is the great
+one in Orion (<a href="#Fig_146">Fig.&nbsp;146</a>), whose position is shown on the
+star map between Rigel and &zeta;&nbsp;Orionis. Look for it with
+an opera glass or even with the unaided eye. This is sometimes
+called an <i>amorphous</i>&mdash;i.&nbsp;e., shapeless&mdash;nebula, because
+it presents no definite form which the eye can grasp and
+little trace of structure or organization. It is "without
+form and void" at least in its central portions, although on
+its edges curved filaments may be traced streaming away<span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span>
+from the brighter parts of the central region. This nebula,
+as shown in <a href="#Fig_146">Fig.&nbsp;146</a>, covers an area about equal to that of
+the full moon, without counting as any part of this the
+companion nebula shown at one side, but photographs
+made with suitable exposures show that faint outlying parts
+of the nebula extend in curved lines over the larger part of
+the constellation Orion. Indeed, over a large part of the
+entire sky the background is faintly covered with nebulous
+light whose brighter portions, if each were counted as a
+separate nebula, would carry the total number of such objects
+well into the hundreds of thousands.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_146" id="Fig_146"></a>
+<a href="images/i378-full.jpg"><img src="images/i378.jpg" width="500" height="378" alt="Fig. 146.&mdash;The Orion nebula." title="Fig. 146.&mdash;The Orion nebula." /></a>
+<span class="caption"><span class="smcap">Fig. 146.</span>&mdash;The Orion nebula.</span>
+</div>
+
+<p>The Pleiades (<a href="#PLATE_IV">Plate&nbsp;IV</a>) present a case of a resolvable
+star cluster projected against such a nebulous background
+whose varying intensity should be noted in the figure. A
+part of this nebulous matter is shown in wisps extending
+from one star to the next, after the fashion of a bridge, and
+leaving little doubt that the nebula is actually a part of the
+cluster and not merely a background for it.</p>
+
+<div class="figcenter" style="width: 600px;"><a name="PLATE_IV" id="PLATE_IV"></a>
+<a href="images/i379-full.jpg"><img src="images/i379.jpg" width="600" height="489" alt="THE PLEIADES
+
+(AFTER A PHOTOGRAPH)" title="THE PLEIADES
+
+(AFTER A PHOTOGRAPH)" /></a>
+<span class="caption">THE PLEIADES
+
+(AFTER A PHOTOGRAPH)</span>
+</div>
+
+<p><a href="#Fig_147">Fig.&nbsp;147</a> shows a series of so-called double nebulę perhaps
+comparable with double stars, although the most
+recent photographic work seems to indicate that they are<span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span>
+really faint spiral nebulę in which only the brightest parts
+are shown by the telescope.</p>
+
+<p>According to Keeler, the spiral is the prevailing type
+of nebulę, and while <a href="#Fig_144">Fig.&nbsp;144</a> presents the most perfect example
+of such a nebula, the
+student should not fail to
+note that the Andromeda nebula
+(<a href="#Fig_140">Fig.&nbsp;140</a>) shows distinct
+traces of a spiral structure,
+only here we do not see its
+true shape, the nebula being
+turned nearly edgewise toward
+us so that its presumably circular
+outline is foreshortened
+into a narrow ellipse.</p>
+
+<div class="figright" style="width: 300px;"><a name="Fig_147" id="Fig_147"></a>
+<a href="images/i381.jpg"><img src="images/i381.jpg" width="300" height="413" alt="Fig. 147.&mdash;Double nebulę.
+Herschel." title="Fig. 147.&mdash;Double nebulę.
+Herschel." /></a>
+<span class="caption"><span class="smcap">Fig. 147.</span>&mdash;Double nebulę.
+<span class="smcap">Herschel.</span></span>
+</div>
+
+<p>Another type of nebula of
+some consequence presents in
+the telescope round disks like
+those of Uranus or Neptune,
+and this appearance has given
+them the name <i>planetary nebulę</i>.
+The comet in <a href="#Fig_138">Fig.&nbsp;138</a>, if smaller, would represent
+fairly well the nebulę of this type. Sometimes a planetary
+nebula has a star at its center, and sometimes it appears
+hollow, like a smoke ring, and is then called a ring nebula.
+The most famous of these is in the constellation Lyra, not
+far from Vega.</p>
+
+<p><a name="S_216" id="S_216"></a>216. <b>Spectra of nebulę.</b>&mdash;A star cluster, like the one in
+Hercules, shows, of course, stellar spectra, and even when
+irresolvable the spectrum is a continuous one, testifying to
+the presence of stars, although they stand too close together
+to be separately seen. But in a certain number of
+nebulę the spectrum is altogether different, a discontinuous
+one containing only a few bright lines, showing that
+here the nebular light comes from glowing gases which
+are subject to no considerable pressure. The planetary<span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span>
+nebulę all have spectra of this kind and make up about
+half of all the known gaseous nebulę. It is worthy of
+note that a century ago Sir William Herschel had observed
+a green shimmer in the light of certain nebulę which led
+him to believe that they were "not of a starry nature," a
+conclusion which has been abundantly confirmed by the
+spectroscope. The green shimmer is, in fact, caused by a
+line in the green part of the spectrum that is always present
+and is always the brightest part of the spectrum of
+gaseous nebulę.</p>
+
+<p>In faint nebulę this line constitutes the whole of their
+visible spectrum, but in brighter ones two or three other
+and fainter lines are usually associated with it, and a very
+bright nebula, like that in Orion, may show a considerable
+number of extra lines, but for the most part they can not
+be identified in the spectrum of any terrestrial substances.
+An exception to this is found in the hydrogen lines, which
+are well marked in most spectra of gaseous nebulę, and
+there are indications of one or two other known substances.</p>
+
+<p><a name="S_217" id="S_217"></a>217. <b>Density of nebulę.</b>&mdash;It is known from laboratory
+experiments that diminishing the pressure to which an incandescent
+gas is subject, diminishes the number of lines
+contained in its spectrum, and we may surmise from the
+very simple character and few lines of these nebular spectra
+that the gas which produces them has a very small
+density. But this is far from showing that the nebula
+itself is correspondingly attenuated, for we must not assume
+that this shining gas is all that exists in the nebula;
+so far as telescope or camera are concerned, there may be
+associated with it any amount of dark matter which can
+not be seen because it sends to us no light. It is easy
+to think in this connection of meteoric dust or the stuff of
+which comets are made, for these seem to be scattered
+broadcast on every side of the solar system and may, perchance,
+extend out to the region of the nebulę.<span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span></p>
+
+<p>But, whatever may be associated in the nebula with the
+glowing gas which we see, the total amount of matter, invisible
+as well as visible, must be very small, or rather its
+average density must be very small, for the space occupied
+by such a nebula as that of Orion is so great that if the
+average density of its matter were equal to that of air the
+resulting mass by its attraction would exert a sensible effect
+upon the motion of the sun through space. The brighter
+parts of this nebula as seen from the earth subtend an angle
+of about half a degree, and while we know nothing of its
+distance from us, it is easy to see that the farther it is away
+the greater must be its real dimensions, and that this increase
+of bulk and mass with increasing distance will just
+compensate the diminishing intensity of gravity at great
+distances, so that for a given angular diameter&mdash;e.&nbsp;g., half
+a degree&mdash;the force with which this nebula attracts the sun
+depends upon its density but not at all upon its distance.
+Now, the nebula must attract the sun in some degree, and
+must tend to move it and the planets in an orbit about
+the attracting center so that year after year we should see
+the nebula from slightly different points of view, and this
+changed point of view should produce a change in the apparent
+direction of the nebula from us&mdash;i.&nbsp;e., a proper motion,
+whose amount would depend upon the attracting force,
+and therefore upon the density of the attracting matter.
+Observations of the Orion nebula show that its proper
+motion is wholly inappreciable, certainly far less than half
+a second of arc per year, and corresponding to this amount
+of proper motion the mean density of the nebula must be
+some millions of times (10<sup>10</sup> according to Ranyard) less than
+that of air at sea level&mdash;i.&nbsp;e., the average density throughout
+the nebula is comparable with that of those upper parts
+of the earth's atmosphere in which meteors first become
+visible.</p>
+
+<p><a name="S_218" id="S_218"></a>218. <b>Motion of nebulę.</b>&mdash;The extreme minuteness of
+their proper motions is a characteristic feature of all<span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span>
+nebulę. Indeed, there is hardly a known case of sensible
+proper motion of one of these bodies, although a dozen or
+more of them show velocities in the line of sight ranging
+in amount from +30 to -40 miles per second, the plus
+sign indicating an increasing distance. While a part of
+these velocities may be only apparent and due to the motion
+of earth and sun through space, a part at least is real
+motion of the nebulę themselves. These seem to move
+through the celestial spaces in much the same way and
+with the same velocities as do the stars, and their smaller
+proper motions across the line of sight (angular motions)
+are an index of their great distance from us. No one has
+ever succeeded in measuring the parallax of a nebula or
+star cluster.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_148" id="Fig_148"></a>
+<a href="images/i384-full.jpg"><img src="images/i384.jpg" width="500" height="445" alt="Fig. 148.&mdash;A part of the Milky Way." title="Fig. 148.&mdash;A part of the Milky Way." /></a>
+<span class="caption"><span class="smcap">Fig. 148.</span>&mdash;A part of the Milky Way.</span>
+</div>
+
+<p>The law of gravitation presumably holds sway within
+these bodies, and the fact that their several parts and the
+stars which are involved within them, although attracted
+by each other, have shown little or no change of position<span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span>
+during the past century, is further evidence of their low
+density and feeble attraction. In a few cases, however,
+there seem to be in progress within a nebula changes of
+brightness, so that what was formerly a faint part has become
+a brighter one, or <i>vice versa</i>; but, on the whole, even
+these changes are very small.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_149" id="Fig_149"></a>
+<a href="images/i385-full.jpg"><img src="images/i385.jpg" width="500" height="499" alt="Fig. 149.&mdash;The Milky Way near &theta;&nbsp;Ophiuchi.&mdash;Barnard." title="Fig. 149.&mdash;The Milky Way near &theta;&nbsp;Ophiuchi.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 149.</span>&mdash;The Milky Way near &theta;&nbsp;Ophiuchi.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p><a name="S_219" id="S_219"></a>219. <b>The Milky Way.</b>&mdash;Closely related to nebulę and
+star clusters is another feature of the sky, the <i>galaxy</i> or
+<i>Milky Way</i>, with whose appearance to the unaided eye the
+student should become familiar by direct study of the thing
+itself. Figs.&nbsp;<a href="#Fig_148">148</a> and&nbsp;<a href="#Fig_149">149</a> are from photographs of two
+small parts of it, and serve to bring out the small stars of
+which it is composed. Every star shown in these pictures
+is invisible to the naked eye, although their combined light
+is easily seen. The general course of the galaxy across the
+heavens is shown in the star maps, but these contain no
+indication of the wealth of detail which even the naked eye
+may detect in it. Bright and faint parts, dark rifts which<span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span>
+cut it into segments, here and there a hole as if the ribbon
+of light had been shot away&mdash;such are some of the features
+to be found by attentive examination.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_150" id="Fig_150"></a>
+<a href="images/i386-full.jpg"><img src="images/i386.jpg" width="500" height="498" alt="Fig. 150.&mdash;The Milky Way near &beta;&nbsp;Cygni.&mdash;Barnard." title="Fig. 150.&mdash;The Milky Way near &beta;&nbsp;Cygni.&mdash;Barnard." /></a>
+<span class="caption"><span class="smcap">Fig. 150.</span>&mdash;The Milky Way near &beta;&nbsp;Cygni.&mdash;<span class="smcap">Barnard.</span></span>
+</div>
+
+<p>Speaking generally, the course of the Milky Way is a
+great circle completely girdling the sky and having its
+north pole in the constellation Coma Berenices. The
+width of this stream of light is very different in different
+parts of the heavens, amounting where it is widest, in Lyra
+and Cygnus, to something more than 30°, although its
+boundaries are too vague and ill defined to permit much
+accuracy of measurement. Observe the very bright part
+between &beta;&nbsp;and &gamma;&nbsp;Cygni, nearly opposite Vega, and note
+how even an opera glass will partially resolve the nebulous
+light into a great number of stars, which are here rather
+brighter than in other parts of its course. But the resolution
+into stars is only partial, and there still remains a
+background of unresolved shimmer. <a href="#Fig_150">Fig.&nbsp;150</a> is a photograph<span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span>
+of a small part of this region in which, although
+each fleck of light represents a separate star, the galaxy is
+not completely resolved. Compare with this region, rich
+in stars, the nearly empty space between the branches of
+the galaxy a little west of Altair. Another hole in the
+Milky Way may be found a little north and east of &alpha;&nbsp;Cygni,
+and between the extremes of abundance and poverty here
+noted there may be found every gradation of nebulous
+light.</p>
+
+<p>The Milky Way is not so simple in its structure as might
+at first be thought, but a clear and moonless night is
+required to bring out its details. The nature of these
+details, the structure of the galaxy, its shape and extent,
+the arrangement of its parts, and their relation to stars
+and nebulę in general, have been subjects of much speculation
+by astronomers and others who have sought to trace
+out in this way what is called the <i>construction of the
+heavens</i>.</p>
+
+<p><a name="S_220" id="S_220"></a>220. <b>Distribution of the stars.</b>&mdash;How far out into space
+do the stars extend? Are they limited or infinite in number?
+Do they form a system of mutually related parts, or
+are they bunched promiscuously, each for itself, without
+reference to the others? Here is what has been well called
+"the most important problem of stellar astronomy, the
+acquisition of well-founded ideas about the distribution of
+the stars." While many of the ideas upon this subject
+which have been advanced by eminent astronomers and
+which are still current in the books are certainly wrong,
+and few of their speculations along this line are demonstrably
+true, the theme itself is of such grandeur and permanent
+interest as to demand at least a brief consideration.
+But before proceeding to its speculative side we
+need to collect facts upon which to build, and these, however
+inadequate, are in the main simple and not far to seek.</p>
+
+<p>Parallaxes, proper motions, motions in the line of sight,
+while pertinent to the problem of stellar distribution, are<span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span>
+of small avail, since they are far too scanty in number and
+relate only to limited classes of stars, usually the very
+bright ones or those nearest to the sun. Almost the sole
+available data are contained in the brightness of the stars
+and the way in which they seem scattered in the sky. The
+most casual survey of the heavens is enough to show that
+the stars are not evenly sprinkled upon it. The lucid stars
+are abundant in some regions, few in others, and the laborious
+star gauges, actual counting of the stars in sample
+regions of the sky, which have been made by the Herschels,
+Celoria, and others, suffice to show that this lack of uniformity
+in distribution is even more markedly true of the
+telescopic stars.</p>
+
+<p>The rate of increase in the number of stars from one
+magnitude to the next, as shown in <a href="#S_187">§&nbsp;187</a>, is proof of
+another kind of irregularity in their distribution. It is not
+difficult to show, mathematically, that if in distant regions
+of space the stars were on the average as numerous and as
+bright as they are in the regions nearer to the sun, then
+the stars of any particular magnitude ought to be four
+times as numerous as those of the next brighter magnitude&mdash;e.&nbsp;g.,
+four times as many sixth-magnitude stars as there
+are fifth-magnitude ones. But, as we have already seen in
+<a href="#S_187">§&nbsp;187</a>, by actual count there are only three times as many,
+and from the discrepancy between these numbers, an actual
+threefold increase instead of a fourfold one, we must conclude
+that on the whole the stars near the sun are either
+bigger or brighter or more numerous than in the remoter
+depths of space.</p>
+
+<p><a name="S_221" id="S_221"></a>221. <b>The stellar system.</b>&mdash;But the arrangement of the
+stars is not altogether lawless and chaotic; there are traces
+of order and system, and among these the Milky Way is the
+dominant feature. Telescope and photographic plate alike
+show that it is made up of stars which, although quite irregularly
+scattered along its course, are on the average
+some twenty times as numerous in the galaxy as at its<span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span>
+poles, and which thin out as we recede from it on either
+side, at first rapidly and then more slowly. This tendency
+to cluster along the Milky Way is much more pronounced
+among the very faint telescopic stars than among the
+brighter ones, for the lucid stars and the telescopic ones
+down to the tenth or eleventh magnitude, while very
+plainly showing the clustering tendency, are not more than
+three times as numerous in the galaxy as in the constellations
+most remote from it. It is remarkable as showing
+the condensation of the brightest stars that one half of all
+the stars in the sky which are brighter than the second
+magnitude are included within a belt extending 12° on
+either side of the center line of the galaxy.</p>
+
+<p>In addition to this general condensation of stars toward
+the Milky Way, there are peculiarities in the distribution of
+certain classes of stars which are worth attention. Planetary
+nebulę and new stars are seldom, if ever, found far
+from the Milky Way, and stars with bright lines in their
+spectra especially affect this region of the sky. Stars with
+spectra of the first type&mdash;Sirian stars&mdash;are much more
+strongly condensed toward the Milky Way than are stars
+of the solar type, and in consequence of this the Milky
+Way is peculiarly rich in light of short wave lengths. Resolvable
+star clusters are so much more numerous in the
+galaxy than elsewhere, that its course across the sky would
+be plainly indicated by their grouping upon a map showing
+nothing but clusters of this kind.</p>
+
+<p>On the other hand, nebulę as a class show a distinct
+aversion for the galaxy, and are found most abundantly in
+those parts of the sky farthest from it, much as if they
+represented raw material which was lacking along the
+Milky Way, because already worked up to make the stars
+which are there so numerous.</p>
+
+<p><a name="S_222" id="S_222"></a>222. <b>Relation of the sun to the Milky Way.</b>&mdash;The fact
+that the galaxy is a <i>great circle</i> of the sky, but only of moderate
+width, shows that it is a widely extended and comparatively<span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span>
+thin stratum of stars within which the solar system
+lies, a member of the galactic system, and probably not
+very far from its center. This position, however, is not to
+be looked upon as a permanent one, since the sun's motion,
+which lies nearly in the plane of the Milky Way, is ceaselessly
+altering its relation to the center of that system, and
+may ultimately carry us outside its limits.</p>
+
+<p>The Milky Way itself is commonly thought to be a
+ring, or series of rings, like the coils of the great spiral
+nebula in Andromeda, and separated from us by a space far
+greater than the thickness of the ring itself. Note in Figs.&nbsp;<a href="#Fig_149">149</a>
+and&nbsp;<a href="#Fig_150">150</a> how the background is made up of bright and
+dark parts curiously interlaced, and presenting much the
+appearance of a thin sheet of cloud through which we look
+to barren space beyond. While, mathematically, this appearance
+can not be considered as proof that the galaxy
+is in fact a distant ring, rather than a sheet of starry
+matter stretching continuously from the nearer stellar
+neighbors of the sun into the remotest depths of space,
+nevertheless, most students of the question hold it to be
+such a ring of stars, which are relatively close together
+while its center is comparatively vacant, although even
+here are some hundreds of thousands of stars which on the
+whole have a tendency to cluster near its plane and to
+crowd together a little more densely than elsewhere in the
+region where the sun is placed.</p>
+
+<p><a name="S_223" id="S_223"></a>223. <b>Dimensions of the galaxy.</b>&mdash;The dimensions of this
+stellar system are wholly unknown, but there can be no
+doubt that it extends farther in the plane of the Milky
+Way than at right angles to that plane, for stars of the fifteenth
+and sixteenth magnitudes are common in the galaxy,
+and testify by their feeble light to their great distance
+from the earth, while near the poles of the Milky Way there
+seem to be few stars fainter than the twelfth magnitude.
+Herschel, with his telescope of 18 inches aperture, could
+count in the Milky Way more than a dozen times as many<span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span>
+stars per square degree as could Celoria with a telescope of
+4 inches aperture; but around the poles of the galaxy the
+two telescopes showed practically the same number of stars,
+indicating that here even the smaller telescope reached to
+the limits of the stellar system. Very recently, indeed, the
+telescope with which <a href="#Fig_140">Fig.&nbsp;140</a> was photographed seems to
+have reached the farthest limit of the Milky Way, for on a
+photographic plate of one of its richest regions Roberts
+finds it completely resolved into stars which stand out upon
+a black background with no trace of nebulous light between
+them.</p>
+
+<p><a name="S_224" id="S_224"></a>224. <b>Beyond the Milky Way.</b>&mdash;Each additional step into
+the depths of space brings us into a region of which less is
+known, and what lies beyond the Milky Way is largely a
+matter of conjecture. We shrink from thinking it an infinite
+void, endless emptiness, and our intellectual sympathies
+go out to Lambert's speculation of a universe filled
+with stellar systems, of which ours, bounded by the galaxy,
+is only one. There is, indeed, little direct evidence that
+other such systems exist, but the Andromeda nebula is not
+altogether unlike a galaxy with a central cloud of stars,
+and in the southern hemisphere, invisible in our latitudes,
+are two remarkable stellar bodies like the Milky Way in
+appearance, but cut off from all apparent connection with
+it, much as we might expect to find independent stellar
+systems, if such there be.</p>
+
+<p>These two bodies are known as the Magellanic clouds,
+and individually bear the names of Major and Minor Nubecula.
+According to Sir John Herschel, "the Nubecula
+Major, like the Minor, consists partly of large tracts and
+ill-defined patches of irresolvable nebula, and of nebulosity
+in every stage of resolution up to perfectly resolved stars
+like the Milky Way, as also of regular and irregular nebulę ... of
+globular clusters in every stage of resolvability, and
+of clustering groups sufficiently insulated and condensed to
+come under the designation of clusters of stars." Its outlines<span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span>
+are vague and somewhat uncertain, but surely include
+an area of more than 40 square degrees&mdash;i.&nbsp;e., as much as
+the bowl of the Big Dipper&mdash;and within this area Herschel
+counted several hundred nebulę and clusters "which far
+exceeds anything that is to be met with in any other region
+of the heavens." Although its excessive complexity of detail
+baffled Herschel's attempts at artistic delineation, it
+has yielded to the modern photographic processes, which
+show the Nubecula Major to be an enormous spiral nebula
+made up of subordinate stars, nebulę, and clusters, as is
+the Milky Way.</p>
+
+<p>Compared with the Andromeda nebula, its greater angular
+extent suggests a smaller distance, although for the
+present all efforts at determining the parallax of either
+seem hopeless. But the spiral form which is common to
+both suggests that the Milky Way itself may be a gigantic
+spiral nebula near whose center lies the sun, a humble
+member of a great cluster of stars which is roughly globular
+in shape, but flattened at the poles of the galaxy
+and completely encircled by its coils. However plausible
+such a view may appear, it is for the present, at least, pure
+hypothesis, although vigorously advocated by Easton, who
+bases his argument upon the appearance of the galaxy
+itself.</p>
+
+<p><a name="S_225" id="S_225"></a>225. <b>Absorption of starlight.</b>&mdash;We have had abundant
+occasion to learn that at least within the confines of the
+solar system meteoric matter, cosmic dust, is profusely scattered,
+and it appears not improbable that the same is true,
+although in smaller degree, in even the remoter parts of
+space. In this case the light which comes from the farther
+stars over a path requiring many centuries to travel, must
+be in some measure absorbed and enfeebled by the obstacles
+which it encounters on the way. Unless celestial space is
+transparent to an improbable degree the remoter stars do
+not show their true brightness; there is a certain limit
+beyond which no star is able to send its light, and beyond<span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span>
+which the universe must be to us a blank. A lighthouse
+throws into the fog its beams only to have them extinguished
+before a single mile is passed, and though the
+celestial lights shine farther, a limit to their reach is none
+the less certain if meteoric dust exists outside the solar
+system. If there is such an absorption of light in space,
+as seems plausible, the universe may well be limitless and
+the number of stellar systems infinite, although the most
+attenuated of dust clouds suffices to conceal from us and
+to shut off from our investigation all save a minor fraction
+of it and them.</p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span></p>
+<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV</h2>
+
+<h3>GROWTH AND DECAY</h3>
+
+
+<p><a name="S_226" id="S_226"></a>226. <b>Nature of the problem.</b>&mdash;To use a common figure of
+speech, the universe is alive. We have found it filled with
+an activity that manifests itself not only in the motions of
+the heavenly bodies along their orbits, but which extends
+to their minutest parts, the molecules and atoms, whose
+vibrations furnish the radiant energy given off by sun and
+stars. Some of these activities, such as the motions of the
+heavenly bodies in their orbits, seem fitted to be of endless
+duration; while others, like the radiation of light and heat,
+are surely temporary, and sooner or later must come to an
+end and be replaced by something different. The study of
+things as they are thus leads inevitably to questions of
+what has been and what is to be. A sound science should
+furnish some account of the universe of yesterday and
+to-morrow as well as of to-day, and we need not shrink
+from such questions, although answers to them must be
+vague and in great measure speculative.</p>
+
+<p>The historian of America finds little difficulty with events
+of the nineteenth century or even the eighteenth, but the
+sources of information about America in the fifteenth century
+are much less definite; the tenth century presents
+almost a blank, and the history of American mankind in
+the first century of the Christian era is wholly unknown.
+So, as we attempt to look into the past or the future of the
+heavens, we must expect to find the mists of obscurity grow
+denser with remoter periods until even the vaguest outlines
+of its development are lost, and we are compelled to say,<span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span>
+beyond this lies the unknown. Our account of growth and
+decay in the universe, therefore, can not aspire to cover the
+whole duration of things, but must be limited in its scope
+to certain chapters whose epochs lie near to the time in
+which we live, and even for these we need to bear constantly
+in mind the logical bases of such an inquiry and
+the limitations which they impose upon us.</p>
+
+<p><a name="S_227" id="S_227"></a>227. <b>Logical bases and limitations.</b>&mdash;The first of these
+bases is: An adequate knowledge of the present universe.
+Our only hope of reading the past and future lies in an
+understanding of the present; not necessarily a complete
+knowledge of it, but one which is sound so far as it goes.
+Our position is like that of a detective who is called upon
+to unravel a mystery or crime, and who must commence
+with the traces that have been left behind in its commission.
+The foot print, the blood stain, the broken glass must
+be examined and compared, and fashioned into a theory of
+how they came to be; and as a wrong understanding of
+these elements is sure to vitiate the theories based upon
+them, so a false science of the universe as it now is, will
+surely give a false account of what it has been; while a
+correct but incomplete knowledge of the present does not
+wholly bar an understanding of the past, but only puts us
+in the position of the detective who correctly understands
+what he sees but fails to take note of other facts which
+might greatly aid him.</p>
+
+<p>The second basis of our inquiry is: The assumed permanence
+of natural laws. The law of gravitation certainly
+held true a century ago as well as a year ago, and for aught
+we know to the contrary it may have been a law of the universe
+for untold millions of years; but that it has prevailed
+for so long a time is a pure assumption, although a necessary
+one for our purpose. So with those other laws of
+mathematics and mechanics and physics and chemistry to
+which we must appeal; if there was ever a time or place
+in which they did not hold true, that time and place lie<span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span>
+beyond the scope of our inquiry, and are in the domain
+inaccessible to scientific research. It is for this reason
+that science knows nothing and can know nothing of a
+creation or an end of the universe, but considers only its
+orderly development within limited periods of time. What
+kind of a past universe would, under the operation of
+known laws, develop into the present one, is the question
+with which we have to deal, and of it we may say with
+Helmholtz: "From the standpoint of science this is no
+idle speculation but an inquiry concerning the limitations
+of its methods and the scope of its known laws."</p>
+
+<p>To ferret out the processes by which the heavenly bodies
+have been brought to their present condition we seek first
+of all for lines of development now in progress which tend
+to change the existing order of things into something different,
+and, having found these, to trace their effects into
+both past and future. Any force, however small, or any
+process, however slow, may produce great results if it works
+always and ceaselessly in the same direction, and it is in
+these processes, whose trend is never reversed, that we find
+a partial clew to both past and future.</p>
+
+<p><a name="S_228" id="S_228"></a>228. <b>The sun's development.</b>&mdash;The first of these to claim
+our attention is the shrinking of the sun's diameter which,
+as we have seen in <a href="#CHAPTER_X">Chapter&nbsp;X</a>, is the means by which the
+solar output of radiant energy is maintained from year to
+year. Its amount, only a few feet per annum, is far too
+small to be measured with any telescope; but it is cumulative,
+working century after century in the same direction,
+and, given time enough, it will produce in the future, and
+must have produced in the past, enormous transformations
+in the sun's bulk and equally significant changes in its
+physical condition.</p>
+
+<p>Thus, as we attempt to trace the sun's history into the
+past, the farther back we go the greater shall we expect to
+find its diameter and the greater the space (volume)
+through which its molecules are spread. By reason of this<span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span>
+expansion its density must have been less then than now,
+and by going far enough back we may even reach a time at
+which the density was comparable with what we find in the
+nebulę of to-day. If our ideas of the sun's present mechanism
+are sound, then, as a necessary consequence of these,
+its past career must have been a process of condensation in
+which its component particles were year by year packed
+closer together by their own attraction for each other. As
+we have seen in <a href="#S_126">§&nbsp;126</a>, this condensation necessarily developed
+heat, a part of which was radiated away as fast as produced,
+while the remainder was stored up, and served to
+raise the temperature of the sun to what we find it now.
+At the present time this temperature is a chief obstacle to
+further shrinkage, and so powerfully opposes the gravitative
+forces as to maintain nearly an equilibrium with them,
+thus causing a very slow rate of further condensation. But
+it is not probable that this was always so. In the early
+stages of the sun's history, when the temperature was low,
+contraction of its bulk must have been more rapid, and
+attempts have been made by the mathematicians to measure
+its rate of progress and to determine how long a time has
+been consumed in the development of the present sun from
+a primitive nebulous condition in which it filled a space of
+greater diameter than Neptune's orbit. Of course, numerical
+precision is not to be expected in results of this kind,
+but, from a consideration of the greatest amount of heat
+that could be furnished by the shrinkage of a mass equal to
+that of the sun, it seems that the period of this development
+is to be measured in tens of millions or possibly hundreds
+of millions of years, but almost certainly does not
+reach a thousand millions.</p>
+
+<p><a name="S_229" id="S_229"></a>229. <b>The sun's future.</b>&mdash;The future duration of the sun
+as a source of radiant energy is surely to be measured in
+far smaller numbers than these. Its career as a dispenser
+of light and heat is much more than half spent, for the
+shrinkage results in an ever-increasing density, which<span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span>
+makes its gaseous substance approximate more and more
+toward the behavior of a liquid or solid, and we recall that
+these forms of matter can not by any further condensation
+restore the heat whose loss through radiation caused them
+to contract. They may continue to shrink, but their temperature
+must fall, and when the sun's substance becomes
+too dense to obey the laws of gaseous matter its surface
+must cool rapidly as a consequence of the radiation into
+surrounding space, and must congeal into a crust which,
+although at first incandescent, will speedily become dark
+and opaque, cutting off the light of the central portions,
+save as it may be rent from time to time by volcanic
+outbursts of the still incandescent mass beneath. But
+such outbursts can be of short duration only, and its final
+condition must be that of a dark body, like the earth or
+moon, no longer available as a source of radiant energy.
+Even before the formation of a solid crust it is quite possible
+that the output of light and heat may be seriously
+diminished by the formation of dense vapors completely
+enshrouding it, as is now the case with Jupiter and Saturn.
+It is believed that these planets were formerly incandescent,
+and at the present time are in a state of development
+through which the earth has passed and toward which the
+sun is moving. According to Newcomb, the future during
+which the sun can continue to furnish light and heat at its
+present rate is not likely to exceed 10,000,000 years.</p>
+
+<p>This idea of the sun as a developing body whose present
+state is only temporary, furnishes a clew to some of the
+vexing problems of solar physics. Thus the sun-spot period,
+the distribution of the spots in latitude, and the peculiar
+law of rotation of the sun in different latitudes, may be,
+and very probably are, results not of anything now operating
+beneath its photosphere, but of something which happened
+to it in the remote past&mdash;e.&nbsp;g., an unsymmetrical
+shrinkage or possibly a collision with some other body. At
+sea the waves continue to toss long after the storm which<span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span>
+produced them has disappeared, and, according to the
+mathematical researches of Wilsing, a profound agitation
+of the sun's mass might well require tens of thousands, or
+even hundreds of thousands of years to subside, and during
+this time its effects would be visible, like the waves, as phenomena
+for which the actual condition of things furnishes
+no apparent cause.</p>
+
+<p><a name="S_230" id="S_230"></a>230. <b>The nebular hypothesis.</b>&mdash;The theory of the sun's
+progressive contraction as a necessary result of its radiation
+of energy is comparatively modern, but more than a century
+ago philosophic students of Nature had been led in
+quite a different way to the belief that in the earlier stages
+of its career the sun must have been an enormously extended
+body whose outer portions reached even beyond the
+orbit of the remotest planet. Laplace, whose speculations
+upon this subject have had a dominant influence during
+the nineteenth century, has left, in a popular treatise upon
+astronomy, an admirable statement of the phenomena of
+planetary motion, which suggest and lead up to the nebular
+theory of the sun's development, and in presenting this
+theory we shall follow substantially his line of thought,
+but with some freedom of translation and many omissions.</p>
+
+<p>He says: "To trace out the primitive source of the planetary
+movements, we have the following five phenomena:
+(1)&nbsp;These movements all take place in the same direction
+and nearly in the same plane. (2)&nbsp;The movements of the
+satellites are in the same direction as those of the planets.
+(3)&nbsp;The rotations of the planets and the sun are in the
+same direction as the orbital motions and nearly in the same
+plane. (4)&nbsp;Planets and satellites alike have nearly circular
+orbits. (5)&nbsp;The orbits of comets are wholly unlike these by
+reason of their great eccentricities and inclinations to the
+ecliptic." That these coincidences should be purely the
+result of chance seemed to Laplace incredible, and, seeking
+a cause for them, he continues: "Whatever its nature may
+be, since it has produced or controlled the motions of the<span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span>
+planets, it must have reached out to all these bodies, and, in
+view of the prodigious distances which separate them, the
+cause can have been nothing else than a fluid of great extent
+which must have enveloped the sun like an atmosphere.
+A consideration of the planetary motions leads us to think
+that ... the sun's atmosphere formerly extended far beyond
+the orbits of all the planets and has shrunk by degrees
+to its present dimensions." This is not very different from
+the idea developed in <a href="#S_228">§&nbsp;228</a> from a consideration of the
+sun's radiant energy; but in Laplace's day the possibility
+of generating the sun's heat by contraction of its bulk was
+unknown, and he was compelled to assume a very high temperature
+for the primitive nebulous sun, while we now know
+that this is unnecessary. Whether the primitive nebula
+was hot or cold the shrinkage would take place in much
+the same way, and would finally result in a star or sun of
+very high temperature, but its development would be slower
+if it were hot in the beginning than if it were cold.</p>
+
+<p>But again Laplace: "How did the sun's atmosphere
+determine the rotations and revolutions of planets and
+satellites? If these bodies had been deeply immersed in
+this atmosphere its resistance to their motion would have
+made them fall into the sun, and we may therefore conjecture
+that the planets were formed, one by one, at the outer
+limits of the solar atmosphere by the condensation of zones
+of vapor which were cast off in the plane of the sun's equator."
+Here he proceeds to show by an appeal to dynamical
+principles that something of this kind must happen, and
+that the matter sloughed off by the nebula in the form of a
+ring, perhaps comparable to the rings of Saturn or the
+asteroid zone, would ultimately condense into a planet,
+which in its turn might shrink and cast off rings to produce
+satellites.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="LAPLACE" id="LAPLACE"></a>
+<a href="images/i401-full.jpg"><img src="images/i401.jpg" width="500" height="620" alt="PIERRE SIMON LAPLACE (1749-1827)." title="PIERRE SIMON LAPLACE (1749-1827)." /></a>
+<span class="caption">PIERRE SIMON LAPLACE (1749-1827).</span>
+</div>
+
+<p>Planets and satellites would then all have similar motions,
+as noted at the beginning of this section, since in
+every case this motion is an inheritance from a common<span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span>
+source, the rotation of the primitive nebula about its own
+axis. "All the bodies which circle around a planet having
+been thus formed from rings which its atmosphere successively
+abandoned as rotation became more and more rapid,
+this rotation should take place in less time than is required
+for the orbital revolution of any of the bodies which have
+been cast off, and this holds true for the sun as compared
+with the planets."</p>
+
+<p><a name="S_231" id="S_231"></a>231. <b>Objections to the nebular hypothesis.</b>&mdash;In Laplace's
+time this slower rate of motion was also supposed to hold
+true for Saturn's rings as compared with the rotation of
+Saturn itself, but, as we have seen in <a href="#CHAPTER_XI">Chapter&nbsp;XI</a>, this ring is
+made up of a great number of independent particles which
+move at different rates of speed, and comparing, through
+Kepler's Third Law, the motion of the inner edge of the
+ring with the known periodic time of the satellites, we may
+find that these particles must rotate about Saturn more
+rapidly than the planet turns upon its axis. Similarly the
+inner satellite of Mars completes its revolution in about
+one third of a Martian day, and we find in cases like this
+grounds for objection to the nebular theory. Compare also
+Laplace's argument with the peculiar rotations of Uranus,
+Neptune, and their satellites (<a href="#CHAPTER_XI">Chapter&nbsp;XI</a>). Do these fortify
+or weaken his case?</p>
+
+<p>Despite these objections and others equally serious that
+have been raised, the nebular theory agrees with the facts
+of Nature at so many points that astronomers upon the
+whole are strongly inclined to accept its major outlines as
+being at least an approximation to the course of development
+actually followed by the solar system; but at some
+points&mdash;e.&nbsp;g., the formation of planets and satellites through
+the casting off of nebulous rings&mdash;the objections are so
+many and strong as to call for revision and possibly serious
+modification of the theory.</p>
+
+<p>One proposed modification, much discussed in recent
+years, consists in substituting for the primitive <i>gaseous</i><span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span>
+nebula imagined by Laplace, a very diffuse cloud of meteoric
+matter which in the course of its development would
+become transformed into the gaseous state by rising temperature.
+From this point of view much of the meteoric
+dust still scattered throughout the solar system may be
+only the fragments left over in fashioning the sun and
+planets. Chamberlin and Moulton, who have recently
+given much attention to this subject, in dissenting from
+some of Laplace's views, consider that the primitive nebulous
+condition must have been one in which the matter of
+the system was "so brought together as to give low mass,
+high momentum, and irregular distribution to the outer
+part, and high mass, low momentum, and sphericity to the
+central part," and they suggest a possible oblique collision
+of a small nebula with the outer parts of a large one.</p>
+
+<p><a name="S_232" id="S_232"></a>232. <b>Bode's law.</b>&mdash;We should not leave the theory of
+Laplace without noting the light it casts upon one point
+otherwise obscure&mdash;the meaning of Bode's law (<a href="#S_134">§&nbsp;134</a>).
+This law, stated in mathematical form, makes a geometrical
+series, and similar geometrical series apply to the
+distances of the satellites of Jupiter and Saturn from
+these planets. Now, Roche has shown by the application
+of physical laws to the shrinkage of a gaseous body that
+its radius at any time may be expressed by means of a
+certain mathematical formula very similar to Bode's law,
+save that it involves the amount of time that has elapsed
+since the beginning of the shrinking process. By comparing
+this formula with the one corresponding to Bode's law
+he reaches the conclusion that the peculiar spacing of the
+planets expressed by that law means that they were formed
+at successive <i>equal</i> intervals of time&mdash;i.&nbsp;e., that Mars is as
+much older than the earth as the earth is older than
+Venus, etc. The failure of Bode's law in the case of
+Neptune would then imply that the interval of time between
+the formation of Neptune and Uranus was shorter
+than that which has prevailed for the other planets. But<span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span>
+too much stress should not be placed upon this conclusion.
+So long as the manner in which the planets came into being
+continues an open question, conclusions about their time
+of birth must remain of doubtful validity.</p>
+
+<p><a name="S_233" id="S_233"></a>233. <b>Tidal friction between earth and moon.</b>&mdash;An important
+addition to theories of development within the solar
+system has been worked out by Prof. G.&nbsp;H. Darwin, who,
+starting with certain very simple assumptions as to the
+present condition of things in earth and moon, derives
+from these, by a strict process of mathematical reasoning,
+far-reaching conclusions of great interest and importance.
+The key to these conclusions lies in recognition of the fact
+that through the influence of the tides (<a href="#S_42">§&nbsp;42</a>) there is now
+in progress and has been in progress for a very long time, a
+gradual transfer of motion (moment of momentum) from
+the earth to the moon. The earth's motion of rotation is
+being slowly destroyed by the friction of the tides, as the
+motion of a bicycle is destroyed by the friction of a brake,
+and, in consequence of this slowing down, the moon is
+pushed farther and farther away from the earth, so that
+it now moves in a larger orbit than it had some millions
+of years ago.</p>
+
+<p><a href="#Fig_24">Fig.&nbsp;24</a> has been used to illustrate the action of the
+moon in raising tides upon the earth, but in accordance
+with the third law of motion (<a href="#S_36">§&nbsp;36</a>) this action must be
+accompanied by an equal and contrary reaction whose
+nature may readily be seen from the same figure. The
+moon moves about its orbit from west to east and the
+earth rotates about its axis in the same direction, as
+shown by the curved arrow in the figure. The tidal wave,
+<i>I</i>, therefore points a little <i>in advance</i> of the moon's position
+in its orbit and by its attraction must tend to pull the
+moon ahead in its orbital motion a little faster than it
+would move if the whole substance of the earth were
+placed inside the sphere represented by the broken circle
+in the figure. It is true that the tidal wave at <i>I''</i> pulls<span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span>
+back and tends to neutralize the effect of the wave at <i>I</i>,
+but on the whole the tidal wave nearer the moon has the
+stronger influence, and the moon on the whole moves a
+very little faster, and by virtue of this added impetus
+draws continually a little farther away from the earth
+than it would if there were no tides.</p>
+
+<p><a name="S_234" id="S_234"></a>234. <b>Consequences of tidal friction upon the earth.</b>&mdash;This
+process of moving the moon away from the earth is a
+cumulative one, going on century after century, and with
+reference to it the moon's orbit must be described not as
+a circle or ellipse, or any other curve which returns into
+itself, but as a spiral, like the balance spring of a watch,
+each of whose coils is a little larger than the preceding
+one, although this excess is, to be sure, very small, because
+the tides themselves are small and the tidal influence
+feeble when compared with the whole attraction
+of the earth for the moon. But, given time enough,
+even this small force may accomplish great results, and
+something like 100,000,000 years of past opportunity
+would have sufficed for the tidal forces to move the moon
+from close proximity with the earth out to its present position.</p>
+
+<p>For millions of years to come, if moon and earth endure
+so long, the distance between them must go on increasing,
+although at an ever slower rate, since the farther away the
+moon goes the smaller will be the tides and the slower the
+working out of their results. On the other hand, when
+the moon was nearer the earth than now, tidal influences
+must have been greater and their effects more rapidly
+produced than at the present time, particularly if, as
+seems probable, at some past epoch the earth was hot and
+plastic like Jupiter and Saturn. Then, instead of tides in
+the water of the sea, such as we now have, the whole substance
+of the earth would respond to the moon's attraction
+in <i>bodily tides</i> of semi-fluid matter not only higher, but with
+greater internal friction of their molecules one upon another,<span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span>
+and correspondingly greater effect in checking the
+earth's rotation.</p>
+
+<p>But, whether the tide be a bodily one or confined to the
+waters of the sea, so long as the moon causes it to flow
+there will be a certain amount of friction which will affect
+the earth much as a brake affects a revolving wheel, slowing
+down its motion, and producing thus a longer day as
+well as a longer month on account of the moon's increased
+distance. Slowing down the earth's rotation is the direct
+action of the moon upon the earth. Pushing the moon
+away is the form in which the earth's equal and contrary
+reaction manifests itself.</p>
+
+<p><a name="S_235" id="S_235"></a>235. <b>Consequences of tidal friction upon the moon.</b>&mdash;When
+the moon was plastic the earth must have raised in it a
+bodily tide manifold greater than the lunar tides upon the
+earth, and, as we have seen in <a href="#CHAPTER_IX">Chapter&nbsp;IX</a>, this tide has
+long since worn out the greater part of the moon's rotation
+and brought our satellite to the condition in which it presents
+always the same face toward the earth.</p>
+
+<p>These two processes, slowing down the rotation and
+pushing away the disturbing body, are inseparable&mdash;one
+requires the other; and it is worth noting in this connection
+that when for any reason the tide ceases to flow, and
+the tidal wave takes up a permanent position, as it has in
+the moon (<a href="#S_99">§&nbsp;99</a>), its work is ended, for when there is no
+motion of the wave there can be no friction to further
+reduce the rate of rotation of the one body, and no reaction
+to that friction to push away the other. But this permanent
+and stationary tidal wave in the moon, or elsewhere,
+means that the satellite presents always the same face
+toward its planet, moving once about its orbit in the time
+required for one revolution upon its axis, and the tide
+raised by the moon upon the earth tends to produce here
+the result long since achieved in our satellite, to make our
+day and month of equal length, and to make the earth
+turn always the same side toward the moon. But the<span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span>
+moon's tidal force is small compared with that of the earth,
+and has a vastly greater momentum to overcome, so that
+its work upon the earth is not yet complete. According
+to Thomson and Tait, the moon must be pushed off another
+hundred thousand miles, and the day lengthened out
+by tidal influence to seven of our present weeks before the
+day and the lunar month are made of equal length, and
+the moon thereby permanently hidden from one hemisphere
+of the earth.</p>
+
+<p><a name="S_236" id="S_236"></a>236. <b>The earth-moon system.</b>&mdash;Retracing into the past
+the course of development of the earth and moon, it is possible
+to reach back by means of the mathematical theory
+of tidal friction to a time at which these bodies were much
+nearer to each other than now, but it has not been found
+possible to trace out the mode of their separation from one
+body into two, as is supposed in the nebular theory. In
+the earliest part of their history accessible to mathematical
+analysis they are distinct bodies at some considerable distance
+from each other, with the earth rotating about an
+axis more nearly perpendicular to the moon's orbit and to
+the ecliptic than is now the case. Starting from such a
+condition, the lunar tides, according to Darwin, have been
+instrumental in tipping the earth's rotation axis into its
+present oblique position, and in determining the eccentricity
+of the moon's orbit and its position with respect to
+the ecliptic as well as the present length of day and month.</p>
+
+<p><a name="S_237" id="S_237"></a>237. <b>Tidal friction upon the planets.</b>&mdash;The satellites of the
+outer planets are equally subject to influences of this kind,
+and there appears to be independent evidence that some of
+them, at least, turn always the same face toward their
+respective planets, indicating that the work of tidal friction
+has here been accomplished. We saw in <a href="#CHAPTER_XI">Chapter&nbsp;XI</a> that
+it is at present an open question whether the inner planets,
+Venus and Mercury, do not always turn the same face
+toward the sun, their day and year being of equal length.
+In addition to the direct observational evidence upon this<span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span>
+point, Schiaparelli has sought to show by an appeal to tidal
+theory that such is probably the case, at least for Mercury,
+since the tidal forces which tend to bring about this result
+in that planet are about as great as the forces which have
+certainly produced it in the case of the moon and Saturn's
+satellite, Japetus. The same line of reasoning would show
+that every satellite in the solar system, save possibly the
+newly discovered ninth satellite of Saturn, must, as a consequence
+of tidal friction, turn always the same face toward
+its planet.</p>
+
+<p><a name="S_238" id="S_238"></a>238. <b>The solar tide.</b>&mdash;The sun also raises tides in the
+earth, and their influence must be similar in character to
+that of the lunar tides, checking the rotation of the earth
+and thrusting earth and sun apart, although quantitatively
+these effects are small compared with those of the moon.
+They must, however, continue so long as the solar tide
+lasts, possibly until the day and year are made of equal
+length&mdash;i.&nbsp;e., they may continue long after the lunar tidal
+influence has ceased to push earth and moon apart. Should
+this be the case, a curious inverse effect will be produced.
+The day being then longer than the month, the moon will
+again raise a tide in the earth which will run around it
+<i>from west to east</i>, opposite to the course of the present tide,
+thus tending to accelerate the earth's rotation, and by its
+reaction to bring the moon back toward the earth again,
+and ultimately to fall upon it.</p>
+
+<p>We may note that an effect of this kind must be in
+progress now between Mars and its inner satellite, Phobos,
+whose time of orbital revolution is only one third of a Martian
+day. It seems probable that this satellite is in the last
+stages of its existence as an independent body, and must
+ultimately fall into Mars.</p>
+
+<p><a name="S_239" id="S_239"></a>239. <b>Roche's limit.</b>&mdash;In looking forward to such a catastrophe,
+however, due regard must be paid to a dynamical
+principle of a different character. The moon can never be
+precipitated upon the earth entire, since before it reaches<span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span>
+us it will have been torn asunder by the excess of the
+earth's attraction for the near side of its satellite over that
+which it exerts upon the far side. As the result of Roche's
+mathematical analysis we are able to assign a limiting distance
+between any planet and its satellite within which the
+satellite, if it turns always the same face toward the planet,
+can not come without being broken into fragments. If we
+represent the radius of the planet by&nbsp;<i>r</i>, and the quotient
+obtained by dividing the density of the planet by the density
+of the satellite by&nbsp;<i>q</i>, then</p>
+
+<p class="center">Roche's limit = 2.44 <i>r</i> &#8731;&nbsp;<i>q</i>.</p>
+
+<p>Thus in the case of earth and moon we find from the densities
+given in <a href="#S_95">§&nbsp;95</a>, <i>q</i>&nbsp;=&nbsp;1.65, and with <i>r</i>&nbsp;=&nbsp;3,963 miles we
+obtain 11,400 miles as the nearest approach which the moon
+could make to the earth without being broken up by the
+difference of the earth's attractions for its opposite sides.</p>
+
+<p>We must observe, however, that Roche's limit takes no
+account of molecular forces, the adhesion of one molecule
+to another, by virtue of which a stick or stone resists fracture,
+but is concerned only with the gravitative forces by
+which the molecules are attracted toward the moon's center
+and toward the earth. Within a stone or rock of moderate
+size these gravitative forces are insignificant, and cohesion
+is the chief factor in preserving its integrity, but in a large
+body like the moon, the case is just reversed, cohesion plays
+a small part and gravitation a large one in holding the
+body together. We may conclude, therefore, that at a
+proper distance these forces are capable of breaking up the
+moon, or any other large body, into fragments of a size
+such that molecular cohesion instead of gravitation is the
+chief agent in preserving them from further disintegration.</p>
+
+<p><a name="S_240" id="S_240"></a>240. <b>Saturn's rings.</b>&mdash;Saturn's rings are of peculiar interest
+in this connection. The outer edge of the ring system
+lies just inside of Roche's limit for this planet, and we
+have already seen that the rings are composed of small fragments<span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span>
+independent of each other. Whatever may have
+been the process by which the nine satellites of Saturn
+came into existence, we have in Roche's limit the explanation
+why the material of the ring was not worked up into
+satellites; the forces exerted by Saturn would tear into
+pieces any considerable satellite thus formed and equally
+would prevent the formation of one from raw material.</p>
+
+<p>Saturn's rings present the only case within the solar
+system where matter is known to be revolving about a
+planet at a distance less than Roche's limit, and it is an
+interesting question whether these rings can remain as a
+permanent part of the planet's system or are only a temporary
+feature. The drawings of Saturn made two centuries
+ago agree among themselves in representing the rings as
+larger than they now appear, and there is some reason to
+suppose that as a consequence of mutual disturbances&mdash;collisions&mdash;their
+momentum is being slowly wasted so that
+ultimately they must be precipitated into the planet. But
+the direct evidence of such a progress that can be drawn
+from present data is too scanty to justify positive conclusions
+in the matter. On the other hand, Nolan suggests
+that in the outer parts of the ring small satellites might be
+formed whose tidal influence upon Saturn would suffice to
+push them away from the ring beyond Roche's limit, and
+that the very small inner satellites of Saturn may have
+been thus formed at the expense of the ring.</p>
+
+<p>The inner satellite of Mars is very close to Roche's limit
+for that planet, and, as we have seen above, must be approaching
+still nearer to the danger line.</p>
+
+<p><a name="S_241" id="S_241"></a>241. <b>The moon's development.</b>&mdash;The fine series of photographs
+of the moon obtained within the last few years at
+Paris, have been used by the astronomers of that observatory
+for a minute study of the lunar formations, much as
+geologists study the surface of the earth to determine something
+about the manner in which it was formed. Their
+conclusions are, in general, that at some past time the moon<span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span>
+was a hot and fluid body which, as it cooled and condensed,
+formed a solid crust whose further shrinkage compressed
+the liquid nucleus and led to a long series of fractures in
+the crust and outbursts of liquid matter, whose latest and
+feeblest stages produced the lunar craters, while traces of
+the earlier ones, connected with a general settling of the
+crust, although nearly obliterated, are still preserved in certain
+large but vague features of the lunar topography, such
+as the distribution of the seas, etc. They find also in certain
+markings of the surface what they consider convincing
+evidence of the existence in past times of a lunar atmosphere.
+But this seems doubtful, since the force of gravity
+at the moon's surface is so small that an atmosphere similar
+to that of the earth, even though placed upon the moon,
+could not permanently endure, but would be lost by the
+gradual escape of its molecules into the surrounding space.</p>
+
+<p>The molecules of a gas are quite independent one of
+another, and are in a state of ceaseless agitation, each one
+darting to and fro, colliding with its neighbors or with
+whatever else opposes its forward motion, and traveling
+with velocities which, on the average, amount to a good
+many hundreds of feet per second, although in the case of
+any individual molecule they may be much less or much
+greater than the average value, an occasional molecule having
+possibly a velocity several times as great as the average.
+In the upper regions of our own atmosphere, if one of these
+swiftly moving particles of oxygen or nitrogen were headed
+away from the earth with a velocity of seven miles per second,
+the whole attractive power of the earth would be
+insufficient to check its motion, and it would therefore,
+unless stopped by some collision, escape from the earth and
+return no more. But, since this velocity of seven miles per
+second is more than thirty times as great as the average
+velocity of the molecules of air, it must be very seldom indeed
+that one is found to move so swiftly, and the loss of
+the earth's atmosphere by leakage of this sort is insignificant.<span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span>
+But upon the moon, or any other body where the
+force of gravity is small, conditions are quite different, and
+in our satellite a velocity of little more than one mile per
+second would suffice to carry a molecule away from the
+outer limits of its atmosphere. This velocity, only five times
+the average, would be frequently attained, particularly in
+former times when the moon's temperature was high, for
+then the average velocity of all the molecules would be considerably
+increased, and the amount of leakage might become,
+and probably would become, a serious matter, steadily
+depleting the moon's atmosphere and leading finally to
+its present state of exhaustion. It is possible that the
+moon may at one time have had an atmosphere, but if so it
+could have been only a temporary possession, and the same
+line of reasoning may be applied to the asteroids and to
+most of the satellites of the solar system, and also, though
+in less degree, to the smaller planets, Mercury and Mars.</p>
+
+<p><a name="S_242" id="S_242"></a>242. <b>Stellar development.</b>&mdash;We have already considered
+in this chapter the line of development followed by one
+star, the sun, and treating this as a typical case, it is commonly
+believed that the life history of a star, in so far as it
+lies within our reach, begins with a condition in which its
+matter is widely diffused, and presumably at a low temperature.
+Contracting in bulk under the influence of its own
+gravitative forces, the star's temperature rises to a maximum,
+and then falls off in later stages until the body ceases
+to shine and passes over to the list of dark stars whose
+existence can only be detected in exceptional cases, such
+as are noted in <a href="#CHAPTER_XIII">Chapter&nbsp;XIII</a>. The most systematic development
+of this idea is due to Lockyer, who looks upon all
+the celestial bodies&mdash;sun, moon and planets, stars, nebulę,
+and comets&mdash;as being only collections of meteoric matter in
+different stages of development, and who has sought by
+means of their spectra to classify these bodies and to determine
+their stage of advancement. While the fundamental
+ideas involved in this "meteoritic hypothesis" are not seriously<span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span>
+controverted, the detailed application of its principles
+is open to more question, and for the most part those
+astronomers who hold that in the present state of knowledge
+stellar spectra furnish a key to a star's age or degree
+of advancement do not venture beyond broad general statements.</p>
+
+<div class="figcenter" style="width: 500px;"><a name="Fig_151" id="Fig_151"></a>
+<a href="images/i414-full.jpg"><img src="images/i414.jpg" width="500" height="349" alt="Fig. 151.&mdash;Types of stellar spectra substantially according to Secchi." title="Fig. 151.&mdash;Types of stellar spectra substantially according to Secchi." /></a>
+<span class="caption"><span class="smcap">Fig. 151.</span>&mdash;Types of stellar spectra substantially according to <span class="smcap">Secchi</span>.</span>
+</div>
+
+<p><a name="S_243" id="S_243"></a>243. <b>Stellar spectra.</b>&mdash;Thus the types of stellar spectra
+shown in <a href="#Fig_151">Fig.&nbsp;151</a> are supposed to illustrate successive
+stages in the development of an average star. Type&nbsp;I corresponds
+to the period in which its temperature is near the
+maximum; Type&nbsp;II belongs to a later stage in which the
+temperature has commenced to fall; and Type&nbsp;III to the
+period immediately preceding extinction.</p>
+
+<p>While human life, or even the duration of the human
+race, is too short to permit a single star to be followed
+through all the stages of its career, an adequate picture of
+that development might be obtained by examining many
+stars, each at a different stage of progress, and, following<span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span>
+this idea, numerous subdivisions of the types of stellar
+spectra shown in <a href="#Fig_151">Fig.&nbsp;151</a> have been proposed in order to
+represent with more detail the process of stellar growth
+and decay; but for the most part these subdivisions and
+their interpretation are accepted by astronomers with much
+reserve.</p>
+
+<p>It is significant that there are comparatively few stars
+with spectra of Type&nbsp;III, for this is what we should expect
+to find if the development of a star through the last stages
+of its visible career occupied but a small fraction of its
+total life. From the same point of view the great number
+of stars with spectra of the first type would point to a long
+duration of this stage of life. The period in which the
+sun belongs, represented by Type&nbsp;II, probably has a duration
+intermediate between the others. Since most of the
+variable stars, save those of the Algol class, have spectra of
+the third type, we conclude that variability, with its associated
+ruddy color and great atmospheric absorption of light,
+is a sign of old age and approaching extinction. The Algol
+or eclipse variables, on the other hand, having spectra of the
+first type, are comparatively young stars, and, as we shall
+see a little later, the shortness of their light periods in some
+measure confirms this conclusion drawn from their spectra.</p>
+
+<p>We have noted in <a href="#S_196">§&nbsp;196</a> that the sun's near neighbors
+are prevailingly stars with spectra of the second type,
+while the Milky Way is mainly composed of first-type stars,
+and from this we may now conclude that in our particular
+part of the entire celestial space the stars are, as a rule,
+somewhat further developed than is the case elsewhere.</p>
+
+<p><a name="S_244" id="S_244"></a>244. <b>Double stars.</b>&mdash;The double stars present special
+problems of development growing out of the effects of tidal
+friction, which must operate in them much as it does between
+earth and moon, tending steadily to increase the distance
+between the components of such a star. So, too,
+in such a system as is shown in <a href="#Fig_132">Fig.&nbsp;132</a>, gravity must
+tend to make each component of the double star shrink to<span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span>
+smaller dimensions, and this shrinkage must result in
+faster rotation and increased tidal friction, which in turn
+must push the components apart, so that in view of the
+small density and close proximity of those particular stars
+we may fairly regard a star like &beta;&nbsp;Lyrę as in the early stages
+of its career and destined with increasing age to lose its
+variability of light, since the eclipses which now take place
+must cease with increasing distance between the components
+unless the orbit is turned exactly edgewise toward the
+earth. Close proximity and the resulting shortness of periodic
+time in a double star seem, therefore, to be evidence
+of its youth, and since this shortness of periodic time is
+characteristic of both Algol variables and spectroscopic
+binaries as a class, we may set them down as being, upon
+the whole, stars in the early stages of their career. On
+the other hand, it is generally true that the larger the orbit,
+and the greater the periodic time in the orbit, the
+farther is the star advanced in its development.</p>
+
+<p>In his theory of tidal friction, Darwin has pointed out
+that whenever the periodic time in the orbit is more than
+twice as long as the time required for rotation about the
+axis, the effect of the tides is to increase the eccentricity of
+the orbit, and, following this indication, See has urged that
+with increasing distance between the components of a
+double star their orbits about the common center of gravity
+must grow more and more eccentric, so that we have in
+the shape of such orbits a new index of stellar development;
+the more eccentric the orbit, the farther advanced
+are the stars. It is important to note in this connection
+that among the double stars whose orbits have been computed
+there seems to run a general rule&mdash;the larger the
+orbit the greater is its eccentricity&mdash;a relation which must
+hold true if tidal friction operates as above supposed, and
+which, being found to hold true, confirms in some degree
+the criteria of stellar age which are furnished by the theory
+of tidal friction.<span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span></p>
+
+<p><a name="S_245" id="S_245"></a>245. <b>Nebulę.</b>&mdash;The nebular hypothesis of Laplace has
+inclined astronomers to look upon nebulę in general as
+material destined to be worked up into stars, but which is
+now in a very crude and undeveloped stage. Their great
+bulk and small density seem also to indicate that gravitation
+has not yet produced in them results at all comparable with
+what we see in sun and stars. But even among nebulę
+there are to be found very different stages of development.
+The irregular nebula, shapeless and void like that of
+Orion; the spiral, ring, and planetary nebulę and the star
+cluster, clearly differ in amount of progress toward their
+final goal. But it is by no means sure that these several
+types are different stages in one line of development; for
+example, the primitive nebula which grows into a spiral
+may never become a ring or planetary nebula, and <i>vice
+versa</i>. So too there is no reason to suppose that a star
+cluster will ever break up into isolated stars such as those
+whose relation to each other is shown in <a href="#Fig_122">Fig.&nbsp;122</a>.</p>
+
+<p><a name="S_246" id="S_246"></a>246. <b>Classification.</b>&mdash;Considering the heavenly bodies
+with respect to their stage of development, and arranging
+them in due order, we should probably find lowest down in
+the scale of progress the irregular nebulę of chaotic appearance
+such as that represented in <a href="#Fig_146">Fig.&nbsp;146</a>. Above
+these in point of development stand the spiral, ring, and
+planetary nebulę, although the exact sequence in which
+they should be arranged remains a matter of doubt. Still
+higher up in the scale are star clusters whose individual
+members, as well as isolated stars, are to be classified by
+means of their spectra, as shown in <a href="#Fig_151">Fig.&nbsp;151</a>, where the
+order of development of each star is probably from Type&nbsp;I,
+through&nbsp;II, into&nbsp;III and beyond, to extinction of its light
+and the cutting off of most of its radiant energy. Jupiter
+and Saturn are to be regarded as stars which have recently
+entered this dark stage. The earth is further developed
+than these, but it is not so far along as are Mars and Mercury;
+while the moon is to be looked upon as the most<span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span>
+advanced heavenly body accessible to our research, having
+reached a state of decrepitude which may almost be called
+death&mdash;a stage typical of that toward which all the others
+are moving.</p>
+
+<p>Meteors and comets are to be regarded as fragments of
+celestial matter, chips, too small to achieve by themselves
+much progress along the normal lines of development, but
+destined sooner or later, by collision with some larger body,
+to share thenceforth in its fortunes.</p>
+
+<p><a name="S_247" id="S_247"></a>247. <b>Stability of the universe.</b>&mdash;It was considered a great
+achievement in the mathematical astronomy of a century
+ago when Laplace showed that the mutual attractions of
+sun and planets might indeed produce endless perturbations
+in the motions and positions of these bodies, but
+could never bring about collisions among them or greatly
+alter their existing orbits. But in the proof of this great
+theorem two influences were neglected, either of which is
+fatal to its validity. One of these&mdash;tidal friction&mdash;as we
+have already seen, tends to wreck the systems of satellites,
+and the same effect must be produced upon the planets by
+any other influence which tends to impede their orbital
+motion. It is the inertia of the planet in its forward movement
+that balances the sun's attraction, and any diminution
+of the planet's velocity will give this attraction the
+upper hand and must ultimately precipitate the planet
+into the sun. The meteoric matter with which the earth
+comes ceaselessly into collision must have just this influence,
+although its effects are very small, and something
+of the same kind may come from the medium
+which transmits radiant energy through the interstellar
+spaces.</p>
+
+<p>It seems incredible that the luminiferous ether, which
+is supposed to pervade all space, should present absolutely
+no resistance to the motion of stars and planets rushing
+through it with velocities which in many cases exceed
+50,000 miles per hour. If there is a resistance to this motion,<span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span>
+however small, we may extend to the whole visible
+universe the words of Thomson and Tait, who say in their
+great Treatise on Natural Philosophy, "We have no data in
+the present state of science for estimating the relative importance
+of tidal friction and of the resistance of the resisting
+medium through which the earth and moon move;
+but, whatever it may be, there can be but one ultimate
+result for such a system as that of the sun and planets,
+if continuing long enough under existing laws and not
+disturbed by meeting with other moving masses in
+space. That result is the falling together of all into
+one mass, which, although rotating for a time, must in
+the end come to rest relatively to the surrounding medium."</p>
+
+<p>Compare with this the words of a great poet who in
+The Tempest puts into the mouth of Prospero the lines:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"The cloud-capp'd towers, the gorgeous palaces,<br /></span>
+<span class="i0">The solemn temples, the great globe itself,<br /></span>
+<span class="i0">Yea, all which it inherit, shall dissolve;<br /></span>
+<span class="i0">And, like this insubstantial pageant faded,<br /></span>
+<span class="i0">Leave not a rack behind."<br /></span>
+</div></div>
+
+<p><a name="S_248" id="S_248"></a>248. <b>The future.</b>&mdash;In spite of statements like these, it
+lies beyond the scope of scientific research to affirm that
+the visible order of things will ever come to naught, and
+the outcome of present tendencies, as sketched above, may
+be profoundly modified in ages to come, by influences of
+which we are now ignorant. We have already noted that
+the farther our speculation extends into either past or
+future, the more insecure are its conclusions, and the remoter
+consequences of present laws are to be accepted with
+a corresponding reserve. But the one great fact which
+stands out clear in this connection is that of <i>change</i>. The
+old concept of a universe created in finished form and destined
+so to abide until its final dissolution, has passed away
+from scientific thought and is replaced by the idea of slow<span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span>
+development. A universe which is ever becoming something
+else and is never finished, as shadowed forth by
+Goethe in the lines:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Thus work I at the roaring loom of Time,<br /></span>
+<span class="i0">And weave for Deity a living robe sublime."<br /></span>
+</div></div>
+
+
+<div class="footnotes">
+<h4>FOOTNOTES</h4>
+<div class="footnote"><p><a name="Footnote_A_1" id="Footnote_A_1"></a><a href="#FNanchor_A_1"><span class="label">[A]</span></a> The circle and straight line are considered to be special cases of
+these curves, which, taken collectively, are called the conic sections.</p></div>
+
+<div class="footnote"><p><a name="Footnote_B_2" id="Footnote_B_2"></a><a href="#FNanchor_B_2"><span class="label">[B]</span></a> Aristophanes, The Clouds, Whewell's translation.</p></div>
+
+<div class="footnote"><p><a name="Footnote_C_3" id="Footnote_C_3"></a><a href="#FNanchor_C_3"><span class="label">[C]</span></a> Schiaparelli, Osservazioni sulle Stelle Doppie.</p></div>
+</div>
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span></p>
+<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX</h2>
+
+
+<h3><span class="smcap">The Greek Alphabet</span></h3>
+
+<p>The Greek letters are so much used by astronomers in
+connection with the names of the stars, and for other purposes,
+that the Greek alphabet is printed below&mdash;not necessarily
+to be learned, but for convenient reference:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><th colspan="2">Greek.</th><th align="left">Name.</th><th align="center">English.</th></tr>
+<tr><td align="center">&Alpha;</td><td align="left">&alpha;</td><td align="left">Alpha</td><td align="center">a</td></tr>
+<tr><td align="center">&Beta;</td><td align="left">&beta;</td><td align="left">Beta</td><td align="center">b</td></tr>
+<tr><td align="center">&Gamma;</td><td align="left">&gamma;</td><td align="left">Gamma</td><td align="center">g</td></tr>
+<tr><td align="center">&Delta;</td><td align="left">&delta;</td><td align="left">Delta</td><td align="center">d</td></tr>
+<tr><td align="center">&Epsilon;</td><td align="left">&epsilon; or &#1013;</td><td align="left">Epsilon</td><td align="center">&#277;</td></tr>
+<tr><td align="center">&Zeta;</td><td align="left">&zeta;</td><td align="left">Zeta</td><td align="center">z</td></tr>
+<tr><td align="center">&Eta;</td><td align="left">&eta;</td><td align="left">Eta</td><td align="center">&#275;</td></tr>
+<tr><td align="center">&Theta;</td><td align="left">&#977; or &theta;</td><td align="left">Theta</td><td align="center">th</td></tr>
+<tr><td align="center">&Iota;</td><td align="left">&iota;</td><td align="left">Iota</td><td align="center">i</td></tr>
+<tr><td align="center">&Kappa;</td><td align="left">&kappa;</td><td align="left">Kappa</td><td align="center">k</td></tr>
+<tr><td align="center">&Lambda;</td><td align="left">&lambda;</td><td align="left">Lambda</td><td align="center">l</td></tr>
+<tr><td align="center">&Mu;</td><td align="left">&mu;</td><td align="left">Mu</td><td align="center">m</td></tr>
+<tr><td align="center">&Nu;</td><td align="left">&nu;</td><td align="left">Nu</td><td align="center">n</td></tr>
+<tr><td align="center">&Xi;</td><td align="left">&xi;</td><td align="left">Xi</td><td align="center">x</td></tr>
+<tr><td align="center">&Omicron;</td><td align="left">&omicron;</td><td align="left">Omicron</td><td align="center">&#335;</td></tr>
+<tr><td align="center">&Pi;</td><td align="left">&pi;</td><td align="left">Pi</td><td align="center">p</td></tr>
+<tr><td align="center">&Rho;</td><td align="left">&rho;</td><td align="left">Rho</td><td align="center">r</td></tr>
+<tr><td align="center">&Sigma;</td><td align="left">&sigma; or &#962;</td><td align="left">Sigma</td><td align="center">s</td></tr>
+<tr><td align="center">&Tau;</td><td align="left">&tau;</td><td align="left">Tau</td><td align="center">t</td></tr>
+<tr><td align="center">&Upsilon;</td><td align="left">&upsilon;</td><td align="left">Upsilon</td><td align="center">u</td></tr>
+<tr><td align="center">&Phi;</td><td align="left">&phi;</td><td align="left">Phi</td><td align="center">ph</td></tr>
+<tr><td align="center">&Chi;</td><td align="left">&chi;</td><td align="left">Chi</td><td align="center">ch</td></tr>
+<tr><td align="center">&Psi;</td><td align="left">&psi;</td><td align="left">Psi</td><td align="center">ps</td></tr>
+<tr><td align="center">&Omega;</td><td align="left">&omega;</td><td align="left">Omega</td><td align="center">&#333;</td></tr>
+</table></div>
+
+
+<hr style="width: 25%;" />
+<p><span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span></p>
+<h3><span class="smcap">Popular Literature of Astronomy</span></h3>
+
+<p>The following brief bibliography, while making no
+pretense at completeness, may serve as a useful guide to
+supplementary reading:</p>
+
+
+<h4><i>General Treatises</i></h4>
+
+<p><span class="smcap">Young.</span> <i>General Astronomy.</i> An admirable general survey of the
+entire field.</p>
+
+<p><span class="smcap">Newcomb.</span> <i>Popular Astronomy.</i> The second edition of a German
+translation of this work by Engelmann and Vogel is especially valuable.</p>
+
+<p><span class="smcap">Ball.</span> <i>Story of the Heavens.</i> Somewhat easier reading than either
+of the preceding.</p>
+
+<p><span class="smcap">Chambers.</span> <i>Descriptive Astronomy.</i> An elaborate but elementary
+work in three volumes.</p>
+
+<p><span class="smcap">Langley.</span> <i>The New Astronomy.</i> Treats mainly of the physical
+condition of the celestial bodies.</p>
+
+<p><span class="smcap">Proctor</span> and <span class="smcap">Ranyard</span>. <i>Old and New Astronomy.</i></p>
+
+
+<h4><i>Special Treatises</i></h4>
+
+<p><span class="smcap">Proctor.</span> <i>The Moon.</i> A general treatment of the subject.</p>
+
+<p><span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>. <i>The Moon.</i> An admirably illustrated
+but expensive work dealing mainly with the topography and physical
+conditions of the moon. There is a cheaper and very good edition in
+German.</p>
+
+<p><span class="smcap">Young.</span> <i>The Sun.</i> International Scientific Series. The most recent
+and authoritative treatise on this subject.</p>
+
+<p><span class="smcap">Proctor.</span> <i>Other Worlds than Ours.</i> An account of planets, comets,
+etc.</p>
+
+<p><span class="smcap">Newton.</span> <i>Meteor.</i> Encyclopędia Britannica.</p>
+
+<p><span class="smcap">Airy.</span> <i>Gravitation.</i> A non-mathematical exposition of the laws
+of planetary motion.</p>
+
+<p><span class="smcap">Stokes.</span> <i>On Light as a Means of Investigation.</i> Burnett Lectures.
+II.&nbsp;The basis of spectrum analysis.</p>
+
+<p><span class="smcap">Schellen.</span> <i>Spectrum Analysis.</i></p>
+
+<p><span class="smcap">Thomson</span> (Sir W., Lord <span class="smcap">Kelvin</span>), <i>Popular Lectures, etc.</i> Lectures
+on the Tides, The Sun's Heat, etc.<span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span></p>
+
+<p><span class="smcap">Ball.</span> <i>Time and Tide.</i> An exposition of the researches of G.&nbsp;H.
+Darwin upon tidal friction.</p>
+
+<p><span class="smcap">Gore.</span> <i>The Visible Universe.</i> Deals with a class of problems inadequately
+treated in most popular astronomies.</p>
+
+<p><span class="smcap">Darwin.</span> <i>The Tides.</i> An admirable elementary exposition.</p>
+
+<p><span class="smcap">Clerke.</span> <i>The System of the Stars.</i> Stellar astronomy.</p>
+
+<p><span class="smcap">Newcomb.</span> Chapters on the Stars, in <i>Popular Science Monthly</i> for
+1900.</p>
+
+<p><span class="smcap">Clerke.</span> <i>History of Astronomy during the Nineteenth Century.</i>
+An admirable work.</p>
+
+<p><span class="smcap">Wolf.</span> <i>Geschichte der Astronomie.</i> München, 1877. An excellent
+German work.</p>
+
+<hr style="width: 25%;" />
+
+<p><span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span></p>
+
+
+<h3><span class="smcap">A List of Stars for Time Observations</span></h3>
+
+<p class="center">See <a href="#S_20">§&nbsp;20</a>.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides">
+<colgroup></colgroup><colgroup></colgroup><colgroup span="2"></colgroup><colgroup></colgroup>
+<thead>
+<tr><th align="center"><span class="smcap">Name.</span></th><th align="center">Magnitude.</th><th align="center" colspan="2">Right Ascension.</th><th align="center">Declination.</th></tr>
+</thead>
+<tbody>
+<tr><td align="left">&nbsp;</td><td align="right">&nbsp;</td><td align="right">h.</td><td align="right">m.&nbsp;</td><td align="right">°&nbsp;&nbsp;&nbsp;</td></tr>
+<tr><td align="left">&beta; Ceti</td><td align="right">2</td><td align="right">0</td><td align="right">38.6</td><td align="right">-18.5</td></tr>
+<tr><td align="left">&eta; Ceti</td><td align="right">3</td><td align="right">1</td><td align="right">3.6</td><td align="right">-10.7</td></tr>
+<tr><td align="left">&alpha; Ceti</td><td align="right">3</td><td align="right">2</td><td align="right">57.1</td><td align="right">+3.7</td></tr>
+<tr><td align="left">&gamma; Eridani</td><td align="right">3</td><td align="right">3</td><td align="right">53.4</td><td align="right">-13.8</td></tr>
+<tr><td align="left"><i>Aldebaran</i></td><td align="right">1</td><td align="right">4</td><td align="right">30.2</td><td align="right">+16.3</td></tr>
+<tr><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td></tr>
+<tr><td align="left"><i>Rigel</i></td><td align="right">0</td><td align="right">5</td><td align="right">9.7</td><td align="right">-8.3</td></tr>
+<tr><td align="left">&kappa; Orionis</td><td align="right">2</td><td align="right">5</td><td align="right">43.0</td><td align="right">-9.7</td></tr>
+<tr><td align="left">&beta; Canis Majoris</td><td align="right">2</td><td align="right">6</td><td align="right">18.3</td><td align="right">-17.9</td></tr>
+<tr><td align="left"><i>Sirius</i></td><td align="right">-1</td><td align="right">6</td><td align="right">40.7</td><td align="right">-16.6</td></tr>
+<tr><td align="left"><i>Procyon</i></td><td align="right">0</td><td align="right">7</td><td align="right">34.1</td><td align="right">+5.5</td></tr>
+<tr><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td></tr>
+<tr><td align="left">&alpha; Hydrę</td><td align="right">2</td><td align="right">9</td><td align="right">22.7</td><td align="right">-8.2</td></tr>
+<tr><td align="left"><i>Regulus</i></td><td align="right">1</td><td align="right">10</td><td align="right">3.0</td><td align="right">+12.5</td></tr>
+<tr><td align="left">&nu; Hydrę</td><td align="right">3</td><td align="right">10</td><td align="right">44.7</td><td align="right">-15.7</td></tr>
+<tr><td align="left">&#1013; Corvi</td><td align="right">3</td><td align="right">12</td><td align="right">5.0</td><td align="right">-22.1</td></tr>
+<tr><td align="left">&gamma; Corvi</td><td align="right">3</td><td align="right">12</td><td align="right">10.7</td><td align="right">-17.0</td></tr>
+<tr><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td></tr>
+<tr><td align="left"><i>Spica</i></td><td align="right">1</td><td align="right">13</td><td align="right">19.9</td><td align="right">-10.6</td></tr>
+<tr><td align="left">&zeta; Virginis</td><td align="right">3</td><td align="right">13</td><td align="right">29.6</td><td align="right">-0.1</td></tr>
+<tr><td align="left">&alpha; Librę</td><td align="right">3</td><td align="right">14</td><td align="right">45.3</td><td align="right">-15.6</td></tr>
+<tr><td align="left">&beta; Librę</td><td align="right">3</td><td align="right">15</td><td align="right">11.6</td><td align="right">-9.0</td></tr>
+<tr><td align="left"><i>Antares</i></td><td align="right">1</td><td align="right">16</td><td align="right">23.3</td><td align="right">-26.2</td></tr>
+<tr><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td></tr>
+<tr><td align="left">&alpha; Ophiuchi</td><td align="right">2</td><td align="right">17</td><td align="right">30.3</td><td align="right">+12.6</td></tr>
+<tr><td align="left">&#1013; Sagittarii</td><td align="right">2</td><td align="right">18</td><td align="right">17.5</td><td align="right">-34.4</td></tr>
+<tr><td align="left">&delta; Aquilę</td><td align="right">3</td><td align="right">19</td><td align="right">20.5</td><td align="right">+2.9</td></tr>
+<tr><td align="left"><i>Altair</i></td><td align="right">1</td><td align="right">19</td><td align="right">45.9</td><td align="right">+8.6</td></tr>
+<tr><td align="left">&beta; Aquarii</td><td align="right">3</td><td align="right">21</td><td align="right">26.3</td><td align="right">-6.0</td></tr>
+<tr><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td></tr>
+<tr><td align="left">&alpha; Aquarii</td><td align="right">3</td><td align="right">22</td><td align="right">0.6</td><td align="right">-0.8</td></tr>
+<tr><td align="left"><i>Fomalhaut</i></td><td align="right">1</td><td align="right">22</td><td align="right">52.1</td><td align="right">-30.2</td></tr>
+</tbody>
+</table>
+</div>
+
+
+
+<hr style="width: 65%;" />
+<p><span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span></p>
+<h2><a name="INDEX" id="INDEX"></a>INDEX</h2>
+
+
+<p class="center">The references are to section numbers.</p>
+
+
+<ul id="index">
+<li>Absorption of starlight, <a href="#S_225">225</a>.</li>
+
+<li>Absorption spectra, <a href="#S_87">87</a>.</li>
+
+<li>Accelerating force, <a href="#S_35">35</a>.</li>
+
+<li>Adjustment of observations, <a href="#S_2">2</a>.</li>
+
+<li>Albedo of moon, <a href="#S_97">97</a>.
+<ul>
+<li>of Venus, <a href="#S_148">148</a>.</li>
+</ul>
+</li>
+
+<li>Algol, <a href="#S_205">205</a>.</li>
+
+<li>Altitudes, <a href="#S_4">4</a>, <a href="#S_21">21</a>.</li>
+
+<li>Andromeda nebula, <a href="#S_214">214</a>.</li>
+
+<li>Angles, measurement of, <a href="#S_2">2</a>.</li>
+
+<li>Angular diameter, <a href="#S_7">7</a>.</li>
+
+<li>Annular eclipse, <a href="#S_64">64</a>.</li>
+
+<li>Asteroids, <a href="#S_156">156</a>.</li>
+
+<li>Atmosphere of the earth, <a href="#S_49">49</a>.
+<ul>
+<li>of the moon, <a href="#S_103">103</a>.</li>
+<li>of Jupiter, <a href="#S_139">139</a>.</li>
+<li>of Mars, <a href="#S_153">153</a>.</li>
+</ul>
+</li>
+
+<li>Aurora, <a href="#S_51">51</a>.</li>
+
+<li>Azimuth, <a href="#S_5">5</a>, <a href="#S_21">21</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Biela's comet, <a href="#S_181">181</a>.</li>
+
+<li>Bode's law, <a href="#S_134">134</a>, <a href="#S_232">232</a>.</li>
+
+<li>Bredichin's theory of comet tails, <a href="#S_180">180</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Calendar, O.&nbsp;S. and N.&nbsp;S., <a href="#S_61">61</a>.</li>
+
+<li>Capture of comets and meteors, <a href="#S_176">176</a>.</li>
+
+<li>Canals of Mars, <a href="#S_154">154</a>.</li>
+
+<li>Celestial mechanics, <a href="#S_32">32</a>.</li>
+
+<li>Changes upon the moon, <a href="#S_108">108</a>.</li>
+
+<li>Chemical constitution of sun, <a href="#S_116">116</a>.
+<ul><li>of stars, <a href="#S_210">210</a>.</li></ul></li>
+
+<li>Chromosphere, the sun's, <a href="#S_124">124</a>.</li>
+
+<li>Chronology, <a href="#S_59">59</a>.</li>
+
+<li>Classification of stars, <a href="#S_212">212</a>.</li>
+
+<li>Clocks and watches, <a href="#S_74">74</a>.
+<ul><li>sidereal clock, <a href="#S_12">12</a>.</li></ul></li>
+
+<li>Collisions with comets, <a href="#S_183">183</a>.</li>
+
+<li>Colors of stars, <a href="#S_209">209</a>.</li>
+
+<li>Comets, general characteristics, <a href="#S_158">158</a>-<a href="#S_164">164</a>.
+<ul><li>development of, <a href="#S_179">179</a>, <a href="#S_181">181</a>.</li>
+<li>groups, <a href="#S_177">177</a>.</li>
+<li>orbits, <a href="#S_161">161</a>.</li>
+<li>periodic, <a href="#S_176">176</a>.</li>
+<li>spectra, <a href="#S_182">182</a>.</li>
+<li>tails, <a href="#S_180">180</a>.</li></ul></li>
+
+<li>Comets and meteors, relation of, <a href="#S_175">175</a>.</li>
+
+<li>Conic sections, <a href="#S_38">38</a>.</li>
+
+<li>Constellations, <a href="#S_184">184</a>.</li>
+
+<li>Corona, the sun's, <a href="#S_123">123</a>.</li>
+
+<li>Craters, lunar, <a href="#S_105">105</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Dark stars, <a href="#S_201">201</a>.</li>
+
+<li>Day, <a href="#S_52">52</a>, <a href="#S_62">62</a>.</li>
+
+<li>Declination, <a href="#S_21">21</a>.</li>
+
+<li>Development of comet, <a href="#S_179">179</a>.
+<ul><li>of moon, <a href="#S_241">241</a>.</li>
+<li>of nebulę, <a href="#S_245">245</a>.</li>
+<li>of stars, <a href="#S_242">242</a>, <a href="#S_244">244</a>.<span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span></li>
+<li>of sun, <a href="#S_228">228</a>.</li>
+<li>of universe, <a href="#S_226">226</a>.</li></ul></li>
+
+<li>Distribution of stars and nebulę, <a href="#S_220">220</a>.</li>
+
+<li>Diurnal motion, <a href="#S_10">10</a>, <a href="#S_15">15</a>.</li>
+
+<li>Doppler principle, <a href="#S_89">89</a>.</li>
+
+<li>Double nebulę, <a href="#S_215">215</a>.</li>
+
+<li>Double stars, <a href="#S_198">198</a>.
+<ul><li>development of, <a href="#S_244">244</a>.</li></ul></li>
+
+<li>Driving clock, <a href="#S_80">80</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Earth, atmosphere, <a href="#S_48">48</a>.
+<ul><li>mass, <a href="#S_45">45</a>.</li>
+<li>size and shape, <a href="#S_44">44</a>.</li>
+<li>warming of the earth, <a href="#S_47">47</a>.</li></ul></li>
+
+<li>Eclipses, nature of, <a href="#S_63">63</a>.
+<ul><li>annular eclipse, <a href="#S_64">64</a>.</li>
+<li>eclipse limits, <a href="#S_68">68</a>.</li>
+<li>eclipse maps, <a href="#S_70">70</a>, <a href="#S_71">71</a>.</li>
+<li>number of, in a year, <a href="#S_69">69</a>.</li>
+<li>partial eclipse, <a href="#S_64">64</a>.</li>
+<li>prediction of, <a href="#S_70">70</a>, <a href="#S_71">71</a>.</li>
+<li>recurrence of, <a href="#S_72">72</a>.</li>
+<li>shadow cone, <a href="#S_64">64</a>, <a href="#S_66">66</a>.</li>
+<li>total eclipse, <a href="#S_64">64</a>.</li>
+<li>uses of, <a href="#S_73">73</a>.</li></ul></li>
+
+<li>Eclipses of Jupiter's satellites, <a href="#S_141">141</a>.</li>
+
+<li>Eclipse theory of variable stars, <a href="#S_205">205</a>.</li>
+
+<li>Ecliptic, <a href="#S_26">26</a>.
+<ul><li>obliquity of, <a href="#S_25">25</a>.</li></ul></li>
+
+<li>Ellipse, <a href="#S_33">33</a>.</li>
+
+<li>Epochs for planetary motion, <a href="#S_30">30</a>.</li>
+
+<li>Energy, radiant, <a href="#S_75">75</a>.
+<ul><li>condensation of, <a href="#S_76">76</a>.</li></ul></li>
+
+<li>Epicycle, <a href="#S_32">32</a>.</li>
+
+<li>Equation of time, <a href="#S_53">53</a>.</li>
+
+<li>Equator, <a href="#S_16">16</a>, <a href="#S_21">21</a>.</li>
+
+<li>Equatorial mounting, <a href="#S_80">80</a>.</li>
+
+<li>Equinoxes, <a href="#S_25">25</a>.</li>
+
+<li>Ether, <a href="#S_75">75</a>.</li>
+
+<li>Evening star, <a href="#S_31">31</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Faculę, <a href="#S_122">122</a>.</li>
+
+<li>Falling bodies, law of, <a href="#S_35">35</a>.</li>
+
+<li>Finding the stars, <a href="#S_14">14</a>.</li>
+
+<li>Fraunhofer lines, <a href="#S_87">87</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Galaxy, <a href="#S_219">219</a>.</li>
+
+<li>Geography of the sky, <a href="#S_16">16</a>.</li>
+
+<li>Graphical representation, <a href="#S_6">6</a>.</li>
+
+<li>Grating, diffraction, <a href="#S_84">84</a>.</li>
+
+<li>Gravitation, law of, <a href="#S_37">37</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Harvest moon, <a href="#S_93">93</a>.</li>
+
+<li>Heat of the sun, <a href="#S_118">118</a>, <a href="#S_126">126</a>.</li>
+
+<li>Helmholtz, contraction theory of the sun, <a href="#S_126">126</a>, <a href="#S_228">228</a>.</li>
+
+<li>Horizon, <a href="#S_4">4</a>, <a href="#S_21">21</a>.</li>
+
+<li>Hour angle, <a href="#S_21">21</a>.</li>
+
+<li>Hour circle, <a href="#S_21">21</a>.</li>
+
+<li>Hyperbola, <a href="#S_38">38</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Japetus, satellite of Saturn, <a href="#S_145">145</a>.</li>
+
+<li>Jupiter, <a href="#S_136">136</a>.
+<ul><li>atmosphere, <a href="#S_139">139</a>.</li>
+<li>belts, <a href="#S_137">137</a>.</li>
+<li>invisible from fixed stars, <a href="#S_197">197</a>.</li>
+<li>orbit of, <a href="#S_29">29</a>.</li>
+<li>physical condition, <a href="#S_139">139</a>.</li>
+<li>rotation and flattening, <a href="#S_138">138</a>.</li>
+<li>satellites, <a href="#S_140">140</a>.</li>
+<li>surface markings, <a href="#S_137">137</a>.</li></ul></li>
+
+<li>&nbsp;</li>
+
+<li>Kepler's laws, <a href="#S_233">33</a>, <a href="#S_111">111</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Latitude, determination of, <a href="#S_18">18</a>.</li>
+
+<li>Leap year, <a href="#S_61">61</a>.</li>
+
+<li>Lenses, <a href="#S_77">77</a>.</li>
+
+<li>Leonid meteor shower, <a href="#S_172">172</a>.
+<ul><li>perturbations of, <a href="#S_174">174</a>.</li></ul></li>
+
+<li>Librations of moon, <a href="#S_98">98</a>.</li>
+
+<li>Life upon the planets, <a href="#S_157">157</a>.</li>
+
+<li>Light curves, <a href="#S_205">205</a>.</li>
+
+<li>Light, nature of, <a href="#S_75">75</a>.<span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span></li>
+
+<li>Light year, <a href="#S_190">190</a>.</li>
+
+<li>Limits of eclipses, <a href="#S_68">68</a>.</li>
+
+<li>Longitude, <a href="#S_56">56</a>.
+<ul><li>determination of, <a href="#S_58">58</a>.</li></ul></li>
+
+<li>Lunation, <a href="#S_60">60</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Magnifying power of telescope, <a href="#S_79">79</a>.</li>
+
+<li>Magnitude, stellar, <a href="#S_9">9</a>, <a href="#S_186">186</a>.</li>
+
+<li>Mars, atmosphere, temperature, <a href="#S_150">150</a>.
+<ul><li>canals, <a href="#S_154">154</a>.</li>
+<li>orbit, <a href="#S_30">30</a>.</li>
+<li>polar caps, <a href="#S_152">152</a>.</li>
+<li>rotation, <a href="#S_151">151</a>.</li>
+<li>satellites, <a href="#S_155">155</a>.</li>
+<li>surface markings, <a href="#S_150">150</a>.</li></ul></li>
+
+<li>Mass, determination of, <a href="#S_37">37</a>.
+<ul><li>of comets, <a href="#S_164">164</a>.</li>
+<li>of double stars, <a href="#S_200">200</a>.</li>
+<li>of moon, <a href="#S_94">94</a>.</li>
+<li>of planets, <a href="#S_40">40</a>, <a href="#S_133">133</a>.</li></ul></li>
+
+<li>Measurements, accurate, <a href="#S_1">1</a>.</li>
+
+<li>Mercury, <a href="#S_149">149</a>.
+<ul><li>motion of its perihelion, <a href="#S_43">43</a>.</li>
+<li>orbit of, <a href="#S_30">30</a>.</li></ul></li>
+
+<li>Meridian, <a href="#S_19">19</a>, <a href="#S_21">21</a>.</li>
+
+<li><a name="Meteor" id="Meteor"></a>Meteors, nature of, <a href="#S_165">165</a>, <a href="#S_169">169</a>.
+<ul><li>number of, <a href="#S_167">167</a>.</li>
+<li>velocity, <a href="#S_170">170</a>.</li></ul></li>
+
+<li>Meteors and comets, relation of, <a href="#S_175">175</a>.</li>
+
+<li>Meteor showers, radiant, <a href="#S_171">171</a>.
+<ul><li>Leonids, capture of, <a href="#S_172">172</a>, <a href="#S_173">173</a>.</li>
+<li>perturbations, <a href="#S_174">174</a>.</li></ul></li>
+
+<li>Milky Way, <a href="#S_219">219</a>.</li>
+
+<li>Mira, &omicron;&nbsp;Ceti, <a href="#S_204">204</a>.</li>
+
+<li>Mirrors, <a href="#S_77">77</a>.</li>
+
+<li>Month, <a href="#S_60">60</a>.</li>
+
+<li>Moon, <a href="#S_91">91</a>.
+<ul><li>albedo, <a href="#S_97">97</a>.</li>
+<li>atmosphere, <a href="#S_103">103</a>.</li>
+<li>changes in, <a href="#S_108">108</a>.</li>
+<li>density, surface gravity, <a href="#S_95">95</a>.</li>
+<li>development of, <a href="#S_241">241</a>.</li>
+<li>harvest moon, <a href="#S_93">93</a>.</li>
+<li>influence upon the earth, <a href="#S_109">109</a>, <a href="#S_233">233</a>.</li>
+<li>librations, <a href="#S_198">98</a>.</li>
+<li>map of, <a href="#S_101">101</a>.</li>
+<li>mass and size, <a href="#S_94">94</a>.</li>
+<li>motion, <a href="#S_24">24</a>, <a href="#S_92">92</a>.</li>
+<li>mountains and craters, <a href="#S_104">104</a>.</li>
+<li>phases, <a href="#S_91">91</a>, <a href="#S_92">92</a>.</li>
+<li>physical condition, <a href="#S_100">100</a>, <a href="#S_107">107</a>.</li></ul></li>
+
+<li>Month, <a href="#S_60">60</a>.</li>
+
+<li>Morning star, <a href="#S_31">31</a>.</li>
+
+<li>Motion in line of sight, <a href="#S_89">89</a>, <a href="#S_193">193</a>.</li>
+
+<li>Multiple stars, <a href="#S_202">202</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Names of stars, <a href="#S_8">8</a>.</li>
+
+<li>Nebulę, <a href="#S_214">214</a>.
+<ul><li>density, <a href="#S_217">217</a>.</li>
+<li>development of, <a href="#S_245">245</a>.</li>
+<li>motion, <a href="#S_218">218</a>.</li>
+<li>spectra, <a href="#S_216">216</a>.</li>
+<li>types and classes of, <a href="#S_215">215</a>.</li></ul></li>
+
+<li>Nebular hypothesis, <a href="#S_230">230</a>.
+<ul><li>objections to, <a href="#S_231">231</a>.</li></ul></li>
+
+<li>Neptune, <a href="#S_146">146</a>.
+<ul><li>discovery of, <a href="#S_41">41</a>.</li></ul></li>
+
+<li>Newton's laws of motion, <a href="#S_34">34</a>.
+<ul><li>law of gravitation, <a href="#S_37">37</a>, <a href="#S_43">43</a>.</li></ul></li>
+
+<li>Nodes, <a href="#S_39">39</a>.
+<ul><li>relation to eclipses, <a href="#S_67">67</a>, <a href="#S_71">71</a>.</li></ul></li>
+
+<li>Nucleus, of comet, <a href="#S_160">160</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Objective, of telescope, <a href="#S_78">78</a>.</li>
+
+<li>Obliquity of ecliptic, <a href="#S_25">25</a>.</li>
+
+<li>Observations, of stars, <a href="#S_10">10</a>.</li>
+
+<li>Occultation of stars, <a href="#S_103">103</a>.</li>
+
+<li>Orbits, of comets, <a href="#S_161">161</a>.
+<ul><li>of double stars, <a href="#S_199">199</a>.</li>
+<li>of moon, <a href="#S_92">92</a>.<span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span></li>
+<li>of planets, <a href="#S_28">28</a>.</li></ul></li>
+
+<li>Orion nebula, <a href="#S_215">215</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Parabola, <a href="#S_35">35</a>, <a href="#S_38">38</a>, <a href="#S_161">161</a>.</li>
+
+<li>Parabolic velocity, <a href="#S_38">38</a>.</li>
+
+<li>Parallax, <a href="#S_114">114</a>, <a href="#S_188">188</a>.</li>
+
+<li>Penumbra, <a href="#S_64">64</a>, <a href="#S_121">121</a>.</li>
+
+<li>Perihelion, <a href="#S_38">38</a>.</li>
+
+<li>Periodic comets, <a href="#S_176">176</a>.</li>
+
+<li>Personal equation, <a href="#S_82">82</a>.</li>
+
+<li>Perturbations, <a href="#S_39">39</a>.
+<ul><li>of meteors, <a href="#S_174">174</a>.</li></ul></li>
+
+<li>Phases, of the moon, <a href="#S_91">91</a>, <a href="#S_92">92</a>.</li>
+
+<li>Photography, <a href="#S_81">81</a>.
+<ul><li>of stars, <a href="#S_13">13</a>.</li></ul></li>
+
+<li>Photosphere, of sun, <a href="#S_121">121</a>.</li>
+
+<li>Planets, <a href="#S_26">26</a>, <a href="#S_133">133</a>.
+<ul><li>distances from the sun, <a href="#S_134">134</a>.</li>
+<li>how to find, <a href="#S_29">29</a>.</li>
+<li>mass, density, size, <a href="#S_133">133</a>.</li>
+<li>motion of, <a href="#S_27">27</a>, <a href="#S_38">38</a>.</li>
+<li>periodic times of, <a href="#S_30">30</a>.</li></ul></li>
+
+<li>Planetary nebulę, <a href="#S_215">215</a>.</li>
+
+<li>Pleiades, <a href="#S_16">16</a>, <a href="#S_215">215</a>.</li>
+
+<li>Plumb-line apparatus, <a href="#S_11">11</a>, <a href="#S_18">18</a>.</li>
+
+<li>Poles, <a href="#S_21">21</a>.</li>
+
+<li>Precession, <a href="#S_46">46</a>.</li>
+
+<li>Prisms, <a href="#S_84">84</a>.</li>
+
+<li>Problem of three bodies, <a href="#S_39">39</a>.</li>
+
+<li>Prominences, solar, <a href="#S_125">125</a>.</li>
+
+<li>Proper motions, <a href="#S_191">191</a>.</li>
+
+<li>Protractor, <a href="#S_2">2</a>.</li>
+
+<li>Ptolemaic system, <a href="#S_32">32</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Radiant energy, <a href="#S_75">75</a>.</li>
+
+<li>Radiant, of meteor shower, <a href="#S_171">171</a>.</li>
+
+<li>Radius <span title="typo for vector">victor</span>, <a href="#S_33">33</a>.</li>
+
+<li>Reference lines and circles, <a href="#S_17">17</a>.</li>
+
+<li>Refraction, <a href="#S_50">50</a>.</li>
+
+<li>Right ascension, <a href="#S_16">16</a>, <a href="#S_20">20</a>, <a href="#S_21">21</a>.</li>
+
+<li>Roche's limit, <a href="#S_239">239</a>.</li>
+
+<li>Rotation, of earth, <a href="#S_55">55</a>.
+<ul><li>of Mars, <a href="#S_151">151</a>.</li>
+<li>of moon, <a href="#S_99">99</a>.</li>
+<li>of Jupiter, <a href="#S_138">138</a>.</li>
+<li>of Saturn, <a href="#S_144">144</a>.</li>
+<li>of sun, <a href="#S_120">120</a>, <a href="#S_132">132</a>.</li></ul></li>
+
+<li>&nbsp;</li>
+
+<li>Saros, <a href="#S_72">72</a>.</li>
+
+<li>Satellites, of Jupiter, <a href="#S_136">136</a>, <a href="#S_140">140</a>.
+<ul><li>of Mars, <a href="#S_155">155</a>.</li>
+<li>of Saturn, <a href="#S_145">145</a>.</li></ul></li>
+
+<li>Saturn, <a href="#S_142">142</a>.
+<ul><li>ball of, <a href="#S_144">144</a>.</li>
+<li>orbit, <a href="#S_29">29</a>.</li>
+<li>rings, <a href="#S_142">142</a>.</li>
+<li>rotation, <a href="#S_144">144</a>.</li>
+<li>satellites, <a href="#S_145">145</a>.</li></ul></li>
+
+<li>Seasons, on the earth, <a href="#S_47">47</a>.
+<ul><li>on Mars, <a href="#S_151">151</a>.</li></ul></li>
+
+<li>Shadow cone, <a href="#S_64">64</a>, <a href="#S_66">66</a>.</li>
+
+<li>Sidereal time, <a href="#S_20">20</a>, <a href="#S_54">54</a>.</li>
+
+<li>Shooting stars, <a href="#S_158">158</a>. (See <a href="#Meteor">Meteor</a>.)</li>
+
+<li>Spectroscope, <a href="#S_84">84</a>.</li>
+
+<li>Spectroscopic binaries, <a href="#S_203">203</a>.</li>
+
+<li>Spectrum, <a href="#S_84">84</a>, <a href="#S_87">87</a>.
+<ul><li>of comets, <a href="#S_182">182</a>.</li>
+<li>of nebulę, <a href="#S_216">216</a>.</li>
+<li>of stars, <a href="#S_211">211</a>.</li>
+<li>types of, <a href="#S_88">88</a>.</li></ul></li>
+
+<li>Spectrum analysis, <a href="#S_85">85</a>.</li>
+
+<li>Spiral nebulę, <a href="#S_215">215</a>.</li>
+
+<li>Standard time, <a href="#S_57">57</a>.</li>
+
+<li>Stars, <a href="#S_8">8</a>, <a href="#S_184">184</a>.
+<ul><li>classes of, <a href="#S_212">212</a>.</li>
+<li>clusters, <a href="#S_213">213</a>.</li>
+<li>colors, <a href="#S_209">209</a>.</li>
+<li>dark stars, <a href="#S_201">201</a>.</li>
+<li>development of, <a href="#S_242">242</a>.</li>
+<li>distances from the sun, <a href="#S_188">188</a>, <a href="#S_196">196</a>.</li>
+<li>distribution of, <a href="#S_220">220</a>.</li>
+<li>double stars, <a href="#S_198">198</a>, <a href="#S_203">203</a>.</li>
+<li>drift, <a href="#S_194">194</a>.</li>
+<li>magnitudes, <a href="#S_9">9</a>, <a href="#S_196">196</a>.<span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span></li>
+<li>number of, <a href="#S_185">185</a>.</li>
+<li>spectra, <a href="#S_211">211</a>.</li>
+<li>temporary, <a href="#S_208">208</a>.</li>
+<li>variable, <a href="#S_204">204</a>.</li></ul></li>
+
+<li>Starlight, absorption of, <a href="#S_225">225</a>.</li>
+
+<li>Star maps, construction of, <a href="#S_23">23</a>.</li>
+
+<li>Stellar system, extent of, <a href="#S_223">223</a>.</li>
+
+<li>Sun's apparent motion, <a href="#S_25">25</a>.
+<ul><li>real motion, <a href="#S_195">195</a>.</li></ul></li>
+
+<li>Sun, <a href="#S_110">110</a>.
+<ul><li>chemical composition, <a href="#S_116">116</a>.</li>
+<li>chromosphere, <a href="#S_124">124</a>.</li>
+<li>corona, <a href="#S_123">123</a>.</li>
+<li>distance from the earth, <a href="#S_111">111</a>.</li>
+<li>faculę, <a href="#S_119">119</a>, <a href="#S_122">122</a>.</li>
+<li>gaseous constitution, <a href="#S_127">127</a>.</li>
+<li>heat of, <a href="#S_117">117</a>.</li>
+<li>mechanism of, <a href="#S_126">126</a>.</li>
+<li>physical properties, <a href="#S_115">115</a>-<a href="#S_120">120</a>.</li>
+<li>prominences, <a href="#S_125">125</a>.</li>
+<li>rotation, <a href="#S_120">120</a>, <a href="#S_132">132</a>.</li>
+<li>surface of, <a href="#S_119">119</a>.</li>
+<li>temperature, <a href="#S_118">118</a>.</li></ul></li>
+
+<li>Sun spots, <a href="#S_119">119</a>, <a href="#S_121">121</a>.
+<ul><li>period, <a href="#S_129">129</a>, <a href="#S_131">131</a>.</li>
+<li>zones, <a href="#S_130">130</a>.</li></ul></li>
+
+<li>&nbsp;</li>
+
+<li>Telescopes, <a href="#S_78">78</a>.
+<ul><li>equatorial mounting for, <a href="#S_80">80</a>.</li>
+<li>magnifying power of, <a href="#S_79">79</a>.</li></ul></li>
+
+<li>Temperature of Jupiter, <a href="#S_139">139</a>.
+<ul><li>of Mars, <a href="#S_152">152</a>.</li>
+<li>of Mercury, <a href="#S_149">149</a>.</li>
+<li>of moon, <a href="#S_107">107</a>.</li>
+<li>of sun, <a href="#S_118">118</a>.</li></ul></li>
+
+<li>Temporary stars, <a href="#S_208">208</a>.</li>
+
+<li>Terminator, <a href="#S_91">91</a>.</li>
+
+<li>Tenth meter, <a href="#S_75">75</a>.</li>
+
+<li>Tidal friction, <a href="#S_233">233</a>-<a href="#S_238">238</a>.</li>
+
+<li>Tides, <a href="#S_42">42</a>.</li>
+
+<li>Time, sidereal, <a href="#S_120">20</a>, <a href="#S_54">54</a>.
+<ul><li>solar, <a href="#S_52">52</a>.</li>
+<li>determination of, <a href="#S_20">20</a>.</li>
+<li>equation of, <a href="#S_53">53</a>.</li>
+<li>standard, <a href="#S_57">57</a>.</li></ul></li>
+
+<li>Triangulation, <a href="#S_3">3</a>.</li>
+
+<li>Trifid nebula, <a href="#S_215">215</a>.</li>
+
+<li>Twilight, <a href="#S_51">51</a>.</li>
+
+<li>Twinkling, of stars, <a href="#S_48">48</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Universe, development of, <a href="#S_226">226</a>.
+<ul><li>stability of, <a href="#S_247">247</a>.</li></ul></li>
+
+<li>Uranus, <a href="#S_146">146</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Variable stars, <a href="#S_204">204</a>.</li>
+
+<li>Velocity, its relation to orbital motion, <a href="#S_38">38</a>.</li>
+
+<li>Venus, <a href="#S_148">148</a>.
+<ul><li>orbit of, <a href="#S_30">30</a>.</li></ul></li>
+
+<li>Vernal equinox, <a href="#S_21">21</a>, <a href="#S_25">25</a>.</li>
+
+<li>Vertical circle, <a href="#S_21">21</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Wave front, <a href="#S_76">76</a>.</li>
+
+<li>Wave lengths, <a href="#S_75">75</a>, <a href="#S_86">86</a>.</li>
+
+<li>&nbsp;</li>
+
+<li>Year, <a href="#S_25">25</a>.
+<ul><li>leap year, <a href="#S_61">61</a>.</li>
+<li>sidereal year, <a href="#S_59">59</a>.</li>
+<li>tropical year, <a href="#S_60">60</a>.</li></ul></li>
+
+<li>&nbsp;</li>
+
+<li>Zenith, <a href="#S_21">21</a>.</li>
+
+<li>Zodiac, <a href="#S_26">26</a>.</li>
+
+<li>Zodiacal light, <a href="#S_168">168</a>.</li>
+</ul>
+
+
+
+<h4>THE END</h4>
+
+
+
+<div class="figcenter" style="width: 600px;"><a name="PROTRACTOR" id="PROTRACTOR"></a>
+<img src="images/i431.jpg" width="600" height="303" alt="PROTRACTOR
+
+TO ACCOMPANY COMSTOCK&#39;S ASTRONOMY" title="PROTRACTOR
+
+TO ACCOMPANY COMSTOCK&#39;S ASTRONOMY" />
+</div>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock
+
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+Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Text-Book of Astronomy
+
+Author: George C. Comstock
+
+Release Date: January 3, 2011 [EBook #34834]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY ***
+
+
+
+
+    Transcriber's Note: The angle symbol has been replaced
+    with [angle]. Greek letters have been replaced with their
+    transliterations in brackets, e. g. [a] for alpha. The
+    upside-down Omega symbol has been replaced with [mho].
+
+
+
+
+                      TWENTIETH CENTURY TEXT-BOOKS
+
+
+                                EDITED BY
+                     A. F. NIGHTINGALE, PH.D., LL.D.
+            FORMERLY SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO
+
+
+
+                 [Illustration: A TOTAL SOLAR ECLIPSE.
+    After Burckhalter's photographs of the eclipse of May 28, 1900.]
+
+
+
+                      TWENTIETH CENTURY TEXT-BOOKS
+
+
+                             A TEXT-BOOK OF
+                               ASTRONOMY
+
+                                   BY
+                           GEORGE C. COMSTOCK
+
+
+                DIRECTOR OF THE WASHBURN OBSERVATORY AND
+                     PROFESSOR OF ASTRONOMY IN THE
+                        UNIVERSITY OF WISCONSIN
+
+
+                             [Illustration]
+
+
+                                NEW YORK
+                        D. APPLETON AND COMPANY
+                                  1903
+
+
+
+                            COPYRIGHT, 1901
+                       BY D. APPLETON AND COMPANY
+
+
+
+
+PREFACE
+
+
+The present work is not a compendium of astronomy or an outline course
+of popular reading in that science. It has been prepared as a text-book,
+and the author has purposely omitted from it much matter interesting as
+well as important to a complete view of the science, and has endeavored
+to concentrate attention upon those parts of the subject that possess
+special educational value. From this point of view matter which permits
+of experimental treatment with simple apparatus is of peculiar value and
+is given a prominence in the text beyond its just due in a well-balanced
+exposition of the elements of astronomy, while topics, such as the
+results of spectrum analysis, which depend upon elaborate apparatus, are
+in the experimental part of the work accorded much less space than their
+intrinsic importance would justify.
+
+Teacher and student are alike urged to magnify the observational side of
+the subject and to strive to obtain in their work the maximum degree of
+precision of which their apparatus is capable. The instruments required
+are few and easily obtained. With exception of a watch and a protractor,
+all of the apparatus needed may be built by any one of fair mechanical
+talent who will follow the illustrations and descriptions of the text.
+In order that proper opportunity for observations may be had, the study
+should be pursued during the milder portion of the year, between April
+and November in northern latitudes, using clear weather for a direct
+study of the sky and cloudy days for book work.
+
+The illustrations contained in the present work are worthy of as careful
+study as is the text, and many of them are intended as an aid to
+experimental work and accurate measurement, e. g., the star maps, the
+diagrams of the planetary orbits, pictures of the moon, sun, etc. If the
+school possesses a projection lantern, a set of astronomical slides to
+be used in connection with it may be made of great advantage, if the
+pictures are studied as an auxiliary to Nature. Mere display and scenic
+effect are of little value.
+
+A brief bibliography of popular literature upon astronomy may be found
+at the end of this book, and it will be well if at least a part of these
+works can be placed in the school library and systematically used for
+supplementary reading. An added interest may be given to the study if
+one or more of the popular periodicals which deal with astronomy are
+taken regularly by the school and kept within easy reach of the
+students. From time to time the teacher may well assign topics treated
+in these periodicals to be read by individual students and presented to
+the class in the form of an essay.
+
+The author is under obligations to many of his professional friends who
+have contributed illustrative matter for his text, and his thanks are in
+an especial manner due to the editors of the Astrophysical Journal,
+Astronomy and Astrophysics, and Popular Astronomy for permission to
+reproduce here plates which have appeared in those periodicals, and to
+Dr. Charles Boynton, who has kindly read and criticised the proofs.
+
+                                                  GEORGE C. COMSTOCK.
+
+  UNIVERSITY OF WISCONSIN, _February, 1901_.
+
+
+
+
+CONTENTS
+
+
+ CHAPTER                                                        PAGE
+    I.--DIFFERENT KINDS OF MEASUREMENT                             1
+          The measurement of angles and time.
+
+   II.--THE STARS AND THEIR DIURNAL MOTION                        10
+          Finding the stars--Their apparent motion--
+          Latitude--Direction of the meridian--Sidereal
+          time--Definitions.
+
+  III.--FIXED AND WANDERING STARS                                 29
+          Apparent motion of the sun, moon, and
+          planets--Orbits of the planets--How to find
+          the planets.
+
+   IV.--CELESTIAL MECHANICS                                       46
+          Kepler's laws--Newton's laws of motion--The law
+          of gravitation--Orbital motion--Perturbations--
+          Masses of the planets--Discovery of Neptune--
+          The tides.
+
+    V.--THE EARTH AS A PLANET                                     70
+          Size--Mass--Precession--The warming of the
+          earth--The atmosphere--Twilight.
+
+   VI.--THE MEASUREMENT OF TIME                                   86
+          Solar and sidereal time--Longitude--The
+          calendar--Chronology.
+
+  VII.--ECLIPSES                                                 101
+          Their cause and nature--Eclipse limits--Eclipse
+          maps--Recurrence and prediction of eclipses.
+
+ VIII.--INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE     121
+          The clock--Radiant energy--Mirrors and lenses--
+          The telescope--Camera--Spectroscope--Principles
+          of spectrum analysis.
+
+   IX.--THE MOON                                                 150
+          Numerical data--Phases--Motion--Librations--Lunar
+          topography--Physical condition.
+
+    X.--THE SUN                                                  178
+          Numerical data--Chemical nature--Temperature--
+          Visible and invisible parts--Photosphere--Spots--
+          Faculę--Chromosphere--Prominences--Corona--The
+          sun-spot period--The sun's rotation--Mechanical
+          theory of the sun.
+
+   XI.--THE PLANETS                                              212
+          Arrangement of the solar system--Bode's law--
+          Physical condition of the planets--Jupiter--
+          Saturn--Uranus and Neptune--Venus--Mercury--
+          Mars--The asteroids.
+
+  XII.--COMETS AND METEORS                                       251
+          Motion, size, and mass of comets--Meteors--Their
+          number and distribution--Meteor showers--Relation
+          of comets and meteors--Periodic comets--Comet
+          families and groups--Comet tails--Physical nature
+          of comets--Collisions.
+
+ XIII.--THE FIXED STARS                                          291
+          Number of the stars--Brightness--Distance--Proper
+          motion--Motion in line of sight--Double stars--
+          Variable stars--New stars.
+
+  XIV.--STARS AND NEBULĘ                                         330
+          Stellar colors and spectra--Classes of stars--
+          Clusters--Nebulę--Their spectra and physical
+          condition--The Milky Way--Construction of the
+          heavens--Extent of the stellar system.
+
+   XV.--GROWTH AND DECAY                                         358
+          Logical bases and limitations--Development of the
+          sun--The nebular hypothesis--Tidal friction--Roche's
+          limit--Development of the moon--Development of stars
+          and nebulę--The future.
+
+        APPENDIX                                                 383
+
+        INDEX                                                    387
+
+
+
+
+LIST OF LITHOGRAPHIC PLATES
+
+
+                                                         FACING PAGE
+    I.--Northern Constellations                                  124
+   II.--Equatorial Constellations                                190
+  III.--Map of Mars                                              246
+   IV.--The Pleiades                                             344
+        Protractor                       _In pocket at back of book_
+
+
+
+
+LIST OF FULL-PAGE ILLUSTRATIONS
+
+
+                                                         FACING PAGE
+  A Total Solar Eclipse                               _Frontispiece_
+  The Harvard College Observatory, Cambridge, Mass.               24
+  Isaac Newton                                                    46
+  Galileo Galilei                                                 52
+  The Lick Observatory, Mount Hamilton, Cal.                      60
+  The Yerkes Observatory, Williams Bay, Wis.                     100
+  The Moon, one day after First Quarter                          150
+  William Herschel                                               234
+  Pierre Simon Laplace                                           364
+
+
+
+
+ASTRONOMY
+
+
+
+
+CHAPTER I
+
+DIFFERENT KINDS OF MEASUREMENT
+
+
+1. ACCURATE MEASUREMENT.--Accurate measurement is the foundation of
+exact science, and at the very beginning of his study in astronomy the
+student should learn something of the astronomer's kind of measurement.
+He should practice measuring the stars with all possible care, and
+should seek to attain the most accurate results of which his instruments
+and apparatus are capable. The ordinary affairs of life furnish abundant
+illustration of some of these measurements, such as finding the length
+of a board in inches or the weight of a load of coal in pounds and
+measurements of both length and weight are of importance in astronomy,
+but of far greater astronomical importance than these are the
+measurement of angles and the measurement of time. A kitchen clock or a
+cheap watch is usually thought of as a machine to tell the "time of
+day," but it may be used to time a horse or a bicycler upon a race
+course, and then it becomes an instrument to measure the amount of time
+required for covering the length of the course. Astronomers use a clock
+in both of these ways--to tell the time at which something happens or is
+done, and to measure the amount of time required for something; and in
+using a clock for either purpose the student should learn to take the
+time from it to the nearest second or better, if it has a seconds hand,
+or to a small fraction of a minute, by estimating the position of the
+minute hand between the minute marks on the dial. Estimate the fraction
+in tenths of a minute, not in halves or quarters.
+
+EXERCISE 1.--If several watches are available, let one person tap
+sharply upon a desk with a pencil and let each of the others note the
+time by the minute hand to the nearest tenth of a minute and record the
+observations as follows:
+
+    2h. 44.5m.  First tap.   2h. 46.4m.  1.9m.
+    2h. 44.9m.  Second tap.  2h. 46.7m.  1.8m.
+    2h. 46.6m.  Third tap.   2h. 48.6m.  2.0m.
+
+The letters h and m are used as abbreviations for hour and minute. The
+first and second columns of the table are the record made by one
+student, and second and third the record made by another. After all the
+observations have been made and recorded they should be brought together
+and compared by taking the differences between the times recorded for
+each tap, as is shown in the last column. This difference shows how much
+faster one watch is than the other, and the agreement or disagreement of
+these differences shows the degree of accuracy of the observations. Keep
+up this practice until tenths of a minute can be estimated with fair
+precision.
+
+2. ANGLES AND THEIR USE.--An angle is the amount of opening or
+difference of direction between two lines that cross each other. At
+twelve o'clock the hour and minute hand of a watch point in the same
+direction and the angle between them is zero. At one o'clock the minute
+hand is again at XII, but the hour hand has moved to I, one twelfth part
+of the circumference of the dial, and the angle between the hands is one
+twelfth of a circumference. It is customary to imagine the circumference
+of a dial to be cut up into 360 equal parts--i. e., each minute space of
+an ordinary dial to be subdivided into six equal parts, each of which
+is called a degree, and the measurement of an angle consists in finding
+how many of these degrees are included in the opening between its sides.
+At one o'clock the angle between the hands of a watch is thirty degrees,
+which is usually written 30°, at three o'clock it is 90°, at six o'clock
+180°, etc.
+
+A watch may be used to measure angles. How? But a more convenient
+instrument is the protractor, which is shown in Fig. 1, applied to the
+angle _A B C_ and showing that _A B C_ = 85° as nearly as the protractor
+scale can be read.
+
+The student should have and use a protractor, such as is furnished with
+this book, for the numerous exercises which are to follow.
+
+[Illustration: FIG. 1.--A protractor.]
+
+EXERCISE 2.--Draw neatly a triangle with sides about 100 millimeters
+long, measure each of its angles and take their sum. No matter what may
+be the shape of the triangle, this sum should be very nearly
+180°--exactly 180° if the work were perfect--but perfection can seldom
+be attained and one of the first lessons to be learned in any science
+which deals with measurement is, that however careful we may be in our
+work some minute error will cling to it and our results can be only
+approximately correct. This, however, should not be taken as an excuse
+for careless work, but rather as a stimulus to extra effort in order
+that the unavoidable errors may be made as small as possible. In the
+present case the measured angles may be improved a little by adding
+(algebraically) to each of them one third of the amount by which their
+sum falls short of 180°, as in the following example:
+
+            Measured angles.    Correction.  Corrected angles.
+                 °                   °              °
+  A            73.4               + 0.1           73.5
+  B            49.3               + 0.1           49.4
+  C            57.0               + 0.1           57.1
+              -----                              -----
+  Sum         179.7                              180.0
+  Defect      + 0.3
+
+This process is in very common use among astronomers, and is called
+"adjusting" the observations.
+
+[Illustration: FIG. 2.--Triangulation.]
+
+3. TRIANGLES.--The instruments used by astronomers for the measurement
+of angles are usually provided with a telescope, which may be pointed at
+different objects, and with a scale, like that of the protractor, to
+measure the angle through which the telescope is turned in passing from
+one object to another. In this way it is possible to measure the angle
+between lines drawn from the instrument to two distant objects, such as
+two church steeples or the sun and moon, and this is usually called the
+angle between the objects. By measuring angles in this way it is
+possible to determine the distance to an inaccessible point, as shown in
+Fig. 2. A surveyor at _A_ desires to know the distance to _C_, on the
+opposite side of a river which he can not cross. He measures with a tape
+line along his own side of the stream the distance _A B_ = 100 yards and
+then, with a suitable instrument, measures the angle at _A_ between the
+points _C_ and _B_, and the angle at _B_ between _C_ and _A_, finding _B
+A C_ = 73.4°, _A B C_ = 49.3°. To determine the distance _A C_ he draws
+upon paper a line 100 millimeters long, and marks the ends _a_ and _b_;
+with a protractor he constructs at _a_ the angle _b a c_ = 73.4°, and at
+_b_ the angle _a b c_ = 49.3°, and marks by _c_ the point where the two
+lines thus drawn meet. With the millimeter scale he now measures the
+distance _a c_ = 90.2 millimeters, which determines the distance _A C_
+across the river to be 90.2 yards, since the triangle on paper has been
+made similar to the one across the river, and millimeters on the one
+correspond to yards on the other. What is the proposition of geometry
+upon which this depends? The measured distance _A B_ in the surveyor's
+problem is called a base line.
+
+EXERCISE 3.--With a foot rule and a protractor measure a base line and
+the angles necessary to determine the length of the schoolroom. After
+the length has been thus found, measure it directly with the foot rule
+and compare the measured length with the one found from the angles. If
+any part of the work has been carelessly done, the student need not
+expect the results to agree.
+
+[Illustration: FIG. 3.--Finding the moon's distance from the earth.]
+
+In the same manner, by sighting at the moon from widely different parts
+of the earth, as in Fig. 3, the moon's distance from us is found to be
+about a quarter of a million miles. What is the base line in this case?
+
+4. THE HORIZON--ALTITUDES.--In their observations astronomers and
+sailors make much use of the _plane of the horizon_, and practically any
+flat and level surface, such as that of a smooth pond, may be regarded
+as a part of this plane and used as such. A very common observation
+relating to the plane of the horizon is called "taking the sun's
+altitude," and consists in measuring the angle between the sun's rays
+and the plane of the horizon upon which they fall. This angle between a
+line and a plane appears slightly different from the angle between two
+lines, but is really the same thing, since it means the angle between
+the sun's rays and a line drawn in the plane of the horizon toward the
+point directly under the sun. Compare this with the definition given in
+the geographies, "The latitude of a point on the earth's surface is its
+angular distance north or south of the equator," and note that the
+latitude is the angle between the plane of the equator and a line drawn
+from the earth's center to the given point on its surface.
+
+A convenient method of obtaining a part of the plane of the horizon for
+use in observation is as follows: Place a slate or a pane of glass upon
+a table in the sunshine. Slightly moisten its whole surface and then
+pour a little more water upon it near the center. If the water runs
+toward one side, thrust the edge of a thin wooden wedge under this side
+and block it up until the water shows no tendency to run one way rather
+than another; it is then level and a part of the plane of the horizon.
+Get several wedges ready before commencing the experiment. After they
+have been properly placed, drive a pin or tack behind each one so that
+it may not slip.
+
+5. TAKING THE SUN'S ALTITUDE. EXERCISE 4.--Prepare a piece of board 20
+centimeters, or more, square, planed smooth on one face and one edge.
+Drive a pin perpendicularly into the face of the board, near the middle
+of the planed edge. Set the board on edge on the horizon plane and turn
+it edgewise toward the sun so that a shadow of the pin is cast on the
+plane. Stick another pin into the board, near its upper edge, so that
+its shadow shall fall exactly upon the shadow of the first pin, and with
+a watch or clock observe the time at which the two shadows coincide.
+Without lifting the board from the plane, turn it around so that the
+opposite edge is directed toward the sun and set a third pin just as the
+second one was placed, and again take the time. Remove the pins and draw
+fine pencil lines, connecting the holes, as shown in Fig. 4, and with
+the protractor measure the angle thus marked. The student who has
+studied elementary geometry should be able to demonstrate that at the
+mean of the two recorded times the sun's altitude was equal to one half
+of the angle measured in the figure.
+
+[Illustration: FIG. 4.--Taking the sun's altitude.]
+
+When the board is turned edgewise toward the sun so that its shadow is
+as thin as possible, rule a pencil line alongside it on the horizon
+plane. The angle which this line makes with a line pointing due south is
+called the sun's _azimuth_. When the sun is south, its azimuth is zero;
+when west, it is 90°; when east, 270°, etc.
+
+EXERCISE 5.--Let a number of different students take the sun's altitude
+during both the morning and afternoon session and note the time of each
+observation, to the nearest minute. Verify the setting of the plane of
+the horizon from time to time, to make sure that no change has occurred
+in it.
+
+6. GRAPHICAL REPRESENTATIONS.--Make a graph (drawing) of all the
+observations, similar to Fig. 5, and find by bisecting a set of chords
+_g_ to _g_, _e_ to _e_, _d_ to _d_, drawn parallel to _B B_, the time at
+which the sun's altitude was greatest. In Fig. 5 we see from the
+intersection of _M M_ with _B B_ that this time was 11h. 50m.
+
+The method of graphs which is here introduced is of great importance in
+physical science, and the student should carefully observe in Fig. 5
+that the line _B B_ is a scale of times, which may be made long or
+short, provided only the intervals between consecutive hours 9 to 10, 10
+to 11, 11 to 12, etc., are equal. The distance of each little circle
+from _B B_ is taken proportional to the sun's altitude, and may be upon
+any desired scale--e. g., a millimeter to a degree--provided the same
+scale is used for all observations. Each circle is placed accurately
+over that part of the base line which corresponds to the time at which
+the altitude was taken. Square ruled paper is very convenient, although
+not necessary, for such diagrams. It is especially to be noted that from
+the few observations which are represented in the figure a smooth curve
+has been drawn through the circles which represent the sun's altitude,
+and this curve shows the altitude of the sun at every moment between 9
+A. M. and 3 P. M. In Fig. 5 the sun's altitude at noon was 57°. What was
+it at half past two?
+
+[Illustration: FIG. 5.--A graph of the sun's altitude.]
+
+7. DIAMETER OF A DISTANT OBJECT.--By sighting over a protractor, measure
+the angle between imaginary lines drawn from it to the opposite sides of
+a window. Carry the protractor farther away from the window and repeat
+the experiment, to see how much the angle changes. The angle thus
+measured is called "the angle subtended" by the window at the place
+where the measurement was made. If this place was squarely in front of
+the window we may draw upon paper an angle equal to the measured one and
+lay off from the vertex along its sides a distance proportional to the
+distance of the window--e. g., a millimeter for each centimeter of real
+distance. If a cross line be now drawn connecting the points thus found,
+its length will be proportional to the width of the window, and the
+width may be read off to scale, a centimeter for every millimeter in the
+length of the cross line.
+
+The astronomer who measures with an appropriate instrument the angle
+subtended by the moon may in an entirely similar manner find the moon's
+diameter and has, in fact, found it to be 2,163 miles. Can the same
+method be used to find the diameter of the sun? A planet? The earth?
+
+
+
+
+CHAPTER II
+
+THE STARS AND THEIR DIURNAL MOTION
+
+
+8. THE STARS.--From the very beginning of his study in astronomy, and as
+frequently as possible, the student should practice watching the stars
+by night, to become acquainted with the constellations and their
+movements. As an introduction to this study he may face toward the
+north, and compare the stars which he sees in that part of the sky with
+the map of the northern heavens, given on Plate I, opposite page 124.
+Turn the map around, upside down if necessary, until the stars upon it
+match the brighter ones in the sky. Note how the stars are grouped in
+such conspicuous constellations as the Big Dipper (Ursa Major), the
+Little Dipper (Ursa Minor), and Cassiopeia. These three constellations
+should be learned so that they can be recognized at any time.
+
+_The names of the stars._--Facing the star map is a key which contains
+the names of the more important constellations and the names of the
+brighter stars in their constellations. These names are for the most
+part a Greek letter prefixed to the genitive case of the Latin name of
+the constellation. (See the Greek alphabet printed at the end of the
+book.)
+
+9. MAGNITUDES OF THE STARS.--Nearly nineteen centuries ago St. Paul
+noted that "one star differeth from another star in glory," and no more
+apt words can be found to mark the difference of brightness which the
+stars present. Even prior to St. Paul's day the ancient Greek
+astronomers had divided the stars in respect of brightness into six
+groups, which the modern astronomers still use, calling each group a
+_magnitude_. Thus a few of the brightest stars are said to be of the
+first magnitude, the great mass of faint ones which are just visible to
+the unaided eye are said to be of the sixth magnitude, and intermediate
+degrees of brilliancy are represented by the intermediate magnitudes,
+second, third, fourth, and fifth. The student must not be misled by the
+word magnitude. It has no reference to the size of the stars, but only
+to their brightness, and on the star maps of this book the larger and
+smaller circles by which the stars are represented indicate only the
+brightness of the stars according to the system of magnitudes. Following
+the indications of these maps, the student should, in learning the
+principal stars and constellations, learn also to recognize how bright
+is a star of the second, fourth, or other magnitude.
+
+10. OBSERVING THE STARS.--Find on the map and in the sky the stars
+[a] Ursę Minoris, [a] Ursę Majoris, [b] Ursę Majoris. What geometrical
+figure will fit on to these stars? In addition to its regular name,
+[a] Ursę Minoris is frequently called by the special name Polaris, or
+the pole star. Why are the other two stars called "the Pointers"? What
+letter of the alphabet do the five bright stars in Cassiopeia suggest?
+
+EXERCISE 6.--Stand in such a position that Polaris is just hidden behind
+the corner of a building or some other vertical line, and mark upon the
+key map as accurately as possible the position of this line with respect
+to the other stars, showing which stars are to the right and which are
+to the left of it. Record the time (date, hour, and minute) at which
+this observation was made. An hour or two later repeat the observation
+at the same place, draw the line and note the time, and you will find
+that the line last drawn upon the map does not agree with the first one.
+The stars have changed their positions, and with respect to the vertical
+line the Pointers are now in a different direction from Polaris.
+Measure with a protractor the angle between the two lines drawn in the
+map, and use this angle and the recorded times of the observation to
+find how many degrees per hour this direction is changing. It should be
+about 15° per hour. If the observation were repeated 12 hours after the
+first recorded time, what would be the position of the vertical line
+among the stars? What would it be 24 hours later? A week later? Repeat
+the observation on the next clear night, and allowing for the number of
+whole revolutions made by the stars between the two dates, again
+determine from the time interval a more accurate value of the rate at
+which the stars move.
+
+The motion of the stars which the student has here detected is called
+their "diurnal" motion. What is the significance of the word diurnal?
+
+In the preceding paragraph there is introduced a method of great
+importance in astronomical practice--i. e., determining something--in
+this case the rate per hour, from observations separated by a long
+interval of time, in order to get a more accurate value than could be
+found from a short interval. Why is it more accurate? To determine the
+rate at which the planet Mars rotates about its axis, astronomers use
+observations separated by an interval of more than 200 years, during
+which the planet made more than 75,000 revolutions upon its axis. If we
+were to write out in algebraic form an equation for determining the
+length of one revolution of Mars about its axis, the large number,
+75,000, would appear in the equation as a divisor, and in the final
+result would greatly reduce whatever errors existed in the observations
+employed.
+
+Repeat Exercise 6 night after night, and note whether the stars come
+back to the same position at the same hour and minute every night.
+
+[Illustration: FIG. 6. The plumb-line apparatus.]
+
+[Illustration: FIG. 7. The plumb-line apparatus.]
+
+11. THE PLUMB-LINE APPARATUS.--This experiment, and many others, may be
+conveniently and accurately made with no other apparatus than a plumb
+line, and a device for sighting past it. In Figs. 6 and 7 there is
+shown a simple form of such apparatus, consisting essentially of a board
+which rests in a horizontal position upon the points of three screws
+that pass through it. This board carries a small box, to one side of
+which is nailed in vertical position another board 5 or 6 feet long to
+carry the plumb line. This consists of a wire or fish line with any
+heavy weight--e. g., a brick or flatiron--tied to its lower end and
+immersed in a vessel of water placed inside the box, so as to check any
+swinging motion of the weight. In the cover of the box is a small hole
+through which the wire passes, and by turning the screws in the
+baseboard the apparatus may be readily leveled, so that the wire shall
+swing freely in the center of the hole without touching the cover of the
+box. Guy wires, shown in the figure, are applied so as to stiffen the
+whole apparatus. A board with a screw eye at each end may be pivoted to
+the upright, as in Fig. 6, for measuring altitudes; or to the box, as in
+Fig. 7, for observing the time at which a star in its diurnal motion
+passes through the plane determined by the plumb line and the center of
+the screw eye through which the observer looks.
+
+The whole apparatus may be constructed by any person of ordinary
+mechanical skill at a very small cost, and it or something equivalent
+should be provided for every class beginning observational astronomy. To
+use the apparatus for the experiment of § 10, it should be leveled, and
+the board with the screw eyes, attached as in Fig. 7, should be turned
+until the observer, looking through the screw eye, sees Polaris exactly
+behind the wire. Use a bicycle lamp to illumine the wire by night. The
+apparatus is now adjusted, and the observer has only to wait for the
+stars which he desires to observe, and to note by his watch the time at
+which they pass behind the wire. It will be seen that the wire takes the
+place of the vertical edge of the building, and that the board with the
+screw eyes is introduced solely to keep the observer in the right place
+relative to the wire.
+
+12. A SIDEREAL CLOCK.--Clocks are sometimes so made and regulated that
+they show always the same hour and minute when the stars come back to
+the same place, and such a timepiece is called a sidereal clock--i. e.,
+a star-time clock. Would such a clock gain or lose in comparison with an
+ordinary watch? Could an ordinary watch be turned into a sidereal watch
+by moving the regulator?
+
+[Illustration: FIG. 8.--Photographing the circumpolar stars.--BARNARD.]
+
+13. PHOTOGRAPHING THE STARS.--EXERCISE 7.--For any student who uses a
+camera. Upon some clear and moonless night point the camera, properly
+focused, at Polaris, and expose a plate for three or four hours. Upon
+developing the plate you should find a series of circular trails such as
+are shown in Fig. 8, only longer. Each one of these is produced by a
+star moving slowly over the plate, in consequence of its changing
+position in the sky. The center indicated by these curved trails is
+called the pole of the heavens. It is that part of the sky toward which
+is pointed the axis about which the earth rotates, and the motion of the
+stars around the center is only an apparent motion due to the rotation
+of the earth which daily carries the observer and his camera around this
+axis while the stars stand still, just as trees and fences and telegraph
+poles stand still, although to the passenger upon a railway train they
+appear to be in rapid motion. So far as simple observations are
+concerned, there is no method by which the pupil can tell for himself
+that the motion of the stars is an apparent rather than a real one, and,
+following the custom of astronomers, we shall habitually speak as if it
+were a real movement of the stars. How long was the plate exposed in
+photographing Fig. 8?
+
+14. FINDING THE STARS.--On Plate I, opposite page 124, the pole of the
+heavens is at the center of the map, near Polaris, and the heavy trail
+near the center of Fig. 8 is made by Polaris. See if you can identify
+from the map any of the stars whose trails show in the photograph. The
+brighter the star the bolder and heavier its trail.
+
+Find from the map and locate in the sky the two bright stars Capella and
+Vega, which are on opposite sides of Polaris and nearly equidistant from
+it. Do these stars share in the motion around the pole? Are they visible
+on every clear night, and all night?
+
+Observe other bright stars farther from Polaris than are Vega and
+Capella and note their movement. Do they move like the sun and moon? Do
+they rise and set?
+
+In what part of the sky do the stars move most rapidly, near the pole or
+far from it?
+
+How long does it take the fastest moving stars to make the circuit of
+the sky and come back to the same place? How long does it take the slow
+stars?
+
+15. RISING AND SETTING OF THE STARS.--A study of the sky along the lines
+indicated in these questions will show that there is a considerable part
+of it surrounding the pole whose stars are visible on every clear night.
+The same star is sometimes high in the sky, sometimes low, sometimes to
+the east of the pole and at other times west of it, but is always above
+the horizon. Such stars are said to be circumpolar. A little farther
+from the pole each star, when at the lowest point of its circular path,
+dips for a time below the horizon and is lost to view, and the farther
+it is away from the pole the longer does it remain invisible, until, in
+the case of stars 90° away from the pole, we find them hidden below the
+horizon for twelve hours out of every twenty-four (see Fig. 9). The sun
+is such a star, and in its rising and setting acts precisely as does
+every other star at a similar distance from the pole--only, as we shall
+find later, each star keeps always at (nearly) the same distance from
+the pole, while the sun in the course of a year changes its distance
+from the pole very greatly, and thus changes the amount of time it
+spends above and below the horizon, producing in this way the long days
+of summer and the short ones of winter.
+
+[Illustration: FIG. 9.--Diurnal motion of the northern constellations.]
+
+How much time do stars which are more than 90° from the pole spend above
+the horizon?
+
+We say in common speech that the sun rises in the east, but this is
+strictly true only at the time when it is 90° distant from the
+pole--i. e., in March and September. At other seasons it rises north or
+south of east according as its distance from the pole is less or greater
+than 90°, and the same is true for the stars.
+
+16. THE GEOGRAPHY OF THE SKY.--Find from a map the latitude and
+longitude of your schoolhouse. Find on the map the place whose latitude
+is 39° and longitude 77° west of the meridian of Greenwich. Is there any
+other place in the world which has the same latitude and longitude as
+your schoolhouse?
+
+The places of the stars in the sky are located in exactly the manner
+which is illustrated by these geographical questions, only different
+names are used. Instead of latitude the astronomer says _declination_,
+in place of longitude he says _right ascension_, in place of meridian he
+says _hour circle_, but he means by these new names the same ideas that
+the geographer expresses by the old ones.
+
+Imagine the earth swollen up until it fills the whole sky; the earth's
+equator would meet the sky along a line (a great circle) everywhere 90°
+distant from the pole, and this line is called the _celestial equator_.
+Trace its position along the middle of the map opposite page 190 and
+notice near what stars it runs. Every meridian of the swollen earth
+would touch the sky along an hour circle--i. e., a great circle passing
+through the pole and therefore perpendicular to the equator. Note that
+in the map one of these hour circles is marked 0. It plays the same part
+in measuring right ascensions as does the meridian of Greenwich in
+measuring longitudes; it is the beginning, from which they are reckoned.
+Note also, at the extreme left end of the map, the four bright stars in
+the form of a square, one side of which is parallel and close to the
+hour circle, which is marked 0. This is familiarly called the Great
+Square in Pegasus, and may be found high up in the southern sky whenever
+the Big Dipper lies below the pole. Why can it not be seen when Ursa
+Major is above the pole?
+
+Astronomers use the right ascensions of the stars not only to tell in
+what part of the sky the star is placed, but also in time reckonings, to
+regulate their sidereal clocks, and with regard to this use they find
+it convenient to express right ascension not in degrees but in hours,
+24 of which fill up the circuit of the sky and each of which is equal
+to 15° of arc, 24 × 15 = 360. The right ascension of Capella is
+5h. 9m. = 77.2°, but the student should accustom himself to using it
+in hours and minutes as given and not to change it into degrees. He
+should also note that some stars lie on the side of the celestial
+equator toward Polaris, and others are on the opposite side, so that the
+astronomer has to distinguish between north declinations and south
+declinations, just as the geographer distinguishes between north
+latitudes and south latitudes. This is done by the use of the + and -
+signs, a + denoting that the star lies north of the celestial equator,
+i. e., toward Polaris.
+
+[Illustration: FIG. 10.--From a photograph of the Pleiades.]
+
+Find on Plate II, opposite page 190, the Pleiades (Pl[=e]ad[=e]s),
+R. A. = 3h. 42m., Dec. = +23.8°. Why do they not show on Plate I,
+opposite page 124? In what direction are they from Polaris? This is one
+of the finest star clusters in the sky, but it needs a telescope to
+bring out its richness. See how many stars you can count in it with the
+naked eye, and afterward examine it with an opera glass. Compare what
+you see with Fig. 10. Find Antares, R. A. = 16h. 23m. Dec. = -26.2°. How
+far is it, in degrees, from the pole? Is it visible in your sky? If so,
+what is its color?
+
+Find the R. A. and Dec. of [a] Ursę Majoris; of [b] Ursę Majoris; of
+Polaris. Find the Northern Crown, _Corona Borealis_, R. A. = 15h. 30m.,
+Dec. = +27.0°; the Beehive, _Pręsepe_, R. A. = 8h. 33m., Dec. = +20.4°.
+
+These should be looked up, not only on the map, but also in the sky.
+
+17. REFERENCE LINES AND CIRCLES.--As the stars move across the sky in
+their diurnal motion, they carry the framework of hour circles and
+equator with them, so that the right ascension and declination of each
+star remain unchanged by this motion, just as longitudes and latitudes
+remain unchanged by the earth's rotation. They are the same when a star
+is rising and when it is setting; when it is above the pole and when it
+is below it. During each day the hour circle of every star in the
+heavens passes overhead, and at the moment when any particular hour
+circle is exactly overhead all the stars which lie upon it are said to
+be "on the meridian"--i. e., at that particular moment they stand
+directly over the observer's geographical meridian and upon the
+corresponding celestial meridian.
+
+An eye placed at the center of the earth and capable of looking through
+its solid substance would see your geographical meridian against the
+background of the sky exactly covering your celestial meridian and
+passing from one pole through your zenith to the other pole. In Fig. 11
+the inner circle represents the terrestrial meridian of a certain
+place, _O_, as seen from the center of the earth, _C_, and the outer
+circle represents the celestial meridian of _O_ as seen from _C_, only
+we must imagine, what can not be shown on the figure, that the outer
+circle is so large that the inner one shrinks to a mere point in
+comparison with it. If _C P_ represents the direction in which the
+earth's axis passes through the center, then _C E_ at right angles to it
+must be the direction of the equator which we suppose to be turned
+edgewise toward us; and if _C O_ is the direction of some particular
+point on the earth's surface, then _Z_ directly overhead is called the
+_zenith_ of that point, upon the celestial sphere. The line _C H_
+represents a direction parallel to the horizon plane at _O_, and _H C P_
+is the angle which the axis of the earth makes with this horizon plane.
+The arc _O E_ measures the latitude of _O_, and the arc _Z E_ measures
+the declination of _Z_, and since by elementary geometry each of these
+arcs contains the same number of degrees as the angle _E C Z_, we have
+the
+
+_Theorem._--The latitude of any place is equal to the declination of its
+zenith.
+
+_Corollary._--Any star whose declination is equal to your latitude will
+once in each day pass through your zenith.
+
+[Illustration: FIG. 11.--Reference lines and circles.]
+
+18. LATITUDE.--From the construction of the figure
+
+    [angle] _E C Z_ + [angle] _Z C P_ = 90°
+    [angle] _H C P_ + [angle] _Z C P_ = 90°
+
+from which we find by subtraction and transposition
+
+    [angle] _E C Z_ = [angle] _H C P_
+
+and this gives the further
+
+_Theorem._--The latitude of any place is equal to the elevation of the
+pole above its horizon plane.
+
+An observer who travels north or south over the earth changes his
+latitude, and therefore changes the angle between his horizon plane and
+the axis of the earth. What effect will this have upon the position of
+stars in his sky? If you were to go to the earth's equator, in what part
+of the sky would you look for Polaris? Can Polaris be seen from
+Australia? From South America? If you were to go from Minnesota to
+Texas, in what respect would the appearance of stars in the northern sky
+be changed? How would the appearance of stars in the southern sky be
+changed?
+
+[Illustration: FIG. 12.--Diurnal path of Polaris.]
+
+EXERCISE 8.--Determine your latitude by taking the altitude of Polaris
+when it is at some one of the four points of its diurnal path, shown in
+Fig. 12. When it is at _1_ it is said to be at upper culmination, and
+the star [z] Ursę Majoris in the handle of the Big Dipper will be
+directly below it. When at _2_ it is at western elongation, and the
+star Castor is near the meridian. When it is at _3_ it is at lower
+culmination, and the star Spica is on the meridian. When it is at _4_ it
+is at eastern elongation, and Altair is near the meridian. All of these
+stars are conspicuous ones, which the student should find upon the map
+and learn to recognize in the sky. The altitude observed at either _2_
+or _4_ may be considered equal to the latitude of the place, but the
+altitude observed when Polaris is at the positions marked _1_ and _3_
+must be corrected for the star's distance from the pole, which may be
+assumed equal to 1.3°.
+
+The plumb-line apparatus described at page 12 is shown in Fig. 6
+slightly modified, so as to adapt it to measuring the altitudes of
+stars. Note that the board with the screw eye at one end has been
+transferred from the box to the vertical standard, and has a screw eye
+at each end. When the apparatus has been properly leveled, so that the
+plumb line hangs at the middle of the hole in the box cover, the board
+is to be pointed at the star by sighting through the centers of the two
+screw eyes, and a pencil line is to be ruled along its edge upon the
+face of the vertical standard. After this has been done turn the
+apparatus halfway around so that what was the north side now points
+south, level it again and revolve the board about the screw which holds
+it to the vertical standard, until the screw eyes again point to the
+star. Rule another line along the same edge of the board as before and
+with a protractor measure the angle between these lines. Use a bicycle
+lamp if you need artificial light for your work. The student who has
+studied plane geometry should be able to prove that one half of the
+angle between these lines is equal to the altitude of the star.
+
+After you have determined your latitude from Polaris, compare the result
+with your position as shown upon the best map available. With a little
+practice and considerable care the latitude may be thus determined
+within one tenth of a degree, which is equivalent to about 7 miles. If
+you go 10 miles north or south from your first station you should find
+the pole higher up or lower down in the sky by an amount which can be
+measured with your apparatus.
+
+19. THE MERIDIAN LINE.--To establish a true north and south line upon
+the ground, use the apparatus as described at page 13, and when Polaris
+is at upper or lower culmination drive into the ground two stakes in
+line with the star and the plumb line. Such a meridian line is of great
+convenience in observing the stars and should be laid out and
+permanently marked in some convenient open space from which, if
+possible, all parts of the sky are visible. June and November are
+convenient months for this exercise, since Polaris then comes to
+culmination early in the evening.
+
+20. TIME.--What is _the time_ at which school begins in the morning?
+What do you mean by "_the time_"?
+
+The sidereal time at any moment is the right ascension of the hour
+circle which at that moment coincides with the meridian. When the hour
+circle passing through Sirius coincides with the meridian, the sidereal
+time is 6h. 40m., since that is the right ascension of Sirius, and in
+astronomical language Sirius is "_on the meridian_" at 6h. 40m. sidereal
+time. As may be seen from the map, this 6h. 40m. is the right ascension
+of Sirius, and if a clock be set to indicate 6h. 40m. when Sirius
+crosses the meridian, it will show sidereal time. If the clock is
+properly regulated, every other star in the heavens will come to the
+meridian at the moment when the time shown by the clock is equal to the
+right ascension of the star. A clock properly regulated for this purpose
+will gain about four minutes per day in comparison with ordinary clocks,
+and when so regulated it is called a sidereal clock. The student should
+be provided with such a clock for his future work, but one such clock
+will serve for several persons, and a nutmeg clock or a watch of the
+cheapest kind is quite sufficient.
+
+[Illustration: THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.]
+
+EXERCISE 9.--Set such a clock to sidereal time by means of the transit
+of a star over your meridian. For this experiment it is presupposed that
+a meridian line has been marked out on the ground as in § 19, and the
+simplest mode of performing the experiment required is for the observer,
+having chosen a suitable star in the southern part of the sky, to place
+his eye accurately over the northern end of the meridian line and to
+estimate as nearly as possible the beginning and end of the period
+during which the star appears to stand exactly above the southern end of
+the line. The middle of this period may be taken as the time at which
+the star crossed the meridian and at this moment the sidereal time is
+equal to the right ascension of the star. The difference between this
+right ascension and the observed middle instant is the error of the
+clock or the amount by which its hands must be set back or forward in
+order to indicate true sidereal time.
+
+A more accurate mode of performing the experiment consists in using the
+plumb-line apparatus carefully adjusted, as in Fig. 7, so that the line
+joining the wire to the center of the screw eye shall be parallel to the
+meridian line. Observe the time by the clock at which the star
+disappears behind the wire as seen through the center of the screw eye.
+If the star is too high up in the sky for convenient observation, place
+a mirror, face up, just north of the screw eye and observe star, wire
+and screw eye by reflection in it.
+
+The numerical right ascension of the observed star is needed for this
+experiment, and it may be measured from the star map, but it will
+usually be best to observe one of the stars of the table at the end of
+the book, and to obtain its right ascension as follows: The table gives
+the right ascension and declination of each star as they were at the
+beginning of the year 1900, but on account of the precession (see
+Chapter V), these numbers all change slowly with the lapse of time, and
+on the average the right ascension of each star of the table must be
+increased by one twentieth of a minute for each year after 1900--i. e.,
+in 1910 the right ascension of the first star of the table will be
+0h. 38.6m. + (10/20)m. = 0h. 39.1m. The declinations also change
+slightly, but as they are only intended to help in finding the star on
+the star maps, their change may be ignored.
+
+Having set the clock approximately to sidereal time, observe one or two
+more stars in the same way as above. The difference between the observed
+time and the right ascension, if any is found, is the "correction" of
+the clock. This correction ought not to exceed a minute if due care has
+been taken in the several operations prescribed. The relation of the
+clock to the right ascension of the stars is expressed in the following
+equation, with which the student should become thoroughly familiar:
+
+    A = T ± U
+
+_T_ stands for the time by the clock at which the star crossed the
+meridian. _A_ is the right ascension of the star, and _U_ is the
+correction of the clock. Use the + sign in the equation whenever the
+clock is too slow, and the - sign when it is too fast. _U_ may be found
+from this equation when _A_ and _T_ are given, or _A_ may be found when
+_T_ and _U_ are given. It is in this way that astronomers measure the
+right ascensions of the stars and planets.
+
+Determine _U_ from each star you have observed, and note how the several
+results agree one with another.
+
+21. DEFINITIONS.--To define a thing or an idea is to give a description
+sufficient to identify it and distinguish it from every other possible
+thing or idea. If a definition does not come up to this standard it is
+insufficient. Anything beyond this requirement is certainly useless and
+probably mischievous.
+
+Let the student define the following geographical terms, and let him
+also criticise the definitions offered by his fellow-students: Equator,
+poles, meridian, latitude, longitude, north, south, east, west.
+
+Compare the following astronomical definitions with your geographical
+definitions, and criticise them in the same way. If you are not able to
+improve upon them, commit them to memory:
+
+_The Poles_ of the heavens are those points in the sky toward which the
+earth's axis points. How many are there? The one near Polaris is called
+the north pole.
+
+_The Celestial Equator_ is a great circle of the sky distant 90° from
+the poles.
+
+_The Zenith_ is that point of the sky, overhead, toward which a plumb
+line points. Why is the word overhead placed in the definition? Is there
+more than one zenith?
+
+_The Horizon_ is a great circle of the sky 90° distant from the zenith.
+
+_An Hour Circle_ is any great circle of the sky which passes through the
+poles. Every star has its own hour circle.
+
+_The Meridian_ is that hour circle which passes through the zenith.
+
+_A Vertical Circle_ is any great circle that passes through the zenith.
+Is the meridian a vertical circle?
+
+_The Declination_ of a star is its angular distance north or south of
+the celestial equator.
+
+_The Right Ascension_ of a star is the angle included between its hour
+circle and the hour circle of a certain point on the equator which is
+called the _Vernal Equinox_. From spherical geometry we learn that this
+angle is to be measured either at the pole where the two hour circles
+intersect, as is done in the star map opposite page 124, or along the
+equator, as is done in the map opposite page 190. Right ascension is
+always measured from the vernal equinox in the direction opposite to
+that in which the stars appear to travel in their diurnal motion--i. e.,
+from west toward east.
+
+_The Altitude_ of a star is its angular distance above the horizon.
+
+_The Azimuth_ of a star is the angle between the meridian and the
+vertical circle passing through the star. A star due south has an
+azimuth of 0°. Due west, 90°. Due north, 180°. Due east, 270°.
+
+What is the azimuth of Polaris in degrees?
+
+What is the azimuth of the sun at sunrise? At sunset? At noon? Are these
+azimuths the same on different days?
+
+_The Hour Angle_ of a star is the angle between its hour circle and the
+meridian. It is measured from the meridian in the direction in which the
+stars appear to travel in their diurnal motion--i. e., from east toward
+west.
+
+What is the hour angle of the sun at noon? What is the hour angle of
+Polaris when it is at the lowest point in its daily motion?
+
+22. EXERCISES.--The student must not be satisfied with merely learning
+these definitions. He must learn to see these points and lines in his
+mind as if they were visibly painted upon the sky. To this end it will
+help him to note that the poles, the zenith, the meridian, the horizon,
+and the equator seem to stand still in the sky, always in the same place
+with respect to the observer, while the hour circles and the vernal
+equinox move with the stars and keep the same place among them. Does the
+apparent motion of a star change its declination or right ascension?
+What is the hour angle of the sun when it has the greatest altitude?
+Will your answer to the preceding question be true for a star? What is
+the altitude of the sun after sunset? In what direction is the north
+pole from the zenith? From the vernal equinox? Where are the points in
+which the meridian and equator respectively intersect the horizon?
+
+
+
+
+CHAPTER III
+
+FIXED AND WANDERING STARS
+
+
+23. STAR MAPS.--Select from the map some conspicuous constellation that
+will be conveniently placed for observation in the evening, and make on
+a large scale a copy of all the stars of the constellation that are
+shown upon the map. At night compare this copy with the sky, and mark in
+upon your paper all the stars of the constellation which are not already
+there. Both the original drawing and the additions made to it by night
+should be carefully done, and for the latter purpose what is called the
+method of allineations may be used with advantage--i. e., the new star
+is in line with two already on the drawing and is midway between them,
+or it makes an equilateral triangle with two others, or a square with
+three others, etc.
+
+A series of maps of the more prominent constellations, such as Ursa
+Major, Cassiopea, Pegasus, Taurus, Orion, Gemini, Canis Major, Leo,
+Corvus, Bootes, Virgo, Hercules, Lyra, Aquila, Scorpius, should be
+constructed in this manner upon a uniform scale and preserved as a part
+of the student's work. Let the magnitude of the stars be represented on
+the maps as accurately as may be, and note the peculiarity of color
+which some stars present. For the most part their color is a very pale
+yellow, but occasionally one may be found of a decidedly ruddy
+hue--e. g., Aldebaran or Antares. Such a star map, not quite complete,
+is shown in Fig. 13.
+
+So, too, a sharp eye may detect that some stars do not remain always of
+the same magnitude, but change their brightness from night to night,
+and this not on account of cloud or mist in the atmosphere, but from
+something in the star itself. Algol is one of the most conspicuous of
+these _variable stars_, as they are called.
+
+[Illustration: FIG. 13.--Star map of the region about Orion.]
+
+24. THE MOON'S MOTION AMONG THE STARS.--Whenever the moon is visible
+note its position among the stars by allineations, and plot it on the
+key map opposite page 190. Keep a record of the day and hour
+corresponding to each such observation. You will find, if the work is
+correctly done, that the positions of the moon all fall near the curved
+line shown on the map. This line is called the ecliptic.
+
+After several such observations have been made and plotted, find by
+measurement from the map how many degrees per day the moon moves. How
+long would it require to make the circuit of the heavens and come back
+to the starting point?
+
+On each night when you observe the moon, make on a separate piece of
+paper a drawing of it about 10 centimeters in diameter and show in the
+drawing every feature of the moon's face which you can see--e. g., the
+shape of the illuminated surface (phase); the direction among the stars
+of the line joining the horns; any spots which you can see upon the
+moon's face, etc. An opera glass will prove of great assistance in this
+work.
+
+Use your drawings and the positions of the moon plotted upon the map to
+answer the following questions: Does the direction of the line joining
+the horns have any special relation to the ecliptic? Does the amount of
+illuminated surface of the moon have any relation to the moon's angular
+distance from the sun? Does it have any relation to the time at which
+the moon sets? Do the spots on the moon when visible remain always in
+the same place? Do they come and go? Do they change their position with
+relation to each other? Can you determine from these spots that the moon
+rotates about an axis, as the earth does? In what direction does its
+axis point? How long does it take to make one revolution about the axis?
+Is there any day and night upon the moon?
+
+Each of these questions can be correctly answered from the student's own
+observations without recourse to any book.
+
+25. THE SUN AND ITS MOTION.--Examine the face of the sun through a
+smoked glass to see if there is anything there that you can sketch.
+
+By day as well as by night the sky is studded with stars, only they can
+not be seen by day on account of the overwhelming glare of sunlight, but
+the position of the sun among the stars may be found quite as
+accurately as was that of the moon, by observing from day to day its
+right ascension and declination, and this should be practiced at noon on
+clear days by different members of the class.
+
+EXERCISE 10.--The right ascension of the sun may be found by observing
+with the sidereal clock the time of its transit over the meridian. Use
+the equation in § 20, and substitute in place of _U_ the value of the
+clock correction found from observations of stars on a preceding or
+following night. If the clock gains or loses _with respect to sidereal
+time_, take this into account in the value of _U_.
+
+EXERCISE 11.--To determine the sun's declination, measure its altitude
+at the time it crosses the meridian. Use either the method of Exercise
+4, or that used with Polaris in Exercise 8. The student should be able
+to show from Fig. 11 that the declination is equal to the sum of the
+altitude and the latitude of the place diminished by 90°, or in an
+equation
+
+    Declination = Altitude + Latitude - 90°.
+
+If the declination as found from this equation is a negative number it
+indicates that the sun is on the south side of the equator.
+
+The right ascension and declination of the sun as observed on each day
+should be plotted on the map and the date, written opposite it. If the
+work has been correctly done, the plotted points should fall upon the
+curved line (ecliptic) which runs lengthwise of the map. This line, in
+fact, represents the sun's path among the stars.
+
+Note that the hours of right ascension increase from 0 up to 24, while
+the numbers on the clock dial go only from 0 to 12, and then repeat 0 to
+12 again during the same day. When the sidereal time is 13 hours, 14
+hours, etc., the clock will indicate 1 hour, 2 hours, etc., and 12 hours
+must then be added to the time shown on the dial.
+
+If observations of the sun's right ascension and declination are made
+in the latter part of either March or September the student will find
+that the sun crosses the equator at these times, and he should determine
+from his observations, as accurately as possible, the date and hour of
+this crossing and the point on the equator at which the sun crosses it.
+These points are called the equinoxes, Vernal Equinox and Autumnal
+Equinox for the spring and autumn crossings respectively, and the
+student will recall that the vernal equinox is the point from which
+right ascensions are measured. Its position among the stars is found by
+astronomers from observations like those above described, only made with
+much more elaborate apparatus.
+
+Similar observations made in June and December show that the sun's
+midday altitude is about 47° greater in summer than in winter. They show
+also that the sun is as far north of the equator in June as he is south
+of it in December, from which it is easily inferred that his path, the
+ecliptic, is inclined to the equator at an angle of 23°.5, one half of
+47°. This angle is called the obliquity of the ecliptic. The student may
+recall that in the geographies the torrid zone is said to extend 23°.5
+on either side of the earth's equator. Is there any connection between
+these limits and the obliquity of the ecliptic? Would it be correct to
+define the torrid zone as that part of the earth's surface within which
+the sun may at some season of the year pass through the zenith?
+
+EXERCISE 12.--After a half dozen observations of the sun have been
+plotted upon the map, find by measurement the rate, in degrees per day,
+at which the sun moves along the ecliptic. How many days will be
+required for it to move completely around the ecliptic from vernal
+equinox back to vernal equinox again? Accurate observations with the
+elaborate apparatus used by professional astronomers show that this
+period, which is called a _tropical year_, is 365 days 5 hours 48
+minutes 46 seconds. Is this the same as the ordinary year of our
+calendars?
+
+26. THE PLANETS.--Any one who has watched the sky and who has made the
+drawings prescribed in this chapter can hardly fail to have found in the
+course of his observations some bright stars not set down on the printed
+star maps, and to have found also that these stars do not remain fixed
+in position among their fellows, but wander about from one constellation
+to another. Observe the motion of one of these planets from night to
+night and plot its positions on the star map, precisely as was done for
+the moon. What kind of path does it follow?
+
+Both the ancient Greeks and the modern Germans have called these bodies
+wandering stars, and in English we name them planets, which is simply
+the Greek word for wanderer, bent to our use. Besides the sun and moon
+there are in the heavens five planets easily visible to the naked eye
+and, as we shall see later, a great number of smaller ones visible only
+in the telescope. More than 2,000 years ago astronomers began observing
+the motion of sun, moon, and planets among the stars, and endeavored to
+account for these motions by the theory that each wandering star moved
+in an orbit about the earth. Classical and medięval literature are
+permeated with this idea, which was displaced only after a long struggle
+begun by Copernicus (1543 A. D.), who taught that the moon alone of
+these bodies revolves about the earth, while the earth and the other
+planets revolve around the sun. The ecliptic is the intersection of the
+plane of the earth's orbit with the sky, and the sun appears to move
+along the ecliptic because, as the earth moves around its orbit, the sun
+is always seen projected against the opposite side of it. The moon and
+planets all appear to move near the ecliptic because the planes of their
+orbits nearly coincide with the plane of the earth's orbit, and a narrow
+strip on either side of the ecliptic, following its course completely
+around the sky, is called the _zodiac_, a word which may be regarded as
+the name of a narrow street (16° wide) within which all the wanderings
+of the visible planets are confined and outside of which they never
+venture. Indeed, Mars is the only planet which ever approaches the edge
+of the street, the others traveling near the middle of the road.
+
+[Illustration: FIG. 14.--The apparent motion of a planet.]
+
+27. A TYPICAL CASE OF PLANETARY MOTION.--The Copernican theory,
+enormously extended and developed through the Newtonian law of
+gravitation (see Chapter IV), has completely supplanted the older
+Ptolemaic doctrine, and an illustration of the simple manner in which it
+accounts for the apparently complicated motions of a planet among the
+stars is found in Figs. 14 and 15, the first of which represents the
+apparent motion of the planet Mars through the constellations Aries and
+Pisces during the latter part of the year 1894, while the second shows
+the true motions of Mars and the earth in their orbits about the sun
+during the same period. The straight line in Fig. 14, with cross ruling
+upon it, is a part of the ecliptic, and the numbers placed opposite it
+represent the distance, in degrees, from the vernal equinox. In Fig. 15
+the straight line represents the direction from the sun toward the
+vernal equinox, and the angle which this line makes with the line
+joining earth and sun is called the earth's longitude. The imaginary
+line joining the earth and sun is called the earth's radius vector, and
+the pupil should note that the longitude and length of the radius vector
+taken together show the direction and distance of the earth from the
+sun--i. e., they fix the relative positions of the two bodies. The same
+is nearly true for Mars and would be wholly true if the orbit of Mars
+lay in the same plane with that of the earth. How does Fig. 14 show that
+the orbit of Mars does not lie exactly in the same plane with the orbit
+of the earth?
+
+EXERCISE 13.--Find from Fig. 15 what ought to have been the apparent
+course of Mars among the stars during the period shown in the two
+figures, and compare what you find with Fig. 14. The apparent position
+of Mars among the stars is merely its direction from the earth, and this
+direction is represented in Fig. 14 by the distance of the planet from
+the ecliptic and by its longitude.
+
+[Illustration: FIG. 15.--The real motion of a planet.]
+
+The longitude of Mars for each date can be found from Fig. 15 by
+measuring the angle between the straight line _S V_ and the line drawn
+from the earth to Mars. Thus for October 12th we may find with the
+protractor that the angle between the line _S V_ and the line joining
+the earth to Mars is a little more than 30°, and in Fig. 14 the position
+of Mars for this date is shown nearly opposite the cross line
+corresponding to 30° on the ecliptic. Just how far below the ecliptic
+this position of Mars should fall can not be told from Fig. 15, which
+from necessity is constructed as if the orbits of Mars and the earth lay
+in the same plane, and Mars in this case would always appear to stand
+exactly on the ecliptic and to oscillate back and forth as shown in Fig.
+14, but without the up-and-down motion there shown. In this way plot in
+Fig. 14 the longitudes of Mars as seen from the earth for other dates
+and observe how the forward motion of the two planets in their orbits
+accounts for the apparently capricious motion of Mars to and fro among
+the stars.
+
+[Illustration: FIG. 16.--The orbits of Jupiter and Saturn.]
+
+28. THE ORBITS OF THE PLANETS.--Each planet, great or small, moves in
+its own appropriate orbit about the sun, and the exact determination of
+these orbits, their sizes, shapes, positions, etc., has been one of the
+great problems of astronomy for more than 2,000 years, in which
+successive generations of astronomers have striven to push to a still
+higher degree of accuracy the knowledge attained by their predecessors.
+Without attempting to enter into the details of this problem we may say,
+generally, that every planet moves in a plane passing through the sun,
+and for the six planets visible to the naked eye these planes nearly
+coincide, so that the six orbits may all be shown without much error as
+lying in the flat surface of one map. It is, however, more convenient to
+use two maps, such as Figs. 16 and 17, one of which shows the group of
+planets, Mercury, Venus, the earth, and Mars, which are near the sun,
+and on this account are sometimes called the inner planets, while the
+other shows the more distant planets, Jupiter and Saturn, together with
+the earth, whose orbit is thus made to serve as a connecting link
+between the two diagrams. These diagrams are accurately drawn to scale,
+and are intended to be used by the student for accurate measurement in
+connection with the exercises and problems which follow.
+
+In addition to the six planets shown in the figures the solar system
+contains two large planets and several hundred small ones, for the most
+part invisible to the naked eye, which are omitted in order to avoid
+confusing the diagrams.
+
+29. JUPITER AND SATURN.--In Fig. 16 the sun at the center is encircled
+by the orbits of the three planets, and inclosing all of these is a
+circular border showing the directions from the sun of the
+constellations which lie along the zodiac. The student must note
+carefully that it is only the directions of these constellations that
+are correctly shown, and that in order to show them at all they have
+been placed very much too close to the sun. The cross lines extending
+from the orbit of the earth toward the sun with Roman numerals opposite
+them show the positions of the earth in its orbit on the first day of
+January (_I_), first day of February (_II_), etc., and the similar lines
+attached to the orbits of Jupiter and Saturn with Arabic numerals show
+the positions of those planets on the first day of January of each year
+indicated, so that the figure serves to show not only the orbits of the
+planets, but their actual positions in their orbits for something more
+than the first decade of the twentieth century.
+
+The line drawn from the sun toward the right of the figure shows the
+direction to the vernal equinox. It forms one side of the angle which
+measures a planet's longitude.
+
+[Illustration: FIG. 17.--The orbits of the inner planets.]
+
+EXERCISE 14.--Measure with your protractor the longitude of the earth on
+January 1st. Is this longitude the same in all years? Measure the
+longitude of Jupiter on January 1, 1900; on July 1, 1900; on September
+25, 1906.
+
+Draw neatly on the map a pencil line connecting the position of the
+earth for January 1, 1900, with the position of Jupiter for the same
+date, and produce the line beyond Jupiter until it meets the circle of
+the constellations. This line represents the direction of Jupiter from
+the earth, and points toward the constellation in which the planet
+appears at that date. But this representation of the place of Jupiter in
+the sky is not a very accurate one, since on the scale of the diagram
+the stars are in fact more than 100,000 times as far off as they are
+shown in the figure, and the pencil mark does not meet the line of
+constellations at the same intersection it would have if this line were
+pushed back to its true position. To remedy this defect we must draw
+another line from the sun parallel to the one first drawn, and its
+intersection with the constellations will give very approximately the
+true position of Jupiter in the sky.
+
+EXERCISE 15.--Find the present positions of Jupiter and Saturn, and look
+them up in the sky by means of your star maps. The planets will appear
+in the indicated constellations as very bright stars not shown on the
+map.
+
+Which of the planets, Jupiter and Saturn, changes its direction from the
+sun more rapidly? Which travels the greater number of miles per day?
+When will Jupiter and Saturn be in the same constellation? Does the
+earth move faster or slower than Jupiter?
+
+The distance of Jupiter or Saturn from the earth at any time may be
+readily obtained from the figure. Thus, by direct measurement with the
+millimeter scale we find for January 1, 1900, the distance of Jupiter
+from the earth is 6.1 times the distance of the sun from the earth, and
+this may be turned into miles by multiplying it by 93,000,000, which is
+approximately the distance of the sun from the earth. For most purposes
+it is quite as well to dispense with this multiplication and call the
+distance 6.1 astronomical units, remembering that the astronomical unit
+is the distance of the sun from the earth.
+
+EXERCISE 16.--What is Jupiter's distance from the earth at its nearest
+approach? What is the greatest distance it ever attains? Is Jupiter's
+least distance from the earth greater or less than its least distance
+from Saturn?
+
+On what day in the year 1906 will the earth be on line between Jupiter
+and the sun? On this day Jupiter is said to be in _opposition_--i. e.,
+the planet and the sun are on opposite sides of the earth, and Jupiter
+then comes to the meridian of any and every place at midnight. When the
+sun is between the earth and Jupiter (at what date in 1906?) the planet
+is said to be in _conjunction_ with the sun, and of course passes the
+meridian with the sun at noon. Can you determine from the figure the
+time at which Jupiter comes to the meridian at other dates than
+opposition and conjunction? Can you determine when it is visible in the
+evening hours? Tell from the figure what constellation is on the
+meridian at midnight on January 1st. Will it be the same constellation
+in every year?
+
+
+30. MERCURY, VENUS, AND MARS.--Fig. 17, which represents the orbits of
+the inner planets, differs from Fig. 16 only in the method of fixing the
+positions of the planets in their orbits at any given date. The motion
+of these planets is so rapid, on account of their proximity to the sun,
+that it would not do to mark their positions as was done for Jupiter and
+Saturn, and with the exception of the earth they do not always return to
+the same place on the same day in each year. It is therefore necessary
+to adopt a slightly different method, as follows: The straight line
+extending from the sun toward the vernal equinox, _V_, is called the
+prime radius, and we know from past observations that the earth in its
+motion around the sun crosses this line on September 23d in each year,
+and to fix the earth's position for September 23d in the diagram we have
+only to take the point at which the prime radius intersects the earth's
+orbit. A month later, on October 23d, the earth will no longer be at
+this point, but will have moved on along its orbit to the point marked
+30 (thirty days after September 23d). Sixty days after September 23d it
+will be at the point marked 60, etc., and for any date we have only to
+find the number of days intervening between it and the preceding
+September 23d, and this number will show at once the position of the
+earth in its orbit. Thus for the date July 4, 1900, we find
+
+    1900, July 4 - 1899, September 23 = 284 days,
+
+and the little circle marked upon the earth's orbit between the numbers
+270 and 300 shows the position of the earth on that date.
+
+In what constellation was the sun on July 4, 1900? What zodiacal
+constellation came to the meridian at midnight on that date? What other
+constellations came to the meridian at the same time?
+
+The positions of the other planets in their orbits are found in the same
+manner, save that they do not cross the prime radius on the same date in
+each year, and the times at which they do cross it must be taken from
+the following table:
+
+                      TABLE OF EPOCHS
+
+  -----------------------------------------------------------
+    A. D. | Mercury.   |  Venus.   |   Earth.   |  Mars.
+  --------+------------+-----------+------------+------------
+  Period  | 88.0 days. |224.7 days.|365.25 days.| 687.1 days.
+   1900   | Feb. 18th. | Jan. 11th.| Sept. 23d. | April 28th.
+   1901   | Feb. 5th.  | April 5th.| Sept. 23d. |   ...
+   1902   | Jan. 23d.  | June 29th.| Sept. 23d. | March 16th.
+   1903   | April 8th. | Feb. 8th. | Sept. 23d. |   ...
+   1904   | March 25th.| May 3d.   | Sept. 23d. | Feb. 1st.
+   1905   | March 12th.| July 26th.| Sept. 23d. | Dec. 19th.
+   1906   | Feb. 27th. | March 8th.| Sept. 23d. |   ...
+   1907   | Feb. 14th. | May 31st. | Sept. 23d. | Nov. 6th.
+   1908   | Feb. 1st.  | Jan. 11th.| Sept. 23d. |   ...
+   1909   | Jan. 18th. | April 4th.| Sept. 23d. | Sept. 23d.
+   1910   | Jan. 5th.  | June 28th.| Sept. 23d. |   ...
+  -----------------------------------------------------------
+
+The first line of figures in this table shows the number of days that
+each of these planets requires to make a complete revolution about the
+sun, and it appears from these numbers that Mercury makes about four
+revolutions in its orbit per year, and therefore crosses the prime
+radius four times in each year, while the other planets are decidedly
+slower in their movements. The following lines of the table show for
+each year the date at which each planet first crossed the prime radius
+in that year; the dates of subsequent crossings in any year can be found
+by adding once, twice, or three times the period to the given date, and
+the table may be extended to later years, if need be, by continuously
+adding multiples of the period. In the case of Mars it appears that
+there is only about one year out of two in which this planet crosses the
+prime radius.
+
+After the date at which the planet crosses the prime radius has been
+determined its position for any required date is found exactly as in the
+case of the earth, and the constellation in which the planet will appear
+from the earth is found as explained above in connection with Jupiter
+and Saturn.
+
+The broken lines in the figure represent the construction for finding
+the places in the sky occupied by Mercury, Venus, and Mars on July 4,
+1900. Let the student make a similar construction and find the positions
+of these planets at the present time. Look them up in the sky and see if
+they are where your work puts them.
+
+31. EXERCISES.--The "evening star" is a term loosely applied to any
+planet which is visible in the western sky soon after sunset. It is easy
+to see that such a planet must be farther toward the east in the sky
+than is the sun, and in either Fig. 16 or Fig. 17 any planet which
+viewed from the position of the earth lies to the left of the sun and
+not more than 50° away from it will be an evening star. If to the right
+of the sun it is a morning star, and may be seen in the eastern sky
+shortly before sunrise.
+
+What planet is the evening star _now_? Is there more than one evening
+star at a time? What is the morning star now?
+
+Do Mercury, Venus, or Mars ever appear in opposition? What is the
+maximum angular distance from the sun at which Venus can ever be seen?
+Why is Mercury a more difficult planet to see than Venus? In what month
+of the year does Mars come nearest to the earth? Will it always be
+brighter in this month than in any other? Which of all the planets comes
+nearest to the earth?
+
+The earth always comes to the same longitude on the same day of each
+year. Why is not this true of the other planets?
+
+The student should remember that in one respect Figs. 16 and 17 are not
+altogether correct representations, since they show the orbits as all
+lying in the same plane. If this were strictly true, every planet would
+move, like the sun, always along the ecliptic; but in fact all of the
+orbits are tilted a little out of the plane of the ecliptic and every
+planet in its motion deviates a little from the ecliptic, first to one
+side then to the other; but not even Mars, which is the most erratic in
+this respect, ever gets more than eight degrees away from the ecliptic,
+and for the most part all of them are much closer to the ecliptic than
+this limit.
+
+
+
+
+CHAPTER IV
+
+CELESTIAL MECHANICS
+
+
+32. THE BEGINNINGS OF CELESTIAL MECHANICS.--From the earliest dawn of
+civilization, long before the beginnings of written history, the motions
+of sun and moon and planets among the stars from constellation to
+constellation had commanded the attention of thinking men, particularly
+of the class of priests. The religions of which they were the guardians
+and teachers stood in closest relations with the movements of the stars,
+and their own power and influence were increased by a knowledge of them.
+
+[Illustration: ISAAC NEWTON (1643-1727).]
+
+Out of these professional needs, as well as from a spirit of scientific
+research, there grew up and flourished for many centuries a study of the
+motions of the planets, simple and crude at first, because the
+observations that could then be made were at best but rough ones, but
+growing more accurate and more complex as the development of the
+mechanic arts put better and more precise instruments into the hands of
+astronomers and enabled them to observe with increasing accuracy the
+movements of these bodies. It was early seen that while for the most
+part the planets, including the sun and moon, traveled through the
+constellations from west to east, some of them sometimes reversed their
+motion and for a time traveled in the opposite way. This clearly can not
+be explained by the simple theory which had early been adopted that a
+planet moves always in the same direction around a circular orbit having
+the earth at its center, and so it was said to move around in a small
+circular orbit, called an epicycle, whose center was situated upon
+and moved along a circular orbit, called the deferent, within which the
+earth was placed, as is shown in Fig. 18, where the small circle is the
+epicycle, the large circle is the deferent, _P_ is the planet, and _E_
+the earth. When this proved inadequate to account for the really
+complicated movements of the planets, another epicycle was put on top of
+the first one, and then another and another, until the supposed system
+became so complicated that Copernicus, a Polish astronomer, repudiated
+its fundamental theorem and taught that the motions of the planets take
+place in circles around the sun instead of about the earth, and that the
+earth itself is only one of the planets moving around the sun in its own
+appropriate orbit and itself largely responsible for the seemingly
+erratic movements of the other planets, since from day to day we see
+them and observe their positions from different points of view.
+
+[Illustration: FIG. 18.--Epicycle and deferent.]
+
+33. KEPLER'S LAWS.--Two generations later came Kepler with his three
+famous laws of planetary motion:
+
+I. Every planet moves in an ellipse which has the sun at one of its
+foci.
+
+II. The radius vector of each planet moves over equal areas in equal
+times.
+
+III. The squares of the periodic times of the planets are proportional
+to the cubes of their mean distances from the sun.
+
+These laws are the crowning glory, not only of Kepler's career, but of
+all astronomical discovery from the beginning up to his time, and they
+well deserve careful study and explanation, although more modern
+progress has shown that they are only approximately true.
+
+EXERCISE 17.--Drive two pins into a smooth board an inch apart and
+fasten to them the ends of a string a foot long. Take up the slack of
+the string with the point of a lead pencil and, keeping the string drawn
+taut, move the pencil point over the board into every possible position.
+The curve thus traced will be an ellipse having the pins at the two
+points which are called its foci.
+
+In the case of the planetary orbits one focus of the ellipse is vacant,
+and, in accordance with the first law, the center of the sun is at the
+other focus. In Fig. 17 the dot, inside the orbit of Mercury, which is
+marked _a_, shows the position of the vacant focus of the orbit of Mars,
+and the dot _b_ is the vacant focus of Mercury's orbit. The orbits of
+Venus and the earth are so nearly circular that their vacant foci lie
+very close to the sun and are not marked in the figure. The line drawn
+from the sun to any point of the orbit (the string from pin to pencil
+point) is a _radius vector_. The point midway between the pins is the
+_center_ of the ellipse, and the distance of either pin from the center
+measures the _eccentricity_ of the ellipse.
+
+Draw several ellipses with the same length of string, but with the pins
+at different distances apart, and note that the greater the eccentricity
+the flatter is the ellipse, but that all of them have the same length.
+
+If both pins were driven into the same hole, what kind of an ellipse
+would you get?
+
+The Second Law was worked out by Kepler as his answer to a problem
+suggested by the first law. In Fig. 17 it is apparent from a mere
+inspection of the orbit of Mercury that this planet travels much faster
+on one side of its orbit than on the other, the distance covered in ten
+days between the numbers 10 and 20 being more than fifty per cent
+greater than that between 50 and 60. The same difference is found,
+though usually in less degree, for every other planet, and Kepler's
+problem was to discover a means by which to mark upon the orbit the
+figures showing the positions of the planet at the end of equal
+intervals of time. His solution of this problem, contained in the second
+law, asserts that if we draw radii vectors from the sun to each of the
+marked points taken at equal time intervals around the orbit, then the
+area of the sector formed by two adjacent radii vectores and the arc
+included between them is equal to the area of each and every other such
+sector, the short radii vectores being spread apart so as to include a
+long arc between them while the long radii vectores have a short arc. In
+Kepler's form of stating the law the radius vector is supposed to travel
+with the planet and in each day to sweep over the same fractional part
+of the total area of the orbit. The spacing of the numbers in Fig. 17
+was done by means of this law.
+
+For the proper understanding of Kepler's Third Law we must note that the
+"mean distance" which appears in it is one half of the long diameter of
+the orbit and that the "periodic time" means the number of days or years
+required by the planet to make a complete circuit in its orbit.
+Representing the first of these by _a_ and the second by _T_, we have,
+as the mathematical equivalent of the law,
+
+    a^{3} ÷ T^{2} = C
+
+where the quotient, _C_, is a number which, as Kepler found, is the same
+for every planet of the solar system. If we take the mean distance of
+the earth from the sun as the unit of distance, and the year as the unit
+of time, we shall find by applying the equation to the earth's motion,
+_C_ = 1. Applying this value to any other planet we shall find in the
+same units, _a_ = _T_^{2/3}, by means of which we may determine the
+distance of any planet from the sun when its periodic time, _T_, has
+been learned from observation.
+
+EXERCISE 18.--Uranus requires 84 years to make a revolution in its
+orbit. What is its mean distance from the sun? What are the mean
+distances of Mercury, Venus, and Mars? (See Chapter III for their
+periodic times.) Would it be possible for two planets at different
+distances from the sun to move around their orbits in the same time?
+
+A circle is an ellipse in which the two foci have been brought together.
+Would Kepler's laws hold true for such an orbit?
+
+34. NEWTON'S LAWS OF MOTION.--Kepler studied and described the motion of
+the planets. Newton, three generations later (1727 A. D.), studied and
+described the mechanism which controls that motion. To Kepler and his
+age the heavens were supernatural, while to Newton and his successors
+they are a part of Nature, governed by the same laws which obtain upon
+the earth, and we turn to the ordinary things of everyday life as the
+foundation of celestial mechanics.
+
+Every one who has ridden a bicycle knows that he can coast farther upon
+a level road if it is smooth than if it is rough; but however smooth and
+hard the road may be and however fast the wheel may have been started,
+it is sooner or later stopped by the resistance which the road and the
+air offer to its motion, and when once stopped or checked it can be
+started again only by applying fresh power. We have here a familiar
+illustration of what is called
+
+THE FIRST LAW OF MOTION.--"Every body continues in its state of rest or
+of uniform motion in a straight line except in so far as it may be
+compelled by force to change that state." A gust of wind, a stone, a
+careless movement of the rider may turn the bicycle to the right or the
+left, but unless some disturbing force is applied it will go straight
+ahead, and if all resistance to its motion could be removed it would go
+always at the speed given it by the last power applied, swerving neither
+to the one hand nor the other.
+
+When a slow rider increases his speed we recognize at once that he has
+applied additional power to the wheel, and when this speed is slackened
+it equally shows that force has been applied against the motion. It is
+force alone which can produce a change in either velocity or direction
+of motion; but simple as this law now appears it required the genius of
+Galileo to discover it and of Newton to give it the form in which it is
+stated above.
+
+35. THE SECOND LAW OF MOTION, which is also due to Galileo and Newton,
+is:
+
+"Change of motion is proportional to force applied and takes place in
+the direction of the straight line in which the force acts." Suppose a
+man to fall from a balloon at some great elevation in the air; his own
+weight is the force which pulls him down, and that force operating at
+every instant is sufficient to give him at the end of the first second
+of his fall a downward velocity of 32 feet per second--i. e., it has
+changed his state from rest, to motion at this rate, and the motion is
+toward the earth because the force acts in that direction. During the
+next second the ceaseless operation of this force will have the same
+effect as in the first second and will add another 32 feet to his
+velocity, so that two seconds from the time he commenced to fall he will
+be moving at the rate of 64 feet per second, etc. The column of figures
+marked _v_ in the table below shows what his velocity will be at the end
+of subsequent seconds. The changing velocity here shown is the change of
+motion to which the law refers, and the velocity is proportional to the
+time shown in the first column of the table, because the amount of force
+exerted in this case is proportional to the time during which it
+operated. The distance through which the man will fall in each second is
+shown in the column marked _d_, and is found by taking the average of
+his velocity at the beginning and end of this second, and the total
+distance through which he has fallen at the end of each second, marked
+_s_ in the table, is found by taking the sum of all the preceding values
+of _d_. The velocity, 32 feet per second, which measures the change of
+motion in each second, also measures the _accelerating force_ which
+produces this motion, and it is usually represented in formulę by the
+letter _g_. Let the student show from the numbers in the table that the
+accelerating force, the time, _t_, during which it operates, and the
+space, _s_, fallen through, satisfy the relation
+
+    s = 1/2 gt^{2},
+
+which is usually called the law of falling bodies. How does the table
+show that _g_ is equal to 32?
+
+            TABLE
+
+    _t_   _v_   _d_   _s_
+
+     0      0     0     0
+     1     32    16    16
+     2     64    48    64
+     3     96    80   144
+     4    128   112   256
+     5    160   144   400
+    etc.  etc.  etc.  etc.
+
+If the balloon were half a mile high how long would it take to fall to
+the ground? What would be the velocity just before reaching the ground?
+
+[Illustration: GALILEO GALILEI (1564-1642).]
+
+Fig. 19 shows the path through the air of a ball which has been struck
+by a bat at the point _A_, and started off in the direction _A B_ with a
+velocity of 200 feet per second. In accordance with the first law of
+motion, if it were acted upon by no other force than the impulse given
+by the bat, it should travel along the straight line _A B_ at the
+uniform rate of 200 feet per second, and at the end of the fourth second
+it should be 800 feet from _A_, at the point marked 4, but during these
+four seconds its weight has caused it to fall 256 feet, and its actual
+position, 4', is 256 feet below the point 4. In this way we find its
+position at the end of each second, 1', 2', 3', 4', etc., and drawing a
+line through these points we shall find the actual path of the ball
+under the influence of the two forces to be the curved line _A C_. No
+matter how far the ball may go before striking the ground, it can not
+get back to the point _A_, and the curve _A C_ therefore can not be a
+part of a circle, since that curve returns into itself. It is, in fact,
+a part of a _parabola_, which, as we shall see later, is a kind of orbit
+in which comets and some other heavenly bodies move. A skyrocket moves
+in the same kind of a path, and so does a stone, a bullet, or any other
+object hurled through the air.
+
+[Illustration: FIG. 19.--The path of a ball.]
+
+36. THE THIRD LAW OF MOTION.--"To every action there is always an equal
+and contrary reaction; or the mutual actions of any two bodies are
+always equal and oppositely directed." This is well illustrated in the
+case of a man climbing a rope hand over hand. The direct force or action
+which he exerts is a downward pull upon the rope, and it is the reaction
+of the rope to this pull which lifts him along it. We shall find in a
+later chapter a curious application of this law to the history of the
+earth and moon.
+
+It is the great glory of Sir Isaac Newton that he first of all men
+recognized that these simple laws of motion hold true in the heavens as
+well as upon the earth; that the complicated motion of a planet, a
+comet, or a star is determined in accordance with these laws by the
+forces which act upon the bodies, and that these forces are essentially
+the same as that which we call weight. The formal statement of the
+principle last named is included in--
+
+37. NEWTON'S LAW OF GRAVITATION.--"Every particle of matter in the
+universe attracts every other particle with a force whose direction is
+that of a line joining the two, and whose magnitude is directly as the
+product of their masses, and inversely as the square of their distance
+from each other." We know that we ourselves and the things about us are
+pulled toward the earth by a force (weight) which is called, in the
+Latin that Newton wrote, _gravitas_, and the word marks well the true
+significance of the law of gravitation. Newton did not discover a new
+force in the heavens, but he extended an old and familiar one from a
+limited terrestrial sphere of action to an unlimited and celestial one,
+and furnished a precise statement of the way in which the force
+operates. Whether a body be hot or cold, wet or dry, solid, liquid, or
+gaseous, is of no account in determining the force which it exerts,
+since this depends solely upon mass and distance.
+
+The student should perhaps be warned against straining too far the
+language which it is customary to employ in this connection. The law of
+gravitation is certainly a far-reaching one, and it may operate in every
+remotest corner of the universe precisely as stated above, but
+additional information about those corners would be welcome to
+supplement our rather scanty stock of knowledge concerning what happens
+there. We may not controvert the words of a popular preacher who says,
+"When I lift my hand I move the stars in Ursa Major," but we should not
+wish to stand sponsor for them, even though they are justified by a
+rigorous interpretation of the Newtonian law.
+
+The word _mass_, in the statement of the law of gravitation, means the
+quantity of matter contained in the body, and if we represent by the
+letters _m“_ and _m““_ the respective quantities of matter contained in
+the two bodies whose distance from each other is _r_, we shall have, in
+accordance with the law of gravitation, the following mathematical
+expression for the force, _F_, which acts between them:
+
+    F = k {m“m““/r^{2}}.
+
+This equation, which is the general mathematical expression for the law
+of gravitation, may be made to yield some curious results. Thus, if we
+select two bullets, each having a mass of 1 gram, and place them so that
+their centers are 1 centimeter apart, the above expression for the force
+exerted between them becomes
+
+    F = k {(1 × 1)/1^{2}} = k,
+
+from which it appears that the coefficient _k_ is the force exerted
+between these bodies. This is called the gravitation constant, and it
+evidently furnishes a measure of the specific intensity with which one
+particle of matter attracts another. Elaborate experiments which have
+been made to determine the amount of this force show that it is
+surprisingly small, for in the case of the two bullets whose mass of 1
+gram each is supposed to be concentrated into an indefinitely small
+space, gravity would have to operate between them continuously for more
+than forty minutes in order to pull them together, although they were
+separated by only 1 centimeter to start with, and nothing save their own
+inertia opposed their movements. It is only when one or both of the
+masses _m“_, _m““_ are very great that the force of gravity becomes
+large, and the weight of bodies at the surface of the earth is
+considerable because of the great quantity of matter which goes to make
+up the earth. Many of the heavenly bodies are much more massive than the
+earth, as the mathematical astronomers have found by applying the law of
+gravitation to determine numerically their masses, or, in more popular
+language, to "weigh" them.
+
+The student should observe that the two terms mass and weight are not
+synonymous; mass is defined above as the quantity of matter contained in
+a body, while weight is the force with which the earth attracts that
+body, and in accordance with the law of gravitation its weight depends
+upon its distance from the center of the earth, while its mass is quite
+independent of its position with respect to the earth.
+
+By the third law of motion the earth is pulled toward a falling body
+just as strongly as the body is pulled toward the earth--i. e., by a
+force equal to the weight of the body. How much does the earth rise
+toward the body?
+
+38. THE MOTION OF A PLANET.--In Fig. 20 _S_ represents the sun and _P_ a
+planet or other celestial body, which for the moment is moving along the
+straight line _P 1_. In accordance with the first law of motion it would
+continue to move along this line with uniform velocity if no external
+force acted upon it; but such a force, the sun's attraction, is acting,
+and by virtue of this attraction the body is pulled aside from the line
+_P 1_.
+
+Knowing the velocity and direction of the body's motion and the force
+with which the sun attracts it, the mathematician is able to apply
+Newton's laws of motion so as to determine the path of the body, and a
+few of the possible orbits are shown in the figure where the short cross
+stroke marks the point of each orbit which is nearest to the sun. This
+point is called the _perihelion_.
+
+Without any formal application of mathematics we may readily see that
+the swifter the motion of the body at _P_ the shorter will be the time
+during which it is subjected to the sun's attraction at close range, and
+therefore the force exerted by the sun, and the resulting change of
+motion, will be small, as in the orbits _P 1_ and _P 2_.
+
+On the other hand, _P 5_ and _P 6_ represent orbits in which the
+velocity at _P_ was comparatively small, and the resulting change of
+motion greater than would be possible for a more swiftly moving body.
+
+What would be the orbit if the velocity at _P_ were reduced to nothing
+at all?
+
+What would be the effect if the body starting at _P_ moved directly away
+from _1_?
+
+[Illustration: FIG. 20.--Different kinds of orbits.]
+
+The student should not fail to observe that the sun's attraction tends
+to pull the body at _P_ forward along its path, and therefore increases
+its velocity, and that this influence continues until the planet reaches
+perihelion, at which point it attains its greatest velocity, and the
+force of the sun's attraction is wholly expended in changing the
+direction of its motion. After the planet has passed perihelion the sun
+begins to pull backward and to retard the motion in just the same
+measure that before perihelion passage it increased it, so that the two
+halves of the orbit on opposite sides of a line drawn from the
+perihelion through the sun are exactly alike. We may here note the
+explanation of Kepler's second law: when the planet is near the sun it
+moves faster, and the radius vector changes its direction more rapidly
+than when the planet is remote from the sun on account of the greater
+force with which it is attracted, and the exact relation between the
+rates at which the radius vector turns in different parts of the orbit,
+as given by the second law, depends upon the changes in this force.
+
+When the velocity is not too great, the sun's backward pull, after a
+planet has passed perihelion, finally overcomes it and turns the planet
+toward the sun again, in such a way that it comes back to the point _P_,
+moving in the same direction and with the same speed as before--i. e.,
+it has gone around the sun in an orbit like _P 6_ or _P 4_, an ellipse,
+along which it will continue to move ever after. But we must not fail to
+note that this return into the same orbit is a consequence of the last
+line in the statement of the law of gravitation (p. 54), and that, if
+the magnitude of this force were inversely as the cube of the distance
+or any other proportion than the square, the orbit would be something
+very different. If the velocity is too great for the sun's attraction to
+overcome, the orbit will be a hyperbola, like _P 2_, along which the
+body will move away never to return, while a velocity just at the limit
+of what the sun can control gives an orbit like _P 3_, a parabola, along
+which the body moves with _parabolic velocity_, which is ever
+diminishing as the body gets farther from the sun, but is always just
+sufficient to keep it from returning. If the earth's velocity could be
+increased 41 per cent, from 19 up to 27 miles per second, it would have
+parabolic velocity, and would quit the sun's company.
+
+The summation of the whole matter is that the orbit in which a body
+moves around the sun, or past the sun, depends upon its velocity and if
+this velocity and the direction of the motion at any one point in the
+orbit are known the whole orbit is determined by them, and the position
+of the planet in its orbit for past as well as future times can be
+determined through the application of Newton's laws; and the same is
+true for any other heavenly body--moon, comet, meteor, etc. It is in
+this way that astronomers are able to predict, years in advance, in what
+particular part of the sky a given planet will appear at a given time.
+
+It is sometimes a source of wonder that the planets move in ellipses
+instead of circles, but it is easily seen from Fig. 20 that the planet,
+_P_, could not by any possibility move in a circle, since the direction
+of its motion at _P_ is not at right angles with the line joining it to
+the sun as it must be in a circular orbit, and even if it were
+perpendicular to the radius vector the planet must needs have exactly
+the right velocity given to it at this point, since either more or less
+speed would change the circle into an ellipse. In order to produce
+circular motion there must be a balancing of conditions as nice as is
+required to make a pin stand upon its point, and the really surprising
+thing is that the orbits of the planets should be so nearly circular as
+they are. If the orbit of the earth were drawn accurately to scale, the
+untrained eye would not detect the slightest deviation from a true
+circle, and even the orbit of Mercury (Fig. 17), which is much more
+eccentric than that of the earth, might almost pass for a circle.
+
+[Illustration: FIG. 21. An impossible orbit.]
+
+The orbit _P 2_, which lies between the parabola and the straight line,
+is called in geometry a hyperbola, and Newton succeeded in proving from
+the law of gravitation that a body might move under the sun's attraction
+in a hyperbola as well as in a parabola or ellipse; but it must move in
+some one of these curves; no other orbit is possible.[1] Thus it would
+not be possible for a body moving under the law of gravitation to
+describe about the sun any such orbit as is shown in Fig. 21. If the
+body passes a second time through any point of its orbit, such as _P_ in
+the figure, then it must retrace, time after time, the whole path that
+it first traversed in getting from _P_ around to _P_ again--i. e., the
+orbit must be an ellipse.
+
+  [1] The circle and straight line are considered to be special cases
+      of these curves, which, taken collectively, are called the conic
+      sections.
+
+Newton also proved that Kepler's three laws are mere corollaries from
+the law of gravitation, and that to be strictly correct the third law
+must be slightly altered so as to take into account the masses of the
+planets. These are, however, so small in comparison with that of the
+sun, that the correction is of comparatively little moment.
+
+39. PERTURBATIONS.--In what precedes we have considered the motion of a
+planet under the influence of no other force than the sun's attraction,
+while in fact, as the law of gravitation asserts, every other body in
+the universe is in some measure attracting it and changing its motion.
+The resulting disturbances in the motion of the attracted body are
+called _perturbations_, but for the most part these are insignificant,
+because the bodies by whose disturbing attractions they are caused are
+either very small or very remote, and it is only when our moving planet,
+_P_, comes under the influence of some great disturbing power like
+Jupiter or one of the other planets that the perturbations caused by
+their influence need to be taken into account.
+
+The problem of the motion of three bodies--sun, Jupiter, planet--which
+must then be dealt with is vastly more complicated than that which we
+have considered, and the ablest mathematicians and astronomers have not
+been able to furnish a complete solution for it, although they have
+worked upon the problem for two centuries, and have developed an immense
+amount of detailed information concerning it.
+
+[Illustration: THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.]
+
+In general each planet works ceaselessly upon the orbit of every other,
+changing its size and shape and position, backward and forward in
+accordance with the law of gravitation, and it is a question of serious
+moment how far this process may extend. If the diameter of the earth's
+orbit were very much increased or diminished by the perturbing action of
+the other planets, the amount of heat received from the sun would be
+correspondingly changed, and the earth, perhaps, be rendered unfit
+for the support of life. The tipping of the plane of the earth's orbit
+into a new position might also produce serious consequences; but the
+great French mathematician of a century ago, Laplace, succeeded in
+proving from the law of gravitation that although both of these changes
+are actually in progress they can not, at least for millions of years,
+go far enough to prove of serious consequence, and the same is true for
+all the other planets, unless here and there an asteroid may prove an
+exception to the rule.
+
+The precession (Chapter V) is a striking illustration of a perturbation
+of slightly different character from the above, and another is found in
+connection with the plane of the moon's orbit. It will be remembered
+that the moon in its motion among the stars never goes far from the
+ecliptic, but in a complete circuit of the heavens crosses it twice,
+once in going from south to north and once in the opposite direction.
+The points at which it crosses the ecliptic are called the _nodes_, and
+under the perturbing influence of the sun these nodes move westward
+along the ecliptic about twenty degrees per year, an extraordinarily
+rapid perturbation, and one of great consequence in the theory of
+eclipses.
+
+[Illustration: FIG. 22.--A planet subject to great perturbations by
+Jupiter.]
+
+40. WEIGHING THE PLANETS.--Although these perturbations can not be
+considered dangerous, they are interesting since they furnish a method
+for weighing the planets which produce them. From the law of gravitation
+we learn that the ability of a planet to produce perturbations depends
+directly upon its mass, since the force _F_ which it exerts contains
+this mass, _m“_, as a factor. So, too, the divisor _r^{2}_ in the
+expression for the force shows that the distance between the disturbing
+and disturbed bodies is a matter of great consequence, for the smaller
+the distance the greater the force. When, therefore, the mass of a
+planet such as Jupiter is to be determined from the perturbations it
+produces, it is customary to select some such opportunity as is
+presented in Fig. 22, where one of the small planets, called asteroids,
+is represented as moving in a very eccentric orbit, which at one point
+approaches close to the orbit of Jupiter, and at another place comes
+near to the orbit of the earth. For the most part Jupiter will not exert
+any very great disturbing influence upon a planet moving in such an
+orbit as this, since it is only at rare intervals that the asteroid and
+Jupiter approach so close to each other, as is shown in the figure. The
+time during which the asteroid is little affected by the attraction of
+Jupiter is used to study the motion given to it by the sun's
+attraction--that is, to determine carefully the undisturbed orbit in
+which it moves; but there comes a time at which the asteroid passes
+close to Jupiter, as shown in the figure, and the orbital motion which
+the sun imparts to it will then be greatly disturbed, and when the
+planet next comes round to the part of its orbit near the earth the
+effect of these disturbances upon its apparent position in the sky will
+be exaggerated by its close proximity to the earth. If now the
+astronomer observes the actual position of the asteroid in the sky, its
+right ascension and declination, and compares these with the position
+assigned to the planet by the law of gravitation when the attraction of
+Jupiter is ignored, the differences between the observed right
+ascensions and declinations and those computed upon the theory of
+undisturbed motion will measure the influence that Jupiter has had upon
+the asteroid, and the amount by which Jupiter has shifted it, compared
+with the amount by which the sun has moved it--that is, with the motion
+in its orbit--furnishes the mass of Jupiter expressed as a fractional
+part of the mass of the sun.
+
+There has been determined in this manner the mass of every planet in the
+solar system which is large enough to produce any appreciable
+perturbation, and all these masses prove to be exceedingly small
+fractions of the mass of the sun, as may be seen from the following
+table, in which is given opposite the name of each planet the number by
+which the mass of the sun must be divided in order to get the mass of
+the planet:
+
+    Mercury      7,000,000 (?)
+    Venus          408,000
+    Earth          329,000
+    Mars         3,093,500
+    Jupiter          1,047.4
+    Saturn           3,502
+    Uranus          22,800
+    Neptune         19,700
+
+It is to be especially noted that the mass given for each planet
+includes the mass of all the satellites which attend it, since their
+influence was felt in the perturbations from which the mass was derived.
+Thus the mass assigned to the earth is the combined mass of earth and
+moon.
+
+41. DISCOVERY OF NEPTUNE.--The most famous example of perturbations is
+found in connection with the discovery, in the year 1846, of Neptune,
+the outermost planet of the solar system. For many years the motion of
+Uranus, his next neighbor, had proved a puzzle to astronomers. In
+accordance with Kepler's first law this planet should move in an ellipse
+having the sun at one of its foci, but no ellipse could be found which
+exactly fitted its observed path among the stars, although, to be sure,
+the misfit was not very pronounced. Astronomers surmised that the small
+deviations of Uranus from the best path which theory combined with
+observation could assign, were due to perturbations in its motion
+caused by an unknown planet more remote from the sun--a thing easy to
+conjecture but hard to prove, and harder still to find the unknown
+disturber. But almost simultaneously two young men, Adams in England and
+Le Verrier in France, attacked the problem quite independently of each
+other, and carried it to a successful solution, showing that if the
+irregularities in the motion of Uranus were indeed caused by an unknown
+planet, then that planet must, in September, 1846, be in the direction
+of the constellation Aquarius; and there it was found on September 23d
+by the astronomers of the Berlin Observatory whom Le Verrier had invited
+to search for it, and found within a degree of the exact point which the
+law of gravitation in his hands had assigned to it.
+
+This working backward from the perturbations experienced by Uranus to
+the cause which produced them is justly regarded as one of the greatest
+scientific achievements of the human intellect, and it is worthy of note
+that we are approaching the time at which it may be repeated, for
+Neptune now behaves much as did Uranus three quarters of a century ago,
+and the most plausible explanation which can be offered for these
+anomalies in its path is that the bounds of the solar system must be
+again enlarged to include another disturbing planet.
+
+42. THE SHAPE OF A PLANET.--There is an effect of gravitation not yet
+touched upon, which is of considerable interest and wide application in
+astronomy--viz., its influence in determining the shape of the heavenly
+bodies. The earth is a globe because every part of it is drawn toward
+the center by the attraction of the other parts, and if this attraction
+on its surface were everywhere of equal force the material of the earth
+would be crushed by it into a truly spherical form, no matter what may
+have been the shape in which it was originally made. But such is not the
+real condition of the earth, for its diurnal rotation develops in every
+particle of its body a force which is sometimes called _centrifugal_,
+but which is really nothing more than the inertia of its particles,
+which tend at every moment to keep unchanged the direction of their
+motion and which thus resist the attraction that pulls them into a
+circular path marked out by the earth's rotation, just as a stone tied
+at the end of a string and swung swiftly in a circle pulls upon the
+string and opposes the constraint which keeps it moving in a circle. A
+few experiments with such a stone will show that the faster it goes the
+harder does it pull upon the string, and the same is true of each
+particle of the earth, the swiftly moving ones near the equator having a
+greater centrifugal force than the slow ones near the poles. At the
+equator the centrifugal force is directly opposed to the force of
+gravity, and in effect diminishes it, so that, comparatively, there is
+an excess of gravity at the poles which compresses the earth along its
+axis and causes it to bulge out at the equator until a balance is thus
+restored. As we have learned from the study of geography, in the case of
+the earth, this compression amounts to about 27 miles, but in the larger
+planets, Jupiter and Saturn, it is much greater, amounting to several
+thousand miles.
+
+But rotation is not the only influence that tends to pull a planet out
+of shape. The attraction which the earth exerts upon the moon is
+stronger on the near side and weaker on the far side of our satellite
+than at its center, and this difference of attraction tends to warp the
+moon, as is illustrated in Fig. 23 where _1_, _2_, and _3_ represent
+pieces of iron of equal mass placed in line on a table near a horseshoe
+magnet, _H_. Each piece of iron is attracted by the magnet and is held
+back by a weight to which it is fastened by means of a cord running over
+a pulley, _P_, at the edge of the table. These weights are all to be
+supposed equally heavy and each of them pulls upon its piece of iron
+with a force just sufficient to balance the attraction of the magnet for
+the middle piece, No. _2_. It is clear that under this arrangement No.
+_2_ will move neither to the right nor to the left, since the forces
+exerted upon it by the magnet and the weight just balance each other.
+Upon No. _1_, however, the magnet pulls harder than upon No. _2_,
+because it is nearer and its pull therefore more than balances the force
+exerted by the weight, so that No. _1_ will be pulled away from No. _2_
+and will stretch the elastic cords, which are represented by the lines
+joining _1_ and _2_, until their tension, together with the force
+exerted by the weight, just balances the attraction of the magnet. For
+No. _3_, the force exerted by the magnet is less than that of the
+weight, and it will also be pulled away from No. _2_ until its elastic
+cords are stretched to the proper tension. The net result is that the
+three blocks which, without the magnet's influence, would be held close
+together by the elastic cords, are pulled apart by this outside force as
+far as the resistance of the cords will permit.
+
+[Illustration: FIG. 23.--Tide-raising forces.]
+
+An entirely analogous set of forces produces a similar effect upon the
+shape of the moon. The elastic cords of Fig. 23 stand for the attraction
+of gravitation by which all the parts of the moon are bound together.
+The magnet represents the earth pulling with unequal force upon
+different parts of the moon. The weights are the inertia of the moon in
+its orbital motion which, as we have seen in a previous section, upon
+the whole just balances the earth's attraction and keeps the moon from
+falling into it. The effect of these forces is to stretch out the moon
+along a line pointing toward the earth, just as the blocks were
+stretched out along the line of the magnet, and to make this diameter of
+the moon slightly but permanently longer than the others.
+
+[Illustration: FIG. 24.--The tides.]
+
+THE TIDES.--Similarly the moon and the sun attract opposite sides of the
+earth with different forces and feebly tend to pull it out of shape. But
+here a new element comes into play: the earth turns so rapidly upon its
+axis that its solid parts have no time in which to yield sensibly to the
+strains, which shift rapidly from one diameter to another as different
+parts of the earth are turned toward the moon, and it is chiefly the
+waters of the sea which respond to the distorting effect of the sun's
+and moon's attraction. These are heaped up on opposite sides of the
+earth so as to produce a slight elongation of its diameter, and Fig. 24
+shows how by the earth's rotation this swelling of the waters is swept
+out from under the moon and is pulled back by the moon until it finally
+takes up some such position as that shown in the figure where the effect
+of the earth's rotation in carrying it one way is just balanced by the
+moon's attraction urging it back on line with the moon. This heaping up
+of the waters is called a _tide_. If _I_ in the figure represents a
+little island in the sea the waters which surround it will of course
+accompany it in its diurnal rotation about the earth's axis, but
+whenever the island comes back to the position _I_, the waters will
+swell up as a part of the tidal wave and will encroach upon the land in
+what is called high tide or flood tide. So too when they reach _I““_,
+half a day later, they will again rise in flood tide, and midway between
+these points, at _I“_, the waters must subside, giving low or ebb tide.
+
+The height of the tide raised by the moon in the open sea is only a very
+few feet, and the tide raised by the sun is even less, but along the
+coast of a continent, in bays and angles of the shore, it often happens
+that a broad but low tidal wave is forced into a narrow corner, and then
+the rise of the water may be many feet, especially when the solar tide
+and the lunar tide come in together, as they do twice in every month, at
+new and full moon. Why do they come together at these times instead of
+some other?
+
+Small as are these tidal effects, it is worth noting that they may in
+certain cases be very much greater--e. g., if the moon were as massive
+as is the sun its tidal effect would be some millions of times greater
+than it now is and would suffice to grind the earth into fragments.
+Although the earth escapes this fate, some other bodies are not so
+fortunate, and we shall see in later chapters some evidence of their
+disintegration.
+
+43. THE SCOPE OF THE LAW OF GRAVITATION.--In all the domain of physical
+science there is no other law so famous as the Newtonian law of
+gravitation; none other that has been so dwelt upon, studied, and
+elaborated by astronomers and mathematicians, and perhaps none that can
+be considered so indisputably proved. Over and over again mathematical
+analysis, based upon this law, has pointed out conclusions which, though
+hitherto unsuspected, have afterward been found true, as when Newton
+himself derived as a corollary from this law that the earth ought to be
+flattened at the poles--a thing not known at that time, and not proved
+by actual measurement until long afterward. It is, in fact, this
+capacity for predicting the unknown and for explaining in minutest
+detail the complicated phenomena of the heavens and the earth that
+constitutes the real proof of the law of gravitation, and it is
+therefore worth while to note that at the present time there are a very
+few points at which the law fails to furnish a satisfactory account of
+things observed. Chief among these is the case of the planet Mercury,
+the long diameter of whose orbit is slowly turning around in a way for
+which the law of gravitation as yet furnishes no explanation. Whether
+this is because the law itself is inaccurate or incomplete, or whether
+it only marks a case in which astronomers have not yet properly applied
+the law and traced out its consequences, we do not know; but whether it
+be the one or the other, this and other similar cases show that even
+here, in its most perfect chapter, astronomy still remains an incomplete
+science.
+
+
+
+
+CHAPTER V
+
+THE EARTH AS A PLANET
+
+
+44. THE SIZE OF THE EARTH.--The student is presumed to have learned, in
+his study of geography, that the earth is a globe about 8,000 miles in
+diameter and, without dwelling upon the "proofs" which are commonly
+given for these statements, we proceed to consider the principles upon
+which the measurement of the earth's size and shape are based.
+
+[Illustration: FIG. 25.--Measuring the size of the earth.]
+
+In Fig. 25 the circle represents a meridian section of the earth; _P P“_
+is the axis about which it rotates, and the dotted lines represent a
+beam of light coming from a star in the plane of the meridian, and so
+distant that the dotted lines are all practically parallel to each
+other. The several radii drawn through the points _1_, _2_, _3_,
+represent the direction of the vertical at these points, and the angles
+which these radii produced, make with the rays of starlight are each
+equal to the angular distance of the star from the zenith of the place
+at the moment the star crosses the meridian. We have already seen, in
+Chapter II, how these angles may be measured, and it is apparent from
+the figure that the difference between any two of these angles--e. g.,
+the angles at _1_ and _2_--is equal to the angle at the center, _O_,
+between the points _1_ and _2_. By measuring these angular distances of
+the star from the zenith, the astronomer finds the angles at the center
+of the earth between the stations _1_, _2_, _3_, etc., at which his
+observations are made. If the meridian were a perfect circle the change
+of zenith distance of the star, as one traveled along a meridian from
+the equator to the pole, would be perfectly uniform--the same number of
+degrees for each hundred miles traveled--and observations made in many
+parts of the earth show that this is very nearly true, but that, on the
+whole, as we approach the pole it is necessary to travel a little
+greater distance than is required for a given change in the angle at the
+equator. The earth is, in fact, flattened at the poles to the amount of
+about 27 miles in the length of its diameter, and by this amount, as
+well as by smaller variations due to mountains and valleys, the shape of
+the earth differs from a perfect sphere. These astronomical measurements
+of the curvature of the earth's surface furnish by far the most
+satisfactory proof that it is very approximately a sphere, and furnish
+as its equatorial diameter 7,926 miles.
+
+Neglecting the _compression_, as it is called, i. e., the 27 miles by
+which the equatorial diameter exceeds the polar, the size of the earth
+may easily be found by measuring the distance _1_--_2_ along the
+surface and by combining with this the angle _1 O 2_ obtained through
+measuring the meridian altitudes of any star as seen from _1_ and _2_.
+Draw on paper an angle equal to the measured difference of altitude and
+find how far you must go from its vertex in order to have the distance
+between the sides, measured along an arc of a circle, equal to the
+measured distance between _1_ and _2_. This distance from the vertex
+will be the earth's radius.
+
+EXERCISE 19.--Measure the diameter of the earth by the method given
+above. In order that this may be done satisfactorily, the two stations
+at which observations are made must be separated by a considerable
+distance--i. e., 200 miles. They need not be on the same meridian, but
+if they are on different meridians in place of the actual distance
+between them, there must be used the projection of that distance upon
+the meridian--i. e., the north and south part of the distance.
+
+By co-operation between schools in the Northern and Southern States,
+using a good map to obtain the required distances, the diameter of the
+earth may be measured with the plumb-line apparatus described in Chapter
+II and determined within a small percentage of its true value.
+
+45. THE MASS OF THE EARTH.--We have seen in Chapter IV the possibility
+of determining the masses of the planets as fractional parts of the
+sun's mass, but nothing was there shown, or could be shown, about
+measuring these masses after the common fashion in kilogrammes or tons.
+To do this we must first get the mass of the earth in tons or
+kilogrammes, and while the principles involved in this determination are
+simple enough, their actual application is delicate and difficult.
+
+[Illustration: FIG. 26.--Illustrating the principles involved in
+weighing the earth.]
+
+In Fig. 26 we suppose a long plumb line to be suspended above the
+surface of the earth and to be attracted toward the center of the earth,
+_C_, by a force whose intensity is (Chapter IV)
+
+    F = k mE/R^{2},
+
+where _E_ denotes the mass of the earth, which is to be determined by
+experiment, and _R_ is the radius of the earth, 3,963 miles. If there is
+no disturbing influence present, the plumb line will point directly
+downward, but if a massive ball of lead or other heavy substance is
+placed at one side, _1_, it will attract the plumb line with a force
+equal to
+
+    f = k mB/r^{2},
+
+where _r_ is the distance of its center from the plumb bob and _B_ is
+its mass which we may suppose, for illustration, to be a ton. In
+consequence of this attraction the plumb line will be pulled a little to
+one side, as shown by the dotted line, and if we represent by _l_ the
+length of the plumb line and by _d_ the distance between the original
+and the disturbed positions of the plumb bob we may write the proportion
+
+    F : f :: l : d;
+
+and introducing the values of _F_ and _f_ given above, and solving for
+_E_ the proportion thus transformed, we find
+
+    E = B × l/d × (R/r)^{2}.
+
+In this equation the mass of the ball, _B_, the length of the plumb
+line, _l_, the distance between the center of the ball and the center of
+the plumb bob, _r_, and the radius of the earth, _R_, can all be
+measured directly, and _d_, the amount by which the plumb bob is pulled
+to one side by the ball, is readily found by shifting the ball over to
+the other side, at _2_, and measuring with a microscope how far the
+plumb bob moves. This distance will, of course, be equal to _2 d_.
+
+By methods involving these principles, but applied in a manner more
+complicated as well as more precise, the mass of the earth is found to
+be, in tons, 6,642 × 10^{18}--i. e., 6,642 followed by 18 ciphers, or in
+kilogrammes 60,258 × 10^{20}. The earth's atmosphere makes up about a
+millionth part of this mass.
+
+If the length of the plumb line were 100 feet, the weight of the ball a
+ton, and the distance between the two positions of the ball, _1_ and
+_2_, six feet, how many inches, _d_, would the plumb bob be pulled out
+of place?
+
+Find from the mass of the earth and the data of § 40 the mass of the sun
+in tons. Find also the mass of Mars. The computation can be very greatly
+abridged by the use of logarithms.
+
+46. PRECESSION.--That the earth is isolated in space and has no support
+upon which to rest, is sufficiently shown by the fact that the stars are
+visible upon every side of it, and no support can be seen stretching out
+toward them. We must then consider the earth to be a globe traveling
+freely about the sun in a circuit which it completes once every year,
+and rotating once in every twenty-four hours about an axis which remains
+at all seasons directed very nearly toward the star Polaris. The student
+should be able to show from his own observations of the sun that, with
+reference to the stars, the direction of the sun from the earth changes
+about a degree a day. Does this prove that the earth revolves about the
+sun?
+
+But it is only in appearance that the pole maintains its fixed position
+among the stars. If photographs are taken year after year, after the
+manner of Exercise 7, it will be found that slowly the pole is moving
+(nearly) toward Polaris, and making this star describe a smaller and
+smaller circle in its diurnal path, while stars on the other side of the
+pole (in right ascension 12h.) become more distant from it and describe
+larger circles in their diurnal motion; but the process takes place so
+slowly that the space of a lifetime is required for the motion of the
+pole to equal the angular diameter of the full moon.
+
+Spin a top and note how its rapid whirl about its axis corresponds to
+the earth's diurnal rotation. When the axis about which the top spins is
+truly vertical the top "sleeps"; but if the axis is tipped ever so
+little away from the vertical it begins to wobble, so that if we imagine
+the axis prolonged out to the sky and provided with a pencil point as a
+marker, this would trace a circle around the zenith, along which the
+pole of the top would move, and a little observation will show that the
+more the top is tipped from the vertical the larger does this circle
+become and the more rapidly does the wobbling take place. Were it not
+for the spinning of the top about its axis, it would promptly fall over
+when tipped from the vertical position, but the spin combines with the
+force which pulls the top over and produces the wobbling motion. Spin
+the top in opposite directions, with the hands of a watch and contrary
+to the hands of a watch, and note the effect which is produced upon the
+wobbling.
+
+The earth presents many points of resemblance to the top. Its diurnal
+rotation is the spin about the axis. This axis is tipped 23.5° away from
+the perpendicular to its orbit (obliquity of the ecliptic) just as the
+axis of the top is tipped away from the vertical line. In consequence of
+its rapid spin, the body of the earth bulges out at the equator (27
+miles), and the sun and moon, by virtue of their attraction (see Chapter
+IV), lay hold of this protuberance and pull it down toward the plane of
+the earth's orbit, so that if it were not for the spin this force would
+straighten the axis up and set it perpendicular to the orbit plane. But
+here, as in the case of the top, the spin and the tipping force combine
+to produce a wobble which is called precession, and whose effect we
+recognize in the shifting position of the pole among the stars. The
+motion of precession is very much slower than the wobbling of the top,
+since the tipping force for the earth is relatively very small, and a
+period of nearly 26,000 years is required for a complete circuit of the
+pole about its center of motion. Friction ultimately stops both the spin
+and the wobble of the top, but this influence seems wholly absent in the
+case of the earth, and both rotation and precession go on unchanged from
+century to century, save for certain minor forces which for a time
+change the direction or rate of the precessional motion, first in one
+way and then in another, without in the long run producing any results
+of consequence.
+
+The center of motion, about which the pole travels in a small circle
+having an angular radius of 23.5°, is at that point of the heavens
+toward which a perpendicular to the plane of the earth's orbit points,
+and may be found on the star map in right ascension 18h. 0m. and
+declination 66.5°.
+
+EXERCISE 20.--Find this point on the map, and draw as well as you can
+the path of the pole about it. The motion of the pole along its path is
+toward the constellation Cepheus. Mark the position of the pole along
+this path at intervals of 1,000 years, and refer to these positions in
+dealing with some of the following questions:
+
+Does the wobbling of the top occur in the same direction as the motion
+of precession? Do the tipping forces applied to the earth and top act in
+the same direction? What will be the polar star 12,000 years hence? The
+Great Pyramid of Egypt is thought to have been used as an observatory
+when Alpha Draconis was the bright star nearest the pole. How long ago
+was that?
+
+The motion of the pole of course carries the equator and the equinoxes
+with it, and thus slowly changes the right ascensions and declinations
+of all the stars. On this account it is frequently called the precession
+of the equinoxes, and this motion of the equinox, slow though it is, is
+a matter of some consequence in connection with chronology and the
+length of the year.
+
+Will the precession ever bring back the right ascensions and
+declinations to be again what they now are?
+
+In what direction is the pole moving with respect to the Big Dipper?
+Will its motion ever bring it exactly to Polaris? How far away from
+Polaris will the precession carry the pole? What other bright stars will
+be brought near the pole by the precession?
+
+47. THE WARMING OF THE EARTH.--Winter and summer alike the day is on the
+average warmer than the night, and it is easy to see that this surplus
+of heat comes from the sun by day and is lost by night through radiation
+into the void which surrounds the earth; just as the heat contained in a
+mass of molten iron is radiated away and the iron cooled when it is
+taken out from the furnace and placed amid colder surroundings. The
+earth's loss of heat by radiation goes on ceaselessly day and night,
+and were it not for the influx of solar heat this radiation would
+steadily diminish the temperature toward what is called the "absolute
+zero"--i. e., a state in which all heat has been taken away and beyond
+which there can be no greater degree of cold. This must not be
+confounded with the zero temperatures shown by our thermometers,
+since it lies nearly 500° below the zero of the Fahrenheit scale (-273°
+Centigrade), a temperature which by comparison makes the coldest winter
+weather seem warm, although the ordinary thermometer may register
+many degrees below its zero. The heat radiated by the sun into the
+surrounding space on every side of it is another example of the same
+cooling process, a hot body giving up its heat to the colder space about
+it, and it is the minute fraction of this heat poured out by the sun,
+and in small part intercepted by the earth, which warms the latter and
+produces what we call weather, climate, the seasons, etc.
+
+Observe the fluctuations, the ebb and flow, which are inherent in this
+process. From sunset to sunrise there is nothing to compensate the
+steady outflow of heat, and air and ground grow steadily colder, but
+with the sunrise there comes an influx of solar heat, feeble at first
+because it strikes the earth's surface very obliquely, but becoming more
+and more efficient as the sun rises higher in the sky. But as the air
+and the ground grow warm during the morning hours they part more and
+more readily and rapidly with their store of heat, just as a steam pipe
+or a cup of coffee radiates heat more rapidly when very hot. The warmest
+hour of the day is reached when these opposing tendencies of income and
+expenditure of heat are just balanced; and barring such disturbing
+factors as wind and clouds, the gain in temperature usually extends to
+the time--an hour or two beyond noon--at which the diminishing altitude
+of the sun renders his rays less efficient, when radiation gains the
+upper hand and the temperature becomes for a short time stationary, and
+then commences to fall steadily until the next sunrise.
+
+We have here an example of what is called a periodic change--i. e., one
+which, within a definite and uniform period (24 hours), oscillates from
+a minimum up to a maximum temperature and then back again to a minimum,
+repeating substantially the same variation day after day. But it must be
+understood that minor causes not taken into account above, such as
+winds, water, etc., produce other fluctuations from day to day which
+sometimes obscure or even obliterate the diurnal variation of
+temperature caused by the sun.
+
+Expose the back of your hand to the sun, holding the hand in such a
+position that the sunlight strikes perpendicularly upon it; then turn
+the hand so that the light falls quite obliquely upon it and note how
+much more vigorous is the warming effect of the sun in the first
+position than in the second. It is chiefly this difference of angle that
+makes the sun's warmth more effective when he is high up in the sky than
+when he is near the horizon, and more effective in summer than in
+winter.
+
+We have seen in Chapter III that the sun's motion among the stars takes
+place along a path which carries it alternately north and south of the
+equator to a distance of 23.5°, and the stars show by their earlier
+risings and later settings, as we pass from the equator toward the north
+pole of the heavens, that as the sun moves northward from the equator,
+each day in the northern hemisphere will become a little longer, each
+night a little shorter, and every day the sun will rise higher toward
+the zenith until this process culminates toward the end of June, when
+the sun begins to move southward, bringing shorter days and smaller
+altitudes until the Christmas season, when again it is reversed and the
+sun moves northward. We have here another periodic variation, which runs
+its complete course in a period of a year, and it is easy to see that
+this variation must have a marked effect on the warming of the earth,
+the long days and great altitudes of summer producing the greater warmth
+of that season, while the shorter days and lower altitudes of December,
+by diminishing the daily supply of solar heat, bring on the winter's
+cold. The succession of the seasons, winter following summer and summer
+winter, is caused by the varying altitude of the sun, and this in turn
+is due to the obliquity of the ecliptic, or, what is the same thing, the
+amount by which the axis of the earth is tipped from being perpendicular
+to the plane of its orbit, and the seasons are simply a periodic change
+in the warming of the earth, quite comparable with the diurnal change
+but of longer period.
+
+It is evident that the period within which the succession of winter and
+summer is completed, the year, as we commonly call it, must equal the
+time required by the sun to go from the vernal equinox around to the
+vernal equinox again, since this furnishes a complete cycle of the sun's
+motions north and south from the equator. On account of the westward
+motion of the equinox (precession) this is not quite the same as the
+time required for a complete revolution of the earth in its orbit, but
+is a little shorter (20m. 23s.), since the equinox moves back to meet
+the sun.
+
+48. RELATION OF THE SUN TO CLIMATE.--It is clear that both the northern
+and southern hemispheres of the earth must have substantially the same
+kind of seasons, since the motion of the sun north and south affects
+both alike; but when the sun is north of the equator and warming our
+hemisphere most effectively, his light falls more obliquely upon the
+other hemisphere, the days there are short and winter reigns at the
+time we are enjoying summer, while six months later the conditions are
+reversed.
+
+In those parts of the earth near the equator--the torrid zone--there is
+no such marked change from cold to warm as we experience, because, as
+the sun never gets more than 23.5° away from the celestial equator, on
+every day of the year he mounts high in the tropic skies, always coming
+within 23.5° of the zenith, and usually closer than this, so that there
+is no such periodic change in the heat supply as is experienced in
+higher latitudes, and within the tropics the temperature is therefore
+both higher and more uniform than in our latitude.
+
+In the frigid zones, on the contrary, the sun never rises high in the
+sky; at the poles his greatest altitude is only 23.5°, and during the
+winter season he does not rise at all, so that the temperature is here
+low the whole year round, and during the winter season, when for weeks
+or months at a time the supply of solar light is entirely cut off, the
+temperature falls to a degree unknown in more favored climes.
+
+If the obliquity of the ecliptic were made 10° greater, what would be
+the effect upon the seasons in the temperate zones? What if it were made
+10° less?
+
+Does the precession of the equinoxes have any effect upon the seasons or
+upon the climate of different parts of the earth?
+
+If the axis of the earth pointed toward Arcturus instead of Polaris,
+would the seasons be any different from what they are now?
+
+49. THE ATMOSPHERE.--Although we live upon its surface, we are not
+outside the earth, but at the bottom of a sea of air which forms the
+earth's outermost layer and extends above our heads to a height of many
+miles. The study of most of the phenomena of the atmosphere belongs to
+that branch of physics called meteorology, but there are a few matters
+which fairly come within our consideration of the earth as a planet. We
+can not see the stars save as we look through this atmosphere, and the
+light which comes through it is bent and oftentimes distorted so as to
+present serious obstacles to any accurate telescopic study of the
+heavenly bodies. Frequently this disturbance is visible to the naked
+eye, and the stars are said to twinkle--i. e., to quiver and change
+color many times per second, solely in consequence of a disturbed
+condition of the air and not from anything which goes on in the star.
+This effect is more marked low down in the sky than near the zenith, and
+it is worth noting that the planets show very little of it because the
+light they send to the earth comes from a disk of sensible area, while a
+star, being much smaller and farther from the earth, has its disk
+reduced practically to a mere point whose light is more easily affected
+by local disturbances in the atmosphere than is the broader beam which
+comes from the planets' disk.
+
+50. REFRACTION.--At all times, whether the stars twinkle or not, their
+light is bent in its passage through the atmosphere, so that the stars
+appear to stand higher up in the sky than their true positions. This
+effect, which the astronomer calls refraction, must be allowed for in
+observations of the more precise class, although save at low altitudes
+its amount is a very small fraction of a degree, but near the horizon it
+is much exaggerated in amount and becomes easily visible to the naked
+eye by distorting the disks of the sun and moon from circles into ovals
+with their long diameters horizontal. The refraction lifts both upper
+and lower edge of the sun, but lifts the lower edge more than the upper,
+thus shortening the vertical diameter. See Fig. 27, which shows not only
+this effect, but also the reflection of the sun from the curved surface
+of the sea, still further flattening the image. If the surface of the
+water were flat, the reflected image would have the same shape as the
+sun's disk, and its altered appearance is sometimes cited as a proof
+that the earth's surface is curved.
+
+The total amount of the refraction at the horizon is a little more than
+half a degree, and since the diameters of the sun and moon subtend an
+angle of about half a degree, we have the remarkable result that in
+reality the whole disk of either sun or moon is below the horizon at the
+instant that the lower edge appears to touch the horizon and sunset or
+moonset begins. The same effect exists at sunrise, and as a consequence
+the duration of sunshine or of moonshine is on the average about six
+minutes longer each day than it would be if there were no atmosphere and
+no refraction. A partial offset to this benefit is found in the fact
+that the atmosphere absorbs the light of the heavenly bodies, so that
+stars appear much less bright when near the horizon than when they are
+higher up in the sky, and by reason of this absorption the setting sun
+can be looked at with the naked eye without the discomfort which its
+dazzling luster causes at noon.
+
+[Illustration: FIG. 27.--Flattening of the sun's disk by refraction and
+by reflection from the surface of the sea.]
+
+51. THE TWILIGHT.--Another effect of the atmosphere, even more marked
+than the preceding, is the twilight. As at sunrise the mountain top
+catches the rays of the coming sun before they reach the lowland, and at
+sunset it keeps them after they have faded from the regions below, so
+the particles of dust and vapor, which always float in the atmosphere,
+catch the sunlight and reflect it to the surface of the earth while the
+sun is still below the horizon, giving at the beginning and end of day
+that vague and diffuse light which we call twilight.
+
+[Illustration: FIG. 28.--Twilight phenomena.]
+
+Fig. 28 shows a part of the earth surrounded by such a dust-laden
+atmosphere, which is illuminated on the left by the rays of the sun, but
+which, on the right of the figure, lies in the shadow cast by the earth.
+To an observer placed at _1_ the sun is just setting, and all the
+atmosphere above him is illumined with its rays, which furnish a bright
+twilight. When, by the earth's rotation, this observer has been carried
+to _2_, all the region to the east of his zenith lies in the shadow,
+while to the west there is a part of the atmosphere from which there
+still comes a twilight, but now comparatively faint, because the lower
+part of the atmosphere about our observer lies in the shadow, and it is
+mainly its upper regions from which the light comes, and here the dust
+and moisture are much less abundant than in the lower strata. Still
+later, when the observer has been carried by the earth's rotation to the
+point _3_, every vestige of twilight will have vanished from his sky,
+because all of the illuminated part of the atmosphere is now below his
+horizon, which is represented by the line _3 L_. In the figure the sun
+is represented to be 78° below this horizon line at the end of twilight,
+but this is a gross exaggeration, made for the sake of clearness in the
+drawing--in fact, twilight is usually said to end when the sun is 18°
+below the horizon.
+
+Let the student redraw Fig. 28 on a large scale, so that the points _1_
+and _3_ shall be only 18° apart, as seen from the earth's center. He
+will find that the point _L_ is brought down much closer to the surface
+of the earth, and measuring the length of the line _2 L_, he should find
+for the "height of the atmosphere" about one-eightieth part of the
+radius of the earth--i. e., a little less than 50 miles. This, however,
+is not the true height of the atmosphere. The air extends far beyond
+this, but the particles of dust and vapor which are capable of sending
+sunlight down to the earth seem all to lie below this limit.
+
+The student should not fail to watch the eastern sky after sunset, and
+see the shadow of the earth rise up and fill it while the twilight arch
+retreats steadily toward the west.
+
+[Illustration: FIG. 29.--The cause of long and short twilights.]
+
+_Duration of twilight._--Since twilight ends when the sun is 18° below
+the horizon, any circumstance which makes the sun go down rapidly will
+shorten the duration of twilight, and anything which retards the
+downward motion of the sun will correspondingly prolong it. Chief among
+influences of this kind is the angle which the sun's course makes with
+the horizon. If it goes straight down, as at _a_, Fig. 29, a much
+shorter time will suffice to carry it to a depression of 18° than is
+needed in the case shown at _b_ in the same figure, where the motion is
+very oblique to the horizon. If we consider different latitudes and
+different seasons of the year, we shall find every possible variety of
+circumstance from _a_ to _b_, and corresponding to these, the duration
+of twilight varies from an all-night duration in the summers of Scotland
+and more northern lands to an hour or less in the mountains of Peru. For
+the sake of graphical effect, the shortness of tropical twilight is
+somewhat exaggerated by Coleridge in the lines,
+
+    "The sun's rim dips; the stars rush out:
+     At one stride comes the dark."
+                            _The Ancient Mariner._
+
+In the United States the longest twilights come at the end of June, and
+last for a little more than two hours, while the shortest ones are in
+March and September, amounting to a little more than an hour and a half;
+but at all times the last half hour of twilight is hardly to be
+distinguished from night, so small is the quantity of reflecting matter
+in the upper regions of the atmosphere. For practical convenience it is
+customary to assume in the courts of law that twilight ends an hour
+after sunset.
+
+How long does twilight last at the north pole?
+
+_The Aurora._--One other phenomenon of the atmosphere may be mentioned,
+only to point out that it is not of an astronomical character. The
+Aurora, or northern lights, is as purely an affair of the earth as is a
+thunderstorm, and its explanation belongs to the subject of terrestrial
+magnetism.
+
+
+
+
+CHAPTER VI
+
+THE MEASUREMENT OF TIME
+
+
+52. SOLAR TIME.--To measure any quantity we need a unit in terms of
+which it must be expressed. Angles are measured in degrees, and the
+degree is the unit for angular measurement. For most scientific purposes
+the centimeter is adopted as the unit with which to measure distances,
+and similarly a day is the fundamental unit for the measurement of time.
+Hours, minutes, and seconds are aliquot parts of this unit convenient
+for use in dealing with shorter periods than a day, and the week, month,
+and year which we use in our calendars are multiples of the day.
+
+Strictly speaking, a day is not the time required by the earth to make
+one revolution upon its axis, but it is best defined as the amount of
+time required for a particular part of the sky to make the complete
+circuit from the meridian of a particular place through west and east
+back to the meridian again. The day begins at the moment when this
+specified part of the sky is on the meridian, and "the time" at any
+moment is the hour angle of this particular part of the sky--i. e., the
+number of hours, minutes, etc., that have elapsed since it was on the
+meridian.
+
+The student has already become familiar with the kind of day which is
+based upon the motion of the vernal equinox, and which furnishes
+sidereal time, and he has seen that sidereal time, while very convenient
+in dealing with the motions of the stars, is decidedly inconvenient for
+the ordinary affairs of life since in the reckoning of the hours it
+takes no account of daylight and darkness. One can not tell off-hand
+whether 10 hours, sidereal time, falls in the day or in the night. We
+must in some way obtain a day and a system of time reckoning based upon
+the apparent diurnal motion of the sun, and we may, if we choose, take
+the sun itself as the point in the heavens whose transit over the
+meridian shall mark the beginning and the end of the day. In this system
+"the time" is the number of hours, minutes, etc., which have elapsed
+since the sun was on the meridian, and this is the kind of time which is
+shown by a sun dial, and which was in general use, years ago, before
+clocks and watches became common. Since the sun moves among the stars
+about a degree per day, it is easily seen that the rotating earth will
+have to turn farther in order to carry any particular meridian from the
+sun around to the sun again, than to carry it from a star around to the
+same star, or from the vernal equinox around to the vernal equinox
+again; just as the minute hand of a clock turns farther in going from
+the hour hand round to the hour hand again than it turns in going from
+XII to XII. These solar days and hours and minutes are therefore a
+little longer than the corresponding sidereal ones, and this furnishes
+the explanation why the stars come to the meridian a little earlier, by
+solar time, every night than on the night before, and why sidereal time
+gains steadily upon solar time, this gain amounting to approximately
+3m. 56.5s. per day, or exactly one day per year, since the sun makes the
+complete circuit of the constellations once in a year.
+
+With the general introduction of clocks and watches into use about a
+century ago this kind of solar time went out of common use, since no
+well-regulated clock could keep the time correctly. The earth in its
+orbital motion around the sun goes faster in some parts of its orbit
+than in others, and in consequence the sun appears to move more rapidly
+among the stars in winter than in summer; moreover, on account of the
+convergence of hour circles as we go away from the equator, the same
+amount of motion along the ecliptic produces more effect in winter and
+summer when the sun is north or south, than it does in the spring and
+autumn when the sun is near the equator, and as a combined result of
+these causes and other minor ones true solar time, as it is called, is
+itself not uniform, but falls behind the uniform lapse of sidereal time
+at a variable rate, sometimes quicker, sometimes slower. A true solar
+day, from noon to noon, is 51 seconds shorter in September than in
+December.
+
+[Illustration: FIG. 30.--The equation of time.]
+
+53. MEAN SOLAR TIME.--To remedy these inconveniences there has been
+invented and brought into common use what is called _mean solar time_,
+which is perfectly uniform in its lapse and which, by comparison with
+sidereal time, loses exactly one day per year. "The time" in this system
+never differs much from true solar time, and the difference between the
+two for any particular day may be found in any good almanac, or may be
+read from the curve in Fig. 30, in which the part of the curve above the
+line marked _0m_ shows how many minutes mean solar time is faster than
+true solar time. The correct name for this difference between the two
+kinds of solar time is the _equation of time_, but in the almanacs it is
+frequently marked "sun fast" or "sun slow." In sidereal time and true
+solar time the distinction between A. M. hours (_ante meridiem_ =
+before the sun reaches the meridian) and P. M. hours (_post meridiem_ =
+after the sun has passed the meridian) is not observed, "the time" being
+counted from 0 hours to 24 hours, commencing when the sun or vernal
+equinox is on the meridian. Occasionally the attempt is made to
+introduce into common use this mode of reckoning the hours, beginning
+the day (date) at midnight and counting the hours consecutively up to
+24, when the next date is reached and a new start made. Such a system
+would simplify railway time tables and similar publications; but the
+American public is slow to adopt it, although the system has come into
+practical use in Canada and Spain.
+
+54. TO FIND (APPROXIMATELY) THE SIDEREAL TIME AT ANY MOMENT.--RULE I.
+When the mean solar time is known. Let _W_ represent the time shown by
+an ordinary watch, and represent by _S_ the corresponding sidereal time
+and by _D_ the number of days that have elapsed from March 23d to the
+date in question. Then
+
+    S = W + 69/70 × D × 4.
+
+The last term is expressed in minutes, and should be reduced to hours
+and minutes. Thus at 4 P. M. on July 4th--
+
+                _D_ = 103 days.
+    69/70 × _D_ × 4 = 406m.
+                    = 6h. 46m.
+                _W_ = 4h. 0m.
+                _S_ = 10h. 46m.
+
+The daily gain of sidereal upon mean solar time is 69/70 of 4 minutes,
+and March 23d is the date on which sidereal and mean solar time are
+together, taking the average of one year with another, but it varies a
+little from year to year on account of the extra day introduced in leap
+years.
+
+RULE II. When the stars in the northern sky can be seen. Find [b]
+Cassiopeię, and imagine a line drawn from it to Polaris, and another
+line from Polaris to the zenith. The sidereal time is equal to the angle
+between these lines, provided that that angle must be measured from the
+zenith toward the west. Turn the angle from degrees into hours by
+dividing by 15.
+
+55. THE EARTH'S ROTATION.--We are familiar with the fact that a watch
+may run faster at one time than at another, and it is worth while to
+inquire if the same is not true of our chief timepiece--the earth. It is
+assumed in the sections upon the measurement of time that the earth
+turns about its axis with absolute uniformity, so that mean solar time
+never gains or loses even the smallest fraction of a second. Whether
+this be absolutely true or not, no one has ever succeeded in finding
+convincing proof of a variation large enough to be measured, although it
+has recently been shown that the axis about which it rotates is not
+perfectly fixed within the body of the earth. The solid body of the
+earth wriggles about this axis like a fish upon a hook, so that the
+position of the north pole upon the earth's surface changes within a
+year to the extent of 40 or 50 feet (15 meters) without ever getting
+more than this distance away from its average position. This is probably
+caused by the periodical shifting of masses of air and water from one
+part of the earth to another as the seasons change, and it seems
+probable that these changes will produce some small effect upon the
+rotation of the earth. But in spite of these, for any such moderate
+interval of time as a year or a century, so far as present knowledge
+goes, we may regard the earth's rotation as uniform and undisturbed. For
+longer intervals--e. g., 1,000,000 or 10,000,000 years--the question is
+a very different one, and we shall have to meet it again in another
+connection.
+
+56. LONGITUDE AND TIME.--In what precedes there has been constant
+reference to the meridian. The day begins when the sun is on the
+meridian. Solar time is the angular distance of the sun past the
+meridian. Sidereal time was determined by observing transits of stars
+over a meridian line actually laid out upon the ground, etc. But every
+place upon the earth has its own meridian from which "the time" may be
+reckoned, and in Fig. 31, where the rays of sunlight are represented as
+falling upon a part of the earth's equator through which the meridians
+of New York, Chicago, and San Francisco pass, it is evident that these
+rays make different angles with the meridians, and that the sun is
+farther from the meridian of New York than from that of San Francisco by
+an amount just equal to the angle at _O_ between these meridians. This
+angle is called by geographers the difference of longitude between the
+two places, and the student should note that the word longitude is here
+used in a different sense from that on page 36. From Fig. 31 we obtain
+the
+
+_Theorem._--The difference between "the times" at any two meridians is
+equal to their difference of longitude, and the time at the eastern
+meridian is greater than at the western meridian. Astronomers usually
+express differences of longitude in hours instead of degrees. 1h. = 15°.
+
+The name given to any kind of time should distinguish all the elements
+which enter into it--e. g., New York sidereal time means the hour angle
+of the vernal equinox measured from the meridian of New York, Chicago
+true solar time is the hour angle of the sun reckoned from the meridian
+of Chicago, etc.
+
+[Illustration: FIG. 31.--Longitude and time]
+
+[Illustration: FIG. 32.--Standard time.]
+
+57. STANDARD TIME.--The requirements of railroad traffic have led to the
+use throughout the United States and Canada of four "standard times,"
+each of which is a mean solar time some integral number of hours slower
+than the time of the meridian passing through the Royal Observatory at
+Greenwich, England.
+
+    Eastern time is 5 hours slower than that of Greenwich.
+    Central  "      6  "      "     "    "         "
+    Mountain "      7  "      "     "    "         "
+    Pacific  "      8  "      "     "    "         "
+
+In Fig. 32 the broken lines indicate roughly the parts of the United
+States and Canada in which these several kinds of time are used, and
+illustrate how irregular are the boundaries of these parts.
+
+Standard time is sent daily into all of the more important telegraph
+offices of the United States, and serves to regulate watches and clocks,
+to the almost complete exclusion of local time.
+
+58. TO DETERMINE THE LONGITUDE.--With an ordinary watch observe the time
+of the sun's transit over your local meridian, and correct the observed
+time for the equation of time by means of the curve in Fig. 30. The
+difference between the corrected time and 12 o'clock will be the
+correction of your watch referred to local mean solar time. Compare your
+watch with the time signals in the nearest telegraph office and find its
+correction referred to standard time. The difference between the two
+corrections is the difference between your longitude and that of the
+standard meridian.
+
+N. B.--Don't tamper with the watch by trying to "set it right." No harm
+will be done if it is wrong, provided you take due account of the
+correction as indicated above.
+
+If the correction of the watch changed between your observation and the
+comparison in the telegraph office, what effect would it have upon the
+longitude determination? How can you avoid this effect?
+
+59. CHRONOLOGY.--The Century Dictionary defines chronology as "the
+science of time"--that is, "the method of measuring or computing time
+by regular divisions or periods according to the revolutions of the sun
+or moon."
+
+We have already seen that for the measurement of short intervals of time
+the day and its subdivisions--hours, minutes, seconds--furnish a very
+complete and convenient system. But for longer periods, extending to
+hundreds and thousands of days, a larger unit of time is required, and
+for the most part these longer units have in all ages and among all
+peoples been based upon astronomical considerations. But to this there
+is one marked exception. The week is a simple multiple of the day, as
+the dime is a multiple of the cent, and while it may have had its origin
+in the changing phases of the moon this is at best doubtful, since it
+does not follow these with any considerable accuracy. If the still
+longer units of time--the month and the year--had equally been made to
+consist of an integral number of days much confusion and
+misunderstanding might have been avoided, and the annals of ancient
+times would have presented fewer pitfalls to the historian than is now
+the case. The month is plainly connected with the motion of the moon
+among the stars. The year is, of course, based upon the motion of the
+sun through the heavens and the change of seasons which is thus
+produced; although, as commonly employed, it is not quite the same as
+the time required by the earth to make one complete revolution in its
+orbit. This time of one revolution is called a sidereal year, while, as
+we have already seen in Chapter V, the year which measures the course of
+the seasons is shorter than this on account of the precession of the
+equinoxes. It is called a tropical year with reference to the circuit
+which the sun makes from one tropic to the other and back again.
+
+We can readily understand why primitive peoples should adopt as units of
+time these natural periods, but in so doing they incurred much the same
+kind of difficulty that we should experience in trying to use both
+English and American money in the ordinary transactions of life. How
+many dollars make a pound sterling? How shall we make change with
+English shillings and American dimes, etc.? How much is one unit worth
+in terms of the other?
+
+One of the Greek poets[2] has left us a quaint account of the confusion
+which existed in his time with regard to the place of months and moons
+in the calendar:
+
+    "The moon by us to you her greeting sends,
+    But bids us say that she's an ill-used moon
+    And takes it much amiss that you will still
+    Shuffle her days and turn them topsy-turvy,
+    So that when gods, who know their feast days well,
+    By your false count are sent home supperless,
+    They scold and storm at her for your neglect."
+
+  [2] Aristophanes, The Clouds, Whewell's translation.
+
+60. DAY, MONTH, AND YEAR.--If the day, the month, and the year are to be
+used concurrently, it is necessary to determine how many days are
+contained in the month and year, and when this has been done by the
+astronomer the numbers are found to be very awkward and inconvenient for
+daily use; and much of the history of chronology consists in an account
+of the various devices by which ingenious men have sought to use
+integral numbers to replace the cumbrous decimal fractions which follow.
+
+According to Professor Harkness, for the epoch 1900 A. D.--
+
+    One tropical year = 365.242197 mean solar days.
+     "     "      "   = 365d. 5h. 48m. 45.8s.
+    One lunation      = 29.530588 mean solar days.
+     "     "          = 29d. 12h. 44m. 2.8s.
+
+The word _lunation_ means the average interval from one new moon to the
+next one--i. e., the time required by the moon to go from conjunction
+with the sun round to conjunction again.
+
+A very ancient device was to call a year equal to 365 days, and to have
+months alternately of 29 and 30 days in length, but this was
+unsatisfactory in more than one way. At the end of four years this
+artificial calendar would be about one day ahead of the true one, at the
+end of forty years ten days in error, and within a single lifetime the
+seasons would have appreciably changed their position in the year, April
+weather being due in March, according to the calendar. So, too, the year
+under this arrangement did not consist of any integral number of months,
+12 months of the average length of 29.5 days being 354 days, and 13
+months 383.5 days, thus making any particular month change its position
+from the beginning to the middle and the end of the year within a
+comparatively short time. Some peoples gave up the astronomical year as
+an independent unit and adopted a conventional year of 12 lunar months,
+354 days, which is now in use in certain Mohammedan countries, where it
+is known as the wandering year, with reference to the changing positions
+of the seasons in such a year. Others held to the astronomical year and
+adopted a system of conventional months, such that twelve of them would
+just make up a year, as is done to this day in our own calendar, whose
+months of arbitrary length we are compelled to remember by some such
+jingle as the following:
+
+    "Thirty days hath September,
+    April, June, and November;
+    All the rest have thirty-one
+    Save February,
+    Which alone hath twenty-eight,
+    Till leap year gives it twenty-nine."
+
+
+61. THE CALENDAR.--The foundations of our calendar may fairly be
+ascribed to Julius Cęsar, who, under the advice of the Egyptian
+astronomer Sosigines, adopted the old Egyptian device of a leap year,
+whereby every fourth year was to consist of 366 days, while ordinary
+years were only 365 days long. He also placed the beginning of the year
+at the first of January, instead of in March, where it had formerly
+been, and gave his own name, Julius, to the month which we now call
+July. August was afterward named in honor of his successor, Augustus.
+The names of the earlier months of the year are drawn from Roman
+mythology; those of the later months, September, October, etc., meaning
+seventh month, eighth month, represent the places of these months in the
+year, before Cęsar's reformation, and also their places in some of the
+subsequent calendars, for the widest diversity of practice existed
+during medięval times with regard to the day on which the new year
+should begin, Christmas, Easter, March 25th, and others having been
+employed at different times and places.
+
+The system of leap years introduced by Cęsar makes the average length of
+a year 365.25 days, which differs by about eleven minutes from the true
+length of the tropical year, a difference so small that for ordinary
+purposes no better approximation to the true length of the year need be
+desired. But _any_ deviation from the true length, however small, must
+in the course of time shift the seasons, the vernal and autumnal
+equinox, to another part of the year, and the ecclesiastical authorities
+of medięval Europe found here ground for objection to Cęsar's calendar,
+since the great Church festival of Easter has its date determined with
+reference to the vernal equinox, and with the lapse of centuries Easter
+became more and more displaced in the calendar, until Pope Gregory XIII,
+late in the sixteenth century, decreed another reformation, whereby ten
+days were dropped from the calendar, the day after March 11th being
+called March 21st, to bring back the vernal equinox to the date on which
+it fell in A. D. 325, the time of the Council of Nicęa, which Gregory
+adopted as the fundamental epoch of his calendar.
+
+The calendar having thus been brought back into agreement with that of
+old time, Gregory purposed to keep it in such agreement for the future
+by modifying Cęsar's leap-year rule so that it should run: Every year
+whose number is divisible by 4 shall be a leap year except those years
+whose numbers are divisible by 100 but not divisible by 400. These
+latter years--e. g., 1900--are counted as common years. The calendar
+thus altered is called Gregorian to distinguish it from the older,
+Julian calendar, and it found speedy acceptance in those civilized
+countries whose Church adhered to Rome; but the Protestant powers were
+slow to adopt it, and it was introduced into England and her American
+colonies by act of Parliament in the year 1752, nearly two centuries
+after Gregory's time. In Russia the Julian calendar has remained in
+common use to our own day, but in commercial affairs it is there
+customary to write the date according to both calendars--e. g., July
+4/16, and at the present time strenuous exertions are making in that
+country for the adoption of the Gregorian calendar to the complete
+exclusion of the Julian one.
+
+The Julian and Gregorian calendars are frequently represented by the
+abbreviations O. S. and N. S., old style, new style, and as the older
+historical dates are usually expressed in O. S., it is sometimes
+convenient to transform a date from the one calendar to the other. This
+is readily done by the formula
+
+    G = J + (N - 2) - N/4,
+
+where _G_ and _J_ are the respective dates, _N_ is the number of the
+century, and the remainder is to be neglected in the division by 4. For
+September 3, 1752, O. S., we have
+
+        J = Sept. 3
+    N - 2 = + 15
+    - N/4 = -  4
+    ------------------
+        G = Sept. 14
+
+and September 14 is the date fixed by act of Parliament to correspond to
+September 3, 1752, O. S. Columbus discovered America on October 12,
+1492, O. S. What is the corresponding date in the Gregorian calendar?
+
+62. THE DAY OF THE WEEK.--A problem similar to the above but more
+complicated consists in finding the day of the week on which any given
+date of the Gregorian calendar falls--e. g., October 21, 1492.
+
+The formula for this case is
+
+    7q + r = Y + D + (Y - 1)/4 - (Y - 1)/100 + (Y - 1)/400
+
+where _Y_ denotes the given year, _D_ the number of the day (date) in
+that year, and _q_ and _r_ are respectively the quotient and the
+remainder obtained by dividing the second member of the equation by 7.
+If _r_ = 1 the date falls on Sunday, etc., and if _r_ = 0 the day is
+Saturday. For the example suggested above we have
+
+      Jan.  31
+      Feb.  29
+      Mch.  31
+      April 30
+      May   31
+      June  30
+      July  31
+      Aug.  31
+      Sept. 30
+      Oct.  21
+           ---
+       D = 295
+
+                  Y =  1492
+                + D = + 295
+    + (Y - 1) ÷   4 = + 372
+    - (Y - 1) ÷ 100 = -  14
+    + (Y - 1) ÷ 400 = +   3
+                     -------
+                    7) 2148
+
+                  _q_ =   306
+                  _r_ =     6 = Friday.
+
+Find from some history the day of the week on which Columbus first saw
+America, and compare this with the above.
+
+On what day of the week did last Christmas fall? On what day of the week
+were you born? In the formula for the day of the week why does _q_ have
+the coefficient 7? What principles in the calendar give rise to the
+divisors 4, 100, 400?
+
+For much curious and interesting information about methods of reckoning
+the lapse of time the student may consult the articles Calendar and
+Chronology in any good encyclopędia.
+
+[Illustration: THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.]
+
+
+
+
+CHAPTER VII
+
+ECLIPSES
+
+
+63. THE NATURE OF ECLIPSES.--Every planet has a shadow which travels
+with the planet along its orbit, always pointing directly away from the
+sun, and cutting off from a certain region of space the sunlight which
+otherwise would fill it. For the most part these shadows are invisible,
+but occasionally one of them falls upon a planet or some other body
+which shines by reflected sunlight, and, cutting off its supply of
+light, produces the striking phenomenon which we call an eclipse. The
+satellites of Jupiter, Saturn, and Mars are eclipsed whenever they
+plunge into the shadows cast by their respective planets, and Jupiter
+himself is partially eclipsed when one of his own satellites passes
+between him and the sun, and casts upon his broad surface a shadow too
+small to cover more than a fraction of it.
+
+But the eclipses of most interest to us are those of the sun and moon,
+called respectively solar and lunar eclipses. In Fig. 33 the full moon,
+_M“_, is shown immersed in the shadow cast by the earth, and therefore
+eclipsed, and in the same figure the new moon, _M_, is shown as casting
+its shadow upon the earth and producing an eclipse of the sun. From a
+mere inspection of the figure we may learn that an eclipse of the sun
+can occur only at new moon--i. e., when the moon is on line between the
+earth and sun--and an eclipse of the moon can occur only at full moon.
+Why? Also, the eclipsed moon, _M“_, will present substantially the same
+appearance from every part of the earth where it is at all visible--the
+same from North America as from South America--but the eclipsed sun
+will present very different aspects from different parts of the earth.
+Thus, at _L_, within the moon's shadow, the sunlight will be entirely
+cut off, producing what is called a total eclipse. At points of the
+earth's surface near _J_ and _K_ there will be no interference whatever
+with the sunlight, and no eclipse, since the moon is quite off the line
+joining these regions to any part of the sun. At places between _J_ and
+_L_ or _K_ and _L_ the moon will cut off a part of the sun's light, but
+not all of it, and will produce what is called a partial eclipse, which,
+as seen from the northern parts of the earth, will be an eclipse of the
+lower (southern) part of the sun, and as seen from the southern
+hemisphere will be an eclipse of the northern part of the sun.
+
+[Illustration: FIG. 33.--Different kinds of eclipse.]
+
+The moon revolves around the earth in a plane, which, in the figure, we
+suppose to be perpendicular to the surface of the paper, and to pass
+through the sun along the line _M“ M_ produced. But it frequently
+happens that this plane is turned to one side of the sun, along some
+such line as _P Q_, and in this case the full moon would cut through the
+edge of the earth's shadow without being at any time wholly immersed in
+it, giving a partial eclipse of the moon, as is shown in the figure.
+
+In what parts of the earth would this eclipse be visible? What kinds of
+solar eclipse would be produced by the new moon at _Q_? In what parts of
+the earth would they be visible?
+
+64. THE SHADOW CONE.--The shape and position of the earth's shadow are
+indicated in Fig. 33 by the lines drawn tangent to the circles which
+represent the sun and earth, since it is only between these lines that
+the earth interferes with the free radiation of sunlight, and since both
+sun and earth are spheres, and the earth is much the smaller of the two,
+it is evident that the earth's shadow must be, in geometrical language,
+a cone whose base is at the earth, and whose vertex lies far to the
+right of the figure--in other words, the earth's shadow, although very
+long, tapers off finally to a point and ends. So, too, the shadow of the
+moon is a cone, having its base at the moon and its vertex turned away
+from the sun, and, as shown in the figure, just about long enough to
+reach the earth.
+
+It is easily shown, by the theorem of similar triangles in connection
+with the known size of the earth and sun, that the distance from the
+center of the earth to the vertex of its shadow is always equal to the
+distance of the earth from the sun divided by 108, and, similarly, that
+the length of the moon's shadow is equal to the distance of the moon
+from the sun divided by 400, the moon's shadow being the smaller and
+shorter of the two, because the moon is smaller than the earth. The
+radius of the moon's orbit is just about 1/400th part of the radius of
+the earth's orbit--i. e., the distance of the moon from the earth is
+1/400th part of the distance of the earth from the sun, and it is this
+"chance" agreement between the length of the moon's shadow and the
+distance of the moon from the earth which makes the tip of the moon's
+shadow fall very near the earth at the time of solar eclipses. Indeed,
+the elliptical shape of the moon's orbit produces considerable
+variations in the distance of the moon from the earth, and in
+consequence of these variations the vertex of the shadow sometimes falls
+short of reaching the earth, and sometimes even projects considerably
+beyond its farther side. When the moon's distance is too great for the
+shadow to bridge the space between earth and moon there can be no total
+eclipse of the sun, for there is no shadow which can fall upon the
+earth, even though the moon does come directly between earth and sun.
+But there is then produced a peculiar kind of partial eclipse called
+_annular_, or ring-shaped, because the moon, although eclipsing the
+central parts of the sun, is not large enough to cover the whole of it,
+but leaves the sun's edge visible as a ring of light, which completely
+surrounds the moon. Although, strictly speaking, this is only a partial
+eclipse, it is customary to put total and annular eclipses together in
+one class, which is called central eclipses, since in these eclipses the
+line of centers of sun and moon strikes the earth, while in ordinary
+partial eclipses it passes to one side of the earth without striking it.
+In this latter case we have to consider another cone called the
+_penumbra_--i. e., partial shadow--which is shown in Fig. 33 by the
+broken lines tangent to the sun and moon, and crossing at the point _V_,
+which is the vertex of this cone. This penumbral cone includes within
+its surface all that region of space within which the moon cuts off any
+of the sunlight, and of course it includes the shadow cone which
+produces total eclipses. Wherever the penumbra falls there will be a
+solar eclipse of some kind, and the nearer the place is to the axis of
+the penumbra, the more nearly total will be the eclipse. Since the moon
+stands about midway between the earth and the vertex of the penumbra,
+the diameter of the penumbra where it strikes the earth will be about
+twice as great as the diameter of the moon, and the student should be
+able to show from this that the region of the earth's surface within
+which a partial solar eclipse is visible extends in a straight line
+about 2,100 miles on either side of the region where the eclipse is
+total. Measured along the curved surface of the earth, this distance is
+frequently much greater.
+
+Is it true that if at any time the axis of the shadow cone comes within
+2,100 miles of the earth's surface a partial eclipse will be visible in
+those parts of the earth nearest the axis of the shadow?
+
+65. DIFFERENT CHARACTERISTICS OF LUNAR AND SOLAR ECLIPSES.--One marked
+difference between lunar and solar eclipses which has been already
+suggested, may be learned from Fig. 33. The full moon, _M“_, will be
+seen eclipsed from every part of the earth where it is visible at all at
+the time of the eclipse--that is, from the whole night side of the
+earth; while the eclipsed sun will be seen eclipsed only from those
+parts of the day side of the earth upon which the moon's shadow or
+penumbra falls. Since the point of the shadow at best but little more
+than reaches to the earth, the amount of space upon the earth which it
+can cover at any one moment is very small, seldom more than 100 to 200
+miles in length, and it is only within the space thus actually covered
+by the shadow that the sun is at any given moment totally eclipsed, but
+within this region the sun disappears, absolutely, behind the solid body
+of the moon, leaving to view only such outlying parts and appendages as
+are too large for the moon to cover. At a lunar eclipse, on the other
+hand, the earth coming between sun and moon cuts off the light from the
+latter, but, curiously enough, does not cut it off so completely that
+the moon disappears altogether from sight even in mid-eclipse. The
+explanation of this continued visibility is furnished by the broken
+lines extending, in Fig. 33, from the earth through the moon. These
+represent sunlight, which, entering the earth's atmosphere near the edge
+of the earth (edge as seen from sun and moon), passes through it and
+emerges in a changed direction, refracted, into the shadow cone and
+feebly illumines the moon's surface with a ruddy light like that often
+shown in our red sunsets. Eclipse and sunset alike show that when the
+sun's light shines through dense layers of air it is the red rays which
+come through most freely, and the attentive observer may often see at a
+clear sunset something which corresponds exactly to the bending of the
+sunlight into the shadow cone; just before the sun reaches the horizon
+its disk is distorted from a circle into an oval whose horizontal
+diameter is longer than the vertical one (see § 50).
+
+QUERY.--At a total lunar eclipse what would be the effect upon the
+appearance of the moon if the atmosphere around the edge of the earth
+were heavily laden with clouds?
+
+66. THE TRACK OF THE SHADOW.--We may regard the moon's shadow cone as a
+huge pencil attached to the moon, moving with it along its orbit in the
+direction of the arrowhead (Fig. 34), and as it moves drawing a black
+line across the face of the earth at the time of total eclipse. This
+black line is the path of the shadow and marks out those regions within
+which the eclipse will be total at some stage of its progress. If the
+point of the shadow just reaches the earth its trace will have no
+sensible width, while, if the moon is nearer, the point of the cone will
+be broken off, and, like a blunt pencil, it will draw a broad streak
+across the earth, and this under the most favorable circumstances may
+have a breadth of a little more than 160 miles and a length of 10,000 or
+12,000 miles. The student should be able to show from the known distance
+of the moon (240,000 miles) and the known interval between consecutive
+new moons (29.5 days) that on the average the moon's shadow sweeps past
+the earth at the rate of 2,100 miles per hour, and that in a general way
+this motion is from west to east, since that is the direction of the
+moon's motion in its orbit. The actual velocity with which the moon's
+shadow moves past a given station may, however, be considerably greater
+or less than this, since on the one hand when the shadow falls very
+obliquely, as when the eclipse occurs near sunrise or sunset, the
+shifting of the shadow will be very much greater than the actual motion
+of the moon which produces it, and on the other hand the earth in
+revolving upon its axis carries the spectator and the ground upon which
+he stands along the same direction in which the shadow is moving. At the
+equator, with the sun and moon overhead, this motion of the earth
+subtracts about 1,000 miles per hour from the velocity with which the
+shadow passes by. It is chiefly on this account, the diminished velocity
+with which the shadow passes by, that total solar eclipses last longer
+in the tropics than in higher latitudes, but even under the most
+favorable circumstances the duration of totality does not reach eight
+minutes at any one place, although it may take the shadow several hours
+to sweep the entire length of its path across the earth.
+
+According to Whitmell the greatest possible duration of a total solar
+eclipse is 7m. 40s., and it can attain this limit only when the eclipse
+occurs near the beginning of July and is visible at a place 5° north of
+the equator.
+
+The duration of a lunar eclipse depends mainly upon the position of the
+moon with respect to the earth's shadow. If it strikes the shadow
+centrally, as at _M“_, Fig. 33, a total eclipse may last for about two
+hours, with an additional hour at the beginning and end, during which
+the moon is entering and leaving the earth's shadow. If the moon meets
+the shadow at one side of the axis, as at _P_, the total phase of the
+eclipse may fail altogether, and between these extremes the duration of
+totality may be anything from two hours downward.
+
+[Illustration: FIG. 34.--Relation of the lunar nodes to eclipses.]
+
+67. RELATION OF THE LUNAR NODES TO ECLIPSES.--To show why the moon
+sometimes encounters the earth's shadow centrally and more frequently at
+full moon passes by without touching it at all, we resort to Fig. 34,
+which represents a part of the orbit of the earth about the sun, with
+dates showing the time in each year at which the earth passes the part
+of its orbit thus marked. The orbit of the moon about the earth, _M M“_,
+is also shown, with the new moon, _M_, casting its shadow toward the
+earth and the full moon, _M“_, apparently immersed in the earth's
+shadow. But here appearances are deceptive, and the student who has
+made the observations set forth in Chapter III has learned for himself
+a fact of which careful account must now be taken. The apparent paths of
+the moon and sun among the stars are great circles which lie near each
+other, but are not exactly the same; and since these great circles are
+only the intersections of the sky with the planes of the earth's orbit
+and the moon's orbit, we see that these planes are slightly inclined to
+each other and must therefore intersect along some line passing through
+the center of the earth. This line, _N“ N““_, is shown in the figure,
+and if we suppose the surface of the paper to represent the plane of the
+earth's orbit, we shall have to suppose the moon's orbit to be tipped
+around this line, so that the left side of the orbit lies above and the
+right side below the surface of the paper. But since the earth's shadow
+lies in the plane of its orbit--i. e., in the surface of the paper--the
+full moon of March, _M“_, must have passed below the shadow, and the new
+moon, _M_, must have cast its shadow above the earth, so that neither a
+lunar nor a solar eclipse could occur in that month. But toward the end
+of May the earth and moon have reached a position where the line
+_N“ N““_ points almost directly toward the sun, in line with the shadow
+cones which hide it. Note that the line _N“ N““_ remains very nearly
+parallel to its original position, while the earth is moving along its
+orbit. The full moon will now be very near this line and therefore very
+close to the plane of the earth's orbit, if not actually in it, and must
+pass through the shadow of the earth and be eclipsed. So also the new
+moon will cast its shadow in the plane of the ecliptic, and this shadow,
+falling upon the earth, produced the total solar eclipse of May 28,
+1900.
+
+_N“ N““_ is called the line of nodes of the moon's orbit (§ 39), and the
+two positions of the earth in its orbit, diametrically opposite each
+other, at which _N“ N““_ points exactly toward the sun, we shall call
+the _nodes_ of the lunar orbit. Strictly speaking, the nodes are those
+points of the sky against which the moon's center is projected at the
+moment when in its orbital motion it cuts through the plane of the
+earth's orbit. Bearing in mind these definitions, we may condense much
+of what precedes into the proposition: Eclipses of either sun or moon
+can occur only when the earth is at or near one of the nodes of the
+moon's orbit. Corresponding to these positions of the earth there are in
+each year two seasons, about six months apart, at which times, and at
+these only, eclipses can occur. Thus in the year 1900 the earth passed
+these two points on June 2d and November 24th respectively, and the
+following list of eclipses which occurred in that year shows that all of
+them were within a few days of one or the other of these dates:
+
+        _Eclipses of the Year 1900_
+
+    Total solar eclipse          May 28th.
+    Partial lunar eclipse        June 12th.
+    Annular (solar) eclipse      November 21st.
+
+68. ECLIPSE LIMITS.--If the earth is exactly at the node at the time of
+new moon, the moon's shadow will fall centrally upon it and will produce
+an eclipse visible within the torrid zone, since this is that part of
+the earth's surface nearest the plane of its orbit. If the earth is near
+but not at the node, the new moon will stand a little north or south of
+the plane of the earth's orbit, and its shadow will strike the earth
+farther north or south than before, producing an eclipse in the
+temperate or frigid zones; or the shadow may even pass entirely above or
+below the earth, producing no eclipse whatever, or at most a partial
+eclipse visible near the north or south pole. Just how many days' motion
+the earth may be away from the node and still permit an eclipse is shown
+in the following brief table of eclipse limits, as they are called:
+
+                  _Solar Eclipse Limits_
+
+  If at any new moon the earth is
+
+  Less than 10 days away from a node, a central eclipse is certain.
+  Between 10 and 16 days   "  "  "    some kind of eclipse is certain.
+  Between 16 and 19 days   "  "  "    a partial eclipse is possible.
+  More than 19 days        "  "  "    no eclipse is possible.
+
+                _Lunar Eclipse Limits_
+
+  If at any full moon the earth is
+
+  Less than 4 days away from a node, a total eclipse is certain.
+  Between 4 and 10 days   "  "  "    some kind of eclipse is certain.
+  Between 10 and 14 days  "  "  "    a partial eclipse is possible.
+  More than 14 days       "  "  "    no eclipse is possible.
+
+From this table of eclipse limits we may draw some interesting
+conclusions about the frequency with which eclipses occur.
+
+69. NUMBER OF ECLIPSES IN A YEAR.--Whenever the earth passes a node of
+the moon's orbit a new moon must occur at some time during the 2 × 16
+days that the earth remains inside the limits where some kind of eclipse
+is certain, and there must therefore be an eclipse of the sun every time
+the earth passes a node of the moon's orbit. But, since there are two
+nodes past which the earth moves at least once in each year, there must
+be at least two solar eclipses every year. Can there be more than two?
+On the average, will central or partial eclipses be the more numerous?
+
+A similar line of reasoning will not hold true for eclipses of the moon,
+since it is quite possible that no full moon should occur during the 20
+days required by the earth to move past the node from the western to the
+eastern limit. This omission of a full moon while the earth is within
+the eclipse limits sometimes happens at both nodes in the same year, and
+then we have a year with no eclipse of the moon. The student may note in
+the list of eclipses for 1900 that the partial lunar eclipse of June
+12th occurred 10 days after the earth passed the node, and was therefore
+within the doubtful zone where eclipses may occur and may fail, and
+corresponding to this position the eclipse was a very small one, only a
+thousandth part of the moon's diameter dipping into the shadow of the
+earth. By so much the year 1900 escaped being an illustration of a year
+in which no lunar eclipse occurred.
+
+A partial eclipse of the moon will usually occur about a fortnight
+before or after a total eclipse of the sun, since the full moon will
+then be within the eclipse limit at the opposite node. A partial eclipse
+of the sun will always occur about a fortnight before or after a total
+eclipse of the moon.
+
+[Illustration: FIG. 35.--The eclipse of May 28, 1900.]
+
+70. ECLIPSE MAPS.--It is the custom of astronomers to prepare, in
+advance of the more important eclipses, maps showing the trace of the
+moon's shadow across the earth, and indicating the times of beginning
+and ending of the eclipses, as is shown in Fig. 35. While the actual
+construction of such a map requires much technical knowledge, the
+principles involved are simple enough: the straight line passed through
+the center of sun and moon is the axis of the shadow cone, and the map
+contains little more than a graphical representation of when and where
+this cone meets the surface of the earth. Thus in the map, the "Path of
+Total Eclipse" is the trace of the shadow cone across the face of the
+earth, and the width of this path shows that the earth encountered the
+shadow considerably inside the vertex of the cone. The general direction
+of the path is from west to east, and the slight sinuousities which it
+presents are for the most part due to unavoidable distortion of the
+map caused by the attempt to represent the curved surface of the earth
+upon the flat surface of the paper. On either side of the Path of Total
+Eclipse is the region within which the eclipse was only partial, and the
+broken lines marked Begins at 3h., Ends at 3h., show the intersection of
+the penumbral cone with the surface of the earth at 3 P. M., Greenwich
+time. These two lines inclose every part of the earth's surface from
+which at that time any eclipse whatever could be seen, and at this
+moment the partial eclipse was just beginning at every point on the
+eastern edge of the penumbra and just ending at every point on the
+western edge, while at the center of the penumbra, on the Path of Total
+Eclipse, lay the shadow of the moon, an oval patch whose greatest
+diameter was but little more than 60 miles in length, and within which
+lay every part of the earth where the eclipse was total at that moment.
+
+The position of the penumbra at other hours is also shown on the map,
+although with more distortion, because it then meets the surface of the
+earth more obliquely, and from these lines it is easy to obtain the time
+of beginning and end of the eclipse at any desired place, and to
+estimate by the distance of the place from the Path of Total Eclipse how
+much of the sun's face was obscured.
+
+Let the student make these "predictions" for Washington, Chicago,
+London, and Algiers.
+
+The points in the map marked First Contact, Last Contact, show the
+places at which the penumbral cone first touched the earth and finally
+left it. According to computations made as a basis for the construction
+of the map the Greenwich time of First Contact was 0h. 12.5m. and of
+Last Contact 5h. 35.6m., and the difference between these two times
+gives the total duration of the eclipse upon the earth--i. e., 5 hours
+23.1 minutes.
+
+[Illustration: FIG. 36.--Central eclipses for the first two decades of
+the twentieth century. OPPOLZER.]
+
+71. FUTURE ECLIPSES.--An eclipse map of a different kind is shown in
+Fig. 36, which represents the shadow paths of all the central eclipses
+of the sun, visible during the period 1900-1918 A. D., in those parts of
+the earth north of the south temperate zone. Each continuous black line
+shows the path of the shadow in a total eclipse, from its beginning, at
+sunrise, at the western end of the line to its end, sunset, at the
+eastern end, the little circle near the middle of the line showing the
+place at which the eclipse was total at noon. The broken lines represent
+similar data for the annular eclipses. This map is one of a series
+prepared by the Austrian astronomer, Oppolzer, showing the path of every
+such eclipse from the year 1200 B. C. to 2160 A. D., a period of more
+than three thousand years.
+
+If we examine the dates of the eclipses shown in this map we shall find
+that they are not limited to the particular seasons, May and November,
+in which those of the year 1900 occurred, but are scattered through all
+the months of the year, from January to December. This shows at once
+that the line of nodes, _N“ N““_, of Fig. 34, does not remain in a fixed
+position, but turns round in the plane of the earth's orbit so that in
+different years the earth reaches the node in different months. The
+precession has already furnished us an illustration of a similar change,
+the slow rotation of the earth's axis, producing a corresponding
+shifting of the line in which the planes of the equator and ecliptic
+intersect; and in much the same way, through the disturbing influence of
+the sun's attraction, the line _N“ N““_ is made to revolve westward,
+opposite to the arrowheads in Fig. 34, at the rate of nearly 20° per
+year, so that the earth comes to each node about 19 days earlier in each
+year than in the year preceding, and the eclipse season in each year
+comes on the average about 19 days earlier than in the year before,
+although there is a good deal of irregularity in the amount of change in
+particular years.
+
+72. RECURRENCE OF ECLIPSES.--Before the beginning of the Christian era
+astronomers had found out a rough-and-ready method of predicting
+eclipses, which is still of interest and value. The substance of the
+method is that if we start with any eclipse whatever--e. g., the eclipse
+of May 28, 1900--and reckon forward or backward from that date a period
+of 18 years and 10 or 11 days, we shall find another eclipse quite
+similar in its general characteristics to the one with which we started.
+Thus, from the map of eclipses (Fig. 36), we find that a total solar
+eclipse will occur on June 8, 1918, 18 years and 11 days after the one
+illustrated in Fig. 35. This period of 18 years and 11 days is called
+_saros_, an ancient word which means cycle or repetition, and since
+every eclipse is repeated after the lapse of a saros, we may find the
+dates of all the eclipses of 1918 by adding 11 days to the dates given
+in the table of eclipses for 1900 (§ 67), and it is to be especially
+noted that each eclipse of 1918 will be like its predecessor of 1900 in
+character--lunar, solar, partial, total, etc. The eclipses of any year
+may be predicted by a similar reference to those which occurred eighteen
+years earlier. Consult a file of old almanacs.
+
+The exact length of a saros is 223 lunar months, each of which is a
+little more than 29.5 days long, and if we multiply the exact value of
+this last number (see § 60) by 223, we shall find for the product
+6,585.32 days, which is equal to 18 years 11.32 days when there are four
+leap years included in the 18, or 18 years 10.32 days when the number of
+leap years is five; and in applying the saros to the prediction of
+eclipses, due heed must be paid to the number of intervening leap years.
+To explain why eclipses are repeated at the end of the saros, we note
+that the occurrence of an eclipse depends solely upon the relative
+positions of the earth, moon, and node of the moon's orbit, and the
+eclipse will be repeated as often as these three come back to the
+position which first produced it. This happens at the end of every
+saros, since the saros is, approximately, the least common multiple of
+the length of the year, the length of the lunar month, and the length of
+time required by the line of nodes to make a complete revolution around
+the ecliptic. If the saros were exactly a multiple of these three
+periods, every eclipse would be repeated over and over again for
+thousands of years; but such is not the case, the saros is not an exact
+multiple of a year, nor is it an exact multiple of the time required for
+a revolution of the line of nodes, and in consequence the restitution
+which comes at the end of the saros is not a perfect one. The earth at
+the 223d new moon is in fact about half a day's motion farther west,
+relative to the node, than it was at the beginning, and the resulting
+eclipse, while very similar, is not precisely the same as before. After
+another 18 years, at the second repetition, the earth is a day farther
+from the node than at first, and the eclipse differs still more in
+character, etc. This is shown in Fig. 37, which represents the apparent
+positions of the disks of the sun and moon as seen from the center of
+the earth at the end of each sixth saros, 108 years, where the upper row
+of figures represents the number of repetitions of the eclipse from the
+beginning, marked _0_, to the end, _72_. The solar eclipse limits, 10,
+16, 19 days, are also shown, and all those eclipses which fall between
+the 10-day limits will be central as seen from some part of the earth,
+those between 16 and 19 partial wherever seen, while between 10 and 16
+they may be either total or partial. Compare the figure with the
+following description given by Professor Newcomb: "A series of such
+eclipses commences with a very small eclipse near one pole of the earth.
+Gradually increasing for about eleven recurrences, it will become
+central near the same pole. Forty or more central eclipses will then
+recur, the central line moving slowly toward the other pole. The series
+will then become partial, and finally cease. The entire duration of the
+series will be more than a thousand years. A new series commences, on
+the average, at intervals of thirty years."
+
+[Illustration: FIG. 37.--Graphical illustration of the saros.]
+
+A similar figure may be constructed to represent the recurrence of lunar
+eclipses; but here, in consequence of the smaller eclipse limits, we
+shall find that a series is of shorter duration, a little over eight
+centuries as compared with twelve centuries, which is the average
+duration of a series of solar eclipses.
+
+One further matter connected with the saros deserves attention. During
+the period of 6,585.32 days the earth has 6,585 times turned toward the
+sun the same face upon which the moon's shadow fell at the beginning of
+the saros, but at the end of the saros the odd 0.32 of a day gives the
+earth time to make about a third of a revolution more before the eclipse
+is repeated, and in consequence the eclipse is seen in a different
+region of the earth, on the average about 116° farther west in
+longitude. Compare in Fig. 36 the regions in which the eclipses of 1900
+and 1918 are visible.
+
+Is this change in the region where the repeated eclipse is visible, true
+of lunar eclipses as well as solar?
+
+73. USE OF ECLIPSES.--At all times and among all peoples eclipses, and
+particularly total eclipses of the sun, have been reckoned among the
+most impressive phenomena of Nature. In early times and among
+uncultivated people they were usually regarded with apprehension, often
+amounting to a terror and frenzy, which civilized travelers have not
+scrupled to use for their own purposes with the aid of the eclipse
+predictions contained in their almanacs, threatening at the proper time
+to destroy the sun or moon, and pointing to the advancing eclipse as
+proof that their threats were not vain. In our own day and our own land
+these feelings of awe have not quite disappeared, but for the most part
+eclipses are now awaited with an interest and pleasure which, contrasted
+with the former feelings of mankind, furnish one of the most striking
+illustrations of the effect of scientific knowledge in transforming
+human fear and misery into a sense of security and enjoyment.
+
+But to the astronomer an eclipse is more than a beautiful illustration
+of the working of natural laws; it is in varying degree an opportunity
+of adding to his store of knowledge respecting the heavenly bodies. The
+region immediately surrounding the sun is at most times closed to
+research by the blinding glare of the sun's own light, so that a planet
+as large as the moon might exist here unseen were it not for the
+occasional opportunity presented by a total eclipse which shuts off the
+excessive light and permits not only a search for unknown planets but
+for anything and everything which may exist around the sun. More than
+one astronomer has reported the discovery of such planets, and at least
+one of these has found a name and a description in some of the books,
+but at the present time most astronomers are very skeptical about the
+existence of any such object of considerable size, although there is
+some reason to believe that an enormous number of little bodies, ranging
+in size from grains of sand upward, do move in this region, as yet
+unseen and offering to the future problems for investigation.
+
+But in other directions the study of this region at the times of total
+eclipse has yielded far larger returns, and in the chapter on the sun we
+shall have to consider the marvelous appearances presented by the solar
+prominences and by the corona, an appendage of the sun which reaches out
+from his surface for millions of miles but is never seen save at an
+eclipse. Photographs of the corona are taken by astronomers at every
+opportunity, and reproductions of some of these may be found in Chapter
+X.
+
+Annular eclipses and lunar eclipses are of comparatively little
+consequence, but any recorded eclipse may become of value in connection
+with chronology. We date our letters in a particular year of the
+twentieth century, and commonly suppose that the years are reckoned from
+the birth of Christ; but this is an error, for the eclipses which were
+observed of old and by the chroniclers have been associated with events
+of his life, when examined by the astronomers are found quite
+inconsistent with astronomic theory. They are, however, reconciled with
+it if we assume that our system of dates has its origin four years after
+the birth of Christ, or, in other words, that Christ was born in the
+year 4 B. C. A mistake was doubtless made at the time the Christian era
+was introduced into chronology. At many other points the chance record
+of an eclipse in the early annals of civilization furnishes a similar
+means of controlling and correcting the dates assigned by the historian
+to events long past.
+
+
+
+
+CHAPTER VIII
+
+INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE
+
+
+74. TWO FAMILIAR INSTRUMENTS.--In previous chapters we have seen that a
+clock and a divided circle (protractor) are needed for the observations
+which an astronomer makes, and it is worth while to note here that the
+geography of the sky and the science of celestial motions depend
+fundamentally upon these two instruments. The protractor is a simple
+instrument, a humble member of the family of divided circles, but untold
+labor and ingenuity have been expended on this family to make possible
+the construction of a circle so accurately divided that with it angles
+may be measured to the tenth of a second instead of to the tenth of a
+degree--i. e., 3,600 times as accurate as the protractor furnishes.
+
+The building of a good clock is equally important and has cost a like
+amount of labor and pains, so that it is a far cry from Galileo and his
+discovery that a pendulum "keeps time" to the modern clock with its
+accurate construction and elaborate provision against disturbing
+influences of every kind. Every such timepiece, whether it be of the
+nutmeg variety which sells for a dollar, or whether it be the standard
+clock of a great national observatory, is made up of the same essential
+parts that fall naturally into four classes, which we may compare with
+the departments of a well-ordered factory: I. A timekeeping department,
+the pendulum or balance spring, whose oscillations must all be of equal
+duration. II. A power department, the weights or mainspring, which,
+when wound, store up the power applied from outside and give it out
+piecemeal as required to keep the first department running. III. A
+publication department, the dial and hands, which give out the time
+furnished by Department I. IV. A transportation department, the wheels,
+which connect the other three and serve as a means of transmitting power
+and time from one to the other. The case of either clock or watch is
+merely the roof which shelters it and forms no department of its
+industry. Of these departments the first is by far the most important,
+and its good or bad performance makes or mars the credit of the clock.
+Beware of meddling with the balance wheel of your watch.
+
+75. RADIANT ENERGY.--But we have now to consider other instruments which
+in practice supplement or displace the simple apparatus hitherto
+employed. Among the most important of these modern instruments are the
+telescope, the spectroscope, and the photographic camera; and since all
+these instruments deal with the light which comes from the stars to the
+earth, we must for their proper understanding take account of the nature
+of that light, or, more strictly speaking, we must take account of the
+radiant energy emitted by the sun and stars, which energy, coming from
+the sun, is translated by our nerves into the two different sensations
+of light and heat. The radiant energy which comes from the stars is not
+fundamentally different from that of the sun, but the amount of energy
+furnished by any star is so small that it is unable to produce through
+our nerves any sensible perception of heat, and for the same reason the
+vast majority of stars are invisible to the unaided eye; they do not
+furnish a sufficient amount of energy to affect the optic nerves. A hot
+brick taken into the hand reveals its presence by the two different
+sensations of heat and pressure (weight); but as there is only one brick
+to produce the two sensations, so there is only one energy to produce
+through its action upon different nerves the two sensations of light
+and heat, and this energy is called _radiant_ because it appears to
+stream forth radially from everything which has the capacity of emitting
+it. For the detailed study of radiant energy the student is referred to
+that branch of science called physics; but some of its elementary
+principles may be learned through the following simple experiment, which
+the student should not fail to perform for himself:
+
+Drop a bullet or other similar object into a bucket of water and observe
+the circular waves which spread from the place where it enters the
+water. These waves are a form of radiant energy, but differing from
+light or heat in that they are visibly confined to a single plane, the
+surface of the water, instead of filling the entire surrounding space.
+By varying the size of the bucket, the depth of the water, the weight of
+the bullet, etc., different kinds of waves, big and little, may be
+produced; but every such set of waves may be described and defined in
+all its principal characteristics by means of three numbers--viz., the
+vertical height of the waves from hollow to crest; the distance of one
+wave from the next; and the velocity with which the waves travel across
+the water. The last of these quantities is called the velocity of
+propagation; the second is called the wave length; one half of the first
+is called the amplitude; and all these terms find important applications
+in the theory of light and heat.
+
+The energy of the falling bullet, the disturbance which it produced on
+entering the water, was carried by the waves from the center to the edge
+of the bucket but not beyond, for the wave can go only so far as the
+water extends. The transfer of energy in this way requires a perfectly
+continuous medium through which the waves may travel, and the whole
+visible universe is supposed to be filled with something called _ether_,
+which serves everywhere as a medium for the transmission of radiant
+energy just as the water in the experiment served as a medium for
+transmitting in waves the energy furnished to it by the falling bullet.
+The student may think of this energy as being transmitted in spherical
+waves through the ether, every glowing body, such as a star, a candle
+flame, an arc lamp, a hot coal, etc., being the origin and center of
+such systems of waves, and determining by its own physical and chemical
+properties the wave length and amplitude of the wave systems given off.
+
+The intensity of any light depends upon the amplitude of the
+corresponding vibration, and its color depends upon the wave length. By
+ingenious devices which need not be here described it has been found
+possible to measure the wave length corresponding to different
+colors--e. g., all of the colors of the rainbow, and some of these wave
+lengths expressed in tenth meters are as follows: A tenth meter is the
+length obtained by dividing a meter into 10^{10} equal parts. 10^{10} =
+10,000,000,000.
+
+                 Color.               Wave length.
+
+    Extreme limit of visible violet      3,900
+    Middle of the violet                 4,060
+      "      "    blue                   4,730
+      "      "    green                  5,270
+      "      "    yellow                 5,810
+      "      "    orange                 5,970
+      "      "    red                    7,000
+    Extreme limit of visible red         7,600
+
+[Illustration: PLATE I. THE NORTHERN CONSTELLATIONS]
+
+The phrase "extreme limit of visible violet" or red used above must be
+understood to mean that in general the eye is not able to detect radiant
+energy having a wave length less than 3,900 or greater than 7,600 tenth
+meters. Radiant energy, however, exists in waves of both greater and
+shorter length than the above, and may be readily detected by apparatus
+not subject to the limitations of the human eye--e. g., a common
+thermometer will show a rise of temperature when its bulb is exposed to
+radiant energy of wave length much greater than 7,600 tenth meters,
+and a photographic plate will be strongly affected by energy of
+shorter wave length than 3,900 tenth meters.
+
+76. REFLECTION AND CONDENSATION OF WAVES.--When the waves produced by
+dropping a bullet into a bucket of water meet the sides of the bucket,
+they appear to rebound and are reflected back toward the center, and if
+the bullet is dropped very near the center of the bucket the reflected
+waves will meet simultaneously at this point and produce there by their
+combined action a wave higher than that which was reflected at the walls
+of the bucket. There has been a condensation of energy produced by the
+reflection, and this increased energy is shown by the greater amplitude
+of the wave. The student should not fail to notice that each portion of
+the wave has traveled out and back over the radius of the bucket, and
+that they meet simultaneously at the center because of this equality of
+the paths over which they travel, and the resulting equality of time
+required to go out and back. If the bullet were dropped at one side of
+the center, would the reflected waves produce _at any point_ a
+condensation of energy?
+
+If the bucket were of elliptical instead of circular cross section and
+the bullet were dropped at one focus of the ellipse there would be
+produced a condensation of reflected energy at the other focus, since
+the sum of the paths traversed by each portion of the wave before and
+after reflection is equal to the sum of the paths traversed by every
+other portion, and all parts of the wave reach the second focus at the
+same time. Upon what geometrical principle does this depend?
+
+The condensation of wave energy in the circular and elliptical buckets
+are special cases under the general principle that such a condensation
+will be produced at any point which is so placed that different parts of
+the wave front reach it simultaneously, whether by reflection or by some
+other means, as shown below.
+
+The student will note that for the sake of greater precision we here
+say _wave front_ instead of wave. If in any wave we imagine a line drawn
+along the crest, so as to touch every drop which at that moment is
+exactly at the crest, we shall have what is called a wave front, and
+similarly a line drawn through the trough between two waves, or through
+any set of drops similarly placed on a wave, constitutes a wave front.
+
+77. MIRRORS AND LENSES.--That form of radiant energy which we recognize
+as light and heat may be reflected and condensed precisely as are the
+waves of water in the exercise considered above, but owing to the
+extreme shortness of the wave length in this case the reflecting surface
+should be very smooth and highly polished. A piece of glass hollowed out
+in the center by grinding, and with a light film of silver chemically
+deposited upon the hollow surface and carefully polished, is often used
+by astronomers for this purpose, and is called a concave mirror.
+
+The radiant energy coming from a star or other distant object and
+falling upon the silvered face of such a mirror is reflected and
+condensed at a point a little in front of the mirror, and there forms an
+image of the star, which may be seen with the unaided eye, if it is held
+in the right place, or may be examined through a magnifying glass.
+Similarly, an image of the sun, a planet, or a distant terrestrial
+object is formed by the mirror, which condenses at its appropriate place
+the radiant energy proceeding from each and every point in the surface
+of the object, and this, in common phrase, produces an image of the
+object.
+
+Another device more frequently used by astronomers for the production of
+images (condensation of energy) is a lens which in its simplest form is
+a round piece of glass, thick in the center and thin at the edge, with a
+cross section, such as is shown at _A B_ in Fig. 38. If we suppose _E G
+D_ to represent a small part of a wave front coming from a very distant
+source of radiant energy, such as a star, this wave front will be
+practically a plane surface represented by the straight line _E D_, but
+in passing through the lens this surface will become warped, since light
+travels slower in glass than in air, and the central part of the beam,
+_G_, in its onward motion will be retarded by the thick center of the
+lens, more than _E_ or _D_ will be retarded by the comparatively thin
+outer edges of _A B_. On the right of the lens the wave front therefore
+will be transformed into a curved surface whose exact character depends
+upon the shape of the lens and the kind of glass of which it is made. By
+properly choosing these the new wave front may be made a part of a
+sphere having its center at the point _F_ and the whole energy of the
+wave front, _E G D_, will then be condensed at _F_, because this point
+is equally distant from all parts of the warped wave front, and
+therefore is in a position to receive them simultaneously. The distance
+of _F_ from _A B_ is called the focal length of the lens, and _F_ itself
+is called the focus. The significance of this last word (Latin, _focus_
+= fireplace) will become painfully apparent to the student if he will
+hold a common reading glass between his hand and the sun in such a way
+that the focus falls upon his hand.
+
+[Illustration: FIG. 38.--Illustrating the theory of lenses.]
+
+All the energy transmitted by the lens in the direction _G F_ is
+concentrated upon a very small area at _F_, and an image of the
+object--e. g., a star, from which the light came--is formed here. Other
+stars situated near the one in question will also send beams of light
+along slightly different directions to the lens, and these will be
+concentrated, each in its appropriate place, in the _focal plane_,
+_F H_, passed through the focus, _F_, perpendicular to the line, _F G_,
+and we shall find in this plane a picture of all the stars or other
+objects within the range of the lens.
+
+[Illustration: FIG. 39.--Essential parts of a reflecting telescope.]
+
+78. TELESCOPES.--The simplest kind of telescope consists of a concave
+mirror to produce images, and a magnifying glass, called an _eyepiece_,
+through which to examine them; but for convenience' sake, so that the
+observer may not stand in his own light, a small mirror is frequently
+added to this combination, as at _H_ in Fig. 39, where the lines
+represent the directions along which the energy is propagated. By
+reflection from this mirror the focal plane and the images are shifted
+to _F_, where they may be examined from one side through the magnifying
+glass _E_.
+
+[Illustration: FIG. 40.--A simple form of refracting telescope.]
+
+Such a combination of parts is called a _reflecting_ telescope, while
+one in which the images are produced by a lens or combination of lenses
+is called a _refracting_ telescope, the adjective having reference to
+the bending, refraction, produced by the glass upon the direction in
+which the energy is propagated. The customary arrangement of parts in
+such a telescope is shown in Fig. 40, where the part marked _O_ is
+called the objective and _V E_ (the magnifying glass) is the eyepiece,
+or ocular, as it is sometimes called.
+
+Most objects with which we have to deal in using a telescope send to it
+not light of one color only, but a mixture of light of many colors,
+many different wave lengths, some of which are refracted more than
+others by the glass of which the lens is composed, and in consequence of
+these different amounts of refraction a single lens does not furnish a
+single image of a star, but gives a confused jumble of red and yellow
+and blue images much inferior in sharpness of outline (definition) to
+the images made by a good concave mirror. To remedy this defect it is
+customary to make the objective of two or more pieces of glass of
+different densities and ground to different shapes as is shown at _O_ in
+Fig. 40. The two pieces of glass thus mounted in one frame constitute a
+compound lens having its own focal plane, shown at _F_ in the figure,
+and similarly the lenses composing the eyepiece have a focal plane
+between the eyepiece and the objective which must also fall at _F_, and
+in the use of a telescope the eyepiece must be pushed out or in until
+its focal plane coincides with that of the objective. This process,
+which is called focusing, is what is accomplished in the ordinary opera
+glass by turning a screw placed between the two tubes, and it must be
+carefully done with every telescope in order to obtain distinct vision.
+
+79. MAGNIFYING POWER.--The amount by which a given telescope magnifies
+depends upon the focal length of the objective (or mirror) and the focal
+length of the eyepiece, and is equal to the ratio of these two
+quantities. Thus in Fig. 40 the distance of the objective from the focal
+plane _F_ is about 16 times as great as the distance of the eyepiece
+from the same plane, and the magnifying power of this telescope is
+therefore 16 diameters. A magnifying power of 16 diameters means that
+the diameter of any object seen in the telescope looks 16 times as large
+as it appears without the telescope, and is nearly equivalent to saying
+that the object appears only one sixteenth as far off. Sometimes the
+magnifying power is assumed to be the number of times that the _area_ of
+an object seems increased; and since areas are proportional to the
+squares of lines, the magnifying power of 16 diameters might be called
+a power of 256. Every large telescope is provided with several eyepieces
+of different focal lengths, ranging from a quarter of an inch to two and
+a half inches, which are used to furnish different magnifying powers as
+may be required for the different kinds of work undertaken with the
+instrument. Higher powers can be used with large telescopes than with
+small ones, but it is seldom advantageous to use with any telescope an
+eyepiece giving a higher power than 60 diameters for each inch of
+diameter of the objective.
+
+The part played by the eyepiece in determining magnifying power will be
+readily understood from the following experiment:
+
+Make a pin hole in a piece of cardboard. Bring a printed page so close
+to one eye that you can no longer see the letters distinctly, and then
+place the pin hole between the eye and the page. The letters which were
+before blurred may now be seen plainly through the pin hole, even when
+the page is brought nearer to the eye than before. As it is brought
+nearer, notice how the letters seem to become larger, solely because
+they are nearer. A pin hole is the simplest kind of a magnifier, and the
+eyepiece in a telescope plays the same part as does the pin hole in the
+experiment; it enables the eye to be brought nearer to the image, and
+the shorter the focal length of the eyepiece the nearer is the eye
+brought to the image and the higher is the magnifying power.
+
+80. THE EQUATORIAL MOUNTING.--Telescopes are of all sizes, from the
+modest opera glass which may be carried in the pocket and which requires
+no other support than the hand, to the giant which must have a special
+roof to shelter it and elaborate machinery to support and direct it
+toward the sky. But for even the largest telescopes this machinery
+consists of the following parts, which are illustrated, with exception
+of the last one, in the small equatorial telescope shown in Fig. 41. It
+is not customary to place a driving clock on so small a telescope as
+this:
+
+(_a_) A supporting pier or tripod.
+
+(_b_) An axis placed parallel to the axis of the earth.
+
+(_c_) Another axis at right angles to _b_ and capable of revolving upon
+_b_ as an axle.
+
+(_d_) The telescope tube attached to _c_ and capable of revolving about
+_c_.
+
+(_e_) Graduated circles attached to _c_ and _b_ to measure the amount by
+which the telescope is turned on these axes.
+
+(_f_) A driving clock so connected with _b_ as to make _c_ (and _d_)
+revolve about _b_ with an angular velocity equal and opposite to that
+with which the earth turns upon its axis.
+
+[Illustration: FIG. 41.--A simple equatorial mounting.]
+
+[Illustration: FIG. 42.--Equatorial mounting of the great telescope of
+the Yerkes Observatory.]
+
+Such a support is called an equatorial mounting, and the student should
+note from the figure that the circles, _e_, measure the hour angle and
+declination of any star toward which the telescope is directed, and
+conversely if the telescope be so set that these circles indicate the
+hour angle and declination of any given star, the telescope will then
+point toward that star. In this way it is easy to find with the
+telescope any moderately bright star, even in broad daylight, although
+it is then absolutely invisible to the naked eye. The rotation of the
+earth about its axis will speedily carry the telescope away from the
+star, but if the driving clock be started, its effect is to turn the
+telescope toward the west just as fast as the earth's rotation carries
+it toward the east, and by these compensating motions to keep it
+directed toward the star. In Fig. 42, which represents the largest and
+one of the most perfect refracting telescopes ever built, let the
+student pick out and identify the several parts of the mounting above
+described. A part of the driving clock may be seen within the head of
+the pier. In Fig. 43 trace out the corresponding parts in the mounting
+of a reflecting telescope.
+
+[Illustration: FIG. 43.--The reflecting telescope of the Paris
+Observatory.]
+
+A telescope is often only a subordinate part of some instrument or
+apparatus, and then its style of mounting is determined by the
+requirements of the special case; but when the telescope is the chief
+thing, and the remainder of the apparatus is subordinate to it, the
+equatorial mounting is almost always adopted, although sometimes the
+arrangement of the parts is very different in appearance from any of
+those shown above. Beware of the popular error that an object held close
+in front of a telescope can be seen by an observer at the eyepiece. The
+numerous stories of astronomers who saw spiders crawling over the
+objective of their telescope, and imagined they were beholding strange
+objects in the sky, are all fictitious, since nothing on or near the
+objective could possibly be seen through the telescope.
+
+81. PHOTOGRAPHY.--A photographic camera consists of a lens and a device
+for holding at its focus a specially prepared plate or film. This plate
+carries a chemical deposit which is very sensitive to the action of
+light, and which may be made to preserve the imprint of any picture
+which the lens forms upon it. If such a sensitive plate is placed at the
+focus of a reflecting telescope, the combination becomes a camera
+available for astronomical photography, and at the present time the
+tendency is strong in nearly every branch of astronomical research to
+substitute the sensitive plate in place of the observer at a telescope.
+A refracting telescope may also be used for astronomical photography,
+and is very much used, but some complications occur here on account of
+the resolution of the light into its constituent colors in passing
+through the objective. Fig. 44 shows such a telescope, or rather two
+telescopes, one photographic, the other visual, supported side by side
+upon the same equatorial mounting.
+
+[Illustration: FIG. 44.--Photographic telescope of the Paris
+Observatory.]
+
+One of the great advantages of photography is found in connection with
+what is called--
+
+82. PERSONAL EQUATION.--It is a remarkable fact, first investigated by
+the German astronomer Bessel, three quarters of a century ago, that
+where extreme accuracy is required the human senses can not be
+implicitly relied upon. The most skillful observers will not agree
+exactly in their measurement of an angle or in estimating the exact
+instant at which a star crossed the meridian; the most skillful artists
+can not draw identical pictures of the same object, etc.
+
+These minor deceptions of the senses are included in the term _personal
+equation_, which is a famous phrase in astronomy, denoting that the
+observations of any given person require to be corrected by means of
+some equation involving his personality.
+
+General health, digestion, nerves, fatigue, all influence the personal
+equation, and it was in reference to such matters that one of the most
+eminent of living astronomers has given this description of his habits
+of observing:
+
+"In order to avoid every physiological disturbance, I have adopted the
+rule to abstain for one or two hours before commencing observations from
+every laborious occupation; never to go to the telescope with stomach
+loaded with food; to abstain from everything which could affect the
+nervous system, from narcotics and alcohol, and especially from the
+abuse of coffee, which I have found to be exceedingly prejudicial to the
+accuracy of observation."[3] A regimen suggestive of preparation for an
+athletic contest rather than for the more quiet labors of an astronomer.
+
+  [3] Schiaparelli, Osservazioni sulle Stelle Doppie.
+
+83. VISUAL AND PHOTOGRAPHIC WORK.--The photographic plate has no stomach
+and no nerves, and is thus free from many of the sources of error which
+inhere in visual observations, and in special classes of work it
+possesses other marked advantages, such as rapidity when many stars are
+to be dealt with simultaneously, permanence of record, and owing to the
+cumulative effect of long exposure of the plate it is possible to
+photograph with a given telescope stars far too faint to be seen through
+it. On the other hand, the eye has the advantage in some respects, such
+as studying the minute details of a fairly bright object--e. g., the
+surface of a planet, or the sun's corona and, for the present at least,
+neither method of observing can exclude the other. For a remarkable case
+of discordance between the results of photographic and visual
+observations compare the pictures of the great nebula in the
+constellation Andromeda, which are given in Chapter XIV. A partial
+explanation of these discordances and other similar ones is that the eye
+is most strongly affected by greenish-yellow light, while the
+photographic plate responds most strongly to violet light; the
+photograph, therefore, represents things which the eye has little
+capacity for seeing, and _vice versa_.
+
+84. THE SPECTROSCOPE.--In some respects the spectroscope is the exact
+counterpart of the telescope. The latter condenses radiant energy and
+the former disperses it. As a measuring instrument the telescope is
+mainly concerned with the direction from which light comes, and the
+different colors of which that light is composed affect it only as an
+obstacle to be overcome in its construction. On the other hand, with the
+spectroscope the direction from which the radiant energy comes is of
+minor consequence, and the all-important consideration is the intrinsic
+character of that radiation. What colors are present in the light and in
+what proportions? What can these colors be made to tell about the nature
+and condition of the body from which they come, be it sun, or star, or
+some terrestrial source of light, such as an arc lamp, a candle flame,
+or a furnace in blast? These are some of the characteristic questions of
+the spectrum analysis, and, as the name implies, they are solved by
+analyzing the radiant energy into its component parts, setting down the
+blue light in one place, the yellow in another, the red in still
+another, etc., and interpreting this array of colors by means of
+principles which we shall have to consider. Something of this process of
+color analysis may be seen in the brilliant hues shown by a soap bubble,
+or reflected from a piece of mother-of-pearl, and still more strikingly
+exhibited in the rainbow, produced by raindrops which break up the
+sunlight into its component colors and arrange them each in its
+appropriate place. Any of these natural methods of decomposing light
+might be employed in the construction of a spectroscope, but in
+spectroscopes which are used for analyzing the light from feeble
+sources, such as a star, or a candle flame, a glass prism of triangular
+cross section is usually employed to resolve the light into its
+component colors, which it does by refracting it as shown at the edges
+of the lens in Fig. 38.
+
+[Illustration: FIG. 45.--Resolution of light into its component colors.]
+
+The course of a beam of light in passing through such a prism is shown
+in Fig. 45. Note that the bending of the light from its original course
+into a new one, which is here shown as produced by the prism, is quite
+similar to the bending shown at the edges of a lens and comes from the
+same cause, the slower velocity of light in glass than in air. It takes
+the light-waves as long to move over the path _A B_ in glass as over the
+longer path _1_, _2_, _3_, _4_, of which only the middle section lies in
+the glass.
+
+Not only does the prism bend the beam of light transmitted by it, but it
+bends in different degree light of different colors, as is shown in the
+figure, where the beam at the left of the prism is supposed to be made
+up of a mixture of blue and red light, while at the right of the prism
+the greater deviation imparted to the blue quite separates the colors,
+so that they fall at different places on the screen, _S S_. The compound
+light has been analyzed into its constituents, and in the same way every
+other color would be put down at its appropriate place on the screen,
+and a beam of white light falling upon the prism would be resolved by it
+into a sequence of colors, falling upon the screen in the order red,
+orange, yellow, green, blue, indigo, violet. The initial letters of
+these names make the word _Roygbiv_, and by means of it their order is
+easily remembered.
+
+[Illustration: FIG. 46.--Principal parts of a spectroscope.]
+
+If the light which is to be examined comes from a star the analysis made
+by the prism is complete, and when viewed through a telescope the image
+of the star is seen to be drawn out into a band of light, which is
+called a _spectrum_, and is red at one end and violet or blue at the
+other, with all the colors of the rainbow intervening in proper order
+between these extremes. Such a prism placed in front of the objective of
+a telescope is called an objective prism, and has been used for stellar
+work with marked success at the Harvard College Observatory. But if the
+light to be analyzed comes from an object having an appreciable extent
+of surface, such as the sun or a planet, the objective prism can not be
+successfully employed, since each point of the surface will produce its
+own spectrum, and these will appear in the _view telescope_ superposed
+and confused one with another in a very objectionable manner. To avoid
+this difficulty there is placed between the prism and the source of
+light an opaque screen, _S_, with a very narrow slit cut in it, through
+which all the light to be analyzed must pass and must also go through a
+lens, _A_, placed between the slit and the prism, as shown in Fig. 46.
+The slit and lens, together with the tube in which they are usually
+supported, are called a _collimator_. By this device a very limited
+amount of light is permitted to pass from the object through the slit
+and lens to the prism and is there resolved into a spectrum, which is in
+effect a series of images of the slit in light of different colors,
+placed side by side so close as to make practically a continuous ribbon
+of light whose width is the length of each individual picture of the
+slit. The length of the ribbon (dispersion) depends mainly upon the
+shape of the prism and the kind of glass of which it is made, and it may
+be very greatly increased and the efficiency of the spectroscope
+enhanced by putting two, three, or more prisms in place of the single
+one above described. When the amount of light is very great, as in the
+case of the sun or an electric arc lamp, it is advantageous to alter
+slightly the arrangement of the spectroscope and to substitute in place
+of the prism a grating--i. e., a metallic mirror with a great number of
+fine parallel lines ruled upon its surface at equal intervals, one from
+another. It is by virtue of such a system of fine parallel grooves that
+mother-of-pearl displays its beautiful color effects, and a brilliant
+spectrum of great purity and high dispersion is furnished by a grating
+ruled with from 10,000 to 20,000 lines to the inch. Fig. 47 represents,
+rather crudely, a part of the spectrum of an arc light furnished by such
+a grating, or rather it shows three different spectra arranged side by
+side, and looking something like a rude ladder. The sides of the ladder
+are the spectra furnished by the incandescent carbons of the lamp, and
+the cross pieces are the spectrum of the electric arc filling the space
+between the carbons. Fig. 48 shows a continuation of the same spectra
+into a region where the radiant energy is invisible to the eye, but is
+capable of being photographed.
+
+[Illustration: FIG. 47.--Green and blue part of the spectrum of an
+electric arc light.]
+
+It is only when a lens is placed between the lamp and the slit of the
+spectroscope that the three spectra are shown distinct from each other
+as in the figure. The purpose of the lens is to make a picture of the
+lamp upon the slit, so that all the radiant energy from any one point of
+the arc may be brought to one part of the slit, and thus appear in the
+resulting spectrum separated from the energy which comes from every
+other part of the arc. Such an instrument is called an _analyzing
+spectroscope_ while one without the lens is called an _integrating
+spectroscope_, since it furnishes to each point of the slit a sample of
+the radiant energy coming from every part of the source of light, and
+thus produces only an average spectrum of that source without
+distinction of its parts. When a spectroscope is attached to a
+telescope, as is often done (see Fig. 49), the eyepiece is removed to
+make way for it, and the telescope objective takes the part of the
+analyzing lens. A camera is frequently combined with such an apparatus
+to photograph the spectra it furnishes, and the whole instrument is then
+called a _spectrograph_.
+
+[Illustration: FIG. 48.--Violet and ultraviolet parts of spectrum of an
+arc lamp.]
+
+[Illustration: FIG. 49.--A spectroscope attached to the Yerkes
+telescope.]
+
+85. SPECTRUM ANALYSIS.--Having seen the mechanism of the spectroscope by
+which the light incident upon it is resolved into its constituent parts
+and drawn out into a series of colors arranged in the order of their
+wave lengths, we have now to consider the interpretation which is to be
+placed upon the various kinds of spectra which may be seen, and here we
+rely upon the experience of physicists and chemists, from whom we learn
+as follows:
+
+The radiant energy which is analyzed by the spectroscope has its source
+in the atoms and molecules which make up the luminous body from which
+the energy is radiated, and these atoms and molecules are able to
+impress upon the ether their own peculiarities in the shape of waves of
+different length and amplitude. We have seen that by varying the
+conditions of the experiment different kinds of waves may be produced in
+a bucket of water; and as a study of these waves might furnish an index
+to the conditions which produced them, so the study of the waves
+peculiar to the light which comes from any source may be made to give
+information about the molecules which make up that source. Thus the
+molecules of iron produce a system of waves peculiar to themselves and
+which can be duplicated by nothing else, and every other substance gives
+off its own peculiar type of energy, presenting a limited and definite
+number of wave lengths dependent upon the nature and condition of its
+molecules. If these molecules are free to behave in their own
+characteristic fashion without disturbance or crowding, they emit light
+of these wave lengths only, and we find in the spectrum a series of
+bright lines, pictures of the slit produced by light of these particular
+wave lengths, while between these bright lines lie dark spaces showing
+the absence from the radiant energy of light of intermediate wave
+lengths. Such a spectrum is shown in the central portion of Fig. 47,
+which, as we have already seen, is produced by the space between the
+carbons of the arc lamp. On the other hand, if the molecules are closely
+packed together under pressure they so interfere with each other as to
+give off a jumble of energy of all wave lengths, and this is translated
+by the spectroscope into a continuous ribbon of light with no dark
+spaces intervening, as in the upper and lower parts of Figs. 47 and 48,
+produced by the incandescent solid carbons of the lamp. These two types
+are known as the continuous and discontinuous spectrum, and we may lay
+down the following principle regarding them:
+
+A discontinuous spectrum, or bright-line spectrum as it is familiarly
+called, indicates that the molecules of the source of light are not
+crowded together, and therefore the light must come from an incandescent
+gas. A continuous spectrum shows only that the molecules are crowded
+together, or are so numerous that the body to which they belong is not
+transparent and gives no further information. The body may be solid,
+liquid, or gaseous, but in the latter case the gas must be under
+considerable pressure or of great extent.
+
+A second principle is: The lines which appear in a spectrum are
+characteristic of the source from which the light came--e. g., the
+double line in the yellow part of the spectrum at the extreme left in
+Fig. 47 is produced by sodium vapor in and around the electric arc and
+is never produced by anything but sodium. When by laboratory experiments
+we have learned the particular set of lines corresponding to iron, we
+may treat the presence of these lines in another spectrum as proof that
+iron is present in the source from which the light came, whether that
+source be a white-hot poker in the next room or a star immeasurably
+distant. The evidence that iron is present lies in the nature of the
+light, and there is no reason to suppose that nature to be altered on
+the way from star to earth. It may, however, be altered by something
+happening to the source from which it comes--e. g., changing temperature
+or pressure may affect, and does affect, the spectrum which such a
+substance as iron emits, and we must be prepared to find the same
+substance presenting different spectra under different conditions, only
+these conditions must be greatly altered in order to produce radical
+changes in the spectrum.
+
+[Illustration: FIG. 50.--The chief lines in the spectrum of
+sunlight.--HERSCHEL.]
+
+86. WAVE LENGTHS.--To identify a line as belonging to and produced by
+iron or any other substance, its position in the spectrum--i. e., its
+wave length--must be very accurately determined, and for the
+identification of a substance by means of its spectrum it is often
+necessary to determine accurately the wave lengths of many lines. A
+complicated spectrum may consist of hundreds or thousands of lines, due
+to the presence of many different substances in the source of light, and
+unless great care is taken in assigning the exact position of these
+lines in the spectrum, confusion and wrong identifications are sure to
+result. For the measurement of the required wave length a tenth meter
+(§ 75) is the unit employed, and a scale of wave lengths expressed in
+this unit is presented in Fig. 50. The accuracy with which some of these
+wave lengths are determined is truly astounding; a ten-billionth of an
+inch! These numerical wave lengths save all necessity for referring to
+the color of any part of the spectrum, and pictures of spectra for
+scientific use are not usually printed in colors.
+
+87. ABSORPTION SPECTRA.--There is another kind of spectrum, of greater
+importance than either of those above considered, which is well
+illustrated by the spectrum of sunlight (Fig. 50). This is a nearly
+continuous spectrum crossed by numerous _dark_ lines due to absorption
+of radiant energy in a comparatively cool gas through which it passes on
+its way to the spectroscope. Fraunhofer, who made the first careful
+study of spectra, designated some of the more conspicuous of these lines
+by letters of the alphabet which are shown in the plate, and which are
+still in common use as names for the lines, not only in the spectrum of
+sunlight but wherever they occur in other spectra. Thus the double line
+marked _D_, wave length 5893, falls at precisely the same place in the
+spectrum as does the double (sodium) line which we have already seen in
+the yellow part of the arc-light spectrum, which line is also called _D_
+and bears a very intimate relation to the dark _D_ line of the solar
+spectrum.
+
+The student who has access to colored crayons should color one edge of
+Fig. 50 in accordance with the lettering there given and, so far as
+possible, he should make the transition from one color to the next a
+gradual one, as it is in the rainbow.
+
+Fig. 50 is far from being a complete representation of the spectrum of
+sunlight. Not only does this spectrum extend both to the right and to
+the left into regions invisible to the human eye, but within the limits
+of the figure, instead of the seventy-five lines there shown, there are
+literally thousands upon thousands of lines, of which only the most
+conspicuous can be shown in such a cut as this.
+
+The dark lines which appear in the spectrum of sunlight can, under
+proper conditions, be made to appear in the spectrum of an arc light,
+and Fig. 51 shows a magnified representation of a small part of such a
+spectrum adjacent to the _D_ (sodium) lines. Down the middle of each of
+these lines runs a black streak whose position (wave length) is
+precisely that of the _D_ lines in the spectrum of sunlight, and whose
+presence is explained as follows:
+
+The very hot sodium vapor at the center of the arc gives off its
+characteristic light, which, shining through the outer and cooler layers
+of sodium vapor, is partially absorbed by these, resulting in a fine
+dark line corresponding exactly in position and wave length to the
+bright lines, and seen against these as a background, since the higher
+temperature at the center of the arc tends to broaden the bright lines
+and make them diffuse. Similarly the dark lines in the spectrum of the
+sun (Fig. 50) point to the existence of a surrounding envelope of
+relatively cool gases, which absorb from the sunlight precisely those
+kinds of radiant energy which they would themselves emit if
+incandescent. The resulting dark lines in the spectrum are to be
+interpreted by the same set of principles which we have above applied to
+the bright lines of a discontinuous spectrum, and they may be used to
+determine the chemical composition of the sun, just as the bright lines
+serve to determine the chemical elements present in the electric arc.
+With reference to the mode of their formation, bright-line and dark-line
+spectra are sometimes called respectively _emission_ and _absorption_
+spectra.
+
+[Illustration: FIG. 51.--The lines reversed.]
+
+88. TYPES OF SPECTRUM.--The sun presents by far the most complex
+spectrum known, and Fig. 50 shows only a small number of the more
+conspicuous lines which appear in it. Spectra of stars, _per contra_,
+appear relatively simple, since their feeble light is insufficient to
+bring out faint details. In Chapters XIII and XIV there are shown types
+of the different kinds of spectra given by starlight, and these are to
+be interpreted by the principles above established. Thus the spectrum of
+the bright star [b] Aurigę shows a continuous spectrum crossed by a few
+heavy absorption lines which are known from laboratory experiments to be
+produced only by hydrogen. There must therefore be an atmosphere of
+relatively cool hydrogen surrounding this star. The spectrum of Pollux
+is quite similar to that of the sun and is to be interpreted as showing
+a physical condition similar to that of the sun, while the spectrum of
+[a] Herculis is quite different from either of the others. In subsequent
+chapters we shall have occasion to consider more fully these different
+types of spectrum.
+
+89. THE DOPPLER PRINCIPLE.--This important principle of the spectrum
+analysis is most readily appreciated through the following experiment:
+
+Listen to the whistle of a locomotive rapidly approaching, and observe
+how the pitch changes and the note becomes more grave as the locomotive
+passes by and commences to recede. During the approach of the whistle
+each successive sound wave has a shorter distance to travel in coming to
+the ear of the listener than had its predecessor, and in consequence the
+waves appear to come in quicker succession, producing a higher note with
+a correspondingly shorter wave length than would be heard if the same
+whistle were blown with the locomotive at rest. On the other hand, the
+wave length is increased and the pitch of the note lowered by the
+receding motion of the whistle. A similar effect is produced upon the
+wave length of light by a rapid change of distance between the source
+from which it comes and the instrument which receives it, so that a
+diminishing distance diminishes very slightly the wave length of every
+line in the spectrum produced by the light, and an increasing distance
+increases these wave lengths, and this holds true whether the change of
+distance is produced by motion of the source of light or by motion of
+the instrument which receives it.
+
+This change of wave length is sometimes described by saying that when a
+body is rapidly approaching, the lines of its spectrum are all displaced
+toward the violet end of the spectrum, and are correspondingly displaced
+toward the red end by a receding motion. The amount of this shifting,
+when it can be measured, measures the velocity of the body along the
+line of sight, but the observations are exceedingly delicate, and it is
+only in recent years that it has been found possible to make them with
+precision. For this purpose there is made to pass through the
+spectroscope light from an artificial source which contains one or more
+chemical elements known to be present in the star which is to be
+observed, and the corresponding lines in the spectrum of this light and
+in the spectrum of the star are examined to determine whether they
+exactly match in position, or show, as they sometimes do, a slight
+displacement, as if one spectrum had been slipped past the other. The
+difficulty of the observations lies in the extremely small amount of
+this slipping, which rarely if ever in the case of a moving star amounts
+to one sixth part of the interval between the close parallel lines
+marked _D_ in Fig. 50. The spectral lines furnished by the headlight of
+a locomotive running at the rate of a hundred miles per hour would be
+displaced by this motion less than one six-thousandth part of the space
+between the _D_ lines, an amount absolutely imperceptible in the most
+powerful spectroscope yet constructed. But many of the celestial bodies
+have velocities so much greater than a hundred miles per hour that these
+may be detected and measured by means of the Doppler principle.
+
+90. OTHER INSTRUMENTS.--Other instruments of importance to the
+astronomer, but of which only casual mention can here be made, are the
+meridian-circle; the transit, one form of which is shown in Fig. 52, and
+the zenith telescope, which furnish refined methods for making
+observations similar in kind to those which the student has already
+learned to make with plumb line and protractor; the sextant, which is
+pre-eminently the sailor's instrument for finding the latitude and
+longitude at sea, by measuring the altitudes of sun and stars above the
+sea horizon; the heliometer, which serves for the very accurate
+measurement of small angles, such as the angular distance between two
+stars not more than one or two degrees apart; and the photometer, which
+is used for measuring the amount of light received from the celestial
+bodies.
+
+[Illustration: FIG. 52.--A combined transit instrument and zenith
+telescope.]
+
+
+
+
+CHAPTER IX
+
+THE MOON
+
+
+91. RESULTS OF OBSERVATION WITH THE UNAIDED EYE.--The student who has
+made the observations of the moon which are indicated in Chapter III has
+in hand data from which much may be learned about the earth's satellite.
+Perhaps the most striking feature brought out by them is the motion of
+the moon among the stars, always from west toward east, accompanied by
+that endless series of changes in shape and brightness--new moon, first
+quarter, full moon, etc.--whose successive stages we represent by the
+words, the phase of the moon. From his own observation the student
+should be able to verify, at least approximately, the following
+statements, although the degree of numerical precision contained in some
+of them can be reached only by more elaborate apparatus and longer study
+than he has given to the subject:
+
+A. The phase of the moon depends upon the distance apart of sun and moon
+in the sky, new moon coming when they are together, and full moon when
+they are as far apart as possible.
+
+[Illustration: THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph
+made at the Paris Observatory.]
+
+B. The moon is essentially a round, dark body, giving off no light of
+its own, but shining solely by reflected sunlight. The proof of this is
+that whenever we see a part of the moon which is turned away from the
+sun it looks dark--e. g., at new moon, sun and moon are in nearly the
+same direction from us and we see little or nothing of the moon, since
+the side upon which the sun shines is turned away from us. At full moon
+the earth is in line between sun and moon, and we see, round and
+bright, the face upon which the sun shines. At other phases, such as the
+quarters, the moon turns toward the earth a part of its night hemisphere
+and a part of its day hemisphere, but in general only that part which
+belongs to the day side of the moon is visible and the peculiar curved
+line which forms the boundary--the "ragged edge," or _terminator_, as it
+is called, is the dividing line between day and night upon the moon.
+
+A partial exception to what precedes is found for a few days after new
+moon when the moon and sun are not very far apart in the sky, for then
+the whole round disk of the moon may often be seen, a small part of it
+brightly illuminated by the sun and the larger part feebly illuminated
+by sunlight which fell first upon the earth and was by it reflected back
+to the moon, giving the pleasing effect which is sometimes called the
+old moon in the new moon's arms. The new moon--i. e., the part illumined
+by the sun--usually appears to belong to a sphere of larger radius than
+the old moon, but this is purely a trick played by the eyes of the
+observer, and the effect disappears altogether in a telescope. Is there
+any similar effect in the few days before new moon?
+
+C. The moon makes the circuit of the sky from a given star around to the
+same star again in a little more than 27 days (27.32166), but the
+interval between successive new moons--i. e., from the sun around to the
+sun again--is more than 29 days (29.53059). This last interval, which is
+called a lunar month or _synodical_ month, indicates what we have
+learned before--that the sun has changed its place among the stars
+during the month, so that it takes the moon an extra two days to
+overtake him after having made the circuit of the sky, just as it takes
+the minute hand of a clock an extra 5 minutes to catch up with the hour
+hand after having made a complete circuit of the dial.
+
+D. Wherever the moon may be in the sky, it turns always the same face
+toward the earth, as is shown by the fact that the dark markings which
+appear on its surface stand always upon (nearly) the same part of its
+disk. It does not always turn the same face toward the sun, for the
+boundary line between the illumined and unillumined parts of the moon
+shifts from one side to the other as the phase changes, dividing at each
+moment day from night upon the moon and illustrating by its slow
+progress that upon the moon the day and the month are of equal length
+(29.5 terrestrial days), instead of being time units of different
+lengths as with us.
+
+[Illustration: FIG. 53.--Motion of moon and earth relative to the sun.]
+
+92. THE MOON'S MOTION.--The student should compare the results of his
+own observations, as well as the preceding section, with Fig. 53, in
+which the lines with dates printed on them are all supposed to radiate
+from the sun and to represent the direction from the sun of earth and
+moon upon the given dates which are arbitrarily assumed for the sake of
+illustration, any other set would do equally well. The black dots, small
+and large, represent the moon revolving about the earth, but having the
+circular path shown in Fig. 34 (ellipse) transformed by the earth's
+forward motion into the peculiar sinuous line here shown. With respect
+to both earth and sun, the moon's orbit deviates but little from a
+circle, since the sinuous curve of Fig. 53 follows very closely the
+earth's orbit around the sun and is almost identical with it. For
+clearness of representation the distance between earth and moon in the
+figure has been made ten times too great, and to get a proper idea of
+the moon's orbit with reference to the sun, we must suppose the moon
+moved up toward the earth until its distance from the line of the
+earth's orbit is only a tenth part of what it is in the figure. When
+this is done, the moon's path becomes almost indistinguishable from that
+of the earth, as may be seen in the figure, where the attempt has been
+made to show both lines, and it is to be especially noted that this
+real orbit of the moon is everywhere concave toward the sun.
+
+The phase presented by the moon at different parts of its path is
+indicated by the row of circles at the right, and the student should
+show why a new moon is associated with June 30th and a full moon with
+July 15th, etc. What was the date of first quarter? Third quarter?
+
+We may find in Fig. 53 another effect of the same kind as that noted
+above in C. Between noon, June 30th, and noon, July 3d, the earth makes
+upon its axis three complete revolutions with respect to the sun, but
+the meridian which points toward the moon at noon on June 30th will not
+point toward it at noon on July 3d, since the moon has moved into a new
+position and is now 37° away from the meridian. Verify this statement by
+measuring, in Fig. 53, with the protractor, the moon's angular distance
+from the meridian at noon on July 3d. When will the meridian overtake
+the moon?
+
+93. HARVEST MOON.--The interval between two successive transits of the
+meridian past the moon is called a lunar day, and the student should
+show from the figure that on the average a lunar day is 51 minutes
+longer than a solar day--i. e., upon the average each day the moon comes
+to the meridian 51 minutes of solar time later than on the day before.
+It is also true that on the average the moon rises and sets 51 minutes
+later each day than on the day before. But there is a good deal of
+irregularity in the retardation of the time of moonrise and moonset,
+since the time of rising depends largely upon the particular point of
+the horizon at which the moon appears, and between two days this point
+may change so much on account of the moon's orbital motion as to make
+the retardation considerably greater or less than its average value. In
+northern latitudes this effect is particularly marked in the month of
+September, when the eastern horizon is nearly parallel with the moon's
+apparent path in the sky, and near the time of full moon in that month
+the moon rises on several successive nights at nearly the same hour, and
+in less degree the same is true for October. This highly convenient
+arrangement of moonlight has caused the full moons of these two months
+to be christened respectively the Harvest Moon and the Hunter's Moon.
+
+94. SIZE AND MASS OF THE MOON.--It has been shown in Chapter I how the
+distance of the moon from the earth may be measured and its diameter
+determined by means of angles, and without enlarging upon the details of
+these observations, we note as their result that the moon is a globe
+2,163 miles in diameter, and distant from the earth on the average about
+240,000 miles. But, as we have seen in Chapter VII, this distance
+changes to the extent of a few thousand miles, sometimes less, sometimes
+greater, mainly on account of the elliptic shape of the moon's orbit
+about the earth, but also in part from the disturbing influence of other
+bodies, such as the sun, which pull the moon to and fro, backward and
+forward, to quite an appreciable extent.
+
+From the known diameter of the moon it is a matter of elementary
+geometry to derive in miles the area of its surface and its volume or
+solid contents. Leaving this as an exercise for the student, we adopt
+the earth as the standard of comparison and find that the diameter of
+the moon is rather more than a quarter, 4/15, that of the earth, the
+area of its surface is a trifle more than 1/14 that of the earth, and
+its volume a little more than 1/49 of the earth's. So much is pure
+geometry, but we may combine with it some mechanical principles which
+enable us to go a step farther and to "weigh" the moon--i. e., determine
+its mass and the average density of the material of which it is made.
+
+We have seen that the moon moves around the sun in a path differing but
+little from the smooth curve shown in Fig. 53, with arrows indicating
+the direction of motion, and it would follow absolutely such a smooth
+path were it not for the attraction of the earth, and in less degree of
+some of the other planets, which swing it about first to one side then
+to the other. But action and reaction are equal; the moon pulls as
+strongly upon the earth as does the earth upon the moon, and if earth
+and moon were of equal mass, the deviation of the earth from the smooth
+curve in the figure would be just as large as that of the moon. It is
+shown in the figure that the moon does displace the earth from this
+curve, and we have only to measure the amount of this displacement of
+the earth and compare it with the displacement suffered by the moon to
+find how much the mass of the one exceeds that of the other. It may be
+seen from the figure that at first quarter, about July 7th, the earth is
+thrust ahead in the direction of its orbital motion, while at the third
+quarter, July 22d, it is pulled back by the action of the moon, and at
+all times it is more or less displaced by this action, so that, in order
+to be strictly correct, we must amend our former statement about the
+moon moving around the earth and make it read, Both earth and moon
+revolve around a point on line between their centers. This point is
+called their _center of gravity_, and the earth and the moon both move
+in ellipses having this center of gravity at their common focus. Compare
+this with Kepler's First Law. These ellipses are similarly shaped, but
+of very different size, corresponding to Newton's third law of motion
+(Chapter IV), so that the action of the earth in causing the small moon
+to move around a large orbit is just equal to the reaction of the moon
+in causing the larger earth to move in the smaller orbit. This is
+equivalent to saying that the dimensions of the two orbits are inversely
+proportional to the masses of the earth and the moon.
+
+By observing throughout the month the direction from the earth to the
+sun or to a near planet, such as Mars or Venus, astronomers have
+determined that the diameter of the ellipse in which the earth moves is
+about 5,850 miles, so that the distance of the earth from the center of
+gravity is 2,925 miles, and the distance of the moon from it is
+240,000-2,925 = 237,075. We may now write in the form of a proportion--
+
+    Mass of earth : Mass of moon :: 237,075 : 2,925,
+
+and find from it that the mass of the earth is 81 times as great as the
+mass of the moon--i. e., leaving kind and quality out of account, there
+is enough material in the earth to make 81 moons. We may note in this
+connection that the diameter of the earth, 7,926 miles, is greater than
+the diameter of the monthly orbit in which the moon causes it to move,
+and therefore the center of gravity of earth and moon always lies inside
+the body of the earth, about 1,000 miles below the surface.
+
+95. DENSITY OF THE MOON.--It is believed that in a general way the moon
+is made of much the same kind of material which goes to make up the
+earth--metals, minerals, rocks, etc.--and a part of the evidence upon
+which this belief is based lies in the density of the moon. By density
+of a substance we mean the amount of it which is contained in a given
+volume--i. e., the weight of a bushel or a cubic centimeter of the
+stuff. The density of chalk is twice as great as the density of water,
+because a cubic centimeter of chalk weighs twice as much as an equal
+volume of water, and similarly in other cases the density is found by
+dividing the mass or weight of the body by the mass or weight of an
+equal volume of water.
+
+We know the mass of the earth (§ 45), and knowing the mass of a cubic
+foot of water, it is easy, although a trifle tedious, to compute what
+would be the mass of a volume of water equal in size to the earth. The
+quotient obtained by dividing one of these masses by the other (mass of
+earth ÷ mass of water) is the average density of the material composing
+the earth, and we find numerically that this is 5.6--i. e., it would
+take 5.6 water earths to attract as strongly as does the real one. From
+direct experiment we know that the average density of the principal
+rocks which make up the crust of the earth is only about half of this,
+showing that the deep-lying central parts of the earth are denser than
+the surface parts, as we should expect them to be, because they have to
+bear the weight of all that lies above them and are compressed by it.
+
+Turning now to the moon, we find in the same way as for the earth that
+its average density is 3.4 as great as that of water.
+
+96. FORCE OF GRAVITY UPON THE MOON.--This number, 3.4, compared with the
+5.6 which we found for the earth, shows that on the whole the moon is
+made of lighter stuff than is the body of the earth, and this again is
+much what we should expect to find, for weight, the force which tends to
+compress the substance of the moon, is less there than here. The weight
+of a cubic yard of rock at the surface of either earth or moon is the
+force with which the earth or moon attracts it, and this by the law of
+gravitation is for the earth--
+
+    W = k × (m m“) / (3963)^{2};
+
+and for the moon--
+
+    w = k × {m (m“/81)} / (1081)^{2};
+
+from which we find by division--
+
+    w = (W / 81) (3963 / 1081)^{2} = (W / 6) (approximately).
+
+The cubic yard of rock, which upon the earth weighs two tons, would, if
+transported to the moon, weigh only one third of a ton, and would have
+only one sixth as much influence in compressing the rocks below it as it
+had upon the earth. Note that this rock when transported to the moon
+would be still attracted by the earth and would have weight toward the
+earth, but it is not this of which we are speaking; by its weight in
+the moon we mean the force with which the moon attracts it. Making due
+allowance for the difference in compression produced by weight, we may
+say that in general, so far as density goes, the moon is very like a
+piece of the earth of equal mass set off by itself alone.
+
+97. ALBEDO.--In another respect the lunar stuff is like that of which
+the earth is made: it reflects the sunlight in much the same way and to
+the same amount. The contrast of light and dark areas on the moon's
+surface shows, as we shall see in another section, the presence of
+different substances upon the moon which reflect the sunlight in
+different degrees. This capacity for reflecting a greater or less
+percentage of the incident sunlight is called _albedo_ (Latin,
+whiteness), and the brilliancy of the full moon might lead one to
+suppose that its albedo is very great, like that of snow or those masses
+of summer cloud which we call thunderheads. But this is only an effect
+of contrast with the dark background of the sky. The same moon by day
+looks pale, and its albedo is, in fact, not very different from that of
+our common rocks--weather-beaten sandstone according to Sir John
+Herschel--so that it would be possible to build an artificial moon of
+rock or brick which would shine in the sunlight much as does the real
+moon.
+
+The effect produced by the differences of albedo upon the moon's face is
+commonly called the "man in the moon," but, like the images presented by
+glowing coals, the face in the moon is anything which we choose to make
+it. Among the Chinese it is said to be a monkey pounding rice; in India,
+a rabbit; in Persia, the earth reflected as in a mirror, etc.
+
+98. LIBRATIONS.--We have already learned that the moon turns always the
+same face toward the earth, and we have now to modify this statement and
+to find that here, as in so many other cases, the thing we learn first
+is only approximately true and needs to be limited or added to or
+modified in some way. In general, Nature is too complex to be completely
+understood at first sight or to be perfectly represented by a simple
+statement. In Fig. 55 we have two photographs of the moon, taken nearly
+three years apart, the right-hand one a little after first quarter and
+the left-hand one a little before third quarter. They therefore
+represent different parts of the moon's surface, but along the ragged
+edge the same region is shown on both photographs, and features common
+to both pictures may readily be found--e. g., the three rings which form
+a right-angled triangle about one third of the way down from the top of
+the cut, and the curved mountain chain just below these. If the moon
+turned exactly the same face toward us in the two pictures, the distance
+of any one of these markings from any part of the moon's edge must be
+the same in both pictures; but careful measurement will show that this
+is not the case, and that in the left-hand picture the upper edge of the
+moon is tipped toward us and the lower edge away from us, as if the
+whole moon had been rotated slightly about a horizontal line and must be
+turned back a little (about 7°) in order to match perfectly the other
+part of the picture.
+
+This turning is called a _libration_, and it should be borne in mind
+that the moon librates not only in the direction above measured, north
+and south, but also at right angles to this, east and west, so that we
+are able to see a little farther around every part of the moon's edge
+than would be possible if it turned toward us at all times exactly the
+same face. But in spite of the librations there remains on the farther
+side of the moon an area of 6,000,000 square miles which is forever
+hidden from us, and of whose character we have no direct knowledge,
+although there is no reason to suppose it very different from that which
+is visible, despite the fact that some of the books contain quaint
+speculations to the contrary. The continent of South America is just
+about equal in extent to this unknown region, while North America is a
+fair equivalent for all the rest of the moon's surface, both those
+central parts which are constantly visible, and the zone around the edge
+whose parts sometimes come into sight and are sometimes hidden.
+
+An interesting consequence of the peculiar rotation of the moon is that
+from our side of it the earth is always visible. Sun, stars, and planets
+rise and set there as well as here, but to an observer on the moon the
+earth swings always overhead, shifting its position a few degrees one
+way or the other on account of the libration but running through its
+succession of phases, new earth, first quarter, etc., without ever going
+below the horizon, provided the observer is anywhere near the center of
+the moon's disk.
+
+[Illustration: FIG. 54.--Illustrating the moon's rotation.]
+
+99. CAUSE OF LIBRATIONS.--That the moon should librate is by no means so
+remarkable a fact as that it should at all times turn very nearly the
+same face toward the earth. This latter fact can have but one meaning:
+the moon revolves about an axis as does the earth, but the time required
+for this revolution is just equal to the time required to make a
+revolution in its orbit. Place two coins upon a table with their heads
+turned toward the north, as in Fig. 54, and move the smaller one around
+the larger in such a way that its face shall always look away from the
+larger one. In making one revolution in its orbit the head on this small
+coin will be successively directed toward every point of the compass,
+and when it returns to its initial position the small coin will have
+made just one revolution about an axis perpendicular to the plane of its
+orbit. In no other way can it be made to face always away from the
+figure at the center of its orbit while moving around it.
+
+We are now in a position to understand the moon's librations, for, if
+the small coin at any time moves faster or slower in its orbit than it
+turns about its axis, a new side will be turned toward the center, and
+the same may happen if the central coin itself shifts into a new
+position. This is what happens to the moon, for its orbital motion, like
+that of Mercury (Fig. 17), is alternately fast and slow, and in addition
+to this there are present other minor influences, such as the fact that
+its rotation axis is not exactly perpendicular to the plane of its
+orbit; in addition to this the observer upon the earth is daily carried
+by its rotation from one point of view to another, etc., so that it is
+only in a general way that the rotation upon the axis and motion in the
+orbit keep pace with each other. In a general way a cable keeps a ship
+anchored in the same place, although wind and waves may cause it to
+"librate" about the anchor.
+
+How the moon came to have this exact equality between its times of
+revolution and rotation constitutes a chapter of its history upon which
+we shall not now enter; but the equality having once been established,
+the mechanism by which it is preserved is simple enough.
+
+The attraction of the earth for the moon has very slightly pulled the
+latter out of shape (§ 42), so that the particular diameter, which
+points toward the earth, is a little longer than any other, and thus
+serves as a handle which the earth lays hold of and pulls down into its
+lowest possible position--i. e., the position in which it points toward
+the center of the earth. Just how long this handle is, remains unknown,
+but it may be shown from the law of gravitation that less than a hundred
+yards of elongation would suffice for the work it has to do.
+
+100. THE MOON AS A WORLD.--Thus far we have considered the moon as a
+satellite of the earth, dependent upon the earth, and interesting
+chiefly because of its relation to it. But the moon is something more
+than this; it is a world in itself, very different from the earth,
+although not wholly unlike it. The most characteristic feature of the
+earth's surface is its division into land and water, and nothing of this
+kind can be found upon the moon. It is true that the first generation of
+astronomers who studied the moon with telescopes fancied that the large
+dark patches shown in Fig. 55 were bodies of water, and named them
+oceans, seas, lakes, and ponds, and to the present day we keep those
+names, although it is long since recognized that these parts of the
+moon's surface are as dry as any other. Their dark appearance indicates
+a different kind of material from that composing the lighter parts of
+the moon, material with a different albedo, just as upon the earth we
+have light-colored and dark-colored rocks, marble and slate, which seen
+from the moon must present similar contrasts of brightness. Although
+these dark patches are almost the only features distinguishable with the
+unaided eye, it is far otherwise in the telescope or the photograph,
+especially along the ragged edge where great numbers of rings can be
+seen, which are apparently depressions in the moon and are called
+craters. These we find in great number all over the moon, but, as the
+figure shows, they are seen to the best advantage near the
+_terminator_--i. e., the dividing line between day and night, since the
+long shadows cast here by the rising or setting sun bring out the
+details of the surface better than elsewhere. Carefully examine Fig. 55
+with reference to these features.
+
+[Illustration: FIG. 55.--The moon at first and last quarter. Lick
+Observatory photographs.]
+
+Another feature which exists upon both earth and moon, although far less
+common there than here, is illustrated in the chain of mountains visible
+near the terminator, a little above the center of the moon in both parts
+of Fig. 55. This particular range of mountains, which is called the
+Lunar Apennines, is by far the most prominent one upon the moon,
+although others, the Alps and Caucasus, exist. But for the most part the
+lunar mountains stand alone, each by itself, instead of being grouped
+into ranges, as on the earth. Note in the figure that some of the lunar
+mountains stretch out into the night side of the moon, their peaks
+projecting up into the sunlight, and thus becoming visible, while the
+lowlands are buried in the shadow.
+
+A subordinate feature of the moon's surface is the system of _rays_
+which seem to radiate like spokes from some of the larger craters,
+extending over hill and valley sometimes for hundreds of miles. A
+suggestion of these rays may be seen in Fig. 55, extending from the
+great crater Copernicus a little southwest of the end of the Apennines,
+but their most perfect development is to be seen at the time of full
+moon around the crater Tycho, which lies near the south pole of the
+moon. Look for them with an opera glass.
+
+Another and even less conspicuous feature is furnished by the rills,
+which, under favorable conditions of illumination, appear like long
+cracks on the moon's surface, perhaps analogous to the cańons of our
+Western country.
+
+101. THE MAP OF THE MOON.--Fig. 55 furnishes a fairly good map of a
+limited portion of the moon near the terminator, but at the edges little
+or no detail can be seen. This is always true; the whole of the moon can
+not be seen to advantage at any one time, and to remedy this we need to
+construct from many photographs or drawings a map which shall represent
+the several parts of the moon as they appear at their best. Fig. 56
+shows such a map photographed from a relief model of the moon, and
+representing the principal features of the lunar surface in a way they
+can never be seen simultaneously. Perhaps its most striking feature is
+the shape of the craters, which are shown round in the central parts of
+the map and oval at the edges, with their long diameters parallel to the
+moon's edge. This is, of course, an effect of the curvature of the
+moon's surface, for we look very obliquely at the edge portions, and
+thus see their formations much foreshortened in the direction of the
+moon's radius.
+
+[Illustration: FIG. 56.--Relief map of the moon's surface.--After
+NASMYTH and CARPENTER.]
+
+The north and south poles of the moon are at the top and bottom of the
+map respectively, and a mere inspection of the regions around them will
+show how much more rugged is the southern hemisphere of the moon than
+the northern. It furnishes, too, some indication of how numerous are the
+lunar craters, and how in crowded regions they overlap one another.
+
+The student should pick out upon the map those features which he has
+learned to know in the photograph (Fig. 55)--the Apennines, Copernicus,
+and the continuation of the Apennines, extending into the dark part of
+the moon.
+
+[Illustration: FIG. 57.--Mare Imbrium. Photographed by G. W. RITCHEY.]
+
+102. SIZE OF THE LUNAR FEATURES.--We may measure distances here in the
+same way as upon a terrestrial map, remembering that near the edges the
+scale of the map is very much distorted parallel to the moon's diameter,
+and measurements must not be taken in this direction, but may be taken
+parallel to the edge. Measuring with a millimeter scale, we find on the
+map for the diameter of the crater Copernicus, 2.1 millimeters. To turn
+this into the diameter of the real Copernicus in miles, we measure upon
+the same map the diameter of the moon, 79.7 millimeters, and then have
+the proportion--
+
+    Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,
+
+which when solved gives 57 miles. The real diameter of Copernicus is a
+trifle over 56 miles. At the eastern edge of the moon, opposite the
+Apennines, is a large oval spot called the Mare Crisium (Latin, _ma-re_
+= sea). Measure its length. The large crater to the northwest of the
+Apennines is called Archimedes. Measure its diameter both in the map and
+in the photograph (Fig. 55), and see how the two results agree. The true
+diameter of this crater, east and west, is very approximately 50 miles.
+The great smooth surface to the west of Archimedes is the Mare Imbrium.
+Is it larger or smaller than Lake Superior? Fig. 57 is from a photograph
+of the Mare Imbrium, and the amount of detail here shown at the bottom
+of the sea is a sufficient indication that, in this case at least, the
+water has been drawn off, if indeed any was ever present.
+
+[Illustration: FIG. 58.--Mare Crisium. Lick Observatory photographs.]
+
+Fig. 58 is a representation of the Mare Crisium at a time when night was
+beginning to encroach upon its eastern border, and it serves well to
+show the rugged character of the ring-shaped wall which incloses this
+area.
+
+With these pictures of the smoother parts of the moon's surface we may
+compare Fig. 59, which shows a region near the north pole of the moon,
+and Fig. 60, giving an early morning view of Archimedes and the
+Apennines. Note how long and sharp are the shadows.
+
+[Illustration: FIG. 59.--Illustrating the rugged character of the moon's
+surface.--NASMYTH and CARPENTER.]
+
+103. THE MOON'S ATMOSPHERE.--Upon the earth the sun casts no shadows so
+sharp and black as those of Fig. 60, because his rays are here scattered
+and reflected in all directions by the dust and vapors of the
+atmosphere (§ 51), so that the place from which direct sunlight is cut
+off is at least partially illumined by this reflected light. The shadows
+of Fig. 60 show that upon the moon it must be otherwise, and suggest
+that if the moon has any atmosphere whatever, its density must be
+utterly insignificant in comparison with that of the earth. In its
+motion around the earth the moon frequently eclipses stars (_occults_ is
+the technical word), and if the moon had an atmosphere such as is shown
+in Fig. 61, the light from the star _A_ must shine through this
+atmosphere just before the moon's advancing body cuts it off, and it
+must be refracted by the atmosphere so that the star would appear in a
+slightly different direction (nearer to _B_) than before. The earth's
+atmosphere refracts the starlight under such circumstances by more than
+a degree, but no one has been able to find in the case of the moon any
+effect of this kind amounting to even a fraction of a second of arc.
+While this hardly justifies the statement sometimes made that the moon
+has no atmosphere, we shall be entirely safe in saying that if it has
+one at all its density is less than a thousandth part of that of the
+earth's atmosphere. Quite in keeping with this absence of an atmosphere
+is the fact that clouds never float over the surface of the moon. Its
+features always stand out hard and clear, without any of that haze and
+softness of outline which our atmosphere introduces into all terrestrial
+landscapes.
+
+[Illustration: FIG. 60.--Archimedes and Apennines. NASMYTH and
+CARPENTER.]
+
+104. HEIGHT OF THE LUNAR MOUNTAINS.--Attention has already been called
+to the detached mountain peaks, which in Fig. 55 prolong the range of
+Apennines into the lunar night. These are the beginnings of the Caucasus
+mountains, and from the photograph we may measure as follows the height
+to which they rise above the surrounding level of the moon: Fig. 62
+represents a part of the lunar surface along the boundary line between
+night and day, the horizontal line at the top of the figure representing
+a level ray of sunlight which just touches the moon at _T_ and barely
+illuminates the top of the mountain, _M_, whose height, _h_, is to be
+determined. If we let _R_ stand for the radius of the moon and _s_ for
+the distance, _T M_, we shall have in the right-angled triangle _M T C_,
+
+    R^{2} + s^{2} = (R + h)^{2},
+
+and we need only to measure _s_--that is, the distance from the
+terminator to the detached mountain peak--to make this equation
+determine _h_, since _R_ is already known, being half the diameter of
+the moon--1,081 miles. Practically it is more convenient to use instead
+of this equation another form, which the student who is expert in
+algebra may show to be very nearly equivalent to it:
+
+        _h_ (miles) = s^{2} / 2163,
+    or  _h_ (feet) = 2.44 s^{2}.
+
+The distance _s_ must be expressed in miles in all of these equations.
+In Fig. 55 the distance from the terminator to the first detached peak
+of the Caucasus mountains is 1.7 millimeters = 52 miles, from which we
+find the height of the mountain to be 1.25 miles, or 6,600 feet.
+
+[Illustration: FIG. 61.--Occultations and the moon's atmosphere.]
+
+[Illustration: FIG. 62.--Determining the height of a lunar mountain.]
+
+Two things, however, need to be borne in mind in this connection. On the
+earth we measure the heights of mountains _above sea level_, while on
+the moon there is no sea, and our 6,600 feet is simply the height of the
+mountain top above the level of that particular point in the terminator,
+from which we measure its distance. So too it is evident from the
+appearance of things, that the sunlight, instead of just touching the
+top of the particular mountain whose height we have measured, really
+extends some little distance down from its summit, and the 6,600 feet is
+therefore the elevation of the lowest point on the mountains to which
+the sunlight reaches. The peak itself may be several hundred feet
+higher, and our photograph must be taken at the exact moment when this
+peak appears in the lunar morning or disappears in the evening if we are
+to measure the altitude of the mountain's summit. Measure the height of
+the most northern visible mountain of the Caucasus range. This is one of
+the outlying spurs of the great mountain Calippus, whose principal peak,
+19,000 feet high, is shown in Fig. 55 as the brightest part of the
+Caucasus range.
+
+The highest peak of the lunar Apennines, Huyghens, has an altitude of
+18,000 feet, and the Leibnitz and Doerfel Mountains, near the south pole
+of the moon, reach an altitude 50 per cent greater than this, and are
+probably the highest peaks on the moon. This falls very little short of
+the highest mountain on the earth, although the moon is much smaller
+than the earth, and these mountains are considerably higher than
+anything on the western continent of the earth.
+
+The vagueness of outline of the terminator makes it difficult to measure
+from it with precision, and somewhat more accurate determinations of the
+heights of lunar mountains can be obtained by measuring the length of
+the shadows which they cast, and the depths of craters may also be
+measured by means of the shadows which fall into them.
+
+105. CRATERS.--Fig. 63 shows a typical lunar crater, and conveys a good
+idea of the ruggedness of the lunar landscape. Compare the appearance of
+this crater with the following generalizations, which are based upon the
+accurate measurement of many such:
+
+A. A crater is a real depression in the surface of the moon, surrounded
+usually by an elevated ring which rises above the general level of the
+region outside, while the bottom of the crater is about an equal
+distance below that level.
+
+B. Craters are shallow, their diameters ranging from five times to more
+than fifty times their depth. Archimedes, whose diameter we found to be
+50 miles, has an average depth of about 4,000 feet below the crest of
+its surrounding wall, and is relatively a shallow crater.
+
+[Illustration: FIG. 63.--A typical lunar crater.--NASMYTH and
+CARPENTER.]
+
+C. Craters frequently have one or more hills rising within them which,
+however, rarely, if ever, reach up to the level of the surrounding wall.
+
+D. Whatever may have been the mode of their formation, the craters can
+not have been produced by scooping out material from the center and
+piling it up to make the wall, for in three cases out of four the volume
+of the excavation is greater than the volume of material contained in
+the wall.
+
+106. MOON AND EARTH.--We have gone far enough now to appreciate both the
+likeness and the unlikeness of the moon and earth. They may fairly
+enough be likened to offspring of the same parent who have followed very
+different careers, and in the fullness of time find themselves in very
+different circumstances. The most serious point of difference in these
+circumstances is the atmosphere, which gives to the earth a wealth of
+phenomena altogether lacking in the moon. Clouds, wind, rain, snow,
+dew, frost, and hail are all dependent upon the atmosphere and can not
+be found where it is not. There can be nothing upon the moon at all like
+that great group of changes which we call weather, and the unruffled
+aspect of the moon's face contrasts sharply with the succession of cloud
+and sunshine which the earth would present if seen from the moon.
+
+The atmosphere is the chief agent in the propagation of sound, and
+without it the moon must be wrapped in silence more absolute than can be
+found upon the surface of the earth. So, too, the absence of an
+atmosphere shows that there can be no water or other liquid upon the
+moon, for if so it would immediately evaporate and produce a gaseous
+envelope which we have seen does not exist. With air and water absent
+there can be of course no vegetation or life of any kind upon the moon,
+and we are compelled to regard it as an arid desert, utterly waste.
+
+107. TEMPERATURE OF THE MOON.--A characteristic feature of terrestrial
+deserts, which is possessed in exaggerated degree by the moon, is the
+great extremes of temperature to which they and it are subject. Owing to
+its slow rotation about its axis, a point on the moon receives the solar
+radiation uninterruptedly for more than a fortnight, and that too
+unmitigated by any cloud or vaporous covering. Then for a like period it
+is turned away from the sun and allowed to cool off, radiating into
+interplanetary space without hindrance its accumulated store of heat. It
+is easy to see that the range of temperature between day and night must
+be much greater under these circumstances than it is with us where
+shorter days and clouded skies render day and night more nearly alike,
+to say nothing of the ocean whose waters serve as a great balance wheel
+for equalizing temperatures. Just how hot or how cold the moon becomes
+is hard to determine, and very different estimates are to be found in
+the books. Perhaps the most reliable of these are furnished by the
+recent researches of Professor Very, whose experiments lead him to
+conclude that "its rocky surface at midday, in latitudes where the sun
+is high, is probably hotter than boiling water and only the most
+terrible of earth's deserts, where the burning sands blister the skin,
+and men, beasts, and birds drop dead, can approach a noontide on the
+cloudless surface of our satellite. Only the extreme polar latitudes of
+the moon can have an endurable temperature by day, to say nothing of the
+night, when we should have to become troglodytes to preserve ourselves
+from such intense cold."
+
+While the night temperature of the moon, even very soon after sunset,
+sinks to something like 200° below zero on the centigrade scale, or 320°
+below zero on the Fahrenheit scale, the lowest known temperature upon
+the earth, according to General Greely, is 90° Fahr. below zero,
+recorded in Siberia in January, 1885.
+
+Winter and summer are not markedly different upon the moon, since its
+rotation axis is nearly perpendicular to the plane of the earth's orbit
+about the sun, and the sun never goes far north or south of the moon's
+equator. The month is the one cycle within which all seasonal changes in
+its physical condition appear to run their complete course.
+
+108. CHANGES IN THE MOON.--It is evidently idle to look for any such
+changes in the condition of the moon's surface as with us mark the
+progress of the seasons or the spread of civilization over the
+wilderness. But minor changes there may be, and it would seem that the
+violent oscillations of temperature from day to night ought to have some
+effect in breaking down and crumbling the sharp peaks and crags which
+are there so common and so pronounced. For a century past astronomers
+have searched carefully for changes of this kind--the filling up of some
+crater or the fall of a mountain peak; but while some things of this
+kind have been reported from time to time, the evidence in their behalf
+has not been altogether conclusive. At the present time it is an open
+question whether changes of this sort large enough to be seen from the
+earth are in progress. A crater much less than a mile wide can be seen
+in the telescope, but it is not easy to tell whether so minute an object
+has changed in size or shape during a year or a decade, and even if
+changes are seen they may be apparent rather than real. Fig. 64 contains
+two views of the crater Archimedes, taken under a morning and an
+afternoon sun respectively, and shows a very pronounced difference
+between the two which proceeds solely from a difference of illumination.
+In the presence of such large fictitious changes astronomers are slow to
+accept smaller ones as real.
+
+[Illustration: FIG. 64.--Archimedes in the lunar morning and
+afternoon.--WEINEK.]
+
+It is this absence of change that is responsible for the rugged and
+sharp-cut features of the moon which continue substantially as they were
+made, while upon the earth rain and frost are continually wearing down
+the mountains and spreading their substance upon the lowland in an
+unending process of smoothing off the roughnesses of its surface. Upon
+the moon this process is almost if not wholly wanting, and the moon
+abides to-day much more like its primitive condition than is the earth.
+
+109. THE MOON'S INFLUENCE UPON THE EARTH.--There is a widespread popular
+belief that in many ways the moon exercises a considerable influence
+upon terrestrial affairs: that it affects the weather for good or ill,
+that crops must be planted and harvested, pigs must be killed, and
+timber cut at the right time of the moon, etc. Our common word lunatic
+means moonstruck--i. e., one upon whom the moon has shone while
+sleeping. There is not the slightest scientific basis for any of these
+beliefs, and astronomers everywhere class them with tales of witchcraft,
+magic, and popular delusion. For the most part the moon's influence upon
+the earth is limited to the light which it sends and the effect of its
+gravitation, chiefly exhibited in the ocean tides. We receive from the
+moon a very small amount of second-hand solar heat and there is also a
+trifling magnetic influence, but neither of these last effects comes
+within the range of ordinary observation, and we shall not go far wrong
+in saying that, save the moonlight and the tides, every supposed lunar
+influence upon the earth is either fictitious or too small to be readily
+detected.
+
+
+
+
+CHAPTER X
+
+THE SUN
+
+
+110. DEPENDENCE OF THE EARTH UPON THE SUN.--There is no better
+introduction to the study of the sun than Byron's Ode to Darkness,
+beginning with the lines--
+
+    "I dreamed a dream
+    That was not all a dream.
+    The bright sun was extinguished,"
+
+and proceeding to depict in vivid words the consequences of this
+extinction. The most matter-of-fact language of science agrees with the
+words of the poet in declaring the earth's dependence upon the sun for
+all those varied forms of energy which make it a fit abode for living
+beings. The winds blow and the rivers run; the crops grow, are gathered
+and consumed, by virtue of the solar energy. Factory, locomotive, beast,
+bird, and the human body furnish types of machines run by energy derived
+from the sun; and the student will find it an instructive exercise to
+search for kinds of terrestrial energy which are not derived either
+directly or indirectly from the sun. There are a few such, but they are
+neither numerous nor important.
+
+111. THE SUN'S DISTANCE FROM THE EARTH.--To the astronomer the sun
+presents problems of the highest consequence and apparently of very
+diverse character, but all tending toward the same goal: the framing of
+a mechanical explanation of the sun considered as a machine; what it is,
+and how it does its work. In the forefront of these problems stand those
+numerical determinations of distance, size, mass, density, etc., which
+we have already encountered in connection with the moon, but which must
+here be dealt with in a different manner, because the immensely greater
+distance of the sun makes impossible the resort to any such simple
+method as the triangle used for determining the moon's distance. It
+would be like determining the distance of a steeple a mile away by
+observing its direction first from one eye, then from the other; too
+short a base for the triangle. In one respect, however, we stand upon a
+better footing than in the case of the moon, for the mass of the earth
+has already been found (Chapter IV) as a fractional part of the sun's
+mass, and we have only to invert the fraction in order to find that the
+sun's mass is 329,000 times that of the earth and moon combined, or
+333,000 times that of the earth alone.
+
+If we could rely implicitly upon this number we might make it determine
+for us the distance of the sun through the law of gravitation as
+follows: It was suggested in § 38 that Newton proved Kepler's three laws
+to be imperfect corollaries from the law of gravitation, requiring a
+little amendment to make them strictly correct, and below we give in the
+form of an equation Kepler's statement of the Third Law together with
+Newton's amendment of it. In these equations--
+
+_T_ = Periodic time of any planet;
+
+_a_ = One half the major axis of its orbit;
+
+_m_ = Its mass;
+
+_M_ = The mass of the sun;
+
+_k_ = The gravitation constant corresponding to the particular set of
+units in which _T_, _a_, _m_, and _M_ are expressed.
+
+  (Kepler) a^{3}/T^{2} = h;
+  (Newton) a^{3}/T^{2} = k (M + m).
+
+Kepler's idea was: For every planet which moves around the sun, _a^{3}_
+divided by _T^{2}_ always gives the same quotient, _h_; and he did not
+concern himself with the significance of this quotient further than to
+note that if the particular _a_ and _T_ which belong to any
+planet--e. g., the earth--be taken as the units of length and time, then
+the quotient will be 1. Newton, on the other hand, attached a meaning to
+the quotient, and showed that it is equal to the product obtained by
+multiplying the sum of the two masses, planet and sun, by a number which
+is always the same when we are dealing with the action of gravitation,
+whether it be between the sun and planet, or between moon and earth, or
+between the earth and a roast of beef in the butcher's scales, provided
+only that we use always the same units with which to measure times,
+distances, and masses.
+
+Numerically, Newton's correction to Kepler's Third Law does not amount
+to much in the motion of the planets. Jupiter, which shows the greatest
+effect, makes the circuit of his orbit in 4,333 days instead of 4,335,
+which it would require if Kepler's law were strictly true. But in
+another respect the change is of the utmost importance, since it enables
+us to extend Kepler's law, which relates solely to the sun and its
+planets, to other attracting bodies, such as the earth, moon, and stars.
+Thus for the moon's motion around the earth we write--
+
+    (240,000^{3})/(27.32^{2}) = k (1 + 1/81),
+
+from which we may find that, with the units here employed, the earth's
+mass as the unit of mass, the mean solar day as the unit of time, and
+the mile as the unit of distance--
+
+    k = 1830 × 10^{10}.
+
+If we introduce this value of _k_ into the corresponding equation, which
+represents the motion of the earth around the sun, we shall have--
+
+    a^{3}/(365.25)^{2} = 1830 × 10^{10} (333,000 + 1),
+
+where the large number in the parenthesis represents the number of times
+the mass of the sun is greater than the mass of the earth. We shall find
+by solving this equation that _a_, the mean distance of the sun from the
+earth, is very approximately 93,000,000 miles.
+
+113. ANOTHER METHOD OF DETERMINING THE SUN'S DISTANCE.--This will be
+best appreciated by a reference to Fig. 17. It appears here that the
+earth makes its nearest approach to the orbit of Mars in the month of
+August, and if in any August Mars happens to be in opposition, its
+distance from the earth will be very much less than the distance of the
+sun from the earth, and may be measured by methods not unlike those
+which served for the moon. If now the orbits of Mars and the earth were
+circles having their centers at the sun this distance between them,
+which we may represent by _D_, would be the difference of the radii of
+these orbits--
+
+    D = a““ - a“,
+
+where the accents ““, “ represent Mars and the earth respectively.
+Kepler's Third Law furnishes the relation--
+
+    (a““)^{3}/(T““)^{2} = (a“)^{3}/(T“)^{2};
+
+and since the periodic times of the earth and Mars, _T“_, _T““_, are
+known to a high degree of accuracy, these two equations are sufficient
+to determine the two unknown quantities, _a“_, _a““_--i. e., the
+distance of the sun from Mars as well as from the earth. The first of
+these equations is, of course, not strictly true, on account of the
+elliptical shape of the orbits, but this can be allowed for easily
+enough.
+
+In practice it is found better to apply this method of determining the
+sun's distance through observations of an asteroid rather than
+observations of Mars, and great interest has been aroused among
+astronomers by the discovery, in 1898, of an asteroid, or planet, Eros,
+which at times comes much closer to the earth than does Mars or any
+other heavenly body except the moon, and which will at future
+oppositions furnish a more accurate determination of the sun's distance
+than any hitherto available. Observations for this purpose are being
+made at the present time (October, 1900).
+
+Many other methods of measuring the sun's distance have been devised by
+astronomers, some of them extremely ingenious and interesting, but every
+one of them has its weak point--e. g., the determination of the mass of
+the earth in the first method given above and the measurement of _D_ in
+the second method, so that even the best results at present are
+uncertain to the extent of 200,000 miles or more, and astronomers,
+instead of relying upon any one method, must use all of them, and take
+an average of their results. According to Professor Harkness, this
+average value is 92,796,950 miles, and it seems certain that a line of
+this length drawn from the earth toward the sun would end somewhere
+within the body of the sun, but whether on the nearer or the farther
+side of the center, or exactly at it, no man knows.
+
+114. PARALLAX AND DISTANCE.--It is quite customary among astronomers to
+speak of the sun's parallax, instead of its distance from the earth,
+meaning by parallax its difference of direction as seen from the center
+and surface of the earth--i. e., the angle subtended at the sun by a
+radius of the earth placed at right angles to the line of sight. The
+greater the sun's distance the smaller will this angle be, and it
+therefore makes a substitute for the distance which has the advantage of
+being represented by a small number, 8".8, instead of a large one.
+
+The books abound with illustrations intended to help the reader
+comprehend how great is a distance of 93,000,000 miles, but a single one
+of these must suffice here. To ride 100 miles a day 365 days in the year
+would be counted a good bicycling record, but the rider who started at
+the beginning of the Christian era and rode at that rate toward the sun
+from the year 1 A. D. down to the present moment would not yet have
+reached his destination, although his journey would be about three
+quarters done. He would have crossed the orbit of Venus about the time
+of Charlemagne, and that of Mercury soon after the discovery of America.
+
+115. SIZE AND DENSITY OF THE SUN.--Knowing the distance of the sun, it
+is easy to find from the angle subtended by its diameter (32 minutes of
+arc) that the length of that diameter is 865,000 miles. We recall in
+this connection that the diameter of the moon's _orbit_ is only 480,000
+miles, but little more than half the diameter of the sun, thus affording
+abundant room inside the sun, and to spare, for the moon to perform the
+monthly revolution about its orbit, as shown in Fig. 65.
+
+[Illustration: FIG. 65.--The sun's size.--YOUNG.]
+
+In the same manner in which the density of the moon was found from its
+mass and diameter, the student may find from the mass and diameter of
+the sun given above that its mean density is 1.4 times that of water.
+This is about the same as the density of gravel or soft coal, and is
+just about one quarter of the average density of the earth.
+
+We recall that the small density of the moon was accounted for by the
+diminished weight of objects upon it, but this explanation can not hold
+in the case of the sun, for not only is the density less but the force
+of gravity (weight) is there 28 times as great as upon the earth. The
+athlete who here weighs 175 pounds, if transported to the surface of the
+sun would weigh more than an elephant does here, and would find his
+bones break under his own weight if his muscles were strong enough to
+hold him upright. The tremendous pressure exerted by gravity at the
+surface of the sun must be surpassed below the surface, and as it does
+not pack the material together and make it dense, we are driven to one
+of two conclusions: Either the stuff of which the sun is made is
+altogether unlike that of the earth, not so readily compressed by
+pressure, or there is some opposing influence at work which more than
+balances the effect of gravity and makes the solar stuff much lighter
+than the terrestrial.
+
+116. MATERIAL OF WHICH THE SUN IS MADE.--As to the first of these
+alternatives, the spectroscope comes to our aid and shows in the sun's
+spectrum (Fig. 50) the characteristic line marked _D_, which we know
+always indicates the presence of sodium and identifies at least one
+terrestrial substance as present in the sun in considerable quantity.
+The lines marked _C_ and _F_ are produced by hydrogen, which is one of
+the constituents of water, _E_ shows calcium to be present in the sun,
+_b_ magnesium, etc. In this way it has been shown that about one half of
+our terrestrial elements, mainly the metallic ones, are present as gases
+on or near the sun's surface, but it must not be inferred that elements
+not found in this way are absent from the sun. They may be there,
+probably are there, but the spectroscopic proof of their presence is
+more difficult to obtain. Professor Rowland, who has been prominent in
+the study of the solar spectrum, says: "Were the whole earth heated to
+the temperature of the sun, its spectrum would probably resemble that of
+the sun very closely."
+
+Some of the common terrestrial elements found in the sun are:
+
+      Aluminium.
+      Calcium.
+      Carbon.
+      Copper.
+      Hydrogen.
+      Iron.
+      Lead.
+      Nickel.
+      Potassium.
+      Silicon.
+      Silver.
+      Sodium.
+      Tin.
+      Zinc.
+      Oxygen (?)
+
+Whatever differences of chemical structure may exist between the sun and
+the earth, it seems that we must regard these bodies as more like than
+unlike to each other in substance, and we are brought back to the second
+of our alternatives: there must be some influence opposing the force of
+gravity and making the substance of the sun light instead of heavy, and
+we need not seek far to find it in--
+
+117. THE HEAT OF THE SUN.--That the sun is hot is too evident to require
+proof, and it is a familiar fact that heat expands most substances and
+makes them less dense. The sun's heat falling upon the earth expands it
+and diminishes its density in some small degree, and we have only to
+imagine this process of expansion continued until the earth's diameter
+becomes 58 per cent larger than it now is, to find the earth's density
+reduced to a level with that of the sun. Just how much the temperature
+of the earth must be raised to produce this amount of expansion we do
+not know, neither do we know accurately the temperature of the sun, but
+there can be no doubt that heat is the cause of the sun's low density
+and that the corresponding temperature is very high.
+
+Before we inquire more closely into the sun's temperature, it will be
+well to draw a sharp distinction between the two terms heat and
+temperature, which are often used as if they meant the same thing. Heat
+is a form of energy which may be found in varying degree in every
+substance, whether warm or cold--a block of ice contains a considerable
+amount of heat--while temperature corresponds to our sensations of warm
+and cold, and measures the extent to which heat is concentrated in the
+body. It is the amount of heat per molecule of the body. A barrel of
+warm water contains more heat than the flame of a match, but its
+temperature is not so high. Bearing in mind this distinction, we seek to
+determine not the amount of heat contained in the sun but the sun's
+temperature, and this involves the same difficulty as does the question,
+What is the temperature of a locomotive? It is one thing in the fire box
+and another thing in the driving wheels, and still another at the
+headlight; and so with the sun, its temperature is certainly different
+in different parts--one thing at the center and another at the surface.
+Even those parts which we see are covered by a veil of gases which
+produce by absorption the dark lines of the solar spectrum, and
+seriously interfere both with the emission of energy from the sun and
+with our attempts at measuring the temperature of those parts of the
+surface from which that energy streams.
+
+In view of these and other difficulties we need not be surprised that
+the wildest discordance has been found in estimates of the solar
+temperature made by different investigators, who have assigned to it
+values ranging from 1,400° C. to more than 5,000,000° C. Quite recently,
+however, improved methods and a better understanding of the problem have
+brought about a better agreement of results, and it now seems probable
+that the temperature of the visible surface of the sun lies somewhere
+between 5,000° and 10,000° C., say 15,000° of the Fahrenheit scale.
+
+118. DETERMINING THE SUN'S TEMPERATURE.--One ingenious method which has
+been used for determining this temperature is based upon the principle
+stated above, that every object, whether warm or cold, contains heat and
+gives it off in the form of radiant energy. The radiation from a body
+whose temperature is lower than 500° C. is made up exclusively of energy
+whose wave length is greater than 7,600 tenth meters, and is therefore
+invisible to the eye, although a thermometer or even the human hand can
+often detect it as radiant heat. A brick wall in the summer sunshine
+gives off energy which can be felt as heat but can not be seen. When
+such a body is further heated it continues to send off the same kinds
+(wave lengths) of energy as before, but new and shorter waves are added
+to its radiation, and when it begins to emit energy of wave length 7,500
+or 7,600 tenth meters, it also begins to shine with a dull-red light,
+which presently becomes brighter and less ruddy and changes to white as
+the temperature rises, and waves of still shorter length are thereby
+added to the radiation. We say, in common speech, the body becomes first
+red hot and then white hot, and we thus recognize in a general way that
+the kind or color of the radiation which a body gives off is an index to
+its temperature. The greater the proportion of energy of short wave
+lengths the higher is the temperature of the radiating body. In sunlight
+the maximum of brilliancy to the eye lies at or near the wave length,
+5,600 tenth meters, but the greatest intensity of radiation of all kinds
+(light included) is estimated to fall somewhere between green and blue
+in the spectrum at or near the wave length 5,000 tenth meters, and if we
+can apply to this wave length Paschen's law--temperature reckoned in
+degrees centigrade from the absolute zero is always equal to the
+quotient obtained by dividing the number 27,000,000 by the wave length
+corresponding to maximum radiation--we shall find at once for the
+absolute temperature of the sun's surface 5,400° C.
+
+Paschen's law has been shown to hold true, at least approximately, for
+lower temperatures and longer wave lengths than are here involved, but
+as it is not yet certain that it is strictly true and holds for all
+temperatures, too great reliance must not be attached to the numerical
+result furnished by it.
+
+[Illustration: FIG. 66.--The sun, August 11, 1894. Photographed at the
+Goodsell Observatory.]
+
+[Illustration: FIG. 67.--The sun, August 14, 1894. Photographed at the
+Goodsell Observatory.]
+
+119. THE SUN'S SURFACE.--A marked contrast exists between the faces of
+sun and moon in respect of the amount of detail to be seen upon them,
+the sun showing nothing whatever to correspond with the mountains,
+craters, and seas of the moon. The unaided eye in general finds in the
+sun only a blank bright circle as smooth and unmarked as the surface of
+still water, and even the telescope at first sight seems to show but
+little more. There may usually be found upon the sun's face a certain
+number of black patches called _sun spots_, such as are shown in Figs.
+66 to 69, and occasionally these are large enough to be seen through a
+smoked glass without the aid of a telescope. When seen near the edge of
+the sun they are quite frequently accompanied, as in Fig. 69, by vague
+patches called _faculę_ (Latin, _facula_ = a little torch), which look a
+little brighter than the surrounding parts of the sun. So, too, a good
+photograph of the sun usually shows that the central parts of the disk
+are rather brighter than the edge, as indeed we should expect them to
+be, since the absorption lines in the sun's spectrum have already taught
+us that the visible surface of the sun is enveloped by invisible vapors
+which in some measure absorb the emitted light and render it feebler at
+the edge where it passes through a greater thickness of this envelope
+than at the center. See Fig. 70, where it is shown that the energy
+coming from the edge of the sun to the earth has to traverse a much
+longer path inside the vapors than does that coming from the center.
+
+[Illustration: FIG. 68.--The sun, August 18, 1894. Photographed at the
+Goodsell Observatory.]
+
+Examine the sun spots in the four photographs, Figs. 66 to 69, and note
+that the two spots which appear at the extreme left of the first
+photograph, very much distorted and foreshortened by the curvature of
+the sun's surface, are seen in a different part of the second picture,
+and are not only more conspicuous but show better their true shape.
+
+[Illustration: PLATE II. THE EQUATORIAL CONSTELLATIONS]
+
+120. THE SUN'S ROTATION.--The changed position of these spots shows that
+the sun rotates about an axis at right angles to the direction of the
+spot's motion, and the position of this axis is shown in the figure by a
+faint line ruled obliquely across the face of the sun nearly north and
+south in each of the four photographs. This rotation in the space of
+three days has carried the spots from the edge halfway to the center of
+the disk, and the student should note the progress of the spots in the
+two later photographs, that of August 21st showing them just ready to
+disappear around the farther edge of the sun.
+
+[Illustration: FIG. 69.--The sun, August 21, 1894. Photographed at the
+Goodsell Observatory.]
+
+Plot accurately in one of these figures the positions of the spots as
+shown in the other three, and observe whether the path of the spots
+across the sun's face is a straight line. Is there any reason why it
+should not be straight?
+
+These four pictures may be made to illustrate many things about the sun.
+Thus the sun's axis is not parallel to that of the earth, for the
+letters _N S_ mark the direction of a north and south line across the
+face of the sun, and this line, of course, is parallel to the earth's
+axis, while it is evidently not parallel to the sun's axis. The group of
+spots took more than ten days to move across the sun's face, and as at
+least an equal time must be required to move around the opposite side of
+the sun, it is evident that the period of the sun's rotation is
+something more than 20 days. It is, in fact, rather more than 25 days,
+for this same group of spots reappeared again on the left-hand edge of
+the sun on September 5th.
+
+[Illustration: FIG. 70.--Absorption at the sun's edge.]
+
+121. SUN SPOTS.--Another significant fact comes out plainly from the
+photographs. The spots are not permanent features of the sun's face,
+since they changed their size and shape very appreciably in the few days
+covered by the pictures. Compare particularly the photographs of August
+14th and August 18th, where the spots are least distorted by the
+curvature of the sun's surface. By September 16th this group of spots
+had disappeared absolutely from the sun's face, although when at its
+largest the group extended more than 80,000 miles in length, and several
+of the individual spots were large enough to contain the earth if it had
+been dropped upon them. From Fig. 67 determine in miles the length of
+the group on August 14th. Fig. 71 shows an enlarged view of these spots
+as they appeared on August 17th, and in this we find some details not so
+well shown in the preceding pictures. The larger spots consist of a
+black part called the _nucleus_ or _umbra_ (Latin, shadow), which is
+surrounded by an irregular border called the _penumbra_ (partial
+shadow), which is intermediate in brightness between the nucleus and
+the surrounding parts of the sun. It should not be inferred from the
+picture that the nucleus is really black or even dark. It shines, in
+fact, with a brilliancy greater than that of an electric lamp, but the
+background furnished by the sun's surface is so much brighter that by
+contrast with it the nucleus and penumbra appear relatively dark.
+
+[Illustration: FIG. 71.--Sun spots, August 17, 1894. Goodsell
+Observatory.]
+
+[Illustration: FIG. 72.--Sun spot of March 5, 1873.--From LANGLEY, The
+New Astronomy. By permission of the publishers.]
+
+The bright shining surface of the sun, the background for the spots, is
+called the _photosphere_ (Greek, light sphere), and, as Fig. 71 shows,
+it assumes under a suitable magnifying power a mottled aspect quite
+different from the featureless expanse shown in the earlier pictures.
+The photosphere is, in fact, a layer of little clouds with darker
+spaces between them, and the fine detail of these clouds, their
+complicated structure, and the way in which, when projected against the
+background of a sun spot, they produce its penumbra, are all brought out
+in Fig. 72. Note that the little patch in one corner of this picture
+represents North and South America drawn to the same scale as the sun
+spots.
+
+[Illustration: FIG. 73.--Spectroheliograph, showing distribution of
+faculę upon the sun.--HALE.]
+
+[Illustration: FIG. 74.--Eclipse of July 20, 1878.--TROUVELOT.]
+
+122. FACULĘ.--We have seen in Fig. 69 a few of the bright spots called
+faculę. At the telescope or in the ordinary photograph these can be seen
+only at the edge of the sun, because elsewhere the background furnished
+by the photosphere is so bright that they are lost in it. It is
+possible, however, by an ingenious application of the spectroscope to
+break up the sunlight into a spectrum in such a way as to diminish the
+brightness of this background, much more than the brightness of the
+faculę is diminished, and in this way to obtain a photograph of the
+sun's surface which shall show them wherever they occur, and such a
+photograph, showing faintly the spectral lines, is reproduced in Fig.
+73. The faculę are the bright patches which stretch inconspicuously
+across the face of the sun, in two rather irregular belts with a
+comparatively empty lane between them. This lane lies along the sun's
+equator, and it is upon either side of it between latitudes 5° and 40°
+that faculę seem to be produced. It is significant of their connection
+with sun spots that the spots occur in these particular zones and are
+rarely found outside them.
+
+[Illustration: FIG. 75.--Eclipse of April 16, 1893.--SCHAEBERLE.]
+
+123. INVISIBLE PARTS OF THE SUN. THE CORONA.--Thus far we have been
+dealing with parts of the sun that may be seen and photographed under
+all ordinary conditions. But outside of and surrounding these parts is
+an envelope, or rather several envelopes, of much greater extent than
+the visible sun. These envelopes are for the most part invisible save at
+those times when the brighter central portions of the sun are hidden in
+a total eclipse.
+
+[Illustration: FIG. 76.--Eclipse of January 21, 1898.--CAMPBELL.]
+
+Fig. 74 is from a drawing, and Figs. 75 and 76 are from eclipse
+photographs showing this region, in which the most conspicuous object
+is the halo of soft light called the _corona_, that completely surrounds
+the sun but is seen to be of differing shapes and differing extent at
+the several eclipses here shown, although a large part of these apparent
+differences is due to technical difficulties in photographing, and
+reproducing an object with outlines so vague as those of the corona. The
+outline of the corona is so indefinite and its outer portions so faint
+that it is impossible to assign to it precise dimensions, but at its
+greatest extent it reaches out for several millions of miles and fills a
+space more than twenty times as large as the visible part of the sun.
+Despite its huge bulk, it is of most unsubstantial character, an airy
+nothing through which comets have been known to force their way around
+the sun from one side to the other, literally for millions of miles,
+without having their course influenced or their velocity checked to any
+appreciable extent. This would hardly be possible if the density even at
+the bottom of the corona were greater than that of the best vacuum which
+we are able to produce in laboratory experiments. It seems odd that a
+vacuum should give off so bright a light as the coronal pictures show,
+and the exact character of that light and the nature of the corona are
+still subjects of dispute among astronomers, although it is generally
+agreed that, in part at least, its light is ordinary sunlight faintly
+reflected from the widely scattered molecules composing the substance of
+the corona. It is also probable that in part the light has its origin in
+the corona itself. A curious and at present unconfirmed result announced
+by one of the observers of the eclipse of May 28, 1900, is that _the
+corona is not hot_, its effective temperature being lower than that of
+the instrument used for the observation.
+
+[Illustration: FIG. 77.--Solar prominence of March 25, 1895.--HALE.]
+
+124. THE CHROMOSPHERE.--Between the corona and the photosphere there is
+a thin separating layer called the _chromosphere_ (Greek, color sphere),
+because when seen at an eclipse it shines with a brilliant red light
+quite unlike anything else upon the sun save the _prominences_ which are
+themselves only parts of the chromosphere temporarily thrown above its
+surface, as in a fountain a jet of water is thrown up from the basin and
+remains for a few moments suspended in mid-air. Not infrequently in such
+a fountain foreign matter is swept up by the rush of the water--dirt,
+twigs, small fish, etc.--and in like manner the prominences often carry
+along with them parts of the underlying layers of the sun, photosphere,
+faculę, etc., which reveal their presence in the prominence by adding
+their characteristic lines to the spectrum, like that of the
+chromosphere, which the prominence presents when they are absent. None
+of the eclipse photographs (Figs. 74 to 76) show the chromosphere,
+because the color effect is lacking in them, but a great curving
+prominence may be seen near the bottom of Fig. 75, and smaller ones at
+other parts of the sun's edge.
+
+[Illustration: FIG. 78.--A solar prominence.--HALE.]
+
+125. PROMINENCES.--Fig. 77 shows upon a larger scale one of these
+prominences rising to a height of 160,000 miles above the photosphere;
+and another photograph, taken 18 minutes later, but not reproduced here,
+showed the same prominence grown in this brief interval to a stature of
+280,000 miles. These pictures were not taken during an eclipse, but in
+full sunlight, using the same spectroscopic apparatus which was employed
+in connection with the faculę to diminish the brightness of the
+background without much enfeebling the brilliancy of the prominence
+itself. The dark base from which the prominence seems to spring is not
+the sun's edge, but a part of the apparatus used to cut off the direct
+sunlight.
+
+Fig. 78 contains a series of photographs of another prominence taken
+within an interval of 1 hour 47 minutes and showing changes in size and
+shape which are much more nearly typical of the ordinary prominence than
+was the very unusual change in the case of Fig. 77.
+
+[Illustration: FIG. 79.--Contrasted forms of solar
+prominences.--ZOELLNER.]
+
+The preceding pictures are from photographs, and with them the student
+may compare Fig. 79, which is constructed from drawings made at the
+spectroscope by the German astronomer Zoellner. The changes here shown
+are most marked in the prominence at the left, which is shaped like a
+broken tree trunk, and which appears to be vibrating from one side to
+the other like a reed shaken in the wind. Such a prominence is
+frequently called an _eruptive_ one, a name suggested by its appearance
+of having been blown out from the sun by something like an explosion,
+while the prominence at the right in this series of drawings, which
+appears much less agitated, is called by contrast with the other a
+_quiescent_ prominence. These quiescent prominences are, as a rule, much
+longer-lived than the eruptive ones. One more picture of prominences
+(Fig. 80) is introduced to show the continuous stretch of chromosphere
+out of which they spring.
+
+[Illustration: FIG. 80.--Prominences and chromosphere.--HALE.]
+
+Prominences are seen only at the edge of the sun, because it is there
+alone that the necessary background can be obtained, but they must occur
+at the center of the sun and elsewhere quite as well as at the edge, and
+it is probable that quiescent prominences are distributed over all parts
+of the sun's surface, but eruptive prominences show a strong tendency
+toward the regions of sun spots and faculę as if all three were
+intimately related phenomena.
+
+126. THE SUN AS A MACHINE.--Thus far we have considered the anatomy of
+the sun, dissecting it into its several parts, and our next step should
+be a consideration of its physiology, the relation of the parts to each
+other, and their function in carrying on the work of the solar organism,
+but this step, unfortunately, must be a lame one. The science of
+astronomy to-day possesses no comprehensive and well-established theory
+of this kind, but looks to the future for the solution of this the
+greatest pending problem of solar physics. Progress has been made
+toward its solution, and among the steps of this progress that we shall
+have to consider, the first and most important is the conception of the
+sun as a kind of heat engine.
+
+In a steam engine coal is burned under the boiler, and its chemical
+energy, transformed into heat, is taken up by the water and delivered,
+through steam as a medium, to the engine, which again transforms and
+gives it out as mechanical work in the turning of shafts, the driving of
+machinery, etc. Now, the function of the sun is exactly opposite to that
+of the engine and boiler: it gives out, instead of receiving, radiant
+energy; but, like the engine, it must be fed from some source; it can
+not be run upon nothing at all any more than the engine can run day
+after day without fresh supplies of fuel under its boiler. We know that
+for some thousands of years the sun has been furnishing light and heat
+to the earth in practically unvarying amount, and not to the earth
+alone, but it has been pouring forth these forms of energy in every
+direction, without apparent regard to either use or economy. Of all the
+radiant energy given off by the sun, only two parts out of every
+thousand million fall upon any planet of the solar system, and of this
+small fraction the earth takes about one tenth for the maintenance of
+its varied forms of life and action. Astronomers and physicists have
+sought on every hand for an explanation of the means by which this
+tremendous output of energy is maintained century after century without
+sensible diminution, and have come with almost one mind to the
+conclusion that the gravitative forces which reside in the sun's own
+mass furnish the only adequate explanation for it, although they may be
+in some small measure re-enforced by minor influences, such as the fall
+of meteoric dust and stones into the sun.
+
+Every boy who has inflated a bicycle tire with a hand pump knows that
+the pump grows warm during the operation, on account of the compression
+of the air within the cylinder. A part of the muscular force (energy)
+expended in working the pump reappears in the heat which warms both air
+and pump, and a similar process is forever going on in the sun, only in
+place of muscular force we must there substitute the tremendous
+attraction of gravitation, 28 times as great as upon the earth. "The
+matter in the interior of the sun must be as a shuttlecock between the
+stupendous pressure and the enormously high temperature," the one
+tending to compress and the other to expand it, but with this important
+difference between them: the temperature steadily tends to fall as the
+heat energy is wasted away, while the gravitative force suffers no
+corresponding diminution, and in the long run must gain the upper hand,
+causing the sun to shrink and become more dense. It is this progressive
+shrinking and compression of its molecules into a smaller space which
+supplies the energy contained in the sun's output of light and heat.
+According to Lord Kelvin, each centimeter of shrinkage in the sun's
+diameter furnishes the energy required to keep up its radiation for
+something more than an hour, and, on account of the sun's great
+distance, the shrinkage might go on at this rate for many centuries
+without producing any measurable effect in the sun's appearance.
+
+127. GASEOUS CONSTITUTION OF THE SUN.--But Helmholtz's dynamical theory
+of the maintenance of the sun's heat, which we are here considering,
+includes one essential feature that is not sufficiently stated above. In
+order that the explanation may hold true, it is necessary that the sun
+should be in the main a gaseous body, composed from center to
+circumference of gases instead of solid or liquid parts. Pumping air
+warms the bicycle pump in a way that pumping water or oil will not.
+
+The high temperature of the sun itself furnishes sufficient reason for
+supposing the solar material to be in the gaseous state, but the gas
+composing those parts of the sun below the photosphere must be very
+different in some of its characteristics from the air or other gases
+with which we are familiar at the earth, since its average density is
+1,000 times as great as that of air, and its consistence and mechanical
+behavior must be more like that of honey or tar than that of any gas
+with which we are familiar. It is worth noting, however, that if a hole
+were dug into the crust of the earth to a depth of 15 or 20 miles the
+air at the bottom of the hole would be compressed by that above it to a
+density comparable with that of the solar gases.
+
+128. THE SUN'S CIRCULATION.--It is plain that under the conditions which
+exist in the sun the outer portions, which can radiate their heat freely
+into space, must be cooler than the inner central parts, and this
+difference of temperature must set up currents of hot matter drifting
+upward and outward from within the sun and counter currents of cooler
+matter settling down to take its place. So, too, there must be some
+level at which the free radiation into outer space chills the hot matter
+sufficiently to condense its less refractory gases into clouds made up
+of liquid drops, just as on a cloudy day there is a level in our own
+atmosphere at which the vapor of water condenses into liquid drops which
+form the thin shell of clouds that hovers above the earth's surface,
+while above and below is the gaseous atmosphere. In the case of the sun
+this cloud layer is always present and is that part which we have
+learned to call the photosphere. Above the photosphere lies the
+chromosphere, composed of gases less easily liquefied, hydrogen is the
+chief one, while between photosphere and chromosphere is a thin layer of
+metallic vapors, perhaps indistinguishable from the top crust of the
+photosphere itself, which by absorbing the light given off from the
+liquid photosphere produces the greater part of the Fraunhofer lines in
+the solar spectrum.
+
+From time to time the hot matter struggling up from below breaks through
+the photosphere and, carrying with it a certain amount of the metallic
+vapors, is launched into the upper and cooler regions of the sun,
+where, parting with its heat, it falls back again upon the photosphere
+and is absorbed into it. It is altogether probable that the corona is
+chiefly composed of fine particles ejected from the sun with velocities
+sufficient to carry them to a height of millions of miles, or even
+sufficient to carry them off never to return. The matter of the corona
+must certainly be in a state of the most lively agitation, its particles
+being alternately hurled up from the photosphere and falling back again
+like fireworks, the particles which make up the corona of to-day being
+quite a different set from those of yesterday or last week. It seems
+beyond question that the prominences and faculę too are produced in some
+way by this up-and-down circulation of the sun's matter, and that any
+mechanical explanation of the sun must be worked out along these lines;
+but the problem is an exceedingly difficult one, and must include and
+explain many other features of the sun's activity of which only a few
+can be considered here.
+
+129. THE SUN-SPOT PERIOD.--Sun spots come and go, and at best any
+particular spot is but short-lived, rarely lasting more than a month or
+two, and more often its duration is a matter of only a few days. They
+are not equally numerous at all times, but, like swarms of locusts, they
+seem to come and abound for a season and then almost to disappear, as if
+the forces which produced them were of a periodic character alternately
+active and quiet. The effect of this periodic activity since 1870 is
+shown in Fig. 81, where the horizontal line is a scale of times, and the
+distance of the curve above this line for any year shows the relative
+number of spots which appeared upon the sun in that year. This indicates
+very plainly that 1870, 1883, and 1893 were years of great sun-spot
+activity, while 1879 and 1889 were years in which few spots appeared.
+The older records, covering a period of two centuries, show the same
+fluctuations in the frequency of sun spots and from these records
+curves (which may be found in Young's, The Sun) have been plotted,
+showing a succession of waves extending back for many years.
+
+[Illustration: FIG. 81.--The curve of sun-spot frequency.]
+
+The sun-spot period is the interval of time from the crest or hollow of
+one wave to the corresponding part of the next one, and on the average
+this appears to be a little more than eleven years, but is subject to
+considerable variation. In accordance with this period there is drawn in
+broken lines at the right of Fig. 81 a predicted continuation of the
+sun-spot curve for the first decade of the twentieth century. The
+irregularity shown by the three preceding waves is such that we must not
+expect the actual course of future sun spots to correspond very closely
+to the prediction here made; but in a general way 1901 and 1911 will
+probably be years of few sun spots, while they will be numerous in 1905,
+but whether more or less numerous than at preceding epochs of greatest
+frequency can not be foretold with any approach to certainty so long as
+we remain in our present ignorance of the causes which make the sun-spot
+period.
+
+Determine from Fig. 81 as accurately as possible the length of the
+sun-spot period. It is hard to tell the exact position of a crest or
+hollow of the curve. Would it do to draw a horizontal line midway
+between top and bottom of the curve and determine the length of the
+period from its intersections with the curve--e. g., in 1874 and 1885?
+
+[Illustration: FIG. 82.--Illustrating change of the sun-spot zones.]
+
+130. THE SUN-SPOT ZONES.--It has been already noted that sun spots are
+found only in certain zones of latitude upon the sun, and that faculę
+and eruptive prominences abound in these zones more than elsewhere,
+although not strictly confined to them. We have now to note a
+peculiarity of these zones which ought to furnish a clew to the sun's
+mechanism, although up to the present time it has not been successfully
+traced out. Just before a sun-spot minimum the few spots which appear
+are for the most part clustered near the sun's equator. As these spots
+die out two new groups appear, one north the other south of the sun's
+equator and about 25° or 30° distant from it, and as the period advances
+toward a maximum these groups shift their positions more and more toward
+the equator, thus approaching each other but leaving between them a
+vacant lane, which becomes steadily narrower until at the close of the
+period, when the next minimum is at hand, it reaches its narrowest
+dimensions, but does not altogether close up even then. In Fig. 82 these
+relations are shown for the period falling between 1879 and 1890, by
+means of the horizontal lines; for each year one line in the northern
+and one in the southern hemisphere of the sun, their lengths being
+proportional to the number of spots which appeared in the corresponding
+hemisphere during the year, and their positions on the sun's disk
+showing the average latitude of the spots in question. It is very
+apparent from the figure that during this decade the sun's southern
+hemisphere was much more active than the northern one in the production
+of spots, and this appears to be generally the case, although the
+difference is not usually as great as in this particular decade.
+
+131. INFLUENCE OF THE SUN-SPOT PERIOD.--Sun spots are certainly less hot
+than the surrounding parts of the sun's surface, and, in view of the
+intimate dependence of the earth upon the solar radiation, it would be
+in no way surprising if their presence or absence from the sun's face
+should make itself felt in some degree upon the earth, raising and
+lowering its temperature and quite possibly affecting it in other ways.
+Ingenious men have suggested many such kinds of influence, which,
+according to their investigations, appear to run in cycles of eleven
+years. Abundant and scanty harvests, cyclones, tornadoes, epidemics,
+rainfall, etc., are among these alleged effects, and it is possible that
+there may be a real connection between any or all of them and the
+sun-spot period, but for the most part astronomers are inclined to hold
+that there is only one case in which the evidence is strong enough to
+really establish a connection of this kind. The magnetic condition of
+the earth and its disturbances, which are called magnetic storms, do
+certainly follow in a very marked manner the course of sun-spot
+activity, and perhaps there should be added to this the statement that
+auroras (northern lights) stand in close relation to these magnetic
+disturbances and are most frequent at the times of sun-spot maxima.
+
+Upon the sun, however, the influence of the spot period is not limited
+to things in and near the photosphere, but extends to the outermost
+limits of the corona. Determine from Fig. 81 the particular part of the
+sun-spot period corresponding to the date of each picture of the corona
+and note how the pictures which were taken near times of sun-spot minima
+present a general agreement in the shape and extent of the corona, while
+the pictures taken at a time of maximum activity of the sun spots show a
+very differently shaped and much smaller corona.
+
+132. THE LAW OF THE SUN'S ROTATION.--We have seen in a previous part of
+the chapter how the time required by the sun to make a complete rotation
+upon its axis may be determined from photographs showing the progress of
+a spot or group of spots across its disk, and we have now to add that
+when this is done systematically by means of many spots situated in
+different solar latitudes it leads to a very peculiar and extraordinary
+result. Each particular parallel of latitude has its own period of
+rotation different from that of its neighbors on either side, so that
+there can be no such thing as a fixed geography of the sun's surface.
+Every part of it is constantly taking up a new position with respect to
+every other part, much as if the Gulf of Mexico should be south of the
+United States this year, southeast of it next year, and at the end of a
+decade should have shifted around to the opposite side of the earth from
+us. A meridian of longitude drawn down the Mississippi Valley remains
+always a straight line, or, rather, great circle, upon the surface of
+the earth, while Fig. 83 shows what would become of such a meridian
+drawn through the equatorial parts of the sun's disk. In the first
+diagram it appears as a straight line running down the middle of the
+sun's disk. Twenty-five days later, when the same face of the sun comes
+back into view again, after making a complete revolution about the axis,
+the equatorial parts will have moved so much faster and farther than
+those in higher latitudes that the meridian will be warped as in the
+second diagram, and still more warped after another and another
+revolution, as shown in the figure.
+
+[Illustration: FIG. 83.--Effect of the sun's peculiar rotation in
+warping a meridian, originally straight.]
+
+At least such is the case if the spots truly represent the way in which
+the sun turns round. There is, however, a possibility that the spots
+themselves drift with varying speeds across the face of the sun, and
+that the differences which we find in their rates of motion belong to
+them rather than to the photosphere. Just what happens in the regions
+near the poles is hard to say, for the sun spots only extend about
+halfway from the equator to the poles, and the spectroscope, which may
+be made to furnish a certain amount of information bearing upon the
+case, is not as yet altogether conclusive, nor are the faculę which have
+also been observed for this purpose.
+
+The simple theory that the solar phenomena are caused by an interchange
+of hotter and cooler matter between the photosphere and the lower strata
+of the sun furnishes in its present shape little or no explanation of
+such features as the sun-spot period, the variations in the corona, the
+peculiar character of the sun's rotation, etc., and we have still
+unsolved in the mechanical theory of the sun one of the noblest problems
+of astronomy, and one upon which both observers and theoretical
+astronomers are assiduously working at the present time. A close watch
+is kept upon sun spots and prominences, the corona is observed at every
+total eclipse, and numerous are the ingenious methods which are being
+suggested and tried for observing it without an eclipse in ordinary
+daylight. Attempts, more or less plausible, have been made and are now
+pending to explain photosphere, spots and the reversing layer by means
+of the refraction of light within the sun's outer envelope of gases, and
+it seems altogether probable, in view of these combined activities, that
+a considerable addition to our store of knowledge concerning the sun may
+be expected in the not distant future.
+
+
+
+
+CHAPTER XI
+
+THE PLANETS
+
+
+133. PLANETS.--Circling about the sun, under the influence of his
+attraction, is a family of planets each member of which is, like the
+moon, a dark body shining by reflected sunlight, and therefore
+presenting phases; although only two of them, Mercury and Venus, run
+through the complete series--new, first quarter, full, last
+quarter--which the moon presents. The way in which their orbits are
+grouped about the sun has been considered in Chapter III, and Figs. 16
+and 17 of that chapter may be completed so as to represent all of the
+planets by drawing in Fig. 16 two circles with radii of 7.9 and 12.4
+centimeters respectively, to represent the orbits of the planets Uranus
+and Neptune, which are more remote from the sun than Saturn, and by
+introducing a little inside the orbit of Jupiter about 500 ellipses of
+different sizes, shapes, and positions to represent a group of minor
+planets or asteroids as they are often called. It is convenient to
+regard these asteroids as composing by themselves a class of very small
+planets, while the remaining 8 larger planets fall naturally into two
+other classes, a group of medium-sized ones--Mercury, Venus, Earth, and
+Mars--called inner planets by reason of their nearness to the sun; and
+the outer planets--Jupiter, Saturn, Uranus, Neptune--each of which is
+much larger and more massive than any planet of the inner group. Compare
+in Figs. 84 and 85 their relative sizes. The earth, _E_, is introduced
+into Fig. 85 as a connecting link between the two figures.
+
+Some of these planets, like the earth, are attended by one or more
+moons, technically called satellites, which also shine by reflected
+sunlight and which move about their respective planets in accordance
+with the law of gravitation, much as the moon moves around the earth.
+
+[Illustration: FIG. 84.--The inner planets and the moon.]
+
+[Illustration: FIG. 85.--The outer planets.]
+
+134. DISTANCES OF THE PLANETS FROM THE SUN.--It is a comparatively
+simple matter to observe these planets year after year as they move
+among the stars, and to find from these observations how long each one
+of them requires to make its circuit around the sun--that is, its
+periodic time, _T_, which figures in Kepler's Third Law, and when these
+periodic times have been ascertained, to use them in connection with
+that law to determine the mean distance of each planet from the sun.
+Thus, Jupiter requires 4,333 days to move completely around its orbit;
+and comparing this with the periodic time and mean distance of the earth
+we find--
+
+    a^{3} / (4333^{2}) = (93,000,000^{3}) / (365.25^{2}),
+
+which when solved gives as the mean distance of Jupiter from the sun,
+483,730,000 miles, or 5.20 times as distant as the earth. If we make a
+similar computation for each planet, we shall find that their distances
+from the sun show a remarkable agreement with an artificial series of
+numbers called Bode's law. We write down the numbers contained in the
+first line of figures below, each of which, after the second, is
+obtained by doubling the preceding one, add 4 to each number and point
+off one place of decimals; the resulting number is (approximately) the
+distance of the corresponding planet from the sun.
+
+ Mercury.  Venus.  Earth.  Mars.    Jupiter.  Saturn.  Uranus.  Neptune.
+    0        3       6      12   24   48        96       192      384
+    4        4       4       4    4    4         4         4        4
+ -----------------------------------------------------------------------
+   0.4      0.7     1.0    1.6  2.8  5.2      10.0      19.6     38.8
+   0.4      0.7     1.0    1.5  2.8  5.2       9.5      19.2     30.1
+
+The last line of figures shows the real distance of the planet as
+determined from Kepler's law, the earth's mean distance from the sun
+being taken as the unit for this purpose. With exception of Neptune, the
+agreement between Bode's law and the true distances is very striking,
+but most remarkable is the presence in the series of a number, 2.8, with
+no planet corresponding to it. This led astronomers at the time Bode
+published the law, something more than a century ago, to give new heed
+to a suggestion made long before by Kepler, that there might be an
+unknown planet moving between the orbits of Mars and Jupiter, and a
+number of them agreed to search for such a planet, each in a part of the
+sky assigned him for that purpose. But they were anticipated by Piazzi,
+an Italian, who found the new planet, by accident, on the first day of
+the nineteenth century, moving at a distance from the sun represented by
+the number 2.77.
+
+This planet was the first of the asteroids, and in the century that has
+elapsed hundreds of them have been discovered, while at the present time
+no year passes by without several more being added to the number. While
+some of these are nearer to the sun than is the first one discovered,
+and others are farther from it, their average distance is fairly
+represented by the number 2.8.
+
+Why Bode's law should hold true, or even so nearly true as it does, is
+an unexplained riddle, and many astronomers are inclined to call it no
+law at all, but only a chance coincidence--an illustration of the
+"inherent capacity of figures to be juggled with"; but if so, it is
+passing strange that it should represent the distance of the asteroids
+and of Uranus, which was also an undiscovered planet at the time the law
+was published.
+
+135. THE PLANETS COMPARED WITH EACH OTHER.--When we pass from general
+considerations to a study of the individual peculiarities of the
+planets, we find great differences in the extent of knowledge concerning
+them, and the reason for this is not far to seek. Neptune and Uranus, at
+the outskirts of the solar system, are so remote from us and so feebly
+illumined by the sun that any detailed study of them can go but little
+beyond determining the numbers which represent their size, mass,
+density, the character of their orbits, etc. The asteroids are so small
+that in the telescope they look like mere points of light, absolutely
+indistinguishable in appearance from the fainter stars. Mercury,
+although closer at hand and presenting a disk of considerable size,
+always stands so near the sun that its observation is difficult on this
+account. Something of the same kind is true for Venus, although in much
+less degree; while Mars, Jupiter, and Saturn are comparatively easy
+objects for telescopic study, and our knowledge of them, while far from
+complete, is considerably greater than for the other planets.
+
+Figs. 84 and 85 show the relative sizes of the planets composing the
+inner and outer groups respectively, and furnish the numerical data
+concerning their diameters, masses, densities, etc., which are of most
+importance in judging of their physical condition. Each planet, save
+Saturn, is represented by two circles, of which the outer is drawn
+proportional to the size of the planet, and the inner shows the amount
+of material that must be subtracted from the interior in order that the
+remaining shell shall just float in water. Note the great difference in
+thickness of shell between the two groups. Saturn, having a mean density
+less than that of water, must have something loaded upon it, instead of
+removed, in order that it should float just submerged.
+
+
+JUPITER
+
+136. APPEARANCE.--Commencing our consideration of the individual planets
+with Jupiter, which is by far the largest of them, exceeding both in
+bulk and mass all the others combined, we have in Fig. 86 four
+representations of Jupiter and his family of satellites as they may be
+seen in a very small telescope--e. g., an opera glass--save that the
+little dots which here represent the satellites are numbered _1_, _2_,
+_3_, _4_, in order to preserve their identity in the successive
+pictures.
+
+The chief interest of these pictures lies in the satellites, but,
+reserving them for future consideration, we note that the planet itself
+resembles in shape the full moon, although in respect of brightness it
+sends to us less than 1/6000 part as much light as the moon. From a
+consideration of the motion of Jupiter and the earth in Fig. 16, show
+that Jupiter can not present any such phases as does the moon, but that
+its disk must be at all times nearly full. As seen from Saturn, what
+kind of phases would Jupiter present?
+
+137. THE BELTS.--Even upon the small scale of Fig. 86 we detect the most
+characteristic feature of Jupiter's appearance in the telescope, the two
+bands extending across his face parallel to the line of the satellites,
+and in Fig. 87 these same dark bands may be recognized amid the
+abundance of detail which is here brought out by a large telescope.
+Photography does not succeed as a means of reproducing this detail, and
+for it we have to rely upon the skill of the artist astronomer. The
+lettering shows the Pacific Standard time at which the sketches were
+made, and also the longitude of the meridian of Jupiter passing down the
+center of the planet's disk.
+
+[Illustration: FIG. 86.--Jupiter and his satellites.]
+
+[Illustration: FIG. 87.--Drawings of Jupiter made at the 36-inch
+telescope of the Lick Observatory.--KEELER.]
+
+The dark bands are called technically the belts of Jupiter; and a
+comparison of these belts in the second and third pictures of the group,
+in which nearly the same face of the planet is turned toward us, will
+show that they are subject to considerable changes of form and position
+even within the space of a few days. So, too, by a comparison of such
+markings as the round white spots in the upper parts of the disks, and
+the indentations in the edges of the belts, we may recognize that the
+planet is in the act of turning round, and must therefore have an axis
+about which it turns, and poles, an equator, etc. The belts are in fact
+parallel to the planet's equator; and generalizing from what appears in
+the pictures, we may say that there is always a strongly marked belt on
+each side of the equator with a lighter colored streak between them,
+and that farther from the equator are other belts variable in number,
+less conspicuous, and less permanent than the two first seen. Compare
+the position of the principal belts with the position of the zones of
+sun-spot activity in the sun. A feature of the planet's surface, which
+can not be here reproduced, is the rich color effect to be found upon
+it. The principal belts are a brick-red or salmon color, the intervening
+spaces in general white but richly mottled, and streaked with purples,
+browns, and greens.
+
+The drawings show the planet as it appeared in the telescope, inverted,
+and they must be turned upside down if we wish the points of the compass
+to appear as upon a terrestrial map. Bearing this in mind, note in the
+last picture the great oval spot in the southern hemisphere of Jupiter.
+This is a famous marking, known from its color as the _great red spot_,
+which appeared first in 1878 and has persisted to the present day
+(1900), sometimes the most conspicuous marking on the planet, at others
+reduced to a mere ghost of itself, almost invisible save for the
+indentation which it makes in the southern edge of the belt near it.
+
+138. ROTATION AND FLATTENING AT THE POLES.--One further significant fact
+with respect to Jupiter may be obtained from a careful measurement of
+the drawings; the planet is flattened at the poles, so that its polar
+diameter is about one sixteenth part shorter than the equatorial
+diameter. The flattening of the earth amounts to only one
+three-hundredth part, and the marked difference between these two
+numbers finds its explanation in the greater swiftness of Jupiter's
+rotation about its axis, since in both cases it is this rotation which
+makes the flattening.
+
+It is not easy to determine the precise dimensions of the planet, since
+this involves a knowledge both of its distance from us and of the angle
+subtended by its diameter, but the most recent determinations of this
+kind assign as the equatorial diameter 90,200 miles, and for the polar
+diameter 84,400 miles. Determine from either of these numbers the size
+of the great red spot.
+
+The earth turns on its axis once in 24 hours but no such definite time
+can be assigned to Jupiter, which, like the sun, seems to have different
+rotation periods in different latitudes--9h. 50m. in the equatorial belt
+and 9h. 56m. in the dark belts and higher latitudes. There is some
+indication that the larger part of the visible surface rotates in 9h.
+55.6m., while a broad stream along the equator flows eastward some 270
+miles per hour, and thus comes back to the center of the planet, as seen
+from the earth, five or six minutes earlier than the parts which do not
+share in this motion. Judged by terrestrial standards, 270 miles per
+hour is a great velocity, but Jupiter is constructed on a colossal
+scale, and, too, we have to compare this movement, not to a current
+flowing in the ocean, but to a wind blowing in the upper regions of the
+earth's atmosphere. The visible surface of Jupiter is only the top of a
+cloud formation, and contains nothing solid or permanent, if indeed
+there is anything solid even at the core of the planet. The great red
+spot during the first dozen years of its existence, instead of remaining
+fixed relative to the surrounding formations, drifted two thirds of the
+way around the planet, and having come to a standstill about 1891, it is
+now slowly retracing its path.
+
+139. PHYSICAL CONDITION.--For a better understanding of the physical
+condition of Jupiter, we have now to consider some independent lines of
+evidence which agree in pointing to the conclusion that Jupiter,
+although classed with the earth as a planet, is in its essential
+character much more like the sun.
+
+_Appearance._--The formations which we see in Fig. 87 look like clouds.
+They gather and disappear, and the only element of permanence about them
+is their tendency to group themselves along zones of latitude. If we
+measure the light reflected from the planet we find that its albedo is
+very high, like that of snow or our own cumulus clouds, and it is of
+course greater from the light parts of the disk than from the darker
+bands. The spectroscope shows that the sunlight reflected from these
+darker belts is like that reflected from the lighter parts, save that a
+larger portion of the blue and violet rays has been absorbed out of it,
+thus producing the ruddy tint of the belts, as sunset colors are
+produced on the earth, and showing that here the light has penetrated
+farther into the planet's atmosphere before being thrown back by
+reflection from lower-lying cloud surfaces. The dark bands are therefore
+to be regarded as rifts in the clouds, reaching down to some
+considerable distance and indicating an atmosphere of great depth. The
+great red spot, 28,000 miles long, and obviously thrusting back the
+white clouds on every side of it, year after year, can hardly be a mere
+patch on the face of the planet, but indicates some considerable depth
+of atmosphere.
+
+_Density._--So, too, the small mean density of the planet, only 1.3
+times that of water and actually less than the density of the sun,
+suggests that the larger part of the planet's bulk may be made of gases
+and clouds, with very little solid matter even at the center; but here
+we get into a difficulty from which there seems but one escape. The
+force of gravity at the visible surface of Jupiter may be found from its
+mass and dimensions to be 2.6 times as great as at the surface of the
+earth, and the pressure exerted upon its atmosphere by this force ought
+to compress the lower strata into something more dense than we find in
+the planet. Some idea of this compression may be obtained from Fig. 88,
+where the line marked _E_ shows approximately how the density of the air
+increases as we move from its upper strata down toward the surface of
+the earth through a distance of 16 miles, the density at any level being
+proportional to the distance of the curved line from the straight one
+near it. The line marked _J_ in the same figure shows how the density
+would increase if the force of gravity were as great here as it is in
+Jupiter, and indicates a much greater rate of increase. Starting from
+the upper surface of the cloud in Jupiter's atmosphere, if we descend,
+not 16 miles, but 1,600 or 16,000, what must the density of the
+atmosphere become and how is this to be reconciled with what we know to
+be the very small mean density of the planet?
+
+We are here in a dilemma between density on the one hand and the effects
+of gravity on the other, and the only escape from it lies in the
+assumption that the interior of Jupiter is tremendously hot, and that
+this heat expands the substance of the planet in spite of the pressure
+to which it is subject, making a large planet with a low density,
+possibly gaseous at the very center, but in its outer part surrounded by
+a shell of clouds condensed from the gases by radiating their heat into
+the cold of outer space.
+
+[Illustration: FIG. 88.--Increase of density in the atmospheres of
+Jupiter and the earth.]
+
+This is essentially the same physical condition that we found for the
+sun, and we may add, as further points of resemblance between it and
+Jupiter, that there seems to be a circulation of matter from the hot
+interior of the planet to its cooler surface that is more pronounced in
+the southern hemisphere than in the northern, and that has its periods
+of maximum and minimum activity, which, curiously enough, seem to
+coincide with periods of maximum and minimum sun-spot development. Of
+this, however, we can not be entirely sure, since it is only in recent
+years that it has been studied with sufficient care, and further
+observations are required to show whether the agreement is something
+more than an accidental and short-lived coincidence.
+
+_Temperature._--The temperature of Jupiter must, of course, be much
+lower than that of the sun, since the surface which we see is not
+luminous like the sun's; but below the clouds it is not improbable that
+Jupiter may be incandescent, white hot, and it is surmised with some
+show of probability that a little of its light escapes through the
+clouds from time to time, and helps to produce the striking brilliancy
+with which this planet shines.
+
+140. THE SATELLITES OF JUPITER.--The satellites bear much the same
+relation to Jupiter that the moon bears to the earth, revolving about
+the planet in accordance with the law of gravitation, and conforming to
+Kepler's three laws, as do the planets in their courses about the sun.
+Observe in Fig. 86 the position of satellite No. _1_ on the four dates,
+and note how it oscillates back and forth from left to right of Jupiter,
+apparently making a complete revolution in about two days, while No. _4_
+moves steadily from left to right during the entire period, and has
+evidently made only a fraction of a revolution in the time covered by
+the pictures. This quicker motion, of course, means that No. _1_ is
+nearer to Jupiter than No. _4_, and the numbers given to the satellites
+show the order of their distances from the planet. The peculiar way in
+which the satellites are grouped, always standing nearly in a straight
+line, shows that their orbits must lie nearly in the same plane, and
+that this plane, which is also the plane of the planets' equator, is
+turned edgewise toward the earth.
+
+These satellites enjoy the distinction of being the first objects ever
+discovered with the telescope, having been found by Galileo almost
+immediately after its invention, A. D. 1610. It is quite possible that
+before this time they may have been seen with the naked eye, for in more
+recent years reports are current that they have been seen under
+favorable circumstances by sharp-eyed persons, and very little
+telescopic aid is required to show them. Look for them with an opera or
+field glass. They bear the names Io, Europa, Ganymede, Callisto, which,
+however, are rarely used, and, following the custom of astronomers, we
+shall designate them by the Roman numerals I, II, III, IV.
+
+[Illustration: FIG. 89.--Orbits of Jupiter's satellites.]
+
+For nearly three centuries (1610 to 1892) astronomers spoke of the four
+satellites of Jupiter; but in September, 1892, a fifth one was added to
+the number by Professor Barnard, who, observing with the largest
+telescope then extant, found very close to Jupiter a tiny object only
+1/600 part as bright as the other satellites, but, like them, revolving
+around Jupiter, a permanent member of his system. This is called the
+fifth satellite, and Fig. 89 shows the orbits of these satellites around
+Jupiter, which is here represented on the same scale as the orbits
+themselves. The broken line just inside the orbit of I represents the
+size of the moon's orbit. The cut shows also the periodic times of the
+satellites expressed in days, and furnishes in this respect a striking
+illustration of the great mass of Jupiter. Satellite I is a little
+farther from Jupiter than is the moon from the earth, but under the
+influence of a greater attraction it makes the circuit of its orbit in
+1.77 days, instead of taking 29.53 days, as does the moon. Determine
+from the figure by the method employed in § 111 how much more massive is
+Jupiter than the earth.
+
+Small as these satellites seem in Fig. 86, they are really bodies of
+considerable size, as appears from Fig. 90, where their dimensions are
+compared with those of the earth and moon, save that the fifth satellite
+is not included. This one is so small as to escape all attempts at
+measuring its diameter, but, judging from the amount of light it
+reflects, the period printed with the legend of the figure represents a
+gross exaggeration of this satellite's size.
+
+[Illustration: FIG. 90.--Jupiter's satellites compared with the earth
+and moon.]
+
+Like the moon, each of these satellites may fairly be considered a world
+in itself, and as such a fitting object of detailed study, but,
+unfortunately, their great distance from us makes it impossible, even
+with the most powerful telescope, to see more upon their surfaces than
+occasional vague markings, which hardly suffice to show the rotations of
+the satellites upon their axes.
+
+One striking feature, however, comes out from a study of their influence
+in disturbing each other's motion about Jupiter. Their masses and the
+resulting densities of the satellites are smaller than we should have
+expected to find, the density being less than that of the moon, and
+averaging only a little greater than the density of Jupiter itself. At
+the surface of the third satellite the force of gravity is but little
+less than on the moon, although the moon's density is nearly twice as
+great as that of III, and there can be no question here of accounting
+for the low density through expansion by great heat, as in the case of
+the sun and Jupiter. It has been surmised that these satellites are not
+solid bodies, like the earth and moon, but only shoals of rock and
+stone, loosely piled together and kept from packing into a solid mass by
+the action of Jupiter in raising tides within them. But the explanation
+can hardly be regarded as an accepted article of astronomical belief,
+although it is supported by some observations which tend to show that
+the apparent shapes of the satellites change under the influence of the
+tidal forces impressed upon them.
+
+141. ECLIPSES OF THE SATELLITES.--It may be seen from Fig. 89 that in
+their motion around the planet Jupiter's satellites must from time to
+time pass through his shadow and be eclipsed, and that the shadows of
+the satellites will occasionally fall upon the planet, producing to an
+observer upon Jupiter an eclipse of the sun, but to an observer on the
+earth presenting only the appearance of a round black spot moving slowly
+across the face of the planet. Occasionally also a satellite will pass
+exactly between the earth and Jupiter, and may be seen projected against
+the planet as a background. All of these phenomena are duly predicted
+and observed by astronomers, but the eclipses are the only ones we need
+consider here. The importance of these eclipses was early recognized,
+and astronomers endeavored to construct a theory of their recurrence
+which would permit accurate predictions of them to be made. But in this
+they met with no great success, for while it was easy enough to foretell
+on what night an eclipse of a given satellite would occur, and even to
+assign the hour of the night, it was not possible to make the predicted
+minute agree with the actual time of eclipse until after Roemer, a
+Danish astronomer of the seventeenth century, found where lay the
+trouble. His discovery was, that whenever the earth was on the side of
+its orbit toward Jupiter the eclipses really occurred before the
+predicted time, and when the earth was on the far side of its orbit they
+came a few minutes later than the predicted time. He correctly inferred
+that this was to be explained, not by any influence which the earth
+exerted upon Jupiter and his satellites, but through the fact that the
+light by which we see the satellite and its eclipse requires an
+appreciable time to cross the intervening space, and a longer time when
+the earth is far from Jupiter than when it is near.
+
+For half a century Roemer's views found little credence, but we know now
+that he was right, and that on the average the eclipses come 8m. 18s.
+early when the earth is nearest to Jupiter, and 8m. 18s. late when it is
+on the opposite side of its orbit. This is equivalent to saying that
+light takes 8m. 18s. to cover the distance from the sun to the earth, so
+that at any moment we see the sun not as it then is, but as it was 8
+minutes earlier. It has been found possible in recent years to measure
+by direct experiment the velocity with which light travels--186,337
+miles per second--and multiplying this number by the 498s. (= 8m. 18s.)
+we obtain a new determination of the sun's distance from the earth. The
+product of the two numbers is 92,795,826, in very fair agreement with
+the 93,000,000 miles found in Chapter X; but, as noted there, this
+method, like every other, has its weak side, and the result may be a
+good many thousands of miles in error.
+
+It is worthy of note in this connection that both methods of obtaining
+the sun's distance which were given in Chapter X involve Kepler's Third
+Law, while the result obtained from Jupiter's satellites is entirely
+independent of this law, and the agreement of the several results is
+therefore good evidence both for the truth of Kepler's laws and for the
+soundness of Roemer's explanation of the eclipses. This mode of proof,
+by comparing the numerical results furnished by two or more different
+principles, and showing that they agree or disagree, is of wide
+application and great importance in physical science.
+
+
+SATURN
+
+142. THE RING OF SATURN.--In respect of size and mass Saturn stands next
+to Jupiter, and although far inferior to him in these respects, it
+contains more material than all the remaining planets combined. But the
+unique feature of Saturn which distinguishes it from every other known
+body in the heavens is its ring, which was long a puzzle to the
+astronomers who first studied the planet with a telescope (one of them
+called Saturn a planet with ears), but, was after nearly half a century
+correctly understood and described by Huyghens, whose Latin text we
+translate into--"It is surrounded by a ring, thin, flat, nowhere
+touching it, and making quite an angle with the ecliptic."
+
+[Illustration: FIG. 91.--Aspects of Saturn's rings.]
+
+Compare with this description Fig. 91, which shows some of the
+appearances presented by the ring at different positions of Saturn in
+its orbit. It was their varying aspects that led Huyghens to insert the
+last words of his description, for, if the plane of the ring coincided
+with the plane of the earth's orbit, then at all times the ring must be
+turned edgewise toward the earth, as shown in the middle picture of the
+group. Fig. 92 shows the sun and the orbit of the earth placed near the
+center of Saturn's orbit, across whose circumference are ruled some
+oblique lines representing the plane of the ring, the right end always
+tilted up, no matter where the planet is in its orbit. It is evident
+that an observer upon the earth will see the _N_ side of the ring when
+the planet is at _N_ and the _S_ side when it is at _S_, as is shown in
+the first and third pictures of Fig. 91, while midway between these
+positions the edge of the ring will be presented to the earth.
+
+[Illustration: FIG. 92.--Aspects of the ring in their relation to
+Saturn's orbital motion.]
+
+The last occasion of this kind was in October, 1891, and with the large
+telescope of the Washburn Observatory the writer at that time saw
+Saturn without a trace of a ring surrounding it. The ring is so thin
+that it disappears altogether when turned edgewise. The names of the
+zodiacal constellations are inserted in Fig. 92 in their proper
+direction from the sun, and from these we learn that the ring will
+disappear, or be exceedingly narrow, whenever Saturn is in the
+constellation Pisces or near the boundary line between Leo and Virgo. It
+will be broad and show its northern side when Saturn is in Scorpius or
+Sagittarius, and its southern face when the planet is in Gemini. What
+will be its appearance in 1907 at the date marked in the figure?
+
+143. NATURE OF THE RING.--It is apparent from Figs. 91 and 93 that
+Saturn's ring is really made up of two or more rings lying one inside of
+the other and completely separated by a dark space which, though narrow,
+is as clean and sharp as if cut with a knife. Also, the inner edge of
+the ring fades off into an obscure border called the _dusky ring_ or
+_crape ring_. This requires a pretty good telescope to show it, as may
+be inferred from the fact that it escaped notice for more than two
+centuries during which the planet was assiduously studied with
+telescopes, and was discovered at the Harvard College Observatory as
+recently as 1850.
+
+Although the rings appear oval in all of the pictures, this is mainly an
+effect of perspective, and they are in fact nearly circular with the
+planet at their center. The extreme diameter of the ring is 172,000
+miles, and from this number, by methods already explained (Chapter IX),
+the student should obtain the width of the rings, their distance from
+the ball of the planet, and the diameter of the ball. As to thickness,
+it is evident, from the disappearance of the ring when its edge is
+turned toward the earth, that it is very thin in comparison with its
+diameter, probably not more than 100 miles thick, although no exact
+measurement of this can be made.
+
+[Illustration: FIG. 93.--Saturn.]
+
+From theoretical reasons based upon the law of gravitation astronomers
+have held that the rings of Saturn could not possibly be solid or
+liquid bodies. The strains impressed upon them by the planet's
+attraction would tear into fragments steel rings made after their size
+and shape. Quite recently Professor Keeler has shown, by applying the
+spectroscope (Doppler's principle) to determine the velocity of the
+ring's rotation about Saturn, that the inner parts of the ring move, as
+Kepler's Third Law requires, more rapidly than do the outer parts, thus
+furnishing a direct proof that they are not solid, and leaving no doubt
+that they are made up of separate fragments, each moving about the
+planet in its own orbit, like an independent satellite, but standing so
+close to its neighbors that the whole space reflects the sunlight as
+completely as if it were solid. With this understanding of the rings it
+is easy to see why they are so thin. Like Jupiter, Saturn is greatly
+flattened at the poles, and this flattening, or rather the protuberant
+mass about the equator, lays hold of every satellite near the planet and
+exerts upon it a direct force tending to thrust it down into the plane
+of the planet's equator and hold it there. The ring lies in the plane of
+Saturn's equator because each particle is constrained to move there.
+
+The division of the ring into two parts, an outer and an inner ring, is
+usually explained as follows: Saturn is surrounded by a numerous brood
+of satellites, which by their attractions produce perturbations in the
+material composing the rings, and the dividing line between the outer
+and inner rings falls at the place where by the law of gravitation the
+perturbations would have their greatest effect. The dividing line
+between the rings is therefore a narrow lane, 2,400 miles wide, from
+which the fragments have been swept clean away by the perturbing action
+of the satellites. Less conspicuous divisions are seen from time to time
+in other parts of the ring, where the perturbations, though less, are
+still appreciable. But it is open to some question whether this
+explanation is sufficient.
+
+The curious darkness of the inner or crape ring is easily explained.
+The particles composing it are not packed together so closely as in the
+outer ring, and therefore reflect less sunlight. Indeed, so sparsely
+strewn are the particles in this ring that it is in great measure
+transparent to the sunlight, as is shown by a recorded observation of
+one of the satellites which was distinctly although faintly seen while
+moving through the shadow of the dark ring, but disappeared in total
+eclipse when it entered the shadow cast by the bright ring.
+
+144. THE BALL OF SATURN.--The ball of the planet is in most respects a
+smaller copy of Jupiter. With an equatorial diameter of 76,000 miles, a
+polar diameter of 69,000 miles, and a mass 95 times that of the earth,
+its density is found to be the least of any planet in the solar system,
+only 0.70 of the density of water, and about one half as great as is the
+density of Jupiter. The force of gravity at its surface is only a little
+greater (1.18) than on the earth; and this, in connection with the low
+density, leads, as in the case of Jupiter, to the conclusion that the
+planet must be mainly composed of gases and vapors, very hot within, but
+inclosed by a shell of clouds which cuts off their glow from our eyes.
+
+Like Jupiter in another respect, the planet turns very swiftly upon its
+axis, making a revolution in 10 hours 14 minutes, but up to the present
+it remains unknown whether different parts of the surface have different
+rotation times.
+
+145. THE SATELLITES.--Saturn is attended by a family of nine satellites,
+a larger number than belongs to any other planet, but with one exception
+they are exceedingly small and difficult to observe save with a very
+large telescope. Indeed, the latest one is said to have been discovered
+in 1898 by means of the image which it impressed upon a photographic
+plate, and it has never been _seen_.
+
+Titan, the largest of them, is distant 771,000 miles from the planet and
+bears much the same relation to Saturn that Satellite III bears to
+Jupiter, the similarity in distance, size and mass being rather
+striking, although, of course, the smaller mass of Saturn as compared
+with Jupiter makes the periodic time of Titan--15 days 23 hours--much
+greater than that of III. Can you apply Kepler's Third Law to the motion
+of Titan so as to determine from the data given above, the time required
+for a particle at the outer or inner edge of the ring to revolve once
+around Saturn?
+
+Japetus, the second satellite in point of size, whose distance from
+Saturn is about ten times as great as the moon's distance from the
+earth, presents the remarkable peculiarity of being always brighter in
+one part of its orbit than in another, three or four times as bright
+when west of Saturn as when east of it. This probably indicates that,
+like our own moon, the satellite turns always the same face toward its
+planet, and further, that one side of the satellite reflects the
+sunlight much better than the other side--i. e., has a higher albedo.
+With these two assumptions it is easily seen that the satellite will
+always turn toward the earth one face when west, and the other face when
+east of Saturn, and thus give the observed difference of brightness.
+
+
+URANUS AND NEPTUNE
+
+146. CHIEF CHARACTERISTICS.--The two remaining large planets are
+interesting chiefly as modern additions to the known members of the
+sun's family. The circumstances leading to the discovery of Neptune have
+been touched upon in Chapter IV, and for Uranus we need only note that
+it was found by accident in the year 1781 by William Herschel, who for
+some time after the discovery considered it to be only a comet. It was
+the first planet ever discovered, all of its predecessors having been
+known from prehistoric times.
+
+[Illustration: WILLIAM HERSCHEL (1738-1822).]
+
+Uranus has four satellites, all of them very faint, which present only
+one feature of special importance. Instead of moving in orbits which are
+approximately parallel to the plane of the ecliptic, as do the
+satellites of the inner planets, their orbit planes are tipped up nearly
+perpendicular to the planes of the orbits of both Uranus and the earth.
+The one satellite which Neptune possesses has the same peculiarity in
+even greater degree, for its motion around the planet takes place in the
+direction opposite to that in which all the planets move around the sun,
+much as if the orbit of the satellite had been tipped over through an
+angle of 150°. Turn a watch face down and note how the hands go round in
+the direction opposite to that in which they moved before the face was
+turned through 180°.
+
+Both Uranus and Neptune are too distant to allow much detail to be seen
+upon their surfaces, but the presence of broad absorption bands in their
+spectra shows that they must possess dense atmospheres quite different
+in constitution from the atmosphere of the earth. In respect of density
+and the force of gravity at their surfaces, they are not very unlike
+Saturn, although their density is greater and gravity less than his,
+leading to the supposition that they are for the most part gaseous
+bodies, but cooler and probably more nearly solid than either Jupiter or
+Saturn.
+
+Under favorable circumstances Uranus may be seen with the naked eye by
+one who knows just where to look for it. Neptune is never visible save
+in a telescope.
+
+147. THE INNER PLANETS.--In sharp contrast with the giant planets which
+we have been considering stands the group of four inner planets, or five
+if we count the moon as an independent body, which resemble each other
+in being all small, dense, and solid bodies, which by comparison with
+the great distances separating the outer planets may fairly be described
+as huddled together close to the sun. Their relative sizes are shown in
+Fig. 84, together with the numerical data concerning size, mass,
+density, etc., which we have already found important for the
+understanding of a planet's physical condition.
+
+
+VENUS
+
+[Illustration: FIG. 94.--The phases of Venus.--ANTONIADI.]
+
+148. APPEARANCE.--Omitting the earth, Venus is by far the most
+conspicuous member of this group, and when at its brightest is, with
+exception of the sun and moon, the most brilliant object in the sky, and
+may be seen with the naked eye in broad daylight if the observer knows
+just where to look for it. But its brilliancy is subject to considerable
+variations on account of its changing distance from the earth, and the
+apparent size of its disk varies for the same reason, as may be seen
+from Fig. 94. These drawings bring out well the phases of the planet,
+and the student should determine from Fig. 17 what are the relative
+positions in their orbits of the earth and Venus at which the planet
+would present each of these phases. As a guide to this, observe that the
+dark part of Venus's earthward side is always proportional in area to
+the angle at Venus between the earth and sun. In the first picture of
+Fig. 94 about two thirds of the surface corresponding to the full
+hemisphere of the planet is dark, and the angle at Venus between earth
+and sun is therefore two thirds of 180°--i. e., 120°. In Fig. 17 find a
+place on the orbit of Venus from which if lines be drawn to the sun and
+earth, as there shown, the angle between them will be 120°. Make a
+similar construction for the fourth picture in Fig. 94. Which of these
+two positions is farther from the earth? How do the distances compare
+with the apparent size of Venus in the two pictures? What is the phase
+of Venus to-day?
+
+The irregularities in the shading of the illuminated parts of the disk
+are too conspicuous in Fig. 94, on account of difficulties of
+reproduction; these shadings are at the best hard to see in the
+telescope, and distinct permanent markings upon the planet are wholly
+lacking. This absence of markings makes almost impossible a
+determination of the planet's time of rotation about its axis, and
+astronomers are divided in this respect into two parties, one of which
+maintains that Venus, like the earth, turns upon its axis in some period
+not very different from 24 hours, while the other contends that, like
+the moon, it turns always the same face toward the center of its orbit,
+making a rotation upon its axis in the same period in which it makes a
+revolution about the sun. The reason why no permanent markings are to be
+seen on this planet is easily found. Like Jupiter and Saturn, its
+atmosphere is at all times heavily cloud-laden, so that we seldom, if
+ever, see down to the level of its solid parts. There is, however, no
+reason here to suppose the interior parts hot and gaseous. It is much
+more probable that Venus, like the earth, possesses a solid crust whose
+temperature we should expect to be considerably higher than that of the
+earth, because Venus is nearer the sun. But the cloud layer in its
+atmosphere must modify the temperature in some degree, and we have
+practically no knowledge of the real temperature conditions at the
+surface of the planet.
+
+It is the clouds of Venus which in great measure are responsible for its
+marked brilliancy, since they are an excellent medium for reflecting the
+sunlight, and give to its surface an albedo greater than that of any
+other planet, although Saturn is nearly equal to it.
+
+Of course, the presence of such cloud formations indicates that Venus is
+surrounded by a dense atmosphere, and we have independent evidence of
+this in the shape of its disk when the planet is very nearly between the
+earth and sun. The illuminated part, from tip to tip of the horns, then
+stretches more than halfway around the planet's circumference, and shows
+that a certain amount of light must have been refracted through its
+atmosphere, thus making the horns of the crescent appear unduly
+prolonged. This atmosphere is shown by the spectroscope to be not unlike
+that of the earth, although, possibly, more dense.
+
+
+MERCURY
+
+149. CHIEF CHARACTERISTICS.--Mercury, on account of its nearness to the
+sun, is at all times a difficult object to observe, and Copernicus, who
+spent most of his life in Poland, is said, despite all his efforts, to
+have gone to his grave without ever seeing it. In our more southern
+latitude it can usually be seen for about a fortnight at the time of
+each elongation--i. e., when at its greatest angular distance from the
+sun--and the student should find from Fig. 16 the time at which the next
+elongation occurs and look for the planet, shining like a star of the
+first magnitude, low down in the sky just after sunset or before
+sunrise, according as the elongation is to the east or west of the sun.
+When seen in the morning sky the planet grows brighter day after day
+until it disappears in the sun's rays, while in the evening sky its
+brilliancy as steadily diminishes until the planet is lost. It should
+therefore be looked for in the evening as soon as possible after it
+emerges from the sun's rays.
+
+Mercury, as the smallest of the planets, is best compared with the
+moon, which it does not greatly surpass in size and which it strongly
+resembles in other respects. Careful comparisons of the amount of light
+reflected by the planet in different parts of its orbit show not only
+that its albedo agrees very closely with that of the moon, but also that
+its light changes with the varying phase of the planet in almost exactly
+the same way as the amount of moonlight changes. We may therefore infer
+that its surface is like that of the moon, a rough and solid one, with
+few or no clouds hanging over it, and most probably covered with very
+little or no atmosphere. Like Venus, its rotation period is uncertain,
+with the balance of probability favoring the view that it rotates upon
+its axis once in 88 days, and therefore always turns the same face
+toward the sun.
+
+If such is the case, its climate must be very peculiar: one side roasted
+in a perpetual day, where the direct heating power of the sun's rays,
+when the planet is at perihelion, is ten times as great as on the moon,
+and which six weeks later, when the planet is at its farthest from the
+sun, has fallen off to less than half of this. On the opposite side of
+the planet there must reign perpetual night and perpetual cold,
+mitigated by some slight access of warmth from the day side, and perhaps
+feebly imitating the rapid change of season which takes place on the day
+side of the planet. This view, however, takes no account of a possible
+deviation of the planet's axis from being perpendicular to the plane of
+its orbit, or of the librations which must be produced by the great
+eccentricity of the orbit, either of which would complicate without
+entirely destroying the ideal conditions outlined above.
+
+
+MARS
+
+150. APPEARANCE.--The one remaining member of the inner group, Mars, has
+in recent years received more attention than any other planet, and the
+newspapers and magazines have announced marvelous things concerning it:
+that it is inhabited by a race of beings superior in intelligence to
+men; that the work of their hands may be seen upon the face of the
+planet; that we should endeavor to communicate with them, if indeed they
+are not already sending messages to us, etc.--all of which is certainly
+important, if true, but it rests upon a very slender foundation of
+evidence, a part of which we shall have to consider.
+
+Beginning with facts of which there is no doubt, this ruddy-colored
+planet, which usually shines about as brightly as a star of the first
+magnitude, sometimes displays more than tenfold this brilliancy,
+surpassing every other planet save Venus and presenting at these times
+especially favorable opportunities for the study of its surface. The
+explanation of this increase of brilliancy is, of course, that the
+planet approaches unusually near to the earth, and we have already seen
+from a consideration of Fig. 17 that this can only happen in the months
+of August and September. The last favorable epoch of this kind was in
+1894. From Fig. 17 the student should determine when the next one will
+come.
+
+[Illustration: FIG. 95.--Mars.--SCHAEBERLE.]
+
+Fig. 95 presents nine drawings of the planet made at one of the epochs
+of close approach to the earth, and shows that its face bears certain
+faint markings which, though inconspicuous, are fixed and permanent
+features of the planet. The dark triangular projection in the lower
+half of the second drawing was seen and sketched by Huyghens, 1659
+A. D. In Fig. 96 some of these markings are shown much more plainly, but
+Fig. 95 gives a better idea of their usual appearance in the telescope.
+
+[Illustration: FIG. 96.--Four views of Mars differing 90° in
+longitude.--BARNARD.]
+
+151. ROTATION.--It may be seen readily enough, from a comparison of the
+first two sketches of Fig. 95, that the planet rotates about an axis,
+and from a more extensive study it is found to be very like the earth in
+this respect, turning once in 24h. 37m. around an axis tipped from being
+perpendicular to the plane of its orbit about a degree and a half more
+than is the earth's axis. Since it is this inclination of the axis which
+is the cause of changing seasons upon the earth, there must be similar
+changes, winter and summer, as well as day and night, upon Mars, only
+each season is longer there than here in the same proportion that its
+year is longer than ours--i. e., nearly two to one. It is summer in the
+northern hemisphere of Mars whenever the sun, as seen from Mars, stands
+in that constellation which is nearest the point of the sky toward which
+the planet's axis points. But this axis points toward the constellation
+Cygnus, and Alpha Cygni is the bright star nearest the north pole of
+Mars. As Pisces is the zodiacal constellation nearest to Cygnus, it must
+be summer in the northern hemisphere of Mars when the sun is in Pisces,
+or, turning the proposition about, it must be summer in the _southern_
+hemisphere of Mars when the planet, as seen from the sun, lies in the
+direction of Pisces.
+
+152. THE POLAR CAPS.--One effect of the changing seasons upon Mars is
+shown in Fig. 97, where we have a series of drawings of the region about
+its south pole made in 1894, on dates between May 21st and December
+10th. Show from Fig. 17 that during this time it was summer in the
+region here shown. Mars crossed the prime radius in 1894 on September
+5th. The striking thing in these pictures is the white spot surrounding
+the pole, which shrinks in size from the beginning to near the end of
+the series, and then disappears altogether. The spot came back again a
+year later, and like a similar spot at the north pole of the planet it
+waxes in the winter and wanes during the summer of Mars in endless
+succession.
+
+[Illustration: FIG. 97.--The south polar cap of Mars in 1894.--BARNARD.]
+
+Sir W. Herschel, who studied these appearances a century ago, compared
+them with the snow fields which every winter spread out from the region
+around the terrestrial pole, and in the summer melt and shrink, although
+with us they do not entirely disappear. This explanation of the polar
+caps of Mars has been generally accepted among astronomers, and from it
+we may draw one interesting conclusion: the temperature upon Mars
+between summer and winter oscillates above and below the freezing point
+of water, as it does in the temperate zones of the earth. But this
+conclusion plunges us into a serious difficulty. The temperature of the
+earth is made by the sun, and at the distance of Mars from the sun the
+heating effect of the latter is reduced to less than half what it is at
+the earth, so that, if Mars is to be kept at the same temperature as the
+earth, there must be some peculiar means for storing the solar heat and
+using it more economically than is done here. Possibly there is some
+such mechanism, although no one has yet found it, and some astronomers
+are very confident that it does not exist, and assert that the
+comparison of the polar caps with snow fields is misleading, and that
+the temperature upon Mars must be at least 100°, and perhaps 200° or
+more, below zero.
+
+153. ATMOSPHERE AND CLIMATE.--In this connection one feature of Mars is
+of importance. The markings upon its surface are always visible when
+turned toward the earth, thus showing that the atmosphere contains no
+such amount of cloud as does our own, but on the whole is decidedly
+clear and sunny, and presumably much less dense than ours. We have seen
+in comparing the earth and the moon how important is the service which
+the earth's atmosphere renders in storing the sun's heat and checking
+those great vicissitudes of temperature to which the moon is subject;
+and with this in mind we must regard the smaller density and cloudless
+character of the atmosphere of Mars as unfavorable to the maintenance
+there of a temperature like that of the earth. Indeed, this
+cloudlessness must mean one of two things: either the temperature is so
+low that vapors can not exist in any considerable quantity, or the
+surface of Mars is so dry that there is little water or other liquid to
+be evaporated. The latter alternative is adopted by those astronomers
+who look upon the polar caps as true snow fields, which serve as the
+chief reservoir of the planet's water supply, and who find in Fig. 98
+evidence that as the snow melts and the water flows away over the flat,
+dry surface of the planet, vegetation springs up, as shown by the dark
+markings on the disk, and gradually dies out with the advancing season.
+Note that in the first of these pictures the season upon Mars
+corresponds to the end of May with us, and in the last picture to the
+beginning of August, a period during which in much of our western
+country the luxuriant vegetation of spring is burned out by the
+scorching sun. From this point of view the permanent dark spots are the
+low-lying parts of the planet's surface, in which at all times there is
+a sufficient accumulation of water to support vegetable life.
+
+[Illustration: FIG. 98.--The same face of Mars at three different
+seasons.--LOWELL.]
+
+154. THE CANALS.--In Fig. 98 the lower part of the disk of Mars shows
+certain faint dark lines which are generally called canals, and in Plate
+III there is given a map of Mars showing many of these canals running in
+narrow, dusky streaks across the face of the planet according to a
+pattern almost as geometrical as that of a spider's web. This must not
+be taken for a picture of the planet's appearance in a telescope. No man
+ever saw Mars look like this, but the map is useful as a plain
+representation of things dimly seen. Some of the regions of this map are
+marked Mare (sea), in accordance with the older view which regarded the
+darker parts of the planet--and of the moon--as bodies of water, but
+this is now known to be an error in both cases. The curved surface of a
+planet can not be accurately reproduced upon the flat surface of paper,
+but is always more or less distorted by the various methods of
+"projecting" it which are in use. Compare the map of Mars in Plate III
+with Fig. 99, in which the projection represents very well the
+equatorial parts of the planet, but enormously exaggerates the region
+around the poles.
+
+It is a remarkable feature of the canals that they all begin and end in
+one of these dark parts of the planet's surface; they show no loose ends
+lying on the bright parts of the planet. Another even more remarkable
+feature is that while the larger canals are permanent features of the
+planet's surface, they at times appear "doubled"--i. e., in place of one
+canal two parallel ones side by side, lasting for a time and then giving
+place again to a single canal.
+
+It is exceedingly difficult to frame any reasonable explanation of these
+canals and the varied appearances which they present. The source of the
+wild speculations about Mars, to which reference is made above, is to be
+found in the suggestion frequently made, half in jest and half in
+earnest, that the canals are artificial water courses constructed upon a
+scale vastly exceeding any public works upon the earth, and testifying
+to the presence in Mars of an advanced civilization. The distinguished
+Italian astronomer, Schiaparelli, who has studied these formations
+longer than any one else, seems inclined to regard them as water courses
+lined on either side by vegetation, which flourishes as far back from
+the central channel as water can be supplied from it--a plausible enough
+explanation if the fundamental difficulty about temperature can be
+overcome.
+
+[Illustration: FIG. 99.--A chart of Mars, 1898-'99.--CERULLI.]
+
+[Illustration: PLATE III. MAP OF MARS (AFTER SCHIAPARELLI)]
+
+155. SATELLITES.--In 1877, one of the times of near approach, Professor
+Hall, of Washington, discovered two tiny satellites revolving about Mars
+in orbits so small that the nearer one, Phobos, presents the remarkable
+anomaly of completing the circuit of its orbit in less time than the
+planet takes for a rotation about its axis. This satellite, in fact,
+makes three revolutions in its orbit while the planet turns once upon
+its axis, and it therefore rises in the west and sets in the east, as
+seen from Mars, going from one horizon to the other in a little less
+than 6 hours. The other satellite, Deimos, takes a few hours more than a
+day to make the circuit of its orbit, but the difference is so small
+that it remains continuously above the horizon of any given place upon
+Mars for more than 60 hours at a time, and during this period runs twice
+through its complete set of phases--new, first quarter, full, etc. In
+ordinary telescopes these satellites can be seen only under especially
+favorable circumstances, and are far too small to permit of any direct
+measurement of their size. The amount of light which they reflect has
+been compared with that of Mars and found to be as much inferior to it
+as is Polaris to two full moons, and, judging from this comparison,
+their diameters can not much exceed a half dozen miles, unless their
+albedo is far less than that of Mars, which does not seem probable.
+
+
+THE ASTEROIDS
+
+156. MINOR PLANETS.--These may be dismissed with few words. There are
+about 500 of them known, all discovered since the beginning of the
+nineteenth century, and new ones are still found every year. No one
+pretends to remember the names which have been assigned them, and they
+are commonly represented by a number inclosed in a circle, showing the
+order in which they were discovered--e. g., [circle 1] = Ceres,
+[circle 433] = Eros, etc. For the most part they are little more than
+chips, world fragments, adrift in space, and naturally it was the larger
+and brighter of them that were first discovered. The size of the first
+four of them--Ceres, Pallas, Juno, and Vesta--compared with the size of
+the moon, according to Professor Barnard, is shown in Fig. 100. The
+great majority of them must be much smaller than the smallest of these,
+perhaps not more than a score of miles in diameter.
+
+A few of the asteroids present problems of special interest, such as
+Eros, on account of its close approach to the earth; Polyhymnia, whose
+very eccentric orbit makes it a valuable means for determining the mass
+of Jupiter, etc.; but these are special cases and the average asteroid
+now receives scant attention, although half a century ago, when only a
+few of them were known, they were regarded with much interest, and the
+discovery of a new one was an event of some consequence.
+
+It was then a favorite speculation that they were in fact fragments of
+an ill-fated planet which once filled the gap between the orbits of Mars
+and Jupiter, but which, by some mischance, had been blown into pieces.
+This is now known to be well-nigh impossible, for every fragment which
+after the explosion moved in an elliptical orbit, as all the asteroids
+do move, would be brought back once in every revolution to the place of
+the explosion, and all the asteroid orbits must therefore intersect at
+this place. But there is no such common point of intersection.
+
+[Illustration: FIG. 100.--The size of the first four
+asteroids.--BARNARD.]
+
+157. LIFE ON THE PLANETS.--There is a belief firmly grounded in the
+popular mind, and not without its advocates among professional
+astronomers, that the planets are inhabited by living and intelligent
+beings, and it seems proper at the close of this chapter to inquire
+briefly how far the facts and principles here developed are consistent
+with this belief, and what support, if any, they lend to it.
+
+At the outset we must observe that the word life is an elastic term,
+hard to define in any satisfactory way, and yet standing for something
+which we know here upon the earth. It is this idea, our familiar though
+crude knowledge of life, which lies at the root of the matter. Life, if
+it exists in another planet, must be in its essential character like
+life upon the earth, and must at least possess those features which are
+common to all forms of terrestrial life. It is an abuse of language to
+say that life in Mars may be utterly unlike life in the earth; if it is
+absolutely unlike, it is not life, whatever else it may be. Now, every
+form of life found upon the earth has for its physical basis a certain
+chemical compound, called protoplasm, which can exist and perpetuate
+itself only within a narrow range of temperature, roughly speaking,
+between 0° and 100° centigrade, although these limits can be
+considerably overstepped for short periods of time. Moreover, this
+protoplasm can be active only in the presence of water, or water vapor,
+and we may therefore establish as the necessary conditions for the
+continued existence and reproduction of life in any place that its
+temperature must not be permanently above 100° or below 0°, C., and
+water must be present in that place in some form.
+
+With these conditions before us it is plain that life can not exist in
+the sun on account of its high temperature. It is conceivable that
+active and intelligent beings, salamanders, might exist there, but they
+could not properly be said to live. In Jupiter and Saturn the same
+condition of high temperature prevails, and probably also in Uranus and
+Neptune, so that it seems highly improbable that any of these planets
+should be the home of life.
+
+Of the inner planets, Mercury and the moon seem destitute of any
+considerable atmospheres, and are therefore lacking in the supply of
+water necessary for life, and the same is almost certainly true of all
+the asteroids. There remain Venus, Mars, and the satellites of the outer
+planets, which latter, however, we must drop from consideration as being
+too little known. On Venus there is an atmosphere probably containing
+vapor of water, and it is well within the range of possibility that
+liquid water should exist upon the surface of this planet and that its
+temperature should fall within the prescribed limits. It would, however,
+be straining our actual knowledge to affirm that such is the case, or to
+insist that if such were the case, life would necessarily exist upon the
+planet.
+
+On Mars we encounter the fundamental difficulty of temperature already
+noted in § 152. If in some unknown way the temperature is maintained
+sufficiently high for the polar caps to be real snow, thawing and
+forming again with the progress of the seasons, the necessary conditions
+of life would seem to be fulfilled here and life if once introduced upon
+the planet might abide and flourish. But of positive proof that such is
+the case we have none.
+
+On the whole, our survey lends little encouragement to the belief in
+planetary life, for aside from the earth, of all the hundreds of bodies
+in the solar system, not one is found in which the necessary conditions
+of life are certainly fulfilled, and only two exist in which there is a
+reasonable probability that these conditions may be satisfied.
+
+
+
+
+CHAPTER XII
+
+COMETS AND METEORS
+
+
+158. VISITORS IN THE SOLAR SYSTEM.--All of the objects--sun, moon,
+planets, stars--which we have thus far had to consider, are permanent
+citizens of the sky, and we have no reason to suppose that their present
+appearance differs appreciably from what it was 1,000 years or 10,000
+years ago. But there is another class of objects--comets, meteors--which
+appear unexpectedly, are visible for a time, and then vanish and are
+seen no more. On account of this temporary character the astronomers of
+ancient and medięval times for the most part refused to regard them as
+celestial bodies but classed them along with clouds, fogs,
+Jack-o'-lanterns, and fireflies, as exhalations from the swamps or the
+volcano; admitting them to be indeed important as harbingers of evil to
+mankind, but having no especial significance for the astronomer.
+
+The comet of 1618 A. D. inspired the lines--
+
+    "Eight things there be a Comet brings,
+      When it on high doth horrid range:
+    Wind, Famine, Plague, and Death to Kings,
+      War, Earthquakes, Floods, and Direful Change,"
+
+which, according to White (History of the Doctrine of Comets), were to
+be taught in all seriousness to peasants and school children.
+
+It was by slow degrees, and only after direct measurements of parallax
+had shown some of them to be more distant than the moon, that the tide
+of old opinion was turned and comets were transferred from the sublunary
+to the celestial sphere, and in more recent times meteors also have
+been recognized as coming to us from outside the earth. A meteor, or
+shooting star as it is often called, is one of the commonest of
+phenomena, and one can hardly watch the sky for an hour on any clear and
+moonless night without seeing several of those quick flashes of light
+which look as if some star had suddenly left its place, dashed swiftly
+across a portion of the sky and then vanished. It is this misleading
+appearance that probably is responsible for the name shooting star.
+
+[Illustration: FIG. 101.--Donati's comet.--BOND.]
+
+159. COMETS.--Comets are less common and much longer-lived than meteors,
+lasting usually for several weeks, and may be visible night after night
+for many months, but never for many years, at a time. During the last
+decade there is no year in which less than three comets have appeared,
+and 1898 is distinguished by the discovery of ten of these bodies, the
+largest number ever found in one year. On the average, we may expect a
+new comet to be found about once in every ten weeks, but for the most
+part they are small affairs, visible only in the telescope, and a fine
+large one, like Donati's comet of 1858 (Fig. 101), or the Great Comet of
+September, 1882, which was visible in broad daylight close beside the
+sun, is a rare spectacle, and as striking and impressive as it is rare.
+
+[Illustration: FIG. 102.--Some famous comets.]
+
+Note in Fig. 102 the great variety of aspect presented by some of the
+more famous comets, which are here represented upon a very small scale.
+
+Fig. 103 is from a photograph of one of the faint comets of the year
+1893, which appears here as a rather feeble streak of light amid the
+stars which are scattered over the background of the picture. An
+apparently detached portion of this comet is shown at the extreme left
+of the picture, looking almost like another independent comet. The
+clean, straight line running diagonally across the picture is the flash
+of a bright meteor that chanced to pass within the range of the camera
+while the comet was being photographed.
+
+A more striking representation of a moderately bright telescopic comet
+is contained in Figs. 104 and 105, which present two different views of
+the same comet, showing a considerable change in its appearance. A
+striking feature of Fig. 105 is the star images, which are here drawn
+out into short lines all parallel with each other. During the exposure
+of 2h. 20m. required to imprint this picture upon the photographic
+plate, the comet was continually changing its position among the stars
+on account of its orbital motion, and the plate was therefore moved
+from time to time, so as to follow the comet and make its image always
+fall at the same place. Hence the plate was continually shifted relative
+to the stars whose images, drawn out into lines, show the direction in
+which the plate was moved--i. e., the direction in which the comet was
+moving across the sky. The same effect is shown in the other
+photographs, but less conspicuously than here on account of their
+shorter exposure times.
+
+These pictures all show that one end of the comet is brighter and
+apparently more dense than the other, and it is customary to call this
+bright part the _head_ of the comet, while the brushlike appendage that
+streams away from it is called the comet's _tail_.
+
+[Illustration: FIG. 103.--Brooks's comet, November 13, 1893. BARNARD.]
+
+160. THE PARTS OF A COMET.--It is not every comet that has a tail,
+though all the large ones do, and in Fig. 103 the detached piece of
+cometary matter at the left of the picture represents very well the
+appearance of a tailless comet, a rather large but not very bright star
+of a fuzzy or hairy appearance. The word comet means long-haired or
+hairy star. Something of this vagueness of outline is found in all
+comets, whose exact boundaries are hard to define, instead of being
+sharp and clean-cut like those of a planet or satellite. Often,
+however, there is found in the head of a comet a much more solid
+appearing part, like the round white ball at the center of Fig. 106,
+which is called the nucleus of the comet, and appears to be in some sort
+the center from which its activities radiate. As shown in Figs. 106 and
+107, the nucleus is sometimes surrounded by what are called envelopes,
+which have the appearance of successive wrappings or halos placed about
+it, and odd, spurlike projections, called jets, are sometimes found in
+connection with the envelopes or in place of them. These figures also
+show what is quite a common characteristic of large comets, a dark
+streak running down the axis of the tail, showing that the tail is
+hollow, a mere shell surrounding empty space.
+
+[Illustration: FIG. 104.--Swift's comet, April 17, 1892.--BARNARD.]
+
+The amount of detail shown in Figs. 106 and 107 is, however, quite
+exceptional, and the ordinary comet is much more like Fig. 103 or 104.
+Even a great comet when it first appears is not unlike the detached
+fragment in Fig. 103, a faint and roundish patch of foggy light which
+grows through successive stages to its maximum estate, developing a
+tail, nucleus, envelopes, etc., only to lose them again as it shrinks
+and finally disappears.
+
+[Illustration: FIG. 105.--Swift's comet, April 24, 1892.--BARNARD.]
+
+161. THE ORBITS OF COMETS.--It will be remembered that Newton found, as
+a theoretical consequence of the law of gravitation, that a body moving
+under the influence of the sun's attraction might have as its orbit any
+one of the conic sections, ellipse, parabola, or hyperbola, and among
+the 400 and more comet orbits which have been determined every one of
+these orbit forms appears, but curiously enough there is not a hyperbola
+among them which, if drawn upon paper, could be distinguished by the
+unaided eye from a parabola, and the ellipses are all so long and
+narrow, not one of them being so nearly round as is the most eccentric
+planet orbit, that astronomers are accustomed to look upon the parabola
+as being the normal type of comet orbit, and to regard a comet whose
+motion differs much from a parabola as being abnormal and calling for
+some special explanation.
+
+The fact that comet orbits are parabolas, or differ but little from
+them, explains at once the temporary character and speedy disappearance
+of these bodies. They are visitors to the solar system and visible for
+only a short time, because the parabola in which they travel is not a
+closed curve, and the comet, having passed once along that portion of it
+near the earth and the sun, moves off along a path which ever thereafter
+takes it farther and farther away, beyond the limit of visibility. The
+development of the comet during the time it is visible, the growth and
+disappearance of tail, nucleus, etc., depend upon its changing distance
+from the sun, the highest development and most complex structure being
+presented when it is nearest to the sun.
+
+[Illustration: FIG. 106.--Head of Coggia's comet, July 13,
+1874.--TROUVELOT.]
+
+Fig. 108 shows the path of the Great Comet of 1882 during the period
+in which it was seen, from September 3, 1882, to May 26, 1883. These
+dates--IX, 3, and V, 26--are marked in the figure opposite the parts
+of the orbit in which the comet stood at those times. Similarly, the
+positions of the earth in its orbit at the beginning of September,
+October, November, etc., are marked by the Roman numerals IX, X, XI,
+etc. The line _S V_ shows the direction from the sun to the vernal
+equinox, and _S_ [Ō] is the line along which the plane of the comet's
+orbit intersects the plane of the earth's orbit--i. e., it is the line
+of nodes of the comet orbit. Since the comet approached the sun from the
+south side of the ecliptic, all of its orbit, save the little segment
+which falls to the left of _S_ [Ō], lies below (south) of the plane of
+the earth's orbit, and the part which would be hidden if this plane were
+opaque is represented by a broken line.
+
+[Illustration: FIG. 107.--Head of Donati's comet, September 30, October
+2, 1858.--BOND.]
+
+162. ELEMENTS OF A COMET'S ORBIT.--There is a theorem of geometry to the
+effect that through any three points not in the same straight line one
+circle, and only one, can be drawn. Corresponding to this there is a
+theorem of celestial mechanics, that through any three positions of a
+comet one conic section, and only one, can be passed along which the
+comet can move in accordance with the law of gravitation. This conic
+section is, of course, its orbit, and at the discovery of a comet
+astronomers always hasten to observe its position in the sky on
+different nights in order to obtain the three positions (right
+ascensions and declinations) necessary for determining the particular
+orbit in which it moves. The circle, to which reference was made above,
+is completely ascertained and defined when we know its radius and the
+position of its center. A parabola is not so simply defined, and five
+numbers, called the _elements_ of its orbit, are required to fix
+accurately a comet's path around the sun. Two of these relate to the
+position of the line of nodes and the angle which the orbit plane makes
+with the plane of the ecliptic; a third fixes the direction of the axis
+of the orbit in its plane, and the remaining two, which are of more
+interest to us, are the date at which the comet makes its nearest
+approach to the sun (_perihelion passage_) and its distance from the sun
+at that date (_perihelion distance_). The date, September 17th, placed
+near the center of Fig. 108, is the former of these elements, while the
+latter, which is too small to be accurately measured here, may be found
+from Fig. 109 to be 0.82 of the sun's diameter, or, in terms of the
+earth's distance from the sun, 0.008.
+
+[Illustration: FIG. 108.--Orbits of the earth and the Great Comet of
+1882.]
+
+Fig. 109 shows on a large scale the shape of that part of the orbit near
+the sun and gives the successive positions of the comet, at intervals of
+2/10 of a day, on September 16th and 17th, showing that in less than 10
+hours--17.0 to 17.4--the comet swung around the sun through an angle of
+more than 240°. When at its perihelion it was moving with a velocity of
+300 miles per second! This very unusual velocity was due to the comet's
+extraordinarily close approach to the sun. The earth's velocity in its
+orbit is only 19 miles per second, and the velocity of any comet at any
+distance from the sun, provided its orbit is a parabola, may be found by
+dividing this number by the square root of half the comet's
+distance--e. g., 300 miles per second equals 19 ÷ 0.004^{1/2}.
+
+[Illustration: FIG. 109.--Motion of the Great Comet of 1883 in passing
+around the sun.]
+
+Most of the visible comets have their perihelion distances included
+between 1/3 and 4/3 of the earth's distance from the sun, but
+occasionally one is found, like the second comet of 1885, whose nearest
+approach to the sun lies far outside the earth's orbit, in this case
+halfway out to the orbit of Jupiter; but such a comet must be a very
+large one in order to be seen at all from the earth. There is, however,
+some reason for believing that the number of comets which move around
+the sun without ever coming inside the orbit of Jupiter, or even that of
+Saturn, is much larger than the number of those which come close enough
+to be discovered from the earth. In any case we are reminded of Kepler's
+saying, that comets in the sky are as plentiful as fishes in the sea,
+which seems to be very little exaggerated when we consider that,
+according to Kleiber, out of all the comets which enter the solar system
+probably not more than 2 or 3 per cent are ever discovered.
+
+[Illustration: FIG. 110.--The Great Comet of 1843.]
+
+163. DIMENSIONS OF COMETS.--The comet whose orbit is shown in Figs. 108
+and 109 is the finest and largest that has appeared in recent years. Its
+tail, which at its maximum extent would have more than bridged the space
+between sun and earth (100,000,000 miles), is made very much too short
+in Fig. 109, but when at its best was probably not inferior to that of
+the Great Comet of 1843, shown in Fig. 110. As we shall see later,
+there is a peculiar and special relationship between these two comets.
+
+The head of the comet of 1882 was not especially large--about twice the
+diameter of the ball of Saturn--but its nucleus, according to an
+estimate made by Dr. Elkin when it was very near perihelion, was as
+large as the moon. The head of the comet shown in Fig. 107 was too large
+to be put in the space between the earth and the moon, and the Great
+Comet of 1811 had a head considerably larger than the sun itself. From
+these colossal sizes down to the smallest shred just visible in the
+telescope, comets of all dimensions may be found, but the smaller the
+comet the less the chance of its being discovered, and a comet as small
+as the earth would probably go unobserved unless it approached very
+close to us.
+
+164. THE MASS OF A COMET.--There is no known case in which the mass of a
+comet has ever been measured, yet nothing about them is more sure than
+that they are bodies with mass which is attracted by the sun and the
+planets, and which in its turn attracts both sun and planets and
+produces perturbations in their motion. These perturbations are,
+however, too small to be measured, although the corresponding
+perturbations in the comet's motion are sometimes enormous, and since
+these mutual perturbations are proportional to the masses of comet and
+planet, we are forced to say that, by comparison with even such small
+bodies as the moon or Mercury, the mass of a comet is utterly
+insignificant, certainly not as great as a ten-thousandth part of the
+mass of the earth. In the case of the Great Comet of 1882, if we leave
+its hundred million miles of tail out of account and suppose the entire
+mass condensed into its head, we find by a little computation that the
+average density of the head under these circumstances must have been
+less than 1/1500 of the density of air. In ordinary laboratory practice
+this would be called a pretty good vacuum. A striking observation made
+on September 17, 1882, goes to confirm the very small density of this
+comet. It is shown in Fig. 109 that early on that day the comet crossed
+the line joining earth and sun, and therefore passed in transit over the
+sun's disk. Two observers at the Cape of Good Hope saw the comet
+approach the sun, and followed it with their telescopes until the
+nucleus actually reached the edge of the sun and disappeared, behind it
+as they supposed, for no trace of the comet, not even its nucleus, could
+be seen against the sun, although it was carefully looked for. Now, the
+figure shows that the comet passed between the earth and sun, and its
+densest parts were therefore too attenuated to cut off any perceptible
+fraction of the sun's rays. In other cases stars have been seen through
+the head of a comet, shining apparently with undimmed luster, although
+in some cases they seem to have been slightly refracted out of their
+true positions.
+
+165. METEORS.--Before proceeding further with the study of comets it is
+well to turn aside and consider their humbler relatives, the shooting
+stars. On some clear evening, when the moon is absent from the sky,
+watch the heavens for an hour and count the meteors visible during that
+time. Note their paths, the part of the sky where they appear and where
+they disappear, their brightness, and whether they all move with equal
+swiftness. Out of such simple observations with the unaided eye there
+has grown a large and important branch of astronomical science, some
+parts of which we shall briefly summarize here.
+
+A particular meteor is a local phenomenon seen over only a small part of
+the earth's surface, although occasionally a very big and bright one may
+travel and be visible over a considerable territory. Such a one in
+December, 1876, swept over the United States from Kansas to
+Pennsylvania, and was seen from eleven different States. But the
+ordinary shooting star is much less conspicuous, and, as we know from
+simultaneous observations made at neighboring places, it makes its
+appearance at a height of some 75 miles above the earth's surface,
+occupies something like a second in moving over its path, and then
+disappears at a height of about 50 miles or more, although occasionally
+a big one comes down to the very surface of the earth with force
+sufficient to bury itself in the ground, from which it may be dug up,
+handled, weighed, and turned over to the chemist to be analyzed. The
+pieces thus found show that the big meteors, at least, are masses of
+stone or mineral; iron is quite commonly found in them, as are a
+considerable number of other terrestrial substances combined in rather
+peculiar ways. But no chemical element not found on the earth has ever
+been discovered in a meteor.
+
+166. NATURE OF METEORS.--The swiftness with which the meteors sweep down
+shows that they must come from outside the earth, for even half their
+velocity, if given to them by some terrestrial volcano or other
+explosive agent, would send them completely away from the earth never to
+return. We must therefore look upon them as so many projectiles,
+bullets, fired against the earth from some outside source and arrested
+in their motion by the earth's atmosphere, which serves as a cushion to
+protect the ground from the bombardment which would otherwise prove in
+the highest degree dangerous to both property and life. The speed of the
+meteor is checked by the resistance which the atmosphere offers to its
+motion, and the energy represented by that speed is transformed into
+heat, which in less than a second raises the meteor and the surrounding
+air to incandescence, melts the meteor either wholly or in part, and
+usually destroys its identity, leaving only an impalpable dust, which
+cools off as it settles slowly through the lower atmosphere to the
+ground. The heating effect of the air's resistance is proportional to
+the square of the meteor's velocity, and even at such a moderate speed
+as 1 mile per second the effect upon the meteor is the same as if it
+stood still in a bath of red-hot air. Now, the actual velocity of
+meteors through the air is often 30 or 40 times as great as this, and
+the corresponding effect of the air in raising its temperature is more
+than 1,000 times that of red heat. Small wonder that the meteor is
+brought to lively incandescence and consumed even in a fraction of a
+second.
+
+167. THE NUMBER OF METEORS.--A single observer may expect to see in the
+evening hours about one meteor every 10 minutes on the average,
+although, of course, in this respect much irregularity may occur. Later
+in the night they become more frequent, and after 2 A. M. there are
+about three times as many to be seen as in the evening hours. But no one
+person can keep a watch upon the whole sky, high and low, in front and
+behind, and experience shows that by increasing the number of observers
+and assigning to each a particular part of the sky, the total number of
+meteors counted may be increased about five-fold. So, too, the observers
+at any one place can keep an effective watch upon only those meteors
+which come into the earth's atmosphere within some moderate distance of
+their station, say 50 or 100 miles, and to watch every part of that
+atmosphere would require a large number of stations, estimated at
+something more than 10,000, scattered systematically over the whole face
+of the earth. If we piece together the several numbers above considered,
+taking 14 as a fair average of the hourly number of meteors to be seen
+by a single observer at all hours of the night, we shall find for
+the total number of meteors encountered by the earth in 24 hours,
+14 × 5 × 10,000 × 24 = 16,800,000. Without laying too much stress upon
+this particular number, we may fairly say that the meteors picked up by
+the earth every day are to be reckoned by millions, and since they come
+at all seasons of the year, we shall have to admit that the region
+through which the earth moves, instead of being empty space, is really a
+dust cloud, each individual particle of dust being a prospective meteor.
+
+On the average these individual particles are very small and very far
+apart; a cloud of silver dimes each about 250 miles from its nearest
+neighbor is perhaps a fair representation of their average mass and
+distance from each other, but, of course, great variations are to be
+expected both in the size and in the frequency of the particles. There
+must be great numbers of them that are too small to make shooting stars
+visible to the naked eye, and such are occasionally seen darting by
+chance across the field of view of a telescope.
+
+168. THE ZODIACAL LIGHT is an effect probably due to the reflection of
+sunlight from the myriads of these tiny meteors which occupy the space
+inside the earth's orbit. It is a faint and diffuse stream of light,
+something like the Milky Way, which may be seen in the early evening or
+morning stretching up from the sunrise or sunset point of the horizon
+along the ecliptic and following its course for many degrees, possibly
+around the entire circumference of the sky. It may be seen at any season
+of the year, although it shows to the best advantage in spring evenings
+and autumn mornings. Look for it.
+
+169. GREAT METEORS.--But there are other meteors, veritable fireballs in
+appearance, far more conspicuous and imposing than the ordinary shooting
+star. Such a one exploded over the city of Madrid, Spain, on the morning
+of February 10, 1896, giving in broad sunlight "a brilliant flash which
+was followed ninety seconds later by a succession of terrific noises
+like the discharge of a battery of artillery." Fig. 111 shows a large
+meteor which was seen in California in the early evening of July 27,
+1894, and which left behind it a luminous trail or cloud visible for
+more than half an hour.
+
+Not infrequently large meteors are found traveling together, two or
+three or more in company, making their appearance simultaneously as did
+the California meteor of October 22, 1896, which is described as triple,
+the trio following one another like a train of cars, and Arago cites an
+instance, from the year 1830, where within a short space of time some
+forty brilliant meteors crossed the sky, all moving in the same
+direction with a whistling noise and displaying in their flight all the
+colors of the rainbow.
+
+The mass of great meteors such as these must be measured in hundreds if
+not thousands of pounds, and stories are current, although not very well
+authenticated, of even larger ones, many tons in weight, having been
+found partially buried in the ground. Of meteors which have been
+actually seen to fall from the sky, the largest single fragment
+recovered weighs about 500 pounds, but it is only a fragment of the
+original meteor, which must have been much more massive before it was
+broken up by collision with the atmosphere.
+
+[Illustration: FIG. 111.--The California meteor of July 27, 1894.]
+
+170. THE VELOCITY OF METEORS.--Every meteor, big or little, is subject
+to the law of gravitation, and before it encounters the earth must be
+moving in some kind of orbit having the sun at its focus, the particular
+species of orbit--ellipse, parabola, hyperbola--depending upon the
+velocity and direction of its motion. Now, the direction in which a
+meteor is moving can be determined without serious difficulty from
+observations of its apparent path across the sky made by two or more
+observers, but the velocity can not be so readily found, since the
+meteors go too fast for any ordinary process of timing. But by
+photographing one of them two or three times on the same plate, with an
+interval of only a tenth of a second between exposures, Dr. Elkin has
+succeeded in showing, in a few cases, that their velocities varied from
+20 to 25 miles per second, and must have been considerably greater than
+this before the meteors encountered the earth's atmosphere. This is a
+greater velocity than that of the earth in its orbit, 19 miles per
+second, as might have been anticipated, since the mere fact that meteors
+can be seen at all in the evening hours shows that some of them at least
+must travel considerably faster than the earth, for, counting in the
+direction of the earth's motion, the region of sunset and evening is
+always on the rear side of the earth, and meteors in order to strike
+this region must overtake it by their swifter motion. We have here, in
+fact, the reason why meteors are especially abundant in the morning
+hours; at this time the observer is on the front side of the earth which
+catches swift and slow meteors alike, while the rear is pelted only by
+the swifter ones which follow it.
+
+A comparison of the relative number of morning and evening meteors makes
+it probable that the average meteor moves, relative to the sun, with a
+velocity of about 26 miles per second, which is very approximately the
+average velocity of comets when they are at the earth's distance from
+the sun. Astronomers, therefore, consider meteors as well as comets to
+have the parabola and the elongated ellipse as their characteristic
+orbits.
+
+171. METEOR SHOWERS--THE RADIANT.--There is evident among meteors a
+distinct tendency for individuals, to the number of hundreds or even
+hundreds of millions, to travel together in flocks or swarms, all going
+the same way in orbits almost exactly alike. This gregarious tendency is
+made manifest not only by the fact that from time to time there are
+unusually abundant meteoric displays, but also by a striking peculiarity
+of their behavior at such times. The meteors all seem to come from a
+particular part of the heavens, as if here were a hole in the sky
+through which they were introduced, and from which they flow away in
+every direction, even those which do not visibly start from this place
+having paths among the stars which, if prolonged backward, would pass
+through it. The cause of this appearance may be understood from Fig.
+112, which represents a group of meteors moving together along parallel
+paths toward an observer at _D_. Traveling unseen above the earth until
+they encounter the upper strata of its atmosphere, they here become
+incandescent and speed on in parallel paths, _1_, _2_, _3_, _4_, _5_,
+_6_, which, as seen by the observer, are projected back against the sky
+into luminous streaks that, as is shown by the arrowheads, _b_, _c_,
+_d_, all seem to radiate from the point _a_--i. e., from the point in
+the sky whose direction from the observer is parallel to the paths of
+the meteors.
+
+[Illustration: FIG. 112.--Explanation of the radiant of a meteoric
+shower.--DENNING.]
+
+Such a display is called a meteor shower, and the point _a_ is called
+its radiant. Note how those meteors which appear near the radiant all
+have short paths, while those remote from it in the sky have longer
+ones. Query: As the night wears on and the stars shift toward the west,
+will the radiant share in their motion or will it be left behind? Would
+the luminous part of the path of any of these meteors pass across the
+radiant from one side to the other? Is such a crossing of the radiant
+possible under any circumstances? Fig. 113 shows how the meteor paths
+are grouped around the radiant of a strongly marked shower. Select from
+it the meteors which do not belong to this shower.
+
+[Illustration: FIG. 113.--The radiant of a meteoric shower, showing
+also the paths of three meteors which do not belong to this
+shower.--DENNING.]
+
+Many hundreds of these radiants have been observed in the sky, each of
+which represents an orbit along which a group of meteors moves, and the
+relation of one of these orbits to that of the earth is shown in Fig.
+114. The orbit of the meteors is an ellipse extending out beyond the
+orbit of Uranus, but so eccentric that a part of it comes inside the
+orbit of the earth, and the figure shows only that part of it which lies
+nearest the sun. The Roman numerals which are placed along the earth's
+orbit show the position of the earth at the beginning of the tenth
+month, eleventh month, etc. The meteors flow along their orbit in a long
+procession, whose direction of motion is indicated by the arrow heads,
+and the earth, coming in the opposite direction, plunges into this
+stream and receives the meteor shower when it reaches the intersection
+of the two orbits. The long arrow at the left of the figure represents
+the direction of motion of another meteor shower which encounters the
+earth at this point.
+
+[Illustration: FIG. 114.--The orbits of the earth and the November
+meteors.]
+
+Can you determine from the figure answers to the following questions? On
+what day of the year will the earth meet each of these showers? Will the
+radiant points of the showers lie above or below the plane of the
+earth's orbit? Will these meteors strike the front or the rear of the
+earth? Can they be seen in the evening hours?
+
+From many of the radiants year after year, upon the same day or week in
+each year, there comes a swarm of shooting stars, showing that there
+must be a continuous procession of meteors moving along this orbit, so
+that some are always ready to strike the earth whenever it reaches the
+intersection of its orbit with theirs. Such is the explanation of the
+shower which appears each year in the first half of August, and whose
+meteors are sometimes called Perseids, because their radiant lies in the
+constellation Perseus, and a similar explanation holds for all the star
+showers which are repeated year after year.
+
+172. THE LEONIDS.--There is, however, a kind of star shower, of which
+the Leonids (radiant in Leo) is the most conspicuous type, in which the
+shower, although repeated from year to year, is much more striking in
+some years than in others. Thus, to quote from the historian: "In 1833
+the shower was well observed along the whole eastern coast of North
+America from the Gulf of Mexico to Halifax. The meteors were most
+numerous at about 5 A. M. on November 13th, and the rising sun could not
+blot out all traces of the phenomena, for large meteors were seen now
+and then in full daylight. Within the scope that the eye could contain,
+more than twenty could be seen at a time shooting in every direction.
+Not a cloud obscured the broad expanse, and millions of meteors sped
+their way across in every point of the compass. Their coruscations were
+bright, gleaming, and incessant, and they fell thick as the flakes in
+the early snows of December." But, so far as is known, none of them
+reached the ground. An illiterate man on the following day remarked:
+"The stars continued to fall until none were left. I am anxious to see
+how the heavens will appear this evening, for I believe we shall see no
+more stars."
+
+An eyewitness in the Southern States thus describes the effect of this
+shower upon the plantation negroes: "Upward of a hundred lay prostrate
+upon the ground, some speechless and some with the bitterest cries, but
+with their hands upraised, imploring God to save the world and them. The
+scene was truly awful, for never did rain fall much thicker than the
+meteors fell toward the earth--east, west, north, and south it was the
+same." In the preceding year a similar but feebler shower from the same
+radiant created much alarm in France, and through the old historic
+records its repetitions may be traced back at intervals of 33 or 34
+years, although with many interruptions, to October 12, 902, O. S., when
+"an immense number of falling stars were seen to spread themselves over
+the face of the sky like rain."
+
+Such a star shower differs from the one repeated every year chiefly in
+the fact that its meteors, instead of being drawn out into a long
+procession, are mainly clustered in a single flock which may be long
+enough to require two or three or four years to pass a given point of
+its orbit, but which is far from extending entirely around it, so that
+meteors from this source are abundant only in those years in which the
+flock is at or near the intersection of its orbit with that of the
+earth. The fact that the Leonid shower is repeated at intervals of 33 or
+34 years (it appeared in 1799, 1832-'33, 1866-'67) shows that this is
+the "periodic time" in its orbit, which latter must of course be an
+ellipse, and presumably a long and narrow one. It is this orbit which is
+shown in Fig. 114, and the student should note in this figure that if
+the meteor stream at the point where it cuts through the plane of the
+earth's orbit were either nearer to or farther from the sun than is the
+earth there could be no shower; the earth and the meteors would pass by
+without a collision. Now, the meteors in their motion are subject to
+perturbations, particularly by the large planets Jupiter, Saturn, and
+Uranus, which slightly change the meteor orbit, and it seems certain
+that the changes thus produced will sometimes thrust the swarm inside or
+outside the orbit of the earth, and thus cause a failure of the shower
+at times when it is expected. The meteors were due at the crossing of
+the orbits in November, 1899 and 1900, and, although a few were then
+seen, the shower was far from being a brilliant one, and its failure was
+doubtless caused by the outer planets, which switched the meteors aside
+from the path in which they had been moving for a century. Whether they
+will be again switched back so as to produce future showers is at the
+present time uncertain.
+
+173. CAPTURE OF THE LEONIDS.--But a far more striking effect of
+perturbations is to be found in Fig. 115, which shows the relation of
+the Leonid orbit to those of the principal planets, and illustrates a
+curious chapter in the history of the meteor swarm that has been worked
+out by mathematical analysis, and is probably a pretty good account of
+what actually befell them. Early in the second century of the Christian
+era this flock of meteors came down toward the sun from outer space,
+moving along a parabolic orbit which would have carried it just inside
+the orbit of Jupiter, and then have sent it off to return no more. But
+such was not to be its fate. As it approached the orbit of Uranus, in
+the year 126 A. D., that planet chanced to be very near at hand and
+perturbed the motion of the meteors to such an extent that the character
+of their orbit was completely changed into the ellipse shown in the
+figure, and in this new orbit they have moved from that time to this,
+permanent instead of transient members of the solar system. The
+perturbations, however, did not end with the year in which the meteors
+were captured and annexed to the solar system, but ever since that time
+Jupiter, Saturn, and Uranus have been pulling together upon the orbit,
+and have gradually turned it around into its present position as shown
+in the figure, and it is chiefly this shifting of the orbit's position
+in the thousand years that have elapsed since 902 A. D. that makes the
+meteor shower now come in November instead of in October as it did
+then.
+
+[Illustration: FIG. 115.--Supposed capture of the November meteors by
+Uranus.]
+
+174. BREAKING UP A METEOR SWARM.--How closely packed together these
+meteors were at the time of their annexation to the solar system is
+unknown, but it is certain that ever since that time the sun has been
+exerting upon them a tidal influence tending to break up the swarm and
+distribute its particles around the orbit, as the Perseids are
+distributed, and, given sufficient time, it will accomplish this, but up
+to the present the work is only partly done. A certain number of the
+meteors have gained so much over the slower moving ones as to have made
+an extra circuit of the orbit and overtaken the rear of the procession,
+so that there is a thin stream of them extending entirely around the
+orbit and furnishing in every November a Leonid shower; but by far the
+larger part of the meteors still cling together, although drawn out into
+a stream or ribbon, which, though very thin, is so long that it takes
+some three years to pass through the perihelion of its orbit. It is only
+when the earth plunges through this ribbon, as it should in 1899, 1900,
+1901, that brilliant Leonid showers can be expected.
+
+175. RELATION OF COMETS AND METEORS.--It appears from the foregoing that
+meteors and comets move in similar orbits, and we have now to push the
+analogy a little further and note that in some instances at least they
+move in identically the same orbit, or at least in orbits so like that
+an appreciable difference between them is hardly to be found. Thus a
+comet which was discovered and observed early in the year 1866, moves in
+the same orbit with the Leonid meteors, passing its perihelion about ten
+months ahead of the main body of the meteors. If it were set back in its
+orbit by ten months' motion, _it would be a part of the meteor swarm_.
+Similarly, the Perseid meteors have a comet moving in their orbit
+actually immersed in the stream of meteor particles, and several other
+of the more conspicuous star showers have comets attending them.
+
+Perhaps the most remarkable case of this character is that of a shower
+which comes in the latter part of November from the constellation
+Andromeda, and which from its association with the comet called Biela
+(after the name of its discoverer) is frequently referred to as the
+Bielid shower. This comet, an inconspicuous one moving in an unusually
+small elliptical orbit, had been observed at various times from 1772
+down to 1846 without presenting anything remarkable in its appearance;
+but about the beginning of the latter year, with very little warning, it
+broke in two, and for three months the pieces were watched by
+astronomers moving off, side by side, something more than half as far
+apart as are the earth and moon. It disappeared, made the circuit of its
+orbit, and six years later came back, with the fragments nearly ten
+times as far apart as before, and after a short stay near the earth once
+more disappeared in the distance, never to be seen again, although the
+fragments should have returned to perihelion at least half a dozen times
+since then. In one respect the orbit of the comet was remarkable: it
+passed through the place in which the earth stands on November 27th of
+each year, so that if the comet were at that particular part of its
+orbit on any November 27th, a collision between it and the earth would
+be inevitable. So far as is known, no such collision with the comet has
+ever occurred, but the Bielid meteors which are strung along its orbit
+do encounter the earth on that date, in greater or less abundance in
+different years, and are watched with much interest by the astronomers
+who look upon them as the final appearance of the _débris_ of a worn-out
+comet.
+
+176. PERIODIC COMETS.--The Biela comet is a specimen of the type which
+astronomers call periodic comets--i. e., those which move in small
+ellipses and have correspondingly short periodic times, so that they
+return frequently and regularly to perihelion. The comets which
+accompany the other meteor swarms--Leonids, Perseids, etc.--also belong
+to this class as do some 30 or 40 others which have periodic times less
+than a century. As has been already indicated, these deviations from the
+normal parabolic orbit call for some special explanation, and the
+substance of that explanation is contained in the account of the Leonid
+meteors and their capture by Uranus. Any comet may be thus captured by
+the attraction of a planet near which it passes. It is only necessary
+that the perturbing action of the planet should result in a diminution
+of the comet's velocity, for we have already learned that it is this
+velocity which determines the character of the orbit, and anything less
+than the velocity appropriate to a parabola must produce an
+ellipse--i. e., a closed orbit around which the body will revolve time
+after time in endless succession. We note in Fig. 115 that when the
+Leonid swarm encountered Uranus it passed _in front of_ the planet and
+had its velocity diminished and its orbit changed into an ellipse
+thereby. It might have passed behind Uranus, it would have passed behind
+had it come a little later, and the effect would then have been just the
+opposite. Its velocity would have been increased, its orbit changed to a
+hyperbola, and it would have left the solar system more rapidly than it
+came into it, thrust out instead of held in by the disturbing planet. Of
+such cases we can expect no record to remain, but the captured comet is
+its own witness to what has happened, and bears imprinted upon its orbit
+the brand of the planet which slowed down its motion. Thus in Fig. 115
+the changed orbit of the meteors has its _aphelion_ (part remotest from
+the sun) quite close to the orbit of Uranus, and one of its nodes,
+[mho], the point in which it cuts through the plane of the ecliptic from
+north to south side, is also very near to the same orbit. It is these
+two marks, aphelion and node, which by their position identify Uranus as
+the planet instrumental in capturing the meteor swarm, and the date of
+the capture is found by working back with their respective periodic
+times to an epoch at which planet and comet were simultaneously near
+this node.
+
+Jupiter, by reason of his great mass, is an especially efficient
+capturer of comets, and Fig. 116 shows his group of captives, his
+family of comets as they are sometimes called. The several orbits are
+marked with the names commonly given to the comets. Frequently this is
+the name of their discoverer, but often a different system is
+followed--e. g., the name 1886, IV, means the fourth comet to pass
+through perihelion in the year 1886. The other great planets--Saturn,
+Uranus, Neptune--have also their families of captured comets, and
+according to Schulhof, who does not entirely agree with the common
+opinion about captured comets, the earth has caught no less than nine of
+these bodies.
+
+[Illustration: FIG. 116.--Jupiter's family of comets.]
+
+177. COMET GROUPS.--But there is another kind of comet family, or comet
+group as it is called, which deserves some notice, and which is best
+exemplified by the Great Comet of 1882 and its relatives. No less than
+four other comets are known to be traveling in substantially the same
+orbit with this one, the group consisting of comets 1668, I; 1843, I;
+1880, I; 1882, II; 1887, I. The orbit itself is not quite a parabola,
+but a very elongated ellipse, whose major axis and corresponding
+periodic time can not be very accurately determined from the available
+data, but it certainly extends far beyond the orbit of Neptune, and
+requires not less than 500 years for the comet to complete a revolution
+in it. It was for a time supposed that some one of the recent comets of
+this group of five might be a return of the comet of 1668 brought back
+ahead of time by unknown perturbations. There is still a possibility of
+this, but it is quite out of the question to suppose that the last four
+members of the group are anything other than separate and distinct
+comets moving in practically the same orbit. This common orbit suggests
+a common origin for the comets, but leaves us to conjecture how they
+became separated.
+
+The observed orbits of these five comets present some slight
+discordances among themselves, but if we suppose each comet to move in
+the average of the observed paths it is a simple matter to fix their
+several positions at the present time. They have all receded from the
+sun nearly on line toward the bright star Sirius, and were all of them,
+at the beginning of the year 1900, standing nearly motionless inside of
+a space not bigger than the sun and distant from the sun about 150 radii
+of the earth's orbit. The great rapidity with which they swept through
+that part of their orbit near the sun (see § 162) is being compensated
+by the present extreme slowness of their motions, so that the comets of
+1668 and 1882, whose passages through the solar system were separated by
+an interval of more than two centuries, now stand together near the
+aphelion of their orbits, separated by a distance only 50 per cent
+greater than the diameter of the moon's orbit, and they will continue
+substantially in this position for some two or three centuries to come.
+
+The slowness with which these bodies move when far from the sun is
+strikingly illustrated by an equation of celestial mechanics which for
+parabolic orbits takes the place of Kepler's Third Law--viz.:
+
+    r^3 / T^2 = 178,
+
+where _T_ is the time, in years, required for the comet to move from its
+perihelion to any remote part of the orbit, whose distance from the sun
+is represented, in radii of the earth's orbit, by _r_. If the comet of
+1668 had moved in a parabola instead of the ellipse supposed above, how
+many years would have been required to reach its present distance from
+the sun?
+
+178. RELATION OF COMETS TO THE SOLAR SYSTEM.--The orbits of these comets
+illustrate a tendency which is becoming ever more strongly marked.
+Because comet orbits are nearly parabolas, it used to be assumed that
+they were exactly parabolic, and this carried with it the conclusion
+that comets have their origin outside the solar system. It may be so,
+and this view is in some degree supported by the fact that these nearly
+parabolic orbits of both comets and meteors are tipped at all possible
+angles to the plane of the ecliptic instead of lying near it as do the
+orbits of the planets; and by the further fact that, unlike the planets,
+the comets show no marked tendency to move around their orbits in the
+direction in which the sun rotates upon his axis. There is, in fact, the
+utmost confusion among them in this respect, some going one way and some
+another. The law of the solar system (gravitation) is impressed upon
+their movements, but its order is not.
+
+But as observations grow more numerous and more precise, and comet
+orbits are determined with increasing accuracy, there is a steady gain
+in the number of elliptic orbits at the expense of the parabolic ones,
+and if comets are of extraneous origin we must admit that a very
+considerable percentage of them have their velocities slowed down
+within the solar system, perhaps not so much by the attraction of the
+planets as by the resistance offered to their motion by meteor particles
+and swarms along their paths. A striking instance of what may befall a
+comet in this way is shown in Fig. 117, where the tail of a comet
+appears sadly distorted and broken by what is presumed to have been a
+collision with a meteor swarm. A more famous case of impeded motion is
+offered by the comet which bears the name of Encke. This has a periodic
+time less than that of any other known comet, and at intervals of forty
+months comes back to perihelion, each time moving in a little smaller
+orbit than before, unquestionably on account of some resistance which it
+has suffered.
+
+[Illustration: FIG. 117.--Brooks's comet, October 21, 1893.--BARNARD.]
+
+179. THE DEVELOPMENT OF A COMET.--We saw in § 174 that the sun's action
+upon a meteor swarm tends to break it up into a long stream, and the
+same tendency to break up is true of comets whose attenuated substance
+presents scant resistance to this force. According to the mathematical
+analysis of Roche, if the comet stood still the sun's tidal force would
+tend first to draw it out on line with the sun, just as the earth's
+tidal force pulled the moon out of shape (§ 42), and then it would cause
+the lighter part of the comet's substance to flow away from both ends of
+this long diameter. This destructive action of the sun is not limited to
+comets and meteor streams, for it tends to tear the earth and moon to
+pieces as well; but the densities and the resulting mutual attractions
+of their parts are far too great to permit this to be accomplished.
+
+As a curiosity of mathematical analysis we may note that a spherical
+cloud of meteors, or dust particles weighing a gramme each, and placed
+at the earth's distance from the sun, will be broken up and dissipated
+by the sun's tidal action if the average distance between the particles
+exceeds two yards. Now, the earth is far more dense than such a cloud,
+whose extreme tenuity, however, suggests what we have already learned of
+the small density of comets, and prepares us in their case for an
+outflow of particles at both ends of the diameter directed toward the
+sun. Something of this kind actually occurs, for the tail of a comet
+streams out on the side opposite to the sun, and in general points away
+from the sun, as is shown in Fig. 109, and the envelopes and jets rise
+up toward the sun; but an inspection of Fig. 106 will show that the tail
+and the envelope are too unlike to be produced by one and the same set
+of forces.
+
+It was long ago suggested that the sun possibly exerts upon a comet's
+substance a repelling force in addition to the attracting force which we
+call gravity. We think naturally in this connection of the repelling
+force which a charge of electricity exerts upon a similar charge placed
+on a neighboring body, and we note that if both sun and comet carried a
+considerable store of electricity upon their surfaces this would furnish
+just such a repelling force as seems indicated by the phenomena of
+comets' tails; for the force of gravity would operate between the
+substance of sun and comet, and on the whole would be the controlling
+force, while the electric charges would produce a repulsion, relatively
+feeble for the big particles and strong for the little ones, since an
+electric charge lies wholly on the surface, while gravity permeates the
+whole mass of a body, and the ratio of volume (gravity) to surface
+(electric charge) increases rapidly with increasing size. The repelling
+force would thrust back toward the comet those particles which flowed
+out toward the sun, while it would urge forward those which flowed away
+from it, thus producing the difference in appearance between tail and
+envelopes, the latter being regarded from this standpoint as stunted
+tails strongly curved backward. In recent years the Russian astronomer
+Bredichin has made a careful study of the shape and positions of comets'
+tails and finds that they fit with mathematical precision to the
+theories of electric repulsion.
+
+180. COMET TAILS.--According to Bredichin, a comet's tail is formed by
+something like the following process: In the head of the comet itself a
+certain part of its matter is broken up into fine bits, single molecules
+perhaps, which, as they no longer cling together, may be described as in
+the condition of vapor. By the repellent action of both sun and comet
+these molecules are cast out from the head of the comet and stream away
+in the direction opposite to the sun with different velocities, the
+heavy ones slowly and the light ones faster, much as particles of smoke
+stream away from a smokestack, making for the comet a tail which like a
+trail of smoke is composed of constantly changing particles. The result
+of this process is shown in Fig. 118, where the positions of the comet
+in its orbit on successive days are marked by the Roman numerals, and
+the broken lines represent the paths of molecules _m^{I}_, _m^{II}_,
+_m^{III}_, etc., expelled from it on their several dates and traveling
+thereafter in orbits determined by the combined effect of the sun's
+attraction, the sun's repulsion, and the comet's repulsion. The comet's
+attraction (gravity) is too small to be taken into account. The line
+drawn upward from _VI_ represents the positions of these molecules on
+the sixth day, and shows that all of them are arranged in a tail
+pointing nearly away from the sun. A similar construction for the other
+dates gives the corresponding positions of the tail, always pointing
+away from the sun.
+
+[Illustration: FIG. 118.--Formation of a comet's tail.]
+
+Only the lightest kind of molecules--e. g., hydrogen--could drift away
+from the comet so rapidly as is here shown. The heavier ones, such as
+carbon and iron, would be repelled as strongly by the electric forces,
+but they would be more strongly pulled back by the gravitative forces,
+thus producing a much slower separation between them and the head of the
+comet. Construct a figure such as the above, in which the molecules
+shall recede from the comet only one eighth as fast as in Fig. 118, and
+note what a different position it gives to the comet's tail. Instead of
+pointing directly away from the sun, it will be bent strongly to one
+side, as is the large plume-shaped tail of the Donati comet shown in
+Fig. 101. But observe that this comet has also a nearly straight tail,
+like the theoretical one of Fig. 118. We have here two distinct types of
+comet tails, and according to Bredichin there is still another but
+unusual type, even more strongly bent to one side of the line joining
+comet and sun, and appearing quite short and stubby. The existence of
+these three types, and their peculiarities of shape and position, are
+all satisfactorily accounted for by the supposition that they are made
+of different materials. The relative molecular weights of hydrogen, some
+of the hydrocarbons, and iron, are such that tails composed of these
+molecules would behave just as do the actual tails observed and
+classified into these three types. The spectroscope shows that these
+materials--hydrogen, hydrocarbons, and iron--are present in comets, and
+leaves little room for doubt of the essential soundness of Bredichin's
+theory.
+
+181. DISINTEGRATION OF COMETS.--We must regard the tail as waste matter
+cast off from the comet's head, and although the amount of this matter
+is very small, it must in some measure diminish the comet's mass. This
+process is, of course, most active at the time of perihelion passage,
+and if the comet returns to perihelion time after time, as the periodic
+ones which move in elliptic orbits must do, this waste of material may
+become a serious matter, leading ultimately to the comet's destruction.
+It is significant in this connection that the periodic comets are all
+small and inconspicuous, not one of them showing a tail of any
+considerable dimensions, and it appears probable that they are far
+advanced along the road which, in the case of Biela's comet, led to its
+disintegration. Their fragments are in part strewn through the solar
+system, making some small fraction of its cloud of cosmic dust, and in
+part they have been carried away from the sun and scattered throughout
+the universe along hyperbolic orbits impressed upon them at the time
+they left the comet.
+
+But it is not through the tail only that the disintegrating process is
+worked out. While Biela's comet is perhaps the most striking instance in
+which the head has broken up, it is by no means the only one. The Great
+Comet of 1882 cast off a considerable number of fragments which moved
+away as independent though small comets and other more recent comets
+have been seen to do the same. An even more striking phenomenon was the
+gradual breaking up of the nucleus of the same comet, 1882, II, into a
+half dozen nuclei arranged in line like beads upon a string, and
+pointing along the axis of the tail. See Fig. 119, which shows the
+series of changes observed in the head of this comet.
+
+182. COMETS AND THE SPECTROSCOPE.--The spectrum presented by comets was
+long a puzzle, and still retains something of that character, although
+much progress has been made toward an understanding of it. In general it
+consists of two quite distinct parts--first, a faint background of
+continuous spectrum due to ordinary sunlight reflected from the comet;
+and, second, superposed upon this, three bright bands like the carbon
+band shown at the middle of Fig. 48, only not so sharply defined. These
+bands make a discontinuous spectrum quite similar to that given off by
+compounds of hydrogen and carbon, and of course indicate that a part of
+the comet's light originates in the body itself, which must therefore be
+incandescent, or at least must contain some incandescent portions.
+
+[Illustration: FIG. 119.--The head of the Great Comet of
+1882.--WINLOCK.]
+
+By heating hydrocarbons in our laboratories until they become
+incandescent, something like the comet spectrum may be artificially
+produced, but the best approximation to it is obtained by passing a
+disruptive electrical discharge through a tube in which fragments of
+meteors have been placed. A flash of lightning is a disruptive
+electrical discharge upon a grand scale. Now, meteors and electric
+phenomena have been independently brought to our notice in connection
+with comets, and with this suggestion it is easy to frame a general idea
+of the physical condition of these objects--for example, a cloud of
+meteors of different sizes so loosely clustered that the average density
+of the swarm is very low indeed; the several particles in motion
+relative to each other, as well as to the sun, and disturbed in that
+motion by the sun's tidal action. Each particle carries its own electric
+charge, which may be of higher or lower tension than that of its
+neighbor, and is ready to leap across the intervening gap whenever two
+particles approach each other. To these conditions add the inductive
+effect of the sun's electric charge, which tends to produce a particular
+and artificial distribution of electricity among the comet's particles,
+and we may expect to find an endless succession of sparks, tiny
+lightning flashes, springing from one particle to another, most frequent
+and most vivid when the comet is near the sun, but never strong enough
+to be separately visible. Their number is, however, great enough to make
+the comet in part self-luminous with three kinds of light--i. e., the
+three bright bands of its spectrum, whose wave lengths show in the comet
+the same elements and compounds of the elements--carbon, hydrogen, and
+oxygen--which chemical analysis finds in the fallen meteor. It is not to
+be supposed that these are the only chemical elements in the comet, as
+they certainly are not the only ones in the meteor. They are the easy
+ones to detect under ordinary circumstances, but in special cases, like
+that of the Great Comet of 1882, whose near approach to the sun rendered
+its whole substance incandescent, the spectrum glows with additional
+bright lines of sodium, iron, etc.
+
+183. COLLISIONS.--A question sometimes asked, What would be the effect
+of a collision between the earth and a comet? finds its answer in the
+results reached in the preceding sections. There would be a star
+shower, more or less brilliant according to the number and size of the
+pieces which made up the comet's head. If these were like the remains of
+the Biela comet, the shower might even be a very tame one; but a
+collision with a great comet would certainly produce a brilliant
+meteoric display if its head came in contact with the earth. If the
+comet were built of small pieces whose individual weights did not exceed
+a few ounces or pounds, the earth's atmosphere would prove a perfect
+shield against their attacks, reducing the pieces to harmless dust
+before they could reach the ground, and leaving the earth uninjured by
+the encounter, although the comet might suffer sadly from it. But big
+stones in the comet, meteors too massive to be consumed in their flight
+through the air, might work a very different effect, and by their
+bombardment play sad havoc with parts of the earth's surface, although
+any such result as the wrecking of the earth, or the destruction of all
+life upon it, does not seem probable. The 40 meteors of § 169 may stand
+for a collision with a small comet. Consult the Bible (Joshua x, 11) for
+an example of what might happen with a larger one.
+
+
+
+
+CHAPTER XIII
+
+THE FIXED STARS
+
+
+184. THE CONSTELLATIONS.--In the earlier chapters the student has
+learned to distinguish between wandering stars (planets) and those fixed
+luminaries which remain year after year in the same constellation,
+shining for the most part with unvarying brilliancy, and presenting the
+most perfect known image of immutability. Homer and Job and prehistoric
+man saw Orion and the Pleiades much as we see them to-day, although the
+precession, by changing their relation to the pole of the heavens, has
+altered their risings and settings, and it may be that their luster has
+changed in some degree as they grew old with the passing centuries.
+
+[Illustration: FIG. 120.--Illustrating the division of the sky into
+constellations.]
+
+The division of the sky into constellations dates back to the most
+primitive times, long before the Christian era, and the crooked and
+irregular boundaries of these constellations, shown by the dotted lines
+in Fig. 120, such as no modern astronomer would devise, are an
+inheritance from antiquity, confounded and made worse in its descent to
+our day. The boundaries assigned to constellations near the south pole
+are much more smooth and regular, since this part of the sky, invisible
+to the peoples from whom we inherit, was not studied and mapped until
+more modern times. The old traditions associated with each constellation
+a figure, often drawn from classical mythology, which was supposed to be
+suggested by the grouping of the stars: thus Ursa Major is a great bear,
+stalking across the sky, with the handle of the Dipper for his tail; Leo
+is a lion; Cassiopeia, a lady in a chair; Andromeda, a maiden chained
+to a rock, etc.; but for the most part the resemblances are far-fetched
+and quite too fanciful to be followed by the ordinary eye.
+
+185. THE NUMBER OF STARS.--"As numerous as the stars of heaven" is a
+familiar figure of speech for expressing the idea of countless number,
+but as applied to the visible stars of the sky the words convey quite a
+wrong impression, for, under ordinary circumstances, in a clear sky
+every star to be seen may be counted in the course of a few hours, since
+they do not exceed 3,000 or 4,000, the exact number depending upon
+atmospheric conditions and the keenness of the individual eye. Test your
+own vision by counting the stars of the Pleiades. Six are easily seen,
+and you may possibly find as many as ten or twelve; but however many are
+seen, there will be a vague impression of more just beyond the limit of
+visibility, and doubtless this impression is partly responsible for the
+popular exaggeration of the number of the stars. In fact, much more than
+half of what we call starlight comes from stars which are separately too
+small to be seen, but whose number is so great as to more than make up
+for their individual faintness.
+
+The Milky Way is just such a cloud of faint stars, and the student who
+can obtain access to a small telescope, or even an opera glass, should
+not fail to turn it toward the Milky Way and see for himself how that
+vague stream of light breaks up into shining points, each an independent
+star. These faint stars, which are found in every part of the sky as
+well as in the Milky Way, are usually called _telescopic_, in
+recognition of the fact that they can be seen only in the telescope,
+while the other brighter ones are known as _lucid stars_.
+
+186. MAGNITUDES.--The telescopic stars show among themselves an even
+greater range of brightness than do the lucid ones, and the system of
+magnitudes (§ 9) has accordingly been extended to include them, the
+faintest star visible in the greatest telescope of the present time
+being of the sixteenth or seventeenth magnitude, while, as we have
+already learned, stars on the dividing line between the telescopic and
+the lucid ones are of the sixth magnitude. To compare the amount of
+light received from the stars with that from the planets, and
+particularly from the sun and moon, it has been found necessary to
+prolong the scale of magnitudes backward into the negative numbers, and
+we speak of the sun as having a stellar magnitude represented by the
+number -26.5. The full moon's stellar magnitude is -12, and the planets
+range from -3 (Venus) to +8 (Neptune). Even a very few of the stars are
+so bright that negative magnitudes must be used to represent their true
+relation to the fainter ones. Sirius, for example, the brightest of the
+fixed stars, is of the -1 magnitude, and such stars as Arcturus and Vega
+are of the 0 magnitude.
+
+The relation of these magnitudes to each other has been so chosen that a
+star of any one magnitude is very approximately 2.5 times as bright as
+one of the next fainter magnitude, and this ratio furnishes a convenient
+method of comparing the amount of light received from different stars.
+Thus the brightness of Venus is 2.5 × 2.5 times that of Sirius. The full
+moon is 2.5^{9} times as bright as Venus, etc.; only it should be
+observed that the number 2.5 is not exactly the value of the _light
+ratio_ between two consecutive magnitudes. Strictly this ratio is the
+100^{1/5} = 2.5119+, so that to be entirely accurate we must say that
+a difference of five magnitudes gives a hundredfold difference of
+brightness. In mathematical symbols, if _B_ represents the ratio of
+brightness (quantity of light) of two stars whose magnitudes are _m_ and
+_n_, then
+
+    B = (100)^{(m-n)/5}
+
+How much brighter is an ordinary first-magnitude star, such as Aldebaran
+or Spica, than a star just visible to the naked eye? How many of the
+faintest stars visible in a great telescope would be required to make
+one star just visible to the unaided eye? How many full moons must be
+put in the sky in order to give an illumination as bright as daylight?
+How large a part of the visible hemisphere would they occupy?
+
+187. CLASSIFICATION BY MAGNITUDES.--The brightness of all the lucid
+stars has been carefully measured with an instrument (photometer)
+designed for that special purpose, and the following table shows,
+according to the Harvard Photometry, the number of stars in the whole
+sky, from pole to pole, which are brighter than the several magnitudes
+named in the table:
+
+    The number of stars brighter than magnitude 1.0 is    11
+        "       "          "      "       "     2.0 "     39
+        "       "          "      "       "     3.0 "    142
+        "       "          "      "       "     4.0 "    463
+        "       "          "      "       "     5.0 "  1,483
+        "       "          "      "       "     6.0 "  4,326
+
+It must not be inferred from this table that there are in the whole sky
+only 4,326 stars visible to the naked eye. The actual number is probably
+50 or 60 per cent greater than this, and the normal human eye sees stars
+as faint as the magnitude 6.4 or 6.5, the discordance between this
+number and the previous statement, that the sixth magnitude is the limit
+of the naked-eye vision, having been introduced in the attempt to make
+precise and accurate a classification into magnitudes which was at first
+only rough and approximate. This same striving after accuracy leads to
+the introduction of fractional numbers to represent gradations of
+brightness intermediate between whole magnitudes. Thus of the 2,843
+stars included between the fifth and sixth magnitudes a certain
+proportion are said to be of the 5.1 magnitude, 5.2 magnitude, and so on
+to the 5.9 magnitude, even hundredths of a magnitude being sometimes
+employed.
+
+We have found the number of stars included between the fifth and sixth
+magnitudes by subtracting from the last number of the preceding table
+the number immediately preceding it, and similarly we may find the
+number included between each other pair of consecutive magnitudes, as
+follows:
+
+    Magnitude       0    1    2     3     4       5       6
+    Number of stars   11   28   103   321   1,020   2,843
+    4 × 3^{m}         12   36   108   324     972   2,916
+
+In the last line each number after the first is found by multiplying the
+preceding one by 3, and the approximate agreement of each such number
+with that printed above it shows that on the whole, as far as the table
+goes, the fainter stars are approximately three times as numerous as
+those a magnitude brighter.
+
+The magnitudes of the telescopic stars have not yet been measured
+completely, and their exact number is unknown; but if we apply our
+principle of a threefold increase for each successive magnitude, we
+shall find for the fainter stars--those of the tenth and twelfth
+magnitudes--prodigious numbers which run up into the millions, and even
+these are probably too small, since down to the ninth or tenth magnitude
+it is certain that the number of the telescopic stars increases from
+magnitude to magnitude in more than a threefold ratio. This is balanced
+in some degree by the less rapid increase which is known to exist in
+magnitudes still fainter; and applying our formula without regard to
+these variations in the rate of increase, we obtain as a rude
+approximation to the total number of stars down to the fifteenth
+magnitude, 86,000,000. The Herschels, father and son, actually counted
+the number of stars visible in nearly 8,000 sample regions of the sky,
+and, inferring the character of the whole sky from these samples, we
+find it to contain 58,500,000 stars; but the magnitude of the faintest
+star visible in their telescope, and included in their count, is rather
+uncertain.
+
+How many first-magnitude stars would be needed to give as much light as
+do the 2,843 stars of magnitude 5.0 to 6.0? How many tenth-magnitude
+stars are required to give the same amount of light?
+
+To the modern man it seems natural to ascribe the different brilliancies
+of the stars to their different distances from us; but such was not the
+case 2,000 years ago, when each fixed star was commonly thought to be
+fastened to a "crystal sphere," which carried them with it, all at the
+same distance from us, as it turned about the earth. In breaking away
+from this erroneous idea and learning to think of the sky itself as only
+an atmospheric illusion through which we look to stars at very different
+distances beyond, it was easy to fall into the opposite error and to
+think of the stars as being much alike one with another, and, like
+pebbles on the beach, scattered throughout space with some rough degree
+of uniformity, so that in every direction there should be found in equal
+measure stars near at hand and stars far off, each shining with a luster
+proportioned to its remoteness.
+
+188. DISTANCES OF THE STARS.--Now, in order to separate the true from
+the false in this last mode of thinking about the stars, we need some
+knowledge of their real distances from the earth, and in seeking it we
+encounter what is perhaps the most delicate and difficult problem in the
+whole range of observational astronomy. As shown in Fig. 121, the
+principles involved in determining these distances are not fundamentally
+different from those employed in determining the moon's distance from
+the earth. Thus, the ellipse at the left of the figure represents the
+earth's orbit and the position of the earth at different times of the
+year. The direction of the star _A_ at these several times is shown by
+lines drawn through _A_ and prolonged to the background apparently
+furnished by the sky. A similar construction is made for the star _B_,
+and it is readily seen that owing to the changing position of the
+observer as he moves around the earth's orbit, both _A_ and _B_ will
+appear to move upon the background in orbits shaped like that of the
+earth as seen from the star, but having their size dependent upon the
+star's distance, the apparent orbit of _A_ being larger than that of
+_B_, because _A_ is nearer the earth. By measuring the angular distance
+between _A_ and _B_ at opposite seasons of the year (e. g., the angles
+_A--Jan.--B_, and _A--July--B_) the astronomer determines from the
+change in this angle how much larger is the one path than the other, and
+thus concludes how much nearer is _A_ than _B_. Strictly, the difference
+between the January and July angles is equal to the difference between
+the angles subtended at _A_ and _B_ by the diameter of the earth's
+orbit, and if _B_ were so far away that the angle _Jan.--B--July_ were
+nothing at all we should get immediately from the observations the angle
+_Jan.--A--July_, which would suffice to determine the stars' distance.
+Supposing the diameter of the earth's orbit and the angle at _A_ to be
+known, can you make a graphical construction that will determine the
+distance of _A_ from the earth?
+
+[Illustration: FIG. 121.--Determining a star's parallax.]
+
+The angle subtended at _A_ by the radius of the earth's orbit--i. e.,
+1/2 (_Jan.--A--July_)--is called the star's parallax, and this is
+commonly used by astronomers as a measure of the star's distance instead
+of expressing it in linear units such as miles or radii of the earth's
+orbit. The distance of a star is equal to the radius of the earth's
+orbit divided by the parallax, in seconds of arc, and multiplied by the
+number 206265.
+
+A weak point of this method of measuring stellar distances is that it
+always gives what is called a relative parallax--i. e., the difference
+between the parallaxes of _A_ and _B_; and while it is customary to
+select for _B_ a star or stars supposed to be much farther off than _A_,
+it may happen, and sometimes does happen, that these comparison stars as
+they are called are as near or nearer than _A_, and give a negative
+parallax--i. e., the difference between the angles at _A_ and _B_ proves
+to be negative, as it must whenever the star _B_ is nearer than _A_.
+
+The first really successful determinations of stellar parallax were made
+by Struve and Bessel a little prior to 1840, and since that time the
+distances of perhaps 100 stars have been measured with some degree of
+reliability, although the parallaxes themselves are so small--never as
+great as 1''--that it is extremely difficult to avoid falling into
+error, since even for the nearest star the problem of its distance is
+equivalent to finding the distance of an object more than 5 miles away
+by looking at it first with one eye and then with the other. Too short a
+base line.
+
+189. THE SUN AND HIS NEIGHBORS.--The distances of the sun's nearer
+neighbors among the stars are shown in Fig. 122, where the two circles
+having the sun at their center represent distances from it equal
+respectively to 1,000,000 and 2,000,000 times the distance between earth
+and sun. In the figure the direction of each star from the sun
+corresponds to its right ascension, as shown by the Roman numerals about
+the outer circle; the true direction of the star from the sun can not,
+of course, be shown upon the flat surface of the paper, but it may be
+found by elevating or depressing the star from the surface of the paper
+through an angle, as seen from the sun, equal to its declination, as
+shown in the fifth column of the following table,
+
+                       _The Sun's Nearest Neighbors_
+
+  ---+------------------+----------+-------+-----+----------+---------
+  No.| STAR.            |Magnitude.| R. A. |Dec. | Parallax.|Distance.
+  ---+------------------+----------+-------+-----+----------+---------
+  1  | [a] Centauri     |   0.7    | 14.5h.| -60°|   0.75"  |  0.27
+     |                  |          |       |     |          |
+  2  | Ll. 21,185       |   6.8    | 11.0  | +37 |   0.45   |  0.46
+     |                  |          |       |     |          |
+  3  | 61 Cygni         |   5.0    | 21.0  | +38 |   0.40   |  0.51
+     |                  |          |       |     |          |
+  4  | [ź] Herculis     |   3.6    | 16.7  | +39 |   0.40   |  0.51
+     |                  |          |       |     |          |
+  5  | Sirius           |  -1.4    |  6.7  | -17 |   0.37   |  0.56
+     |                  |          |       |     |          |
+  6  | [S] 2,398        |   8.2    | 18.7  | +59 |   0.35   |  0.58
+     |                  |          |       |     |          |
+  7  | Procyon          |   0.5    |  7.6  | + 5 |   0.34   |  0.60
+     |                  |          |       |     |          |
+  8  | [g] Draconis     |   4.8    | 17.5  | +55 |   0.30   |  0.68
+     |                  |          |       |     |          |
+  9  | Gr. 34           |   7.9    |  0.2  | +43 |   0.29   |  0.71
+     |                  |          |       |     |          |
+  10 | Lac. 9,352       |   7.5    | 23.0  | -36 |   0.28   |  0.74
+     |                  |          |       |     |          |
+  11 | [s] Draconis     |   4.8    | 19.5  | +69 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  12 | A. O. 17,415-6   |   9.0    | 17.6  | +68 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  13 | [ź] Cassiopeię   |   3.4    |  0.7  | +57 |   0.25   |  0.82
+     |                  |          |       |     |          |
+  14 | Altair           |   1.0    | 19.8  | + 9 |   0.21   |  0.97
+     |                  |          |       |     |          |
+  15 | [e] Indi         |   5.2    | 21.9  | -57 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  16 | Gr. 1,618        |   6.7    | 10.1  | +50 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  17 | 10 Ursę Majoris  |   4.2    |  8.9  | +42 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  18 | Castor           |   1.5    |  7.5  | +32 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  19 | Ll. 21,258       |   8.5    | 11.0  | +44 |   0.20   |  1.03
+     |                  |          |       |     |          |
+  20 | [o]^{2} Eridani  |   4.5    |  4.2  | - 8 |   0.19   |  1.08
+     |                  |          |       |     |          |
+  21 | A. O. 11,677     |   9.0    | 11.2  | +66 |   0.19   |  1.08
+     |                  |          |       |     |          |
+  22 | Ll. 18,115       |   8.0    |  9.1  | +53 |   0.18   |  1.14
+     |                  |          |       |     |          |
+  23 | B. D. 36°, 3,883 |   7.1    | 20.0  | +36 |   0.18   |  1.14
+     |                  |          |       |     |          |
+  24 | Gr. 1,618        |   6.5    | 10.1  | +50 |   0.17   |  1.21
+     |                  |          |       |     |          |
+  25 | [b] Cassiopeię   |   2.3    |  0.1  | +59 |   0.16   |  1.28
+     |                  |          |       |     |          |
+  26 | 70 Ophiuchi      |   4.4    | 18.0  | + 2 |   0.16   |  1.28
+     |                  |          |       |     |          |
+  27 | [S] 1,516        |   6.5    | 11.2  | +74 |   0.15   |  1.38
+     |                  |          |       |     |          |
+  28 | Gr. 1,830        |   6.6    | 11.8  | +39 |   0.15   |  1.38
+     |                  |          |       |     |          |
+  29 | [m] Cassiopeię   |   5.4    |  1.0  | +54 |   0.14   |  1.47
+     |                  |          |       |     |          |
+  30 | [e] Eridani      |   4.4    |  3.5  | -10 |   0.14   |  1.47
+     |                  |          |       |     |          |
+  31 | [i] Ursę Majoris |   3.2    |  8.9  | +48 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  32 | [b] Hydri        |   2.9    |  0.3  | -78 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  33 | Fomalhaut        |   1.0    | 22.9  | -30 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  34 | Br. 3,077        |   6.0    | 23.1  | +57 |   0.13   |  1.58
+     |                  |          |       |     |          |
+  35 | [e] Cygni        |   2.5    | 20.8  | +33 |   0.12   |  1.71
+     |                  |          |       |     |          |
+  36 | [b] Comę         |   4.5    | 13.1  | +28 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  37 | [ps]^{5} Aurigę  |   8.8    |  6.6  | +44 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  38 | [p] Herculis     |   3.3    | 17.2  | +37 |   0.11   |  1.87
+     |                  |          |       |     |          |
+  39 | Aldebaran        |   1.1    |  4.5  | +16 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  40 | Capella          |   0.1    |  5.1  | +46 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  41 | B. D. 35°, 4,003 |   9.2    | 20.1  | +35 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  42 | Gr. 1,646        |   6.3    | 10.3  | +49 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  43 | [g] Cygni        |   2.3    | 20.3  | +40 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  44 | Regulus          |   1.2    | 10.0  | +12 |   0.10   |  2.06
+     |                  |          |       |     |          |
+  45 | Vega             |   0.2    | 18.6  | +39 |   0.10   |  2.06
+  ---+------------------+----------+-------+-----+----------+---------
+
+in which the numbers in the first column are those placed adjacent to
+the stars in the diagram to identify them.
+
+[Illustration: FIG. 122.--Stellar neighbors of the sun.]
+
+190. LIGHT YEARS.--The radius of the inner circle in Fig. 122, 1,000,000
+times the earth's distance from the sun, is a convenient unit in which
+to express the stellar distances, and in the preceding table the
+distances of the stars from the sun are expressed in terms of this
+unit. To express them in miles the numbers in the table must be
+multiplied by 93,000,000,000,000. The nearest star, [a] Centauri, is
+25,000,000,000,000 miles away. But there is another unit in more common
+use--i. e., the distance traveled over by light in the period of one
+year. We have already found (§ 141) that it requires light 8m. 18s. to
+come from the sun to the earth, and it is a simple matter to find from
+this datum that in a year light moves over a space equal to 63,368 radii
+of the earth's orbit. This distance is called a _light year_, and the
+distance of the same star, [a] Centauri, expressed in terms of this
+unit, is 4.26 years--i. e., it takes light that long to come from the
+star to the earth.
+
+In Fig. 122 the stellar magnitudes of the stars are indicated by the
+size of the dots--the bigger the dot the brighter the star--and a mere
+inspection of the figure will serve to show that within a radius of 30
+light years from the sun bright stars and faint ones are mixed up
+together, and that, so far as distance is concerned, the sun is only a
+member of this swarm of stars, whose distances apart, each from its
+nearest neighbor, are of the same order of magnitude as those which
+separate the sun from the three or four stars nearest it.
+
+Fig. 122 is not to be supposed complete. Doubtless other stars will be
+found whose distance from the sun is less than 2,000,000 radii of the
+earth's orbit, but it is not probable that they will ever suffice to
+more than double or perhaps treble the number here shown. The vast
+majority of the stars lie far beyond the limits of the figure.
+
+191. PROPER MOTIONS.--It is evident that these stars are too far apart
+for their mutual attractions to have much influence one upon another,
+and that we have here a case in which, according to § 34, each star is
+free to keep unchanged its state of rest or motion with unvarying
+velocity along a straight line. Their very name, _fixed stars_, implies
+that they are at rest, and so astronomers long believed. Hipparchus (125
+B. C.) and Ptolemy (130 A. D.) observed and recorded many allineations
+among the stars, in order to give to future generations a means of
+settling this very question of a possible motion of the stars and a
+resulting change in their relative positions upon the sky. For example,
+they found at the beginning of the Christian era that the four stars,
+Capella, [e] Persei, [a] and [b] Arietis, stood in a straight
+line--i. e., upon a great circle of the sky. Verify this by direct
+reference to the sky, and see how nearly these stars have kept the same
+position for nearly twenty centuries. Three of them may be identified
+from the star maps, and the fourth, [e] Persei, is a third-magnitude
+star between Capella and the other two.
+
+Other allineations given by Ptolemy are: Spica, Arcturus and [b] Bootis;
+Spica, [d] Corvi and [g] Corvi; [a] Librę, Arcturus and [z] Ursę
+Majoris. Arcturus does not now fit very well to these alignments, and
+nearly two centuries ago it, together with Aldebaran and Sirius, was on
+other grounds suspected to have changed its place in the sky since the
+days of Ptolemy. This discovery, long since fully confirmed, gave a
+great impetus to observing with all possible accuracy the right
+ascensions and declinations of the stars, with a view to finding other
+cases of what was called _proper motion_--i. e., a motion peculiar to
+the individual star as contrasted with the change of right ascension and
+declination produced for all stars by the precession.
+
+Since the middle of the eighteenth century there have been made many
+thousands of observations of this kind, whose results have gone into
+star charts and star catalogues, and which are now being supplemented by
+a photographic survey of the sky that is intended to record permanently
+upon photographic plates the position and magnitude of every star in the
+heavens down to the fourteenth magnitude, with a view to ultimately
+determining all their proper motions.
+
+The complete achievement of this result is, of course, a thing of the
+remote future, but sufficient progress in determining these motions has
+been made during the past century and a half to show that nearly every
+lucid star possesses some proper motion, although in most cases it is
+very small, there being less than 100 known stars in which it amounts
+to so much as 1" per annum--i. e., a rate of motion across the sky which
+would require nearly the whole Christian era to alter a star's direction
+from us by so much as the moon's angular diameter. The most rapid known
+proper motion is that of a telescopic star midway between the equator
+and the south pole, which changes its position at the rate of nearly 9"
+per annum, and the next greatest is that of another telescopic star, in
+the northern sky, No. 28 of Fig. 122. It is not until we reach the tenth
+place in a list of large proper motions that we find a bright lucid
+star, No. 1 of Fig. 122. It is a significant fact that for the most part
+the stars with large proper motions are precisely the ones shown in Fig.
+122, which is designed to show stars near the earth. This connection
+between nearness and rapidity of proper motions is indeed what we should
+expect to find, since a given amount of real motion of the star along
+its orbit will produce a larger angular displacement, proper motion, the
+nearer the star is to the earth, and this fact has guided astronomers in
+selecting the stars to be observed for parallax, the proper motion being
+determined first and the parallax afterward.
+
+192. THE PATHS OF THE STARS.--We have already seen reason for thinking
+that the orbit along which a star moves is practically a straight line,
+and from a study of proper motions, particularly their directions across
+the sky, it appears that these orbits point in all possible ways--north,
+south, east, and west--so that some of them are doubtless directed
+nearly toward or from the sun; others are square to the line joining sun
+and star; while the vast majority occupy some position intermediate
+between these two. Now, our relation to these real motions of the stars
+is well illustrated in Fig. 112, where the observer finds in some of the
+shooting stars a tremendous proper motion across the sky, but sees
+nothing of their rapid approach to him, while others appear to stand
+motionless, although, in fact, they are moving quite as rapidly as are
+their fellows. The fixed star resembles the shooting star in this
+respect, that its proper motion is only that part of its real motion
+which lies at right angles to the line of sight, and this needs to be
+supplemented by that other part of the motion which lies parallel to the
+line of sight, in order to give us any knowledge of the star's real
+orbit.
+
+[Illustration: FIG. 123.--Motion of Polaris in the line of sight as
+determined by the spectroscope. FROST.]
+
+193. MOTION IN THE LINE OF SIGHT.--It is only within the last 25 years
+that anything whatever has been accomplished in determining these
+stellar motions of approach or recession, but within that time much
+progress has been made by applying the Doppler principle (§ 89) to the
+study of stellar spectra, and at the present time nearly every great
+telescope in the world is engaged upon work of this kind. The shifting
+of the lines of the spectrum toward the violet or toward the red end of
+the spectrum indicates with certainty the approach or recession of the
+star, but this shifting, which must be determined by comparing the
+star's spectrum with that of some artificial light showing corresponding
+lines, is so small in amount that its accurate measurement is a matter
+of extreme difficulty, as may be seen from Fig. 123. This cut shows
+along its central line a part of the spectrum of Polaris, between wave
+lengths 4,450 and 4,600 tenth meters, while above and below are the
+corresponding parts of the spectrum of an electric spark whose light
+passed through the same spectroscope and was photographed upon the same
+plate with that of Polaris. This comparison spectrum is, as it should
+be, a discontinuous or bright-line one, while the spectrum of the star
+is a continuous one, broken only by dark gaps or lines, many of which
+have no corresponding lines in the comparison spectrum. But a certain
+number of lines in the two spectra do correspond, save that the dark
+line is always pushed a very little toward the direction of shorter wave
+lengths, showing that this star is approaching the earth. This spectrum
+was photographed for the express purpose of determining the star's
+motion in the line of sight, and with it there should be compared Figs.
+124 and 125, which show in the upper part of each a photograph obtained
+without comparison spectra by allowing the star's light to pass through
+some prisms placed just in front of the telescope. The lower section of
+each figure shows an enlargement of the original photograph, bringing
+out its details in a way not visible to the unaided eye. In the enlarged
+spectrum of [b] Aurigę a rate of motion equal to that of the earth in
+its orbit would be represented by a shifting of 0.03 of a millimeter in
+the position of the broad, hazy lines.
+
+[Illustration: FIG. 124.--Spectrum of [b] Aurigę.--PICKERING.]
+
+Despite the difficulty of dealing with such small quantities as the
+above, very satisfactory results are now obtained, and from them it is
+known that the velocities of stars in the line of sight are of the same
+order of magnitude as the velocities of the planets in their orbits,
+ranging all the way from 0 to 60 miles per second--more than 200,000
+miles per hour--which latter velocity, according to Campbell, is the
+rate at which [m] Cassiopeię is approaching the sun.
+
+The student should not fail to note one important difference between
+proper motions and the motions determined spectroscopically: the latter
+are given directly in miles per second, or per hour, while the former
+are expressed in angular measure, seconds of arc, and there can be no
+direct comparison between the two until by means of the known distances
+of the stars their proper motions are converted from angular into linear
+measure. We are brought thus to the very heart of the matter; parallax,
+proper motion, and motion in the line of sight are intimately related
+quantities, all of which are essential to a knowledge of the real
+motions of the stars.
+
+[Illustration: FIG. 125.--Spectrum of Pollux.--PICKERING.]
+
+194. STAR DRIFT.--An illustration of how they may be made to work
+together is furnished by some of the stars--which make up the Great
+Dipper--[b], [g], [e], and [z] Ursę Majoris, whose proper motions have
+long been known to point in nearly the same direction across the sky and
+to be nearly equal in amount. More recently it has been found that these
+stars are all moving toward the sun with approximately the same
+velocity--18 miles per second. One other star of the Dipper, [d] Ursę
+Majoris, shares in the common proper motion, but its velocity in the
+line of sight has not yet been determined with the spectroscope. These
+similar motions make it probable that the stars are really traveling
+together through space along parallel lines; and on the supposition
+that such is the case it is quite possible to write out a set of
+equations which shall involve their known proper motions and motions in
+the line of sight, together with their unknown distances and the unknown
+direction and velocity of their real motion along their orbits. Solving
+these equations for the values of the unknown quantities, it is found
+that the five stars probably lie in a plane which is turned nearly
+edgewise toward us, and that in this plane they are moving about twice
+as fast as the earth moves around the sun, and are at a distance from us
+represented by a parallax of less than 0.02"--i. e., six times as great
+as the outermost circle in Fig. 122. A most extraordinary system of
+stars which, although separated from each other by distances as great as
+the whole breadth of Fig. 122, yet move along in parallel paths which it
+is difficult to regard as the result of chance, and for which it is
+equally difficult to frame an explanation.
+
+[Illustration: FIG. 126.--The Great Dipper, past, present, and future.]
+
+The stars [a] and [ź] of the Great Dipper do not share in this motion,
+and must ultimately part company with the other five, to the complete
+destruction of the Dipper's shape. Fig. 126 illustrates this change of
+shape, the upper part of the figure (_a_) showing these seven stars as
+they were grouped at a remote epoch in the past, while the lower
+section (_c_) shows their position for an equally remote epoch in
+the future. There is no resemblance to a dipper in either of these
+configurations, but it should be observed that in each of them the stars
+[a] and [ź] keep their relative position unaltered, and the other five
+stars also keep together, the entire change of appearance being due to
+the changing positions of these two groups with respect to each other.
+
+This phenomenon of groups of stars moving together is called _star
+drift_, and quite a number of cases of it are found in different parts
+of the sky. The Pleiades are perhaps the most conspicuous one, for here
+some sixty or more stars are found traveling together along similar
+paths. Repeated careful measurements of the relative positions of stars
+in this cluster show that one of the lucid stars and four or five of the
+telescopic ones do not share in this motion, and therefore are not to be
+considered as members of the group, but rather as isolated stars which,
+for a time, chance to be nearly on line with the Pleiades, and probably
+farther off, since their proper motions are smaller.
+
+To rightly appreciate the extreme slowness with which proper motions
+alter the constellations, the student should bear in mind that the
+changes shown in passing from one section of Fig. 126 to the next
+represent the effect of the present proper motions of the stars
+accumulated for a period of 200,000 years. Will the stars continue to
+move in straight paths for so long a time?
+
+195. THE SUN'S WAY.--Another and even more interesting application of
+proper motions and motions in the line of sight is the determination
+from them of the sun's orbit among the stars. The principle involved is
+simple enough. If the sun moves with respect to the stars and carries
+the earth and the other planets year after year into new regions of
+space, our changing point of view must displace in some measure every
+star in the sky save those which happen to be exactly on the line of the
+sun's motion, and even these will show its effect by their apparent
+motion of approach or recession along the line of sight. So far as their
+own orbital motions are concerned, there is no reason to suppose that
+more stars move north than south, or that more go east than west; and
+when we find in their proper motions a distinct tendency to radiate from
+a point somewhere near the bright star Vega and to converge toward a
+point on the opposite side of the sky, we infer that this does not come
+from any general drift of the stars in that direction, but that it marks
+the course of the sun among them. That it is moving along a straight
+line pointing toward Vega, and that at least a part of the velocities
+which the spectroscope shows in the line of sight, comes from the motion
+of the sun and earth. Working along these lines, Kapteyn finds that the
+sun is moving through space with a velocity of 11 miles per second,
+which is decidedly below the average rate of stellar motion--19 miles
+per second.
+
+196. DISTANCE OF SIRIAN AND SOLAR STARS.--By combining this rate of
+motion of the sun with the average proper motions of the stars of
+different magnitudes, it is possible to obtain some idea of the average
+distance from us of a first-magnitude star or a sixth-magnitude star,
+which, while it gives no information about the actual distance of any
+particular star, does show that on the whole the fainter stars are more
+remote. But here a broad distinction must be drawn. By far the larger
+part of the stars belong to one of two well-marked classes, called
+respectively Sirian and solar stars, which are readily distinguished
+from each other by the kind of spectrum they furnish. Thus [b] Aurigę
+belongs to the Sirian class, as does every other star which has a
+spectrum like that of Fig. 124, while Pollux is a solar star presenting
+in Fig. 125 a spectrum like that of the sun, as do the other stars of
+this class.
+
+Two thirds of the sun's near neighbors, shown in Fig. 122, have spectra
+of the solar type, and in general stars of this class are nearer to us
+than are the stars with spectra unlike that of the sun. The average
+distance of a solar star of the first magnitude is very approximately
+represented by the outer circle in Fig. 122, 2,000,000 times the
+distance of the sun from the earth; while the corresponding distance for
+a Sirian star of the first magnitude is represented by the number
+4,600,000.
+
+A third-magnitude star is on the average twice as far away as one of the
+first magnitude, a fifth-magnitude star four times as far off, etc.,
+each additional two magnitudes doubling the average distance of the
+stars, at least down to the eighth magnitude and possibly farther,
+although beyond this limit we have no certain knowledge. Put in another
+way, the naked eye sees many Sirian stars which _may_ have "gone out"
+and ceased to shine centuries ago, for the light by which we now see
+them left those stars before the discovery of America by Columbus. For
+the student of mathematical tastes we note that the results of Kapteyn's
+investigation of the mean distances (_D_) of the stars of magnitude
+(_m_) may be put into two equations:
+
+    For Solar Stars, D = 23 × 2^{m/2}
+
+    For Sirian Stars, D = 52 × 2^{m/2}
+
+where the coefficients 23 and 52 are expressed in light years. How long
+a time is required for light to come from an average solar star of the
+sixth magnitude?
+
+197. CONSEQUENCES OF STELLAR DISTANCE.--The amount of light which comes
+to us from any luminous body varies inversely as the square of its
+distance, and since many of the stars are changing their distance from
+us quite rapidly, it must be that with the lapse of time they will grow
+brighter or fainter by reason of this altered distance. But the
+distances themselves are so great that the most rapid known motion in
+the line of sight would require more than 1,000 years (probably several
+thousand) to produce any perceptible change in brilliancy.
+
+The law in accordance with which this change of brilliancy takes place
+is that the distance must be increased or diminished tenfold in order to
+produce a change of five magnitudes in the brightness of the object, and
+we may apply this law to determine the sun's rank among the stars. If it
+were removed to the distance of an average first-, or second-, or
+third-magnitude star, how would its light compare with that of the
+stars? The average distance of a third-magnitude star of the solar type
+is, as we have seen above, 4,000,000 times the sun's distance from the
+earth, and since 4,000,000 = 10^{6.6}, we find that at this distance the
+sun's stellar magnitude would be altered by 6.6 × 5 magnitudes, and
+would therefore be -26.5 + 33.0 = 6.5--i. e., the sun if removed to the
+average distance of the third-magnitude stars of its type would be
+reduced to the very limit of naked-eye visibility. It must therefore be
+relatively small and feeble as compared with the brightness of the
+average star. It is only its close proximity to us that makes the sun
+look brighter than the stars.
+
+The fixed stars may have planets circling around them, but an
+application of the same principles will show how hopeless is the
+prospect of ever seeing them in a telescope. If the sun's nearest
+neighbor, [a] Centauri, were attended by a planet like Jupiter, this
+planet would furnish to us no more light than does a star of the
+twenty-second magnitude--i. e., it would be absolutely invisible, and
+would remain invisible in the most powerful telescope yet built, even
+though its bulk were increased to equal that of the sun. Let the student
+make the computation leading to this result, assuming the stellar
+magnitude of Jupiter to be -1.7.
+
+198. DOUBLE STARS.--In the constellation Taurus, not far from Aldebaran,
+is the fourth-magnitude star [th] Tauri, which can readily be seen to
+consist of two stars close together. The star [a] Capricorni is plainly
+double, and a sharp eye can detect that one of the faint stars which
+with Vega make a small equilateral triangle, is also a double star.
+Look for them in the sky.
+
+In the strict language of astronomy the term double star would not be
+applied to the first two of these objects, since it is usually
+restricted to those stars whose angular distance from each other is so
+small that in the telescope they appear much as do the stars named above
+to the naked eye--i. e., their angular separation is measured by a few
+seconds or fractions of a single second, instead of the six minutes
+which separate the component stars of [th] Tauri or [a] Capricorni.
+There are found in the sky many thousands of these close double stars,
+of which some are only optically double--i. e., two stars nearly on line
+with the earth but at very different distances from it--while more of
+them are really what they seem, stars near each other, and in many cases
+near enough to influence each other's motion. These are called _binary_
+systems, and in cases of this kind the principles of celestial mechanics
+set forth in Chapter IV hold true, and we may expect to find each
+component of a double star moving in a conic section of some kind,
+having its focus at the common center of gravity of the two stars.
+We are thus presented with problems of orbital motion quite similar
+to those which occur in the solar system, and careful telescopic
+observations are required year after year to fix the relative positions
+of the two stars--i. e., their angular separation, which it is customary
+to call their _distance_, and their direction one from the other, which
+is called _position angle_.
+
+199. ORBITS OF DOUBLE STARS.--The sun's nearest neighbor, [a] Centauri,
+is such a double star, whose position angle and distance have been
+measured by successive generations of astronomers for more than a
+century, and Fig. 127 shows the result of plotting their observations.
+Each black dot that lies on or near the circumference of the long
+ellipse stands for an observed direction and distance of the fainter of
+the two stars from the brighter one, which is represented by the small
+circle at the intersection of the lines inside the ellipse. It appears
+from the figure that during this time the one star has gone completely
+around the other, as a planet goes around the sun, and the true orbit
+must therefore be an ellipse having one of its foci at the center
+of gravity of the two stars. The other star moves in an ellipse of
+precisely similar shape, but probably smaller size, since the dimensions
+of the two orbits are inversely proportional to the masses of the two
+bodies, but it is customary to neglect this motion of the larger star
+and to give to the smaller one an orbit whose diameter is equal to the
+sum of the diameters of the two real orbits. This practice, which has
+been followed in Fig. 127, gives correctly the relative positions of the
+two stars, and makes one orbit do the work of two.
+
+[Illustration: FIG. 127.--The orbit of [a] Centauri.--SEE.]
+
+In Fig. 127 the bright star does not fall anywhere near the focus of the
+ellipse marked out by the smaller one, and from this we infer that the
+figure does not show the true shape of the orbit, which is certainly
+distorted, foreshortened, by the fact that we look obliquely down upon
+its plane. It is possible, however, by mathematical analysis, to find
+just how much and in what direction that plane should be turned in order
+to bring the focus of the ellipse up to the position of the principal
+star, and thus give the true shape and size of the orbit. See Fig. 128
+for a case in which the true orbit is turned exactly edgewise toward the
+earth, and the small star, which really moves in an ellipse like that
+shown in the figure, appears to oscillate to and fro along a straight
+line drawn through the principal star, as shown at the left of the
+figure.
+
+In the case of [a] Centauri the true orbit proves to have a major
+axis 47 times, and a minor axis 40 times, as great as the distance of
+the earth from the sun. The orbit, in fact, is intermediate in size
+between the orbits of Uranus and Neptune, and the periodic time of the
+star in this orbit is 81 years, a little less than the period of Uranus.
+
+[Illustration: FIG. 128.--Apparent orbit and real orbit of the double
+star 42 Comę Berenicis.--SEE.]
+
+200. MASSES OF DOUBLE STARS.--If we apply to this orbit Kepler's Third
+Law in the form given it at page 179, we shall find--
+
+    a^3 / T^2 = (23.5)^3 / (81)^2 = k (M + m),
+
+where _M_ and _m_ represent the masses of the two stars. We have already
+seen that _k_, the gravitation constant, is equal to 1 when the masses
+are measured in terms of the sun's mass taken as unity, and when _T_ and
+_a_ are expressed in years and radii of the earth's orbit respectively,
+and with this value of _k_ we may readily find from the above equation,
+_M_ + _m_ = 2.5--i. e., the combined mass of the two components of
+[a] Centauri is equal to rather more than twice the mass of the
+sun. It is not every double star to which this process of weighing can
+be applied. The major axis of the orbit, _a_, is found from the
+observations in angular measure, 35" in this case, and it is only when
+the parallax of the star is known that this can be converted into the
+required linear units, radii of the earth's orbit, by dividing the
+angular major axis by the parallax; 47 = 35" ÷ 0.75".
+
+Our list of distances (§ 189) contains four double stars whose periodic
+times and major axes have been fairly well determined, and we find in
+the accompanying table the information which they give about the masses
+of double stars and the size of the orbits in which they move:
+
+  ---------------------+-------+-------+----------+-------
+  STAR.                | Major | Minor | Periodic | Mass.
+                       | axis. | axis. | time.    |
+  ---------------------+-------+-------+----------+-------
+  [a] Centauri         |  47   |  40   |   81 y.  |   2
+  70 Ophiuchi          |  56   |  48   |   88     |   3
+  Procyon              |  34   |  31   |   40     |   3
+  Sirius               |  43   |  34   |   52     |   4
+  ---------------------+-------+-------+----------+-------
+
+The orbit of Uranus, diameter = 38, and Neptune, diameter = 60, are of
+much the same size as these double-star orbits; but the planetary orbits
+are nearly circular, while in every case the double stars show a
+substantial difference between the long and short diameters of their
+orbits. This is a characteristic feature of most double-star orbits, and
+seems to stand in some relation to their periodic times, for, on the
+average, the longer the time required by a star to make its orbital
+revolution the more eccentric is its orbit likely to prove.
+
+Another element of the orbits of double stars, which stands in even
+closer relation to the periodic time, is the major axis; the smaller the
+long diameter of the orbit the more rapid is the motion and the shorter
+the periodic time, so that astronomers in search of interesting
+double-star orbits devote themselves by preference to those stars whose
+distance apart is so small that they can barely be distinguished one
+from the other in the telescope.
+
+Although the half-dozen stars contained in the table all have orbits of
+much the same size and with much the same periodic time as those in
+which Uranus and Neptune move, this is by no means true of all the
+double stars, many of which have periods running up into the hundreds if
+not thousands of years, while a few complete their orbital revolutions
+in periods comparable with, or even shorter than, that of Jupiter.
+
+201. DARK STARS.--Procyon, the next to the last star of the preceding
+table, calls for some special mention, as the determination of its mass
+and orbit stands upon a rather different basis from that of the other
+stars. More than half a century ago it was discovered that its proper
+motion was not straight and uniform after the fashion of ordinary stars,
+but presented a series of loops like those marked out by a bright point
+on the rim of a swiftly running bicycle wheel. The hub may move straight
+forward with uniform velocity, but the point near the tire goes up and
+down, and, while sharing in the forward motion of the hub, runs
+sometimes ahead of it, sometimes behind, and such seemed to be the
+motion of Procyon and of Sirius as well. Bessel, who discovered it, did
+not hesitate to apply the laws of motion, and to affirm that this
+visible change of the star's motion pointed to the presence of an unseen
+companion, which produced upon the motions of Sirius and Procyon just
+such effects as the visible companions produce in the motions of double
+stars. A new kind of star, dark instead of bright, was added to the
+astronomer's domain, and its discoverer boldly suggested the possible
+existence of many more. "That countless stars are visible is clearly no
+argument against the existence of as many more invisible ones." "There
+is no reason to think radiance a necessary property of celestial
+bodies." But most astronomers were incredulous, and it was not until
+1862 that, in the testing of a new and powerful telescope just built, a
+dark star was brought to light and the companion of Sirius actually
+seen. The visual discovery of the dark companion of Procyon is of still
+more recent date (November, 1896), when it was detected with the great
+telescope of the Lick Observatory. This discovery is so recent that the
+orbit is still very uncertain, being based almost wholly upon the
+variations in the proper motion of the star, and while the periodic time
+must be very nearly correct, the mass of the stars and dimensions of the
+orbit may require considerable correction.
+
+The companion of Sirius is about ten magnitudes and that of Procyon
+about twelve magnitudes fainter than the star itself. How much more
+light does the bright star give than its faint companion? Despite the
+tremendous difference of brightness represented by the answer to this
+question, the mass of Sirius is only about twice as great as that of its
+companion, and for Procyon the ratio does not exceed five or six.
+
+The visual discovery of the companions to Sirius and Procyon removes
+them from the list of dark stars, but others still remain unseen,
+although their existence is indicated by variable proper motions or by
+variable orbital motion, as in the case of [z] Cancri, where one
+of the components of a triple star moves around the other two in a
+series of loops whose presence indicates a disturbing body which has
+never yet been seen.
+
+202. MULTIPLE STARS.--Combinations of three, four, or more stars close
+to each other, like [z] Cancri, are called multiple stars, and
+while they are far from being as common as are double stars, there is a
+considerable number of them in the sky, 100 or more as against the more
+than 10,000 double stars that are known. That their relative motions are
+subject to the law of gravitation admits of no serious doubt, but
+mathematical analysis breaks down in face of the difficulties here
+presented, and no astronomer has ever been able to determine what will
+be the general character of the motions in such a system.
+
+[Illustration: FIG. 129.--Illustrating the motion of a spectroscopic
+binary.]
+
+203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of
+the Harvard Observatory, announced the discovery of a new class of
+double stars, invisible as such in even the most powerful telescope,
+and producing no perturbations such as have been considered above, but
+showing in their spectrum that two or more bodies must be present in the
+source of light which to the eye is indistinguishable from a single
+star. In Fig. 129 we suppose _A_ and _B_ to be the two components of a
+double star, each moving in its own orbit about their common center of
+gravity, _C_, whose distance from the earth is several million times
+greater than the distance between the stars themselves. Under such
+circumstances no telescope could distinguish between the two stars,
+which would appear fused into one; but the smaller the orbit the more
+rapid would be their motion in it, and if this orbit were turned
+edgewise toward the earth, as is supposed in the figure, whenever the
+stars were in the relative position there shown, _A_ would be rapidly
+approaching the earth by reason of its orbital motion, while _B_ would
+move away from it, so that in accordance with the Doppler principle the
+lines composing their respective spectra would be shifted in opposite
+directions, thus producing a doubling of the lines, each single line
+breaking up into two, like the double-sodium line _D_, only not spaced
+so far apart. When the stars have moved a quarter way round their orbit
+to the points _A“_, _B“_, their velocities are turned at right angles to
+the line of sight and the spectrum returns to the normal type with
+single lines, only to break up again when after another quarter
+revolution their velocities are again parallel with the line of sight.
+The interval of time between consecutive doublings of the lines in the
+spectrum thus furnishes half the time of a revolution in the orbit. The
+distance between the components of a double line shows by means of the
+Doppler principle how fast the stars are traveling, and this in
+connection with the periodic times fixes the size of the orbit, provided
+we assume that it is turned exactly edgewise to the earth. This
+assumption may not be quite true, but even though the orbit should
+deviate considerably from this position, it will still present the
+phenomenon of the double lines whose displacement will now show
+something less than the true velocities of the stars in their orbits,
+since the spectroscope measures only that component of the whole
+velocity which is directed toward the earth, and it is important to note
+that the real orbits and masses of these _spectroscopic binaries_, as
+they are called, will usually be somewhat larger than those indicated by
+the spectroscope, since it is only in exceptional cases that the orbit
+will be turned exactly edgewise to us.
+
+The bright star Capella is an excellent illustration of these
+spectroscopic binaries. At intervals of a little less than a month the
+lines of its spectrum are alternately single and double, their maximum
+separation corresponding to a velocity in the line of sight amounting to
+37 miles per second. Each component of a doubled line appears to be
+shifted an equal amount from the position occupied by the line when it
+is single, thus indicating equal velocities and equal masses for the two
+component stars whose periodic time in their orbit is 104 days. From
+this periodic time, together with the velocity of the star's motion, let
+the student show that the diameter of the orbit--i. e., the distance of
+the stars from each other--is approximately 53,000,000 miles, and that
+their combined mass is a little less than that of [a] Centauri, provided
+that their orbit plane is turned exactly edgewise toward the earth.
+
+There are at the present time (1901) 34 spectroscopic binaries known,
+including among them such stars as Polaris, Capella, Algol, Spica, [b]
+Aurigę, [z] Ursę Majoris, etc., and their number is rapidly increasing,
+about one star out of every seven whose motion in the line of sight is
+determined proving to be a binary or, as in the case of Polaris,
+possibly triple. On account of smaller distance apart their periodic
+times are much shorter than those of the ordinary double stars, and
+range from a few days up to several months--more than two years in the
+case of [ź] Pegasi, which has the longest known period of any star of
+this class.
+
+Spectroscopic binaries agree with ordinary double stars in having masses
+rather greater than that of the sun, but there is as yet no assured case
+of a mass ten times as great as that of the sun.
+
+204. VARIABLE STARS.--Attention has already been drawn (§ 23) to the
+fact that some stars shine with a changing brightness--e. g., Algol, the
+most famous of these _variable stars_, at its maximum of brightness
+furnishes three times as much light as when at its minimum, and other
+variable stars show an even greater range. The star [o] Ceti has
+been named Mira (Latin, _the wonderful_), from its extraordinary range
+of brightness, more than six-hundred-fold. For the greater part of the
+time this star is invisible to the naked eye, but during some three
+months in every year it brightens up sufficiently to be seen, rising
+quite rapidly to its maximum brilliancy, which is sometimes that of a
+second-magnitude star, but more frequently only third or even fourth
+magnitude, and, after shining for a few weeks with nearly maximum
+brilliancy, falling off to become invisible for a time and then return
+to its maximum brightness after an interval of eleven months from the
+preceding maximum. In 1901 it should reach its greatest brilliancy about
+midsummer, and a month earlier than this for each succeeding year. Find
+it by means of the star map, and by comparing its brightness from night
+to night with neighboring stars of about the same magnitude see how it
+changes with respect to them.
+
+The interval of time from maximum to maximum of brightness--331.6 days
+for Mira--is called the star's period, and within its period a star
+regularly variable runs through all its changes of brilliancy, much as
+the weather runs through its cycle of changes in the period of a year.
+But, as there are wet years and dry ones, hot years and cold, so also
+with variable stars, many of them show differences more or less
+pronounced between different periods, and one such difference has
+already been noted in the case of Mira; its maximum brilliancy is
+different in different years. So, too, the length of the period
+fluctuates in many cases, as does every other circumstance connected
+with it, and predictions of what such a variable star will do are
+notoriously unreliable.
+
+205. THE ALGOL VARIABLES.--On the other hand, some variable stars
+present an almost perfect regularity, repeating their changes time after
+time with a precision like that of clockwork. Algol is one type of these
+regular variables, having a period of 68.8154 hours, during six sevenths
+of which time it shines with unchanging luster as a star of the 2.3
+magnitude, but during the remaining 9 hours of each period it runs down
+to the 3.5 magnitude, and comes back again, as is shown by a curve in
+Fig. 130. The horizontal scale here represents hours, reckoned from the
+time of the star's minimum brightness, and the vertical scale shows
+stellar magnitudes. Such a diagram is called the star's light curve, and
+we may read from it that at any time between 5h. and 32h. after the time
+of minimum the star's magnitude is 2.32; at 2h. after a minimum the
+magnitude is 2.88, etc. What is the magnitude an hour and a half before
+the time of minimum? What is the magnitude 43 days after a minimum?
+
+[Illustration: FIG. 130.--The light curve of Algol.]
+
+The arrows shown in Fig. 130 are a feature not usually found with light
+curves, but in this case each one represents a spectroscopic
+determination of the motion of Algol in the line of sight. These
+observations extended over a period of more than two years, but they are
+plotted in the figure with reference to the number of hours each one
+preceded or followed a minimum of the star's light, and each arrow shows
+not only the direction of the star's motion along the line of sight, the
+arrows pointing down denoting approach of the star toward the earth, but
+also its velocity, each square of the ruling corresponding to 10
+kilometers (6.2 miles per second). The differences of velocity shown by
+adjacent arrows come mainly from errors of observation and furnish some
+idea of how consistent among themselves such observations are, but there
+can be no doubt that before minimum the star is moving away from the
+earth, and after minimum is approaching it. It is evident from these
+observations that in Algol we have to do with a spectroscopic binary,
+one of whose components is a dark star which, once in each revolution,
+partially eclipses the bright star and produces thus the variations in
+its light. By combining the spectroscopic observations with the
+variations in the star's light, Vogel finds that the bright star, Algol,
+itself has a diameter somewhat greater than that of the sun, but is of
+low density, so that its mass is less than half that of the sun, while
+the dark star is a very little smaller than the sun and has about a
+quarter of its mass. The distance between the two stars, dark and
+bright, is 3,200,000 miles. Fig. 129, which is drawn to scale, shows the
+relative positions and sizes of these stars as well as the orbits in
+which they move.
+
+The mere fact already noted that close binary systems exist in
+considerable numbers is sufficient to make it probable that a certain
+proportion of these stars would have their orbit planes turned so nearly
+edgewise toward the earth as to produce eclipses, and corresponding to
+this probability there are already known no less than 15 stars of the
+Algol type of eclipse variables, and only a beginning has been made in
+the search for them.
+
+[Illustration: FIG. 131.--The light curve of [b] Lyrę.]
+
+206. VARIABLES OF THE [b] LYRĘ TYPE.--In addition to these there is a
+certain further number of binary variables in which both components are
+bright and where the variation of brightness follows a very different
+course. Capella would be such a variable if its orbit plane were
+directed exactly toward the earth, and the fact that its light is not
+variable shows conclusively that such is not the position of the orbit.
+Fig. 131 represents the light curve of one of the best-known variable
+systems of this second type, that of [b] Lyrę, whose period is 12 days
+21.8 hours, and the student should read from the curve the magnitude of
+the star for different times during this interval. According to Myers,
+this light curve and the spectroscopic observations of the star point to
+the existence of a binary star of very remarkable character, such as is
+shown, together with its orbit and a scale of miles, in Fig. 132. Note
+the tide which each of these stars raises in the other, thus changing
+their shapes from spheres into ellipsoids. The astonishing dimensions of
+these stars are in part compensated by their very low density, which is
+less than that of air, so that their masses are respectively only 10
+times and 21 times that of the sun! But these dimensions and masses
+perhaps require confirmation, since they depend upon spectroscopic
+observations of doubtful interpretation. In Fig. 132 what relative
+positions must the stars occupy in their orbit in order that their
+combined light should give [b] Lyrę its maximum brightness? What
+position will furnish a minimum brightness?
+
+[Illustration: FIG. 132.--The system of [b] Lyrę.--MYERS.]
+
+207. VARIABLES OF LONG AND SHORT PERIODS.--It must not be supposed that
+all variable stars are binaries which eclipse each other. By far the
+larger part of them, like Mira, are not to be accounted for in this way,
+and a distinction which is pretty well marked in the length of their
+periods is significant in this connection. There is a considerable
+number of variable stars with periods shorter than a month, and there
+are many having periods longer than 6 months, but there are very few
+having periods longer than 18 months, or intermediate between 1 month
+and 6 months, so that it is quite customary to divide variable stars
+into two classes--those of long period, 6 months or more, and those of
+short period less than 6 months, and that this distinction corresponds
+to some real difference in the stars themselves is further marked by the
+fact that the long-period variables are prevailingly red in color, while
+the short-period stars are almost without exception white or very pale
+yellow. In fact, the longer the period the redder the star, although it
+is not to be inferred that all red stars are variable; a considerable
+percentage of them shine with constant light. The eclipse explanation of
+variability holds good only for short-period variables, and possibly not
+for all of them, while for the long-period variables there is no
+explanation which commands the general assent of astronomers, although
+unverified hypotheses are plenty.
+
+The number of stars known to be variable is about 400, while a
+considerable number of others are "suspected," and it would not be
+surprising if a large fraction of all the stars should be found to
+fluctuate a little in brightness. The sun's spots may suffice to make it
+a variable star with a period of 11 years.
+
+The discovery of new variables is of frequent occurrence, and may be
+expected to become more frequent when the sky is systematically explored
+for them by the ingenious device suggested by Pickering and illustrated
+in Fig. 133. A given region of the sky--e. g., the Northern Crown--is
+photographed repeatedly upon the same plate, which is shifted a little
+at each new exposure, so that the stars shall fall at new places upon
+it. The finally developed plate shows a row of images corresponding to
+each star, and if the star's light is constant the images in any given
+row will all be of the same size, as are most of those in Fig. 133; but
+a variable star such as is shown by the arrowhead reveals its presence
+by the broken aspect of its row of dots, a minimum brilliancy being
+shown by smaller and a maximum by larger ones. In this particular case,
+at two exposures the star was too faint to print its image upon the
+plate.
+
+[Illustration: FIG. 133.--Discovery of a variable star by means of
+photography.--PICKERING.]
+
+208. NEW STARS.--Next to the variable stars of very long or very
+irregular period stand the so-called _new_ or _temporary stars_, which
+appear for the most part suddenly, and after a brief time either vanish
+altogether or sink to comparative insignificance. These were formerly
+thought to be very remarkable and unusual occurrences--"the birth of a
+new world"--and it is noteworthy that no new star is recorded to have
+been seen from 1670 to 1848 A. D., for since that time there have been
+no less than five of them visible to the naked eye and others
+telescopic. In so far as these new stars are not ordinary variables
+(Mira, first seen in 1596, was long counted as a new star), they are
+commonly supposed due to chance encounters between stars or other cosmic
+bodies moving with considerable velocities along orbits which approach
+very close to each other. The actual collision of two dark bodies moving
+with high velocities is clearly sufficient to produce a luminous
+star--e. g., meteors--and even the close approach of two cooled-off
+stars, might result in tidal actions which would rend open their crusts
+and pour out the glowing matter from within so as to produce temporarily
+a very great accession of brightness.
+
+The most famous of all new stars is that which, according to Tycho
+Brahe's report, appeared in the year 1572, and was so bright when at its
+best as to be seen with the naked eye in broad daylight. It continued
+visible, though with fading light, for about 16 months, and finally
+disappeared to the naked eye, although there is some reason to suppose
+that it can be identified with a ruddy star of the eleventh magnitude in
+the constellation Cassiopeia, whose light still shows traces of
+variability.
+
+No modern temporary star approaches that of Tycho in splendor, but in
+some respects the recent ones surpass it in interest, since it has been
+possible to apply the spectroscope to the analysis of their light and to
+find thereby a much more complex set of conditions in the star than
+would have been suspected from its light changes alone.
+
+One of the most extraordinary of new stars, and the most brilliant one
+since that of Tycho, appeared suddenly in the constellation Perseus in
+February, 1901, and for a short time equaled Capella in brightness. But
+its light rapidly waned, with periodic fluctuations of brightness like
+those of a variable star, and at the present time (September, 1902) it
+is lost to the naked eye, although in the telescope it still shines like
+a star of the ninth or tenth magnitude.
+
+By the aid of powerful photographic apparatus, during the period of its
+waning brilliancy a ring of faint nebulous matter was detected
+surrounding the star and drifting around and away from it much as if a
+series of nebulę had been thrown off by the star at the time of its
+sudden outburst of light. But the extraordinary velocity of this nebular
+motion, nearly a billion miles per hour, makes such an explanation
+almost incredible, and astronomers are more inclined to believe that the
+ring was merely a reflection of the star's own light from a cloud of
+meteoric matter, into which a rapidly moving dark star plunged and,
+after the fashion of terrestrial meteors, was raised to brilliant
+incandescence by the collision. If we assume this to be the true
+explanation of these extraordinary phenomena, it is possible to show
+from the known velocity with which light travels through space and from
+the rate at which the nebula spread, that the distance of Nova Persei,
+as the new star is called, corresponds to a parallax of about one
+one-hundredth of a second, a result that is, in substance, confirmed by
+direct telescopic measurements of its parallax.
+
+Another modern temporary star is Nova Aurigę, which appeared suddenly in
+December, 1891, waned, and in the following April vanished, only to
+reappear three months later for another season of renewed brightness.
+The spectra of both these modern Novę contain both dark and bright lines
+displaced toward opposite ends of the spectrum, and suggesting the
+Doppler effect that would be produced by two or more glowing bodies
+having rapid and opposite motions in the line of sight. But the most
+recent investigations cast discredit on this explanation and leave the
+spectra of temporary stars still a subject of debate among astronomers,
+with respect both to the motion they indicate and the intrinsic nature
+of the stars themselves. The varying aspect of the spectra suggested at
+one time the sun's chromosphere, at another time the conditions that are
+present in nebulę, etc.
+
+
+
+
+CHAPTER XIV
+
+STARS AND NEBULĘ
+
+
+209. STELLAR COLORS.--We have already seen that one star differs from
+another in respect of color as well as brightness, and the diligent
+student of the sky will not fail to observe for himself how the luster
+of Sirius and Rigel is more nearly a pure white than is that of any
+other stars in the heavens, while at the other end of the scale
+[a] Orionis and Aldebaran are strongly ruddy, and Antares presents an
+even deeper tone of red. Between these extremes the light of every star
+shows a mixture of the rainbow hues, in which a very pale yellow is the
+predominant color, shading off, as we have seen, to white at one end of
+the scale and red at the other. There are no green stars, or blue stars,
+or violet stars, save in one exceptional class of cases--viz., where the
+two components of a double star are of very different brightness, it is
+quite the usual thing for them to have different colors, and then,
+almost without exception, the color of the fainter star lies nearer to
+the violet end of the spectrum than does the color of the bright one,
+and sometimes shows a distinctly blue or green hue. A fine type of such
+double star is [b] Cygni, in which the components are respectively
+yellow and blue, and the yellow star furnishes eight times as much light
+as the blue one.
+
+The exception which double stars thus make to the general rule of
+stellar colors, yellow and red, but no color of shorter wave length, has
+never been satisfactorily explained, but the rule itself presents no
+difficulties. Each star is an incandescent body, giving off radiant
+energy of every wave length within the limits of the visible spectrum,
+and, indeed, far beyond these limits. If this radiant energy could come
+unhindered to our eyes every star would appear white, but they are all
+surrounded by atmospheres--analogous to the chromosphere and reversing
+layer of the sun--which absorb a portion of their radiant energy and,
+like the earth's atmosphere, take a heavier toll from the violet than
+from the red end of the spectrum. The greater the absorption in the
+star's atmosphere, therefore, the feebler and the ruddier will be its
+light, and corresponding to this the red stars are as a class fainter
+than the white ones.
+
+210. CHEMISTRY OF THE STARS.--The spectroscope is pre-eminently the
+instrument to deal with this absorption of light in the stellar
+atmospheres, just as it deals with that absorption in the sun's
+atmosphere to which are due the dark lines of the solar spectrum,
+although the faintness of starlight, compared with that of the sun,
+presents a serious obstacle to its use. Despite this difficulty most of
+the lucid stars and many of the telescopic ones have been studied with
+the spectroscope and found to be similar to the sun and the earth as
+respects the material of which they are made. Such familiar chemical
+elements as hydrogen and iron, carbon, sodium, and calcium are scattered
+broadcast throughout the visible universe, and while it would be
+unwarranted by the present state of knowledge to say that the stars
+contain nothing not found in the earth and the sun, it is evident that
+in a broad way their substance is like rather than unlike that composing
+the solar system, and is subject to the same physical and chemical laws
+which obtain here. Galileo and Newton extended to the heavens the
+terrestrial sciences of mathematics and mechanics, but it remained to
+the nineteenth century to show that the physics and chemistry of the sky
+are like the physics and chemistry of the earth.
+
+211. STELLAR SPECTRA.--When the spectra of great numbers of stars are
+compared one with another, it is found that they bear some relation to
+the colors of the stars, as, indeed, we should expect, since spectrum
+and color are both produced by the stellar atmospheres, and it is found
+useful to classify these spectra into three types, as follows:
+
+_Type I. Sirian stars._--Speaking generally, the stars which are white
+or very faintly tinged with yellow, furnish spectra like that of Sirius,
+from which they take their name, or that of [b] Aurigę (Fig. 124), which
+is a continuous spectrum, especially rich in energy of short wave
+length--i. e., violet and ultraviolet light, and is crossed by a
+relatively small number of heavy dark lines corresponding to the
+spectrum of hydrogen. Sometimes, however, these lines are much fainter
+than is here shown, and we find associated with them still other faint
+ones pointing to the presence of other metallic substances in the star's
+atmosphere. These metallic lines are not always present, and sometimes
+even the hydrogen lines themselves are lacking, but the spectrum is
+always rich in violet and ultraviolet light.
+
+Since with increasing temperature a body emits a continually increasing
+proportion of energy of short wave length (§ 118), the richness of these
+spectra in such energy points to a very high temperature in these stars,
+probably surpassing in some considerable measure that of the sun. Stars
+with this type of spectrum are more numerous than all others combined,
+but next to them in point of numbers stands--
+
+_Type II. Solar stars._--To this type of spectrum belong the yellow
+stars, which show spectra like that of the sun, or of Pollux (Fig. 125).
+These are not so rich in violet light as are those of Type I, but in
+complexity of spectrum and in the number of their absorption lines they
+far surpass the Sirian stars. They are supposed to be at a lower
+temperature than the Sirian stars, and a much larger number of chemical
+elements seems present and active in the reversing layer of their
+atmospheres. The strong resemblance which these spectra bear to that of
+the sun, together with the fact that most of the sun's stellar neighbors
+have spectra of this type, justify us in ranking both them and it as
+members of one class, called _solar stars_.
+
+_Type III. Red stars._--A small number of stars show spectra comparable
+with that of [a] Herculis (Fig. 134), in which the blue and the violet
+part of the spectrum is almost obliterated, and the remaining yellow and
+red parts show not only dark lines, but also numerous broad dark bands,
+sharp at one edge, and gradually fading out at the other. It is this
+_selective absorption_, extinguishing the blue and leaving the red end
+of the spectrum, which produces the ruddy color of these stars, while
+the bands in their spectra "are characteristic of chemical combinations,
+and their presence ... proves that at certain elevations in the
+atmospheres of these stars the temperature has sunk so low that chemical
+combinations can be formed and maintained" (Scheiner-Frost). One of the
+chemical compounds here indicated is a hydrocarbon similar to that found
+in comets. In the white and yellow stars the temperatures are so high
+that the same chemical elements, although present, can not unite one
+with another to form compound substances.
+
+[Illustration: FIG. 134.--The spectrum of [a] Herculis.--ESPIN.]
+
+Most of the variable stars are red and have spectra of the third type;
+but this does not hold true for the eclipse variables like Algol, all of
+which are white stars with spectra of the first type. The ordinary
+variable star is therefore one with a dense atmosphere of relatively low
+temperature and complex structure, which produces the prevailing red
+color of these stars by absorbing the major part of their radiant
+energy of short wave length while allowing the longer, red waves to
+escape. Although their exact nature is not understood, there can be
+little doubt that the fluctuation in the light of these stars is due to
+processes taking place within the star itself, but whether above or
+below its photosphere is still uncertain.
+
+212. CLASSES OF STARS.--There is no hard-and-fast dividing line between
+these types of stellar spectra, but the change from one to another is by
+insensible gradations, like the transition from youth to manhood and
+from manhood to old age, and along the line of transition are to be
+found numberless peculiarities and varieties of spectra not enumerated
+above--e. g., a few stars show not only dark absorption lines in their
+spectra but bright lines as well, which, like those in Fig. 48, point to
+the presence of incandescent vapors, even in the outer parts of their
+atmospheres. Among the lucid stars about 75 per cent have spectra of the
+first type, 23 per cent are of the second type, 1 per cent of the third
+type, and the remaining 1 per cent are peculiar or of doubtful
+classification. Among the telescopic stars it is probable that much the
+same distribution holds, but in the present state of knowledge it is not
+prudent to speak with entire confidence upon this point.
+
+That the great number of stars whose spectra have been studied should
+admit of a classification so simple as the above, is an impressive fact
+which, when supplemented by the further fact of a gradual transition
+from one type of spectrum to the next, leaves little room for doubt that
+in the stars we have an innumerable throng of individuals belonging to
+the same species but in different stages of development, and that the
+sun is only one of these individuals, of something less than medium size
+and in a stage of development which is not at all peculiar, since it is
+shared by nearly a fourth of all the stars.
+
+213. STAR CLUSTERS.--In previous chapters we have noted the Pleiades and
+Pręsepe as star clusters visible to the naked eye, and to them we may
+add the Hyades, near Aldebaran, and the little constellation Coma
+Berenices. But more impressive than any of these, although visible only
+in a telescope, is the splendid cluster in Hercules, whose appearance in
+a telescope of moderate size is shown in Fig. 135, while Fig. 136 is a
+photograph of the same cluster taken with a very large reflecting
+telescope. This is only a type of many telescopic clusters which are
+scattered over the sky, and which are made up of stars packed so closely
+together as to become indistinguishable, one from another, at the center
+of the cluster. Within an area which could be covered by a third of the
+full moon's face are crowded in this cluster more than five thousand
+stars which are unquestionably close neighbors, but whose apparent
+nearness to each other is doubtless due to their great distance from us.
+It is quite probable that even at the center of this cluster, where more
+than a thousand stars are included within a radius of 160", the actual
+distances separating adjoining stars are much greater than that
+separating earth and sun, but far less than that separating the sun from
+its nearest stellar neighbor.
+
+[Illustration: FIG 135.--Star cluster in Hercules.]
+
+An interesting discovery of recent date, made by Professor Bailey in
+photographing star clusters, is that some few of them, which are
+especially rich in stars, contain an extraordinary number of variable
+stars, mostly very faint and of short period. Two clusters, one in the
+northern and one in the southern hemisphere, contain each more than a
+hundred variables, and an even more extraordinary case is presented by
+a cluster, called Messier 5, not far from the star [a] Serpentis,
+which contains no less than sixty-three variables, all about of the
+fourteenth magnitude, all having light periods which differ but little
+from half a day, all having light curves of about the same shape, and
+all having a range of brightness from maximum to minimum of about one
+magnitude. An extraordinary set of coincidences which "points
+unmistakably to a common origin and cause of variability."
+
+[Illustration: FIG. 136.--Star cluster in Hercules.--KEELER.]
+
+[Illustration: FIG. 137.--The Andromeda nebula as seen in a very small
+telescope.]
+
+[Illustration: FIG. 138.--The Andromeda nebula and Holmes's comet.
+Photographed by BARNARD.]
+
+[Illustration: FIG. 139.--A drawing of the Andromeda nebula.]
+
+[Illustration: FIG. 140.--A photograph of the Andromeda
+nebula.--ROBERTS.]
+
+214. NEBULĘ.--Returning to Fig. 136, we note that its background has a
+hazy appearance, and that at its center the stars can no longer be
+distinguished, but blend one with another so as to appear like a bright
+cloud. The outer part of the cluster is _resolved_ into stars, while in
+the picture the inner portion is not so resolved, although in the
+original photographic plate the individual stars can be distinguished to
+the very center of the cluster. In many cases, however, this is not
+possible, and we have an _irresolvable cluster_ which it is customary to
+call a _nebula_ (Latin, _little cloud_).
+
+The most conspicuous example of this in the northern heavens is the
+great nebula in Andromeda (R. A. 0^{h} 37^{m}, Dec. + 41°), which may be
+seen with the naked eye as a faint patch of foggy light. Look for it.
+This appears in an opera glass or very small telescope not unlike Fig.
+137, which is reproduced from a sketch. Fig. 138 is from a photograph of
+the same object showing essentially the same shape as in the preceding
+figure, but bringing out more detail. Note the two small nebulę
+adjoining the large one, and at the bottom of the picture an object
+which might easily be taken for another nebula but which is in fact a
+tailless comet that chanced to be passing that part of the sky when the
+picture was taken. Fig. 139 is from another drawing of this nebula,
+although it is hardly to be recognized as a representation of the same
+thing; but its characteristic feature, the two dark streaks near the
+center of the picture, is justified in part by Fig. 140, which is from a
+photograph made with a large reflecting telescope.
+
+[Illustration: FIG. 141.--Types of nebulę.]
+
+A comparison of these several representations of the same thing will
+serve to illustrate the vagueness of its outlines, and how much the
+impressions to be derived from nebulę depend upon the telescopes
+employed and upon the observer's own prepossessions. The differences
+among the pictures can not be due to any change in the nebula itself,
+for half a century ago it was sketched much as shown in the latest of
+them (Fig. 140).
+
+[Illustration: FIG. 142.--The Trifid nebula.--KEELER.]
+
+215. TYPICAL NEBULĘ.--Some of the fantastic forms which nebulę present
+in the telescope are shown on a small scale in Fig. 141, but in recent
+years astronomers have learned to place little reliance upon drawings
+such as these, which are now almost entirely supplanted by photographs
+made with long exposures in powerful telescopes. One of the most
+exquisite of these modern photographs is that of the Trifid nebula in
+Sagittarius (Fig. 142). Note especially the dark lanes that give to this
+nebula its name, Trifid, and which run through its brightest parts,
+breaking it into seemingly independent sections. The area of the sky
+shown in this cut is about 15 per cent less than that covered by the
+full moon.
+
+[Illustration: FIG. 143.--A nebula in Cygnus.--KEELER.]
+
+Fig. 143 shows a very different type of nebula, found in the
+constellation Cygnus, which appears made up of filaments closely
+intertwined, and stretches across the sky for a distance considerably
+greater than the moon's diameter.
+
+[Illustration: FIG. 144.--Spiral nebula in Canes Venatici.--KEELER.]
+
+A much smaller but equally striking nebula is that in the constellation
+Canes Venatici (Fig. 144), which shows a most extraordinary spiral
+structure, as if the stars composing it were flowing in along curved
+lines toward a center of condensation. The diameter of the circular part
+of this nebula, omitting the projection toward the bottom of the
+picture, is about five minutes of arc, a sixth part of the diameter of
+the moon, and its thickness is probably very small compared with its
+breadth, perhaps not much exceeding the width of the spiral streams
+which compose it. Note how the bright stars that appear within the area
+of this nebula fall on the streams of nebulous matter as if they were
+part of them. This characteristic grouping of the stars, which is
+followed in many other nebulę, shows that they are really part and
+parcel of the nebula and not merely on line with it. Fig. 145 shows how
+a great nebula is associated with the star [r] Ophiuchi.
+
+[Illustration: FIG. 145.--Great nebula about the star [r]
+Ophiuchi.--BARNARD.]
+
+Probably the most impressive of all nebulę is the great one in Orion
+(Fig. 146), whose position is shown on the star map between Rigel and
+[z] Orionis. Look for it with an opera glass or even with the unaided
+eye. This is sometimes called an _amorphous_--i. e., shapeless--nebula,
+because it presents no definite form which the eye can grasp and little
+trace of structure or organization. It is "without form and void" at
+least in its central portions, although on its edges curved filaments
+may be traced streaming away from the brighter parts of the central
+region. This nebula, as shown in Fig. 146, covers an area about equal
+to that of the full moon, without counting as any part of this the
+companion nebula shown at one side, but photographs made with suitable
+exposures show that faint outlying parts of the nebula extend in curved
+lines over the larger part of the constellation Orion. Indeed, over a
+large part of the entire sky the background is faintly covered with
+nebulous light whose brighter portions, if each were counted as a
+separate nebula, would carry the total number of such objects well into
+the hundreds of thousands.
+
+[Illustration: FIG. 146.--The Orion nebula.]
+
+The Pleiades (Plate IV) present a case of a resolvable star cluster
+projected against such a nebulous background whose varying intensity
+should be noted in the figure. A part of this nebulous matter is shown
+in wisps extending from one star to the next, after the fashion of a
+bridge, and leaving little doubt that the nebula is actually a part of
+the cluster and not merely a background for it.
+
+[Illustration: THE PLEIADES (AFTER A PHOTOGRAPH)]
+
+Fig. 147 shows a series of so-called double nebulę perhaps comparable
+with double stars, although the most recent photographic work seems to
+indicate that they are really faint spiral nebulę in which only the
+brightest parts are shown by the telescope.
+
+According to Keeler, the spiral is the prevailing type of nebulę, and
+while Fig. 144 presents the most perfect example of such a nebula, the
+student should not fail to note that the Andromeda nebula (Fig. 140)
+shows distinct traces of a spiral structure, only here we do not see its
+true shape, the nebula being turned nearly edgewise toward us so that
+its presumably circular outline is foreshortened into a narrow ellipse.
+
+[Illustration: FIG. 147.--Double nebulę. HERSCHEL.]
+
+Another type of nebula of some consequence presents in the telescope
+round disks like those of Uranus or Neptune, and this appearance has
+given them the name _planetary nebulę_. The comet in Fig. 138, if
+smaller, would represent fairly well the nebulę of this type. Sometimes
+a planetary nebula has a star at its center, and sometimes it appears
+hollow, like a smoke ring, and is then called a ring nebula. The most
+famous of these is in the constellation Lyra, not far from Vega.
+
+216. SPECTRA OF NEBULĘ.--A star cluster, like the one in Hercules,
+shows, of course, stellar spectra, and even when irresolvable the
+spectrum is a continuous one, testifying to the presence of stars,
+although they stand too close together to be separately seen. But in a
+certain number of nebulę the spectrum is altogether different, a
+discontinuous one containing only a few bright lines, showing that here
+the nebular light comes from glowing gases which are subject to no
+considerable pressure. The planetary nebulę all have spectra of this
+kind and make up about half of all the known gaseous nebulę. It is
+worthy of note that a century ago Sir William Herschel had observed a
+green shimmer in the light of certain nebulę which led him to believe
+that they were "not of a starry nature," a conclusion which has been
+abundantly confirmed by the spectroscope. The green shimmer is, in fact,
+caused by a line in the green part of the spectrum that is always
+present and is always the brightest part of the spectrum of gaseous
+nebulę.
+
+In faint nebulę this line constitutes the whole of their visible
+spectrum, but in brighter ones two or three other and fainter lines are
+usually associated with it, and a very bright nebula, like that in
+Orion, may show a considerable number of extra lines, but for the most
+part they can not be identified in the spectrum of any terrestrial
+substances. An exception to this is found in the hydrogen lines, which
+are well marked in most spectra of gaseous nebulę, and there are
+indications of one or two other known substances.
+
+217. DENSITY OF NEBULĘ.--It is known from laboratory experiments that
+diminishing the pressure to which an incandescent gas is subject,
+diminishes the number of lines contained in its spectrum, and we may
+surmise from the very simple character and few lines of these nebular
+spectra that the gas which produces them has a very small density. But
+this is far from showing that the nebula itself is correspondingly
+attenuated, for we must not assume that this shining gas is all that
+exists in the nebula; so far as telescope or camera are concerned, there
+may be associated with it any amount of dark matter which can not be
+seen because it sends to us no light. It is easy to think in this
+connection of meteoric dust or the stuff of which comets are made, for
+these seem to be scattered broadcast on every side of the solar system
+and may, perchance, extend out to the region of the nebulę.
+
+But, whatever may be associated in the nebula with the glowing gas which
+we see, the total amount of matter, invisible as well as visible, must
+be very small, or rather its average density must be very small, for the
+space occupied by such a nebula as that of Orion is so great that if the
+average density of its matter were equal to that of air the resulting
+mass by its attraction would exert a sensible effect upon the motion of
+the sun through space. The brighter parts of this nebula as seen from
+the earth subtend an angle of about half a degree, and while we know
+nothing of its distance from us, it is easy to see that the farther it
+is away the greater must be its real dimensions, and that this increase
+of bulk and mass with increasing distance will just compensate the
+diminishing intensity of gravity at great distances, so that for a given
+angular diameter--e. g., half a degree--the force with which this nebula
+attracts the sun depends upon its density but not at all upon its
+distance. Now, the nebula must attract the sun in some degree, and must
+tend to move it and the planets in an orbit about the attracting center
+so that year after year we should see the nebula from slightly different
+points of view, and this changed point of view should produce a change
+in the apparent direction of the nebula from us--i. e., a proper motion,
+whose amount would depend upon the attracting force, and therefore upon
+the density of the attracting matter. Observations of the Orion nebula
+show that its proper motion is wholly inappreciable, certainly far less
+than half a second of arc per year, and corresponding to this amount of
+proper motion the mean density of the nebula must be some millions of
+times (10^{10} according to Ranyard) less than that of air at sea
+level--i. e., the average density throughout the nebula is comparable
+with that of those upper parts of the earth's atmosphere in which
+meteors first become visible.
+
+218. MOTION OF NEBULĘ.--The extreme minuteness of their proper motions
+is a characteristic feature of all nebulę. Indeed, there is hardly a
+known case of sensible proper motion of one of these bodies, although a
+dozen or more of them show velocities in the line of sight ranging in
+amount from +30 to -40 miles per second, the plus sign indicating an
+increasing distance. While a part of these velocities may be only
+apparent and due to the motion of earth and sun through space, a part at
+least is real motion of the nebulę themselves. These seem to move
+through the celestial spaces in much the same way and with the same
+velocities as do the stars, and their smaller proper motions across the
+line of sight (angular motions) are an index of their great distance
+from us. No one has ever succeeded in measuring the parallax of a nebula
+or star cluster.
+
+[Illustration: FIG. 148.--A part of the Milky Way.]
+
+The law of gravitation presumably holds sway within these bodies, and
+the fact that their several parts and the stars which are involved
+within them, although attracted by each other, have shown little or no
+change of position during the past century, is further evidence of
+their low density and feeble attraction. In a few cases, however, there
+seem to be in progress within a nebula changes of brightness, so that
+what was formerly a faint part has become a brighter one, or _vice
+versa_; but, on the whole, even these changes are very small.
+
+[Illustration: FIG. 149.--The Milky Way near [th] Ophiuchi.--BARNARD.]
+
+219. THE MILKY WAY.--Closely related to nebulę and star clusters is
+another feature of the sky, the _galaxy_ or _Milky Way_, with whose
+appearance to the unaided eye the student should become familiar by
+direct study of the thing itself. Figs. 148 and 149 are from photographs
+of two small parts of it, and serve to bring out the small stars of
+which it is composed. Every star shown in these pictures is invisible to
+the naked eye, although their combined light is easily seen. The general
+course of the galaxy across the heavens is shown in the star maps, but
+these contain no indication of the wealth of detail which even the naked
+eye may detect in it. Bright and faint parts, dark rifts which cut it
+into segments, here and there a hole as if the ribbon of light had been
+shot away--such are some of the features to be found by attentive
+examination.
+
+[Illustration: FIG. 150.--The Milky Way near [b] Cygni.--BARNARD.]
+
+Speaking generally, the course of the Milky Way is a great circle
+completely girdling the sky and having its north pole in the
+constellation Coma Berenices. The width of this stream of light is very
+different in different parts of the heavens, amounting where it is
+widest, in Lyra and Cygnus, to something more than 30°, although its
+boundaries are too vague and ill defined to permit much accuracy of
+measurement. Observe the very bright part between [b] and [g] Cygni,
+nearly opposite Vega, and note how even an opera glass will partially
+resolve the nebulous light into a great number of stars, which are here
+rather brighter than in other parts of its course. But the resolution
+into stars is only partial, and there still remains a background of
+unresolved shimmer. Fig. 150 is a photograph of a small part of this
+region in which, although each fleck of light represents a separate
+star, the galaxy is not completely resolved. Compare with this region,
+rich in stars, the nearly empty space between the branches of the galaxy
+a little west of Altair. Another hole in the Milky Way may be found a
+little north and east of [a] Cygni, and between the extremes of
+abundance and poverty here noted there may be found every gradation of
+nebulous light.
+
+The Milky Way is not so simple in its structure as might at first be
+thought, but a clear and moonless night is required to bring out its
+details. The nature of these details, the structure of the galaxy, its
+shape and extent, the arrangement of its parts, and their relation to
+stars and nebulę in general, have been subjects of much speculation by
+astronomers and others who have sought to trace out in this way what is
+called the _construction of the heavens_.
+
+220. DISTRIBUTION OF THE STARS.--How far out into space do the stars
+extend? Are they limited or infinite in number? Do they form a system of
+mutually related parts, or are they bunched promiscuously, each for
+itself, without reference to the others? Here is what has been well
+called "the most important problem of stellar astronomy, the acquisition
+of well-founded ideas about the distribution of the stars." While many
+of the ideas upon this subject which have been advanced by eminent
+astronomers and which are still current in the books are certainly
+wrong, and few of their speculations along this line are demonstrably
+true, the theme itself is of such grandeur and permanent interest as to
+demand at least a brief consideration. But before proceeding to its
+speculative side we need to collect facts upon which to build, and
+these, however inadequate, are in the main simple and not far to seek.
+
+Parallaxes, proper motions, motions in the line of sight, while
+pertinent to the problem of stellar distribution, are of small avail,
+since they are far too scanty in number and relate only to limited
+classes of stars, usually the very bright ones or those nearest to the
+sun. Almost the sole available data are contained in the brightness of
+the stars and the way in which they seem scattered in the sky. The most
+casual survey of the heavens is enough to show that the stars are not
+evenly sprinkled upon it. The lucid stars are abundant in some regions,
+few in others, and the laborious star gauges, actual counting of the
+stars in sample regions of the sky, which have been made by the
+Herschels, Celoria, and others, suffice to show that this lack of
+uniformity in distribution is even more markedly true of the telescopic
+stars.
+
+The rate of increase in the number of stars from one magnitude to the
+next, as shown in § 187, is proof of another kind of irregularity in
+their distribution. It is not difficult to show, mathematically, that if
+in distant regions of space the stars were on the average as numerous
+and as bright as they are in the regions nearer to the sun, then the
+stars of any particular magnitude ought to be four times as numerous as
+those of the next brighter magnitude--e. g., four times as many
+sixth-magnitude stars as there are fifth-magnitude ones. But, as we have
+already seen in § 187, by actual count there are only three times as
+many, and from the discrepancy between these numbers, an actual
+threefold increase instead of a fourfold one, we must conclude that on
+the whole the stars near the sun are either bigger or brighter or more
+numerous than in the remoter depths of space.
+
+221. THE STELLAR SYSTEM.--But the arrangement of the stars is not
+altogether lawless and chaotic; there are traces of order and system,
+and among these the Milky Way is the dominant feature. Telescope and
+photographic plate alike show that it is made up of stars which,
+although quite irregularly scattered along its course, are on the
+average some twenty times as numerous in the galaxy as at its poles,
+and which thin out as we recede from it on either side, at first rapidly
+and then more slowly. This tendency to cluster along the Milky Way is
+much more pronounced among the very faint telescopic stars than among
+the brighter ones, for the lucid stars and the telescopic ones down to
+the tenth or eleventh magnitude, while very plainly showing the
+clustering tendency, are not more than three times as numerous in the
+galaxy as in the constellations most remote from it. It is remarkable as
+showing the condensation of the brightest stars that one half of all the
+stars in the sky which are brighter than the second magnitude are
+included within a belt extending 12° on either side of the center line
+of the galaxy.
+
+In addition to this general condensation of stars toward the Milky Way,
+there are peculiarities in the distribution of certain classes of stars
+which are worth attention. Planetary nebulę and new stars are seldom, if
+ever, found far from the Milky Way, and stars with bright lines in their
+spectra especially affect this region of the sky. Stars with spectra of
+the first type--Sirian stars--are much more strongly condensed toward
+the Milky Way than are stars of the solar type, and in consequence of
+this the Milky Way is peculiarly rich in light of short wave lengths.
+Resolvable star clusters are so much more numerous in the galaxy than
+elsewhere, that its course across the sky would be plainly indicated by
+their grouping upon a map showing nothing but clusters of this kind.
+
+On the other hand, nebulę as a class show a distinct aversion for the
+galaxy, and are found most abundantly in those parts of the sky farthest
+from it, much as if they represented raw material which was lacking
+along the Milky Way, because already worked up to make the stars which
+are there so numerous.
+
+222. RELATION OF THE SUN TO THE MILKY WAY.--The fact that the galaxy is
+a _great circle_ of the sky, but only of moderate width, shows that it
+is a widely extended and comparatively thin stratum of stars within
+which the solar system lies, a member of the galactic system, and
+probably not very far from its center. This position, however, is not to
+be looked upon as a permanent one, since the sun's motion, which lies
+nearly in the plane of the Milky Way, is ceaselessly altering its
+relation to the center of that system, and may ultimately carry us
+outside its limits.
+
+The Milky Way itself is commonly thought to be a ring, or series of
+rings, like the coils of the great spiral nebula in Andromeda, and
+separated from us by a space far greater than the thickness of the ring
+itself. Note in Figs. 149 and 150 how the background is made up of
+bright and dark parts curiously interlaced, and presenting much the
+appearance of a thin sheet of cloud through which we look to barren
+space beyond. While, mathematically, this appearance can not be
+considered as proof that the galaxy is in fact a distant ring, rather
+than a sheet of starry matter stretching continuously from the nearer
+stellar neighbors of the sun into the remotest depths of space,
+nevertheless, most students of the question hold it to be such a ring of
+stars, which are relatively close together while its center is
+comparatively vacant, although even here are some hundreds of thousands
+of stars which on the whole have a tendency to cluster near its plane
+and to crowd together a little more densely than elsewhere in the region
+where the sun is placed.
+
+223. DIMENSIONS OF THE GALAXY.--The dimensions of this stellar system
+are wholly unknown, but there can be no doubt that it extends farther in
+the plane of the Milky Way than at right angles to that plane, for stars
+of the fifteenth and sixteenth magnitudes are common in the galaxy, and
+testify by their feeble light to their great distance from the earth,
+while near the poles of the Milky Way there seem to be few stars fainter
+than the twelfth magnitude. Herschel, with his telescope of 18 inches
+aperture, could count in the Milky Way more than a dozen times as many
+stars per square degree as could Celoria with a telescope of 4 inches
+aperture; but around the poles of the galaxy the two telescopes showed
+practically the same number of stars, indicating that here even the
+smaller telescope reached to the limits of the stellar system. Very
+recently, indeed, the telescope with which Fig. 140 was photographed
+seems to have reached the farthest limit of the Milky Way, for on a
+photographic plate of one of its richest regions Roberts finds it
+completely resolved into stars which stand out upon a black background
+with no trace of nebulous light between them.
+
+224. BEYOND THE MILKY WAY.--Each additional step into the depths of
+space brings us into a region of which less is known, and what lies
+beyond the Milky Way is largely a matter of conjecture. We shrink from
+thinking it an infinite void, endless emptiness, and our intellectual
+sympathies go out to Lambert's speculation of a universe filled with
+stellar systems, of which ours, bounded by the galaxy, is only one.
+There is, indeed, little direct evidence that other such systems exist,
+but the Andromeda nebula is not altogether unlike a galaxy with a
+central cloud of stars, and in the southern hemisphere, invisible in our
+latitudes, are two remarkable stellar bodies like the Milky Way in
+appearance, but cut off from all apparent connection with it, much as we
+might expect to find independent stellar systems, if such there be.
+
+These two bodies are known as the Magellanic clouds, and individually
+bear the names of Major and Minor Nubecula. According to Sir John
+Herschel, "the Nubecula Major, like the Minor, consists partly of large
+tracts and ill-defined patches of irresolvable nebula, and of nebulosity
+in every stage of resolution up to perfectly resolved stars like the
+Milky Way, as also of regular and irregular nebulę ... of globular
+clusters in every stage of resolvability, and of clustering groups
+sufficiently insulated and condensed to come under the designation of
+clusters of stars." Its outlines are vague and somewhat uncertain, but
+surely include an area of more than 40 square degrees--i. e., as much as
+the bowl of the Big Dipper--and within this area Herschel counted
+several hundred nebulę and clusters "which far exceeds anything that is
+to be met with in any other region of the heavens." Although its
+excessive complexity of detail baffled Herschel's attempts at artistic
+delineation, it has yielded to the modern photographic processes, which
+show the Nubecula Major to be an enormous spiral nebula made up of
+subordinate stars, nebulę, and clusters, as is the Milky Way.
+
+Compared with the Andromeda nebula, its greater angular extent suggests
+a smaller distance, although for the present all efforts at determining
+the parallax of either seem hopeless. But the spiral form which is
+common to both suggests that the Milky Way itself may be a gigantic
+spiral nebula near whose center lies the sun, a humble member of a great
+cluster of stars which is roughly globular in shape, but flattened at
+the poles of the galaxy and completely encircled by its coils. However
+plausible such a view may appear, it is for the present, at least, pure
+hypothesis, although vigorously advocated by Easton, who bases his
+argument upon the appearance of the galaxy itself.
+
+225. ABSORPTION OF STARLIGHT.--We have had abundant occasion to learn
+that at least within the confines of the solar system meteoric matter,
+cosmic dust, is profusely scattered, and it appears not improbable that
+the same is true, although in smaller degree, in even the remoter parts
+of space. In this case the light which comes from the farther stars over
+a path requiring many centuries to travel, must be in some measure
+absorbed and enfeebled by the obstacles which it encounters on the way.
+Unless celestial space is transparent to an improbable degree the
+remoter stars do not show their true brightness; there is a certain
+limit beyond which no star is able to send its light, and beyond which
+the universe must be to us a blank. A lighthouse throws into the fog its
+beams only to have them extinguished before a single mile is passed, and
+though the celestial lights shine farther, a limit to their reach is
+none the less certain if meteoric dust exists outside the solar system.
+If there is such an absorption of light in space, as seems plausible,
+the universe may well be limitless and the number of stellar systems
+infinite, although the most attenuated of dust clouds suffices to
+conceal from us and to shut off from our investigation all save a minor
+fraction of it and them.
+
+
+
+
+CHAPTER XV
+
+GROWTH AND DECAY
+
+
+226. NATURE OF THE PROBLEM.--To use a common figure of speech, the
+universe is alive. We have found it filled with an activity that
+manifests itself not only in the motions of the heavenly bodies along
+their orbits, but which extends to their minutest parts, the molecules
+and atoms, whose vibrations furnish the radiant energy given off by sun
+and stars. Some of these activities, such as the motions of the heavenly
+bodies in their orbits, seem fitted to be of endless duration; while
+others, like the radiation of light and heat, are surely temporary, and
+sooner or later must come to an end and be replaced by something
+different. The study of things as they are thus leads inevitably to
+questions of what has been and what is to be. A sound science should
+furnish some account of the universe of yesterday and to-morrow as well
+as of to-day, and we need not shrink from such questions, although
+answers to them must be vague and in great measure speculative.
+
+The historian of America finds little difficulty with events of the
+nineteenth century or even the eighteenth, but the sources of
+information about America in the fifteenth century are much less
+definite; the tenth century presents almost a blank, and the history of
+American mankind in the first century of the Christian era is wholly
+unknown. So, as we attempt to look into the past or the future of the
+heavens, we must expect to find the mists of obscurity grow denser with
+remoter periods until even the vaguest outlines of its development are
+lost, and we are compelled to say, beyond this lies the unknown. Our
+account of growth and decay in the universe, therefore, can not aspire
+to cover the whole duration of things, but must be limited in its scope
+to certain chapters whose epochs lie near to the time in which we live,
+and even for these we need to bear constantly in mind the logical bases
+of such an inquiry and the limitations which they impose upon us.
+
+227. LOGICAL BASES AND LIMITATIONS.--The first of these bases is: An
+adequate knowledge of the present universe. Our only hope of reading the
+past and future lies in an understanding of the present; not necessarily
+a complete knowledge of it, but one which is sound so far as it goes.
+Our position is like that of a detective who is called upon to unravel a
+mystery or crime, and who must commence with the traces that have been
+left behind in its commission. The foot print, the blood stain, the
+broken glass must be examined and compared, and fashioned into a theory
+of how they came to be; and as a wrong understanding of these elements
+is sure to vitiate the theories based upon them, so a false science of
+the universe as it now is, will surely give a false account of what it
+has been; while a correct but incomplete knowledge of the present does
+not wholly bar an understanding of the past, but only puts us in the
+position of the detective who correctly understands what he sees but
+fails to take note of other facts which might greatly aid him.
+
+The second basis of our inquiry is: The assumed permanence of natural
+laws. The law of gravitation certainly held true a century ago as well
+as a year ago, and for aught we know to the contrary it may have been a
+law of the universe for untold millions of years; but that it has
+prevailed for so long a time is a pure assumption, although a necessary
+one for our purpose. So with those other laws of mathematics and
+mechanics and physics and chemistry to which we must appeal; if there
+was ever a time or place in which they did not hold true, that time and
+place lie beyond the scope of our inquiry, and are in the domain
+inaccessible to scientific research. It is for this reason that science
+knows nothing and can know nothing of a creation or an end of the
+universe, but considers only its orderly development within limited
+periods of time. What kind of a past universe would, under the operation
+of known laws, develop into the present one, is the question with which
+we have to deal, and of it we may say with Helmholtz: "From the
+standpoint of science this is no idle speculation but an inquiry
+concerning the limitations of its methods and the scope of its known
+laws."
+
+To ferret out the processes by which the heavenly bodies have been
+brought to their present condition we seek first of all for lines of
+development now in progress which tend to change the existing order of
+things into something different, and, having found these, to trace their
+effects into both past and future. Any force, however small, or any
+process, however slow, may produce great results if it works always and
+ceaselessly in the same direction, and it is in these processes, whose
+trend is never reversed, that we find a partial clew to both past and
+future.
+
+228. THE SUN'S DEVELOPMENT.--The first of these to claim our attention
+is the shrinking of the sun's diameter which, as we have seen in Chapter
+X, is the means by which the solar output of radiant energy is
+maintained from year to year. Its amount, only a few feet per annum, is
+far too small to be measured with any telescope; but it is cumulative,
+working century after century in the same direction, and, given time
+enough, it will produce in the future, and must have produced in the
+past, enormous transformations in the sun's bulk and equally significant
+changes in its physical condition.
+
+Thus, as we attempt to trace the sun's history into the past, the
+farther back we go the greater shall we expect to find its diameter and
+the greater the space (volume) through which its molecules are spread.
+By reason of this expansion its density must have been less then than
+now, and by going far enough back we may even reach a time at which the
+density was comparable with what we find in the nebulę of to-day. If our
+ideas of the sun's present mechanism are sound, then, as a necessary
+consequence of these, its past career must have been a process of
+condensation in which its component particles were year by year packed
+closer together by their own attraction for each other. As we have seen
+in § 126, this condensation necessarily developed heat, a part of which
+was radiated away as fast as produced, while the remainder was stored
+up, and served to raise the temperature of the sun to what we find it
+now. At the present time this temperature is a chief obstacle to further
+shrinkage, and so powerfully opposes the gravitative forces as to
+maintain nearly an equilibrium with them, thus causing a very slow rate
+of further condensation. But it is not probable that this was always so.
+In the early stages of the sun's history, when the temperature was low,
+contraction of its bulk must have been more rapid, and attempts have
+been made by the mathematicians to measure its rate of progress and to
+determine how long a time has been consumed in the development of the
+present sun from a primitive nebulous condition in which it filled a
+space of greater diameter than Neptune's orbit. Of course, numerical
+precision is not to be expected in results of this kind, but, from a
+consideration of the greatest amount of heat that could be furnished by
+the shrinkage of a mass equal to that of the sun, it seems that the
+period of this development is to be measured in tens of millions or
+possibly hundreds of millions of years, but almost certainly does not
+reach a thousand millions.
+
+229. THE SUN'S FUTURE.--The future duration of the sun as a source of
+radiant energy is surely to be measured in far smaller numbers than
+these. Its career as a dispenser of light and heat is much more than
+half spent, for the shrinkage results in an ever-increasing density,
+which makes its gaseous substance approximate more and more toward the
+behavior of a liquid or solid, and we recall that these forms of matter
+can not by any further condensation restore the heat whose loss through
+radiation caused them to contract. They may continue to shrink, but
+their temperature must fall, and when the sun's substance becomes too
+dense to obey the laws of gaseous matter its surface must cool rapidly
+as a consequence of the radiation into surrounding space, and must
+congeal into a crust which, although at first incandescent, will
+speedily become dark and opaque, cutting off the light of the central
+portions, save as it may be rent from time to time by volcanic outbursts
+of the still incandescent mass beneath. But such outbursts can be of
+short duration only, and its final condition must be that of a dark
+body, like the earth or moon, no longer available as a source of radiant
+energy. Even before the formation of a solid crust it is quite possible
+that the output of light and heat may be seriously diminished by the
+formation of dense vapors completely enshrouding it, as is now the case
+with Jupiter and Saturn. It is believed that these planets were formerly
+incandescent, and at the present time are in a state of development
+through which the earth has passed and toward which the sun is moving.
+According to Newcomb, the future during which the sun can continue to
+furnish light and heat at its present rate is not likely to exceed
+10,000,000 years.
+
+This idea of the sun as a developing body whose present state is only
+temporary, furnishes a clew to some of the vexing problems of solar
+physics. Thus the sun-spot period, the distribution of the spots in
+latitude, and the peculiar law of rotation of the sun in different
+latitudes, may be, and very probably are, results not of anything now
+operating beneath its photosphere, but of something which happened to it
+in the remote past--e. g., an unsymmetrical shrinkage or possibly a
+collision with some other body. At sea the waves continue to toss long
+after the storm which produced them has disappeared, and, according to
+the mathematical researches of Wilsing, a profound agitation of the
+sun's mass might well require tens of thousands, or even hundreds of
+thousands of years to subside, and during this time its effects would be
+visible, like the waves, as phenomena for which the actual condition of
+things furnishes no apparent cause.
+
+230. THE NEBULAR HYPOTHESIS.--The theory of the sun's progressive
+contraction as a necessary result of its radiation of energy is
+comparatively modern, but more than a century ago philosophic students
+of Nature had been led in quite a different way to the belief that in
+the earlier stages of its career the sun must have been an enormously
+extended body whose outer portions reached even beyond the orbit of the
+remotest planet. Laplace, whose speculations upon this subject have had
+a dominant influence during the nineteenth century, has left, in a
+popular treatise upon astronomy, an admirable statement of the phenomena
+of planetary motion, which suggest and lead up to the nebular theory of
+the sun's development, and in presenting this theory we shall follow
+substantially his line of thought, but with some freedom of translation
+and many omissions.
+
+He says: "To trace out the primitive source of the planetary movements,
+we have the following five phenomena: (1) These movements all take place
+in the same direction and nearly in the same plane. (2) The movements of
+the satellites are in the same direction as those of the planets. (3)
+The rotations of the planets and the sun are in the same direction as
+the orbital motions and nearly in the same plane. (4) Planets and
+satellites alike have nearly circular orbits. (5) The orbits of comets
+are wholly unlike these by reason of their great eccentricities and
+inclinations to the ecliptic." That these coincidences should be purely
+the result of chance seemed to Laplace incredible, and, seeking a cause
+for them, he continues: "Whatever its nature may be, since it has
+produced or controlled the motions of the planets, it must have reached
+out to all these bodies, and, in view of the prodigious distances which
+separate them, the cause can have been nothing else than a fluid of
+great extent which must have enveloped the sun like an atmosphere. A
+consideration of the planetary motions leads us to think that ... the
+sun's atmosphere formerly extended far beyond the orbits of all the
+planets and has shrunk by degrees to its present dimensions." This is
+not very different from the idea developed in § 228 from a consideration
+of the sun's radiant energy; but in Laplace's day the possibility of
+generating the sun's heat by contraction of its bulk was unknown, and he
+was compelled to assume a very high temperature for the primitive
+nebulous sun, while we now know that this is unnecessary. Whether the
+primitive nebula was hot or cold the shrinkage would take place in much
+the same way, and would finally result in a star or sun of very high
+temperature, but its development would be slower if it were hot in the
+beginning than if it were cold.
+
+But again Laplace: "How did the sun's atmosphere determine the rotations
+and revolutions of planets and satellites? If these bodies had been
+deeply immersed in this atmosphere its resistance to their motion would
+have made them fall into the sun, and we may therefore conjecture that
+the planets were formed, one by one, at the outer limits of the solar
+atmosphere by the condensation of zones of vapor which were cast off in
+the plane of the sun's equator." Here he proceeds to show by an appeal
+to dynamical principles that something of this kind must happen, and
+that the matter sloughed off by the nebula in the form of a ring,
+perhaps comparable to the rings of Saturn or the asteroid zone, would
+ultimately condense into a planet, which in its turn might shrink and
+cast off rings to produce satellites.
+
+[Illustration: PIERRE SIMON LAPLACE (1749-1827).]
+
+Planets and satellites would then all have similar motions, as noted at
+the beginning of this section, since in every case this motion is an
+inheritance from a common source, the rotation of the primitive
+nebula about its own axis. "All the bodies which circle around a planet
+having been thus formed from rings which its atmosphere successively
+abandoned as rotation became more and more rapid, this rotation should
+take place in less time than is required for the orbital revolution of
+any of the bodies which have been cast off, and this holds true for the
+sun as compared with the planets."
+
+231. OBJECTIONS TO THE NEBULAR HYPOTHESIS.--In Laplace's time this
+slower rate of motion was also supposed to hold true for Saturn's rings
+as compared with the rotation of Saturn itself, but, as we have seen in
+Chapter XI, this ring is made up of a great number of independent
+particles which move at different rates of speed, and comparing, through
+Kepler's Third Law, the motion of the inner edge of the ring with the
+known periodic time of the satellites, we may find that these particles
+must rotate about Saturn more rapidly than the planet turns upon its
+axis. Similarly the inner satellite of Mars completes its revolution in
+about one third of a Martian day, and we find in cases like this grounds
+for objection to the nebular theory. Compare also Laplace's argument
+with the peculiar rotations of Uranus, Neptune, and their satellites
+(Chapter XI). Do these fortify or weaken his case?
+
+Despite these objections and others equally serious that have been
+raised, the nebular theory agrees with the facts of Nature at so many
+points that astronomers upon the whole are strongly inclined to accept
+its major outlines as being at least an approximation to the course of
+development actually followed by the solar system; but at some
+points--e. g., the formation of planets and satellites through the
+casting off of nebulous rings--the objections are so many and strong as
+to call for revision and possibly serious modification of the theory.
+
+One proposed modification, much discussed in recent years, consists in
+substituting for the primitive _gaseous_ nebula imagined by Laplace, a
+very diffuse cloud of meteoric matter which in the course of its
+development would become transformed into the gaseous state by rising
+temperature. From this point of view much of the meteoric dust still
+scattered throughout the solar system may be only the fragments left
+over in fashioning the sun and planets. Chamberlin and Moulton, who have
+recently given much attention to this subject, in dissenting from some
+of Laplace's views, consider that the primitive nebulous condition must
+have been one in which the matter of the system was "so brought together
+as to give low mass, high momentum, and irregular distribution to the
+outer part, and high mass, low momentum, and sphericity to the central
+part," and they suggest a possible oblique collision of a small nebula
+with the outer parts of a large one.
+
+232. BODE'S LAW.--We should not leave the theory of Laplace without
+noting the light it casts upon one point otherwise obscure--the meaning
+of Bode's law (§ 134). This law, stated in mathematical form, makes a
+geometrical series, and similar geometrical series apply to the
+distances of the satellites of Jupiter and Saturn from these planets.
+Now, Roche has shown by the application of physical laws to the
+shrinkage of a gaseous body that its radius at any time may be expressed
+by means of a certain mathematical formula very similar to Bode's law,
+save that it involves the amount of time that has elapsed since the
+beginning of the shrinking process. By comparing this formula with the
+one corresponding to Bode's law he reaches the conclusion that the
+peculiar spacing of the planets expressed by that law means that they
+were formed at successive _equal_ intervals of time--i. e., that Mars is
+as much older than the earth as the earth is older than Venus, etc. The
+failure of Bode's law in the case of Neptune would then imply that the
+interval of time between the formation of Neptune and Uranus was shorter
+than that which has prevailed for the other planets. But too much
+stress should not be placed upon this conclusion. So long as the manner
+in which the planets came into being continues an open question,
+conclusions about their time of birth must remain of doubtful validity.
+
+233. TIDAL FRICTION BETWEEN EARTH AND MOON.--An important addition to
+theories of development within the solar system has been worked out by
+Prof. G. H. Darwin, who, starting with certain very simple assumptions
+as to the present condition of things in earth and moon, derives from
+these, by a strict process of mathematical reasoning, far-reaching
+conclusions of great interest and importance. The key to these
+conclusions lies in recognition of the fact that through the influence
+of the tides (§ 42) there is now in progress and has been in progress
+for a very long time, a gradual transfer of motion (moment of momentum)
+from the earth to the moon. The earth's motion of rotation is being
+slowly destroyed by the friction of the tides, as the motion of a
+bicycle is destroyed by the friction of a brake, and, in consequence of
+this slowing down, the moon is pushed farther and farther away from the
+earth, so that it now moves in a larger orbit than it had some millions
+of years ago.
+
+Fig. 24 has been used to illustrate the action of the moon in raising
+tides upon the earth, but in accordance with the third law of motion
+(§ 36) this action must be accompanied by an equal and contrary reaction
+whose nature may readily be seen from the same figure. The moon moves
+about its orbit from west to east and the earth rotates about its axis
+in the same direction, as shown by the curved arrow in the figure. The
+tidal wave, _I_, therefore points a little _in advance_ of the moon's
+position in its orbit and by its attraction must tend to pull the moon
+ahead in its orbital motion a little faster than it would move if the
+whole substance of the earth were placed inside the sphere represented
+by the broken circle in the figure. It is true that the tidal wave at
+_I““_ pulls back and tends to neutralize the effect of the wave at _I_,
+but on the whole the tidal wave nearer the moon has the stronger
+influence, and the moon on the whole moves a very little faster, and by
+virtue of this added impetus draws continually a little farther away
+from the earth than it would if there were no tides.
+
+234. CONSEQUENCES OF TIDAL FRICTION UPON THE EARTH.--This process of
+moving the moon away from the earth is a cumulative one, going on
+century after century, and with reference to it the moon's orbit must be
+described not as a circle or ellipse, or any other curve which returns
+into itself, but as a spiral, like the balance spring of a watch, each
+of whose coils is a little larger than the preceding one, although this
+excess is, to be sure, very small, because the tides themselves are
+small and the tidal influence feeble when compared with the whole
+attraction of the earth for the moon. But, given time enough, even this
+small force may accomplish great results, and something like 100,000,000
+years of past opportunity would have sufficed for the tidal forces to
+move the moon from close proximity with the earth out to its present
+position.
+
+For millions of years to come, if moon and earth endure so long, the
+distance between them must go on increasing, although at an ever slower
+rate, since the farther away the moon goes the smaller will be the tides
+and the slower the working out of their results. On the other hand, when
+the moon was nearer the earth than now, tidal influences must have been
+greater and their effects more rapidly produced than at the present
+time, particularly if, as seems probable, at some past epoch the earth
+was hot and plastic like Jupiter and Saturn. Then, instead of tides in
+the water of the sea, such as we now have, the whole substance of the
+earth would respond to the moon's attraction in _bodily tides_ of
+semi-fluid matter not only higher, but with greater internal friction of
+their molecules one upon another, and correspondingly greater effect in
+checking the earth's rotation.
+
+But, whether the tide be a bodily one or confined to the waters of the
+sea, so long as the moon causes it to flow there will be a certain
+amount of friction which will affect the earth much as a brake affects a
+revolving wheel, slowing down its motion, and producing thus a longer
+day as well as a longer month on account of the moon's increased
+distance. Slowing down the earth's rotation is the direct action of the
+moon upon the earth. Pushing the moon away is the form in which the
+earth's equal and contrary reaction manifests itself.
+
+235. CONSEQUENCES OF TIDAL FRICTION UPON THE MOON.--When the moon was
+plastic the earth must have raised in it a bodily tide manifold greater
+than the lunar tides upon the earth, and, as we have seen in Chapter IX,
+this tide has long since worn out the greater part of the moon's
+rotation and brought our satellite to the condition in which it presents
+always the same face toward the earth.
+
+These two processes, slowing down the rotation and pushing away the
+disturbing body, are inseparable--one requires the other; and it is
+worth noting in this connection that when for any reason the tide ceases
+to flow, and the tidal wave takes up a permanent position, as it has in
+the moon (§ 99), its work is ended, for when there is no motion of the
+wave there can be no friction to further reduce the rate of rotation of
+the one body, and no reaction to that friction to push away the other.
+But this permanent and stationary tidal wave in the moon, or elsewhere,
+means that the satellite presents always the same face toward its
+planet, moving once about its orbit in the time required for one
+revolution upon its axis, and the tide raised by the moon upon the earth
+tends to produce here the result long since achieved in our satellite,
+to make our day and month of equal length, and to make the earth turn
+always the same side toward the moon. But the moon's tidal force is
+small compared with that of the earth, and has a vastly greater momentum
+to overcome, so that its work upon the earth is not yet complete.
+According to Thomson and Tait, the moon must be pushed off another
+hundred thousand miles, and the day lengthened out by tidal influence to
+seven of our present weeks before the day and the lunar month are made
+of equal length, and the moon thereby permanently hidden from one
+hemisphere of the earth.
+
+236. THE EARTH-MOON SYSTEM.--Retracing into the past the course of
+development of the earth and moon, it is possible to reach back by means
+of the mathematical theory of tidal friction to a time at which these
+bodies were much nearer to each other than now, but it has not been
+found possible to trace out the mode of their separation from one body
+into two, as is supposed in the nebular theory. In the earliest part of
+their history accessible to mathematical analysis they are distinct
+bodies at some considerable distance from each other, with the earth
+rotating about an axis more nearly perpendicular to the moon's orbit and
+to the ecliptic than is now the case. Starting from such a condition,
+the lunar tides, according to Darwin, have been instrumental in tipping
+the earth's rotation axis into its present oblique position, and in
+determining the eccentricity of the moon's orbit and its position with
+respect to the ecliptic as well as the present length of day and month.
+
+337. TIDAL FRICTION UPON THE PLANETS.--The satellites of the outer
+planets are equally subject to influences of this kind, and there
+appears to be independent evidence that some of them, at least, turn
+always the same face toward their respective planets, indicating that
+the work of tidal friction has here been accomplished. We saw in Chapter
+XI that it is at present an open question whether the inner planets,
+Venus and Mercury, do not always turn the same face toward the sun,
+their day and year being of equal length. In addition to the direct
+observational evidence upon this point, Schiaparelli has sought to show
+by an appeal to tidal theory that such is probably the case, at least
+for Mercury, since the tidal forces which tend to bring about this
+result in that planet are about as great as the forces which have
+certainly produced it in the case of the moon and Saturn's satellite,
+Japetus. The same line of reasoning would show that every satellite in
+the solar system, save possibly the newly discovered ninth satellite of
+Saturn, must, as a consequence of tidal friction, turn always the same
+face toward its planet.
+
+238. THE SOLAR TIDE.--The sun also raises tides in the earth, and their
+influence must be similar in character to that of the lunar tides,
+checking the rotation of the earth and thrusting earth and sun apart,
+although quantitatively these effects are small compared with those of
+the moon. They must, however, continue so long as the solar tide lasts,
+possibly until the day and year are made of equal length--i. e., they
+may continue long after the lunar tidal influence has ceased to push
+earth and moon apart. Should this be the case, a curious inverse effect
+will be produced. The day being then longer than the month, the moon
+will again raise a tide in the earth which will run around it _from west
+to east_, opposite to the course of the present tide, thus tending to
+accelerate the earth's rotation, and by its reaction to bring the moon
+back toward the earth again, and ultimately to fall upon it.
+
+We may note that an effect of this kind must be in progress now between
+Mars and its inner satellite, Phobos, whose time of orbital revolution
+is only one third of a Martian day. It seems probable that this
+satellite is in the last stages of its existence as an independent body,
+and must ultimately fall into Mars.
+
+239. ROCHE'S LIMIT.--In looking forward to such a catastrophe, however,
+due regard must be paid to a dynamical principle of a different
+character. The moon can never be precipitated upon the earth entire,
+since before it reaches us it will have been torn asunder by the excess
+of the earth's attraction for the near side of its satellite over that
+which it exerts upon the far side. As the result of Roche's mathematical
+analysis we are able to assign a limiting distance between any planet
+and its satellite within which the satellite, if it turns always the
+same face toward the planet, can not come without being broken into
+fragments. If we represent the radius of the planet by _r_, and the
+quotient obtained by dividing the density of the planet by the density
+of the satellite by _q_, then
+
+    Roche's limit = 2.44 × r × q^{1/3}.
+
+Thus in the case of earth and moon we find from the densities given in
+§ 95, _q_ = 1.65, and with _r_ = 3,963 miles we obtain 11,400 miles as
+the nearest approach which the moon could make to the earth without
+being broken up by the difference of the earth's attractions for its
+opposite sides.
+
+We must observe, however, that Roche's limit takes no account of
+molecular forces, the adhesion of one molecule to another, by virtue of
+which a stick or stone resists fracture, but is concerned only with the
+gravitative forces by which the molecules are attracted toward the
+moon's center and toward the earth. Within a stone or rock of moderate
+size these gravitative forces are insignificant, and cohesion is the
+chief factor in preserving its integrity, but in a large body like the
+moon, the case is just reversed, cohesion plays a small part and
+gravitation a large one in holding the body together. We may conclude,
+therefore, that at a proper distance these forces are capable of
+breaking up the moon, or any other large body, into fragments of a size
+such that molecular cohesion instead of gravitation is the chief agent
+in preserving them from further disintegration.
+
+240. SATURN'S RINGS.--Saturn's rings are of peculiar interest in this
+connection. The outer edge of the ring system lies just inside of
+Roche's limit for this planet, and we have already seen that the rings
+are composed of small fragments independent of each other. Whatever may
+have been the process by which the nine satellites of Saturn came into
+existence, we have in Roche's limit the explanation why the material of
+the ring was not worked up into satellites; the forces exerted by Saturn
+would tear into pieces any considerable satellite thus formed and
+equally would prevent the formation of one from raw material.
+
+Saturn's rings present the only case within the solar system where
+matter is known to be revolving about a planet at a distance less than
+Roche's limit, and it is an interesting question whether these rings can
+remain as a permanent part of the planet's system or are only a
+temporary feature. The drawings of Saturn made two centuries ago agree
+among themselves in representing the rings as larger than they now
+appear, and there is some reason to suppose that as a consequence of
+mutual disturbances--collisions--their momentum is being slowly wasted
+so that ultimately they must be precipitated into the planet. But the
+direct evidence of such a progress that can be drawn from present data
+is too scanty to justify positive conclusions in the matter. On the
+other hand, Nolan suggests that in the outer parts of the ring small
+satellites might be formed whose tidal influence upon Saturn would
+suffice to push them away from the ring beyond Roche's limit, and that
+the very small inner satellites of Saturn may have been thus formed at
+the expense of the ring.
+
+The inner satellite of Mars is very close to Roche's limit for that
+planet, and, as we have seen above, must be approaching still nearer to
+the danger line.
+
+241. THE MOON'S DEVELOPMENT.--The fine series of photographs of the moon
+obtained within the last few years at Paris, have been used by the
+astronomers of that observatory for a minute study of the lunar
+formations, much as geologists study the surface of the earth to
+determine something about the manner in which it was formed. Their
+conclusions are, in general, that at some past time the moon was a hot
+and fluid body which, as it cooled and condensed, formed a solid crust
+whose further shrinkage compressed the liquid nucleus and led to a long
+series of fractures in the crust and outbursts of liquid matter, whose
+latest and feeblest stages produced the lunar craters, while traces of
+the earlier ones, connected with a general settling of the crust,
+although nearly obliterated, are still preserved in certain large but
+vague features of the lunar topography, such as the distribution of the
+seas, etc. They find also in certain markings of the surface what they
+consider convincing evidence of the existence in past times of a lunar
+atmosphere. But this seems doubtful, since the force of gravity at the
+moon's surface is so small that an atmosphere similar to that of the
+earth, even though placed upon the moon, could not permanently endure,
+but would be lost by the gradual escape of its molecules into the
+surrounding space.
+
+The molecules of a gas are quite independent one of another, and are in
+a state of ceaseless agitation, each one darting to and fro, colliding
+with its neighbors or with whatever else opposes its forward motion, and
+traveling with velocities which, on the average, amount to a good many
+hundreds of feet per second, although in the case of any individual
+molecule they may be much less or much greater than the average value,
+an occasional molecule having possibly a velocity several times as great
+as the average. In the upper regions of our own atmosphere, if one of
+these swiftly moving particles of oxygen or nitrogen were headed away
+from the earth with a velocity of seven miles per second, the whole
+attractive power of the earth would be insufficient to check its motion,
+and it would therefore, unless stopped by some collision, escape from
+the earth and return no more. But, since this velocity of seven miles
+per second is more than thirty times as great as the average velocity of
+the molecules of air, it must be very seldom indeed that one is found to
+move so swiftly, and the loss of the earth's atmosphere by leakage of
+this sort is insignificant. But upon the moon, or any other body where
+the force of gravity is small, conditions are quite different, and in
+our satellite a velocity of little more than one mile per second would
+suffice to carry a molecule away from the outer limits of its
+atmosphere. This velocity, only five times the average, would be
+frequently attained, particularly in former times when the moon's
+temperature was high, for then the average velocity of all the molecules
+would be considerably increased, and the amount of leakage might become,
+and probably would become, a serious matter, steadily depleting the
+moon's atmosphere and leading finally to its present state of
+exhaustion. It is possible that the moon may at one time have had an
+atmosphere, but if so it could have been only a temporary possession,
+and the same line of reasoning may be applied to the asteroids and to
+most of the satellites of the solar system, and also, though in less
+degree, to the smaller planets, Mercury and Mars.
+
+242. STELLAR DEVELOPMENT.--We have already considered in this chapter
+the line of development followed by one star, the sun, and treating this
+as a typical case, it is commonly believed that the life history of a
+star, in so far as it lies within our reach, begins with a condition in
+which its matter is widely diffused, and presumably at a low
+temperature. Contracting in bulk under the influence of its own
+gravitative forces, the star's temperature rises to a maximum, and then
+falls off in later stages until the body ceases to shine and passes over
+to the list of dark stars whose existence can only be detected in
+exceptional cases, such as are noted in Chapter XIII. The most
+systematic development of this idea is due to Lockyer, who looks upon
+all the celestial bodies--sun, moon and planets, stars, nebulę, and
+comets--as being only collections of meteoric matter in different stages
+of development, and who has sought by means of their spectra to classify
+these bodies and to determine their stage of advancement. While the
+fundamental ideas involved in this "meteoritic hypothesis" are not
+seriously controverted, the detailed application of its principles is
+open to more question, and for the most part those astronomers who hold
+that in the present state of knowledge stellar spectra furnish a key to
+a star's age or degree of advancement do not venture beyond broad
+general statements.
+
+[Illustration: FIG. 151.--Types of stellar spectra substantially
+according to SECCHI.]
+
+243. STELLAR SPECTRA.--Thus the types of stellar spectra shown in Fig.
+151 are supposed to illustrate successive stages in the development of
+an average star. Type I corresponds to the period in which its
+temperature is near the maximum; Type II belongs to a later stage in
+which the temperature has commenced to fall; and Type III to the period
+immediately preceding extinction.
+
+While human life, or even the duration of the human race, is too short
+to permit a single star to be followed through all the stages of its
+career, an adequate picture of that development might be obtained by
+examining many stars, each at a different stage of progress, and,
+following this idea, numerous subdivisions of the types of stellar
+spectra shown in Fig. 151 have been proposed in order to represent with
+more detail the process of stellar growth and decay; but for the most
+part these subdivisions and their interpretation are accepted by
+astronomers with much reserve.
+
+It is significant that there are comparatively few stars with spectra of
+Type III, for this is what we should expect to find if the development
+of a star through the last stages of its visible career occupied but a
+small fraction of its total life. From the same point of view the great
+number of stars with spectra of the first type would point to a long
+duration of this stage of life. The period in which the sun belongs,
+represented by Type II, probably has a duration intermediate between the
+others. Since most of the variable stars, save those of the Algol class,
+have spectra of the third type, we conclude that variability, with its
+associated ruddy color and great atmospheric absorption of light, is a
+sign of old age and approaching extinction. The Algol or eclipse
+variables, on the other hand, having spectra of the first type, are
+comparatively young stars, and, as we shall see a little later, the
+shortness of their light periods in some measure confirms this
+conclusion drawn from their spectra.
+
+We have noted in § 196 that the sun's near neighbors are prevailingly
+stars with spectra of the second type, while the Milky Way is mainly
+composed of first-type stars, and from this we may now conclude that in
+our particular part of the entire celestial space the stars are, as a
+rule, somewhat further developed than is the case elsewhere.
+
+244. DOUBLE STARS.--The double stars present special problems of
+development growing out of the effects of tidal friction, which must
+operate in them much as it does between earth and moon, tending steadily
+to increase the distance between the components of such a star. So, too,
+in such a system as is shown in Fig. 132, gravity must tend to make each
+component of the double star shrink to smaller dimensions, and this
+shrinkage must result in faster rotation and increased tidal friction,
+which in turn must push the components apart, so that in view of the
+small density and close proximity of those particular stars we may
+fairly regard a star like [b] Lyrę as in the early stages of its
+career and destined with increasing age to lose its variability of
+light, since the eclipses which now take place must cease with
+increasing distance between the components unless the orbit is turned
+exactly edgewise toward the earth. Close proximity and the resulting
+shortness of periodic time in a double star seem, therefore, to be
+evidence of its youth, and since this shortness of periodic time is
+characteristic of both Algol variables and spectroscopic binaries as a
+class, we may set them down as being, upon the whole, stars in the early
+stages of their career. On the other hand, it is generally true that the
+larger the orbit, and the greater the periodic time in the orbit, the
+farther is the star advanced in its development.
+
+In his theory of tidal friction, Darwin has pointed out that whenever
+the periodic time in the orbit is more than twice as long as the time
+required for rotation about the axis, the effect of the tides is to
+increase the eccentricity of the orbit, and, following this indication,
+See has urged that with increasing distance between the components of a
+double star their orbits about the common center of gravity must grow
+more and more eccentric, so that we have in the shape of such orbits a
+new index of stellar development; the more eccentric the orbit, the
+farther advanced are the stars. It is important to note in this
+connection that among the double stars whose orbits have been computed
+there seems to run a general rule--the larger the orbit the greater is
+its eccentricity--a relation which must hold true if tidal friction
+operates as above supposed, and which, being found to hold true,
+confirms in some degree the criteria of stellar age which are furnished
+by the theory of tidal friction.
+
+245. NEBULĘ.--The nebular hypothesis of Laplace has inclined astronomers
+to look upon nebulę in general as material destined to be worked up into
+stars, but which is now in a very crude and undeveloped stage. Their
+great bulk and small density seem also to indicate that gravitation has
+not yet produced in them results at all comparable with what we see in
+sun and stars. But even among nebulę there are to be found very
+different stages of development. The irregular nebula, shapeless and
+void like that of Orion; the spiral, ring, and planetary nebulę and the
+star cluster, clearly differ in amount of progress toward their final
+goal. But it is by no means sure that these several types are different
+stages in one line of development; for example, the primitive nebula
+which grows into a spiral may never become a ring or planetary nebula,
+and _vice versa_. So too there is no reason to suppose that a star
+cluster will ever break up into isolated stars such as those whose
+relation to each other is shown in Fig. 122.
+
+246. CLASSIFICATION.--Considering the heavenly bodies with respect to
+their stage of development, and arranging them in due order, we should
+probably find lowest down in the scale of progress the irregular nebulę
+of chaotic appearance such as that represented in Fig. 146. Above these
+in point of development stand the spiral, ring, and planetary nebulę,
+although the exact sequence in which they should be arranged remains a
+matter of doubt. Still higher up in the scale are star clusters whose
+individual members, as well as isolated stars, are to be classified by
+means of their spectra, as shown in Fig. 151, where the order of
+development of each star is probably from Type I, through II, into III
+and beyond, to extinction of its light and the cutting off of most of
+its radiant energy. Jupiter and Saturn are to be regarded as stars which
+have recently entered this dark stage. The earth is further developed
+than these, but it is not so far along as are Mars and Mercury; while
+the moon is to be looked upon as the most advanced heavenly body
+accessible to our research, having reached a state of decrepitude which
+may almost be called death--a stage typical of that toward which all the
+others are moving.
+
+Meteors and comets are to be regarded as fragments of celestial matter,
+chips, too small to achieve by themselves much progress along the normal
+lines of development, but destined sooner or later, by collision with
+some larger body, to share thenceforth in its fortunes.
+
+247. STABILITY OF THE UNIVERSE.--It was considered a great achievement
+in the mathematical astronomy of a century ago when Laplace showed that
+the mutual attractions of sun and planets might indeed produce endless
+perturbations in the motions and positions of these bodies, but could
+never bring about collisions among them or greatly alter their existing
+orbits. But in the proof of this great theorem two influences were
+neglected, either of which is fatal to its validity. One of these--tidal
+friction--as we have already seen, tends to wreck the systems of
+satellites, and the same effect must be produced upon the planets by any
+other influence which tends to impede their orbital motion. It is the
+inertia of the planet in its forward movement that balances the sun's
+attraction, and any diminution of the planet's velocity will give this
+attraction the upper hand and must ultimately precipitate the planet
+into the sun. The meteoric matter with which the earth comes ceaselessly
+into collision must have just this influence, although its effects are
+very small, and something of the same kind may come from the medium
+which transmits radiant energy through the interstellar spaces.
+
+It seems incredible that the luminiferous ether, which is supposed to
+pervade all space, should present absolutely no resistance to the motion
+of stars and planets rushing through it with velocities which in many
+cases exceed 50,000 miles per hour. If there is a resistance to this
+motion, however small, we may extend to the whole visible universe the
+words of Thomson and Tait, who say in their great Treatise on Natural
+Philosophy, "We have no data in the present state of science for
+estimating the relative importance of tidal friction and of the
+resistance of the resisting medium through which the earth and moon
+move; but, whatever it may be, there can be but one ultimate result for
+such a system as that of the sun and planets, if continuing long enough
+under existing laws and not disturbed by meeting with other moving
+masses in space. That result is the falling together of all into one
+mass, which, although rotating for a time, must in the end come to rest
+relatively to the surrounding medium."
+
+Compare with this the words of a great poet who in The Tempest puts into
+the mouth of Prospero the lines:
+
+    "The cloud-capp'd towers, the gorgeous palaces,
+    The solemn temples, the great globe itself,
+    Yea, all which it inherit, shall dissolve;
+    And, like this insubstantial pageant faded,
+    Leave not a rack behind."
+
+248. THE FUTURE.--In spite of statements like these, it lies beyond the
+scope of scientific research to affirm that the visible order of things
+will ever come to naught, and the outcome of present tendencies, as
+sketched above, may be profoundly modified in ages to come, by
+influences of which we are now ignorant. We have already noted that the
+farther our speculation extends into either past or future, the more
+insecure are its conclusions, and the remoter consequences of present
+laws are to be accepted with a corresponding reserve. But the one great
+fact which stands out clear in this connection is that of _change_. The
+old concept of a universe created in finished form and destined so to
+abide until its final dissolution, has passed away from scientific
+thought and is replaced by the idea of slow development. A universe
+which is ever becoming something else and is never finished, as shadowed
+forth by Goethe in the lines:
+
+    "Thus work I at the roaring loom of Time,
+    And weave for Deity a living robe sublime."
+
+
+
+
+APPENDIX
+
+
+THE GREEK ALPHABET
+
+The Greek letters are so much used by astronomers in connection with the
+names of the stars, and for other purposes, that the Greek alphabet is
+printed below--not necessarily to be learned, but for convenient
+reference:
+
+        Greek.          Name.  English.
+
+    [A]  [a]            Alpha    a
+
+    [B]  [b]            Beta     b
+
+    [G]  [g]            Gamma    g
+
+    [D]  [d]            Delta    d
+
+    [E]  [e] or [e]     Epsilon  [)e]
+
+    [Z]  [z]            Zeta      z
+
+    [Ź]  [ź]            Eta       [=e]
+
+    [Th]  [th] or [th]  Theta     th
+
+    [I]  [i]            Iota      i
+
+    [K]  [k]            Kappa     k
+
+    [L]  [l]            Lambda    l
+
+    [M]  [m]            Mu        m
+
+    [N]  [n]            Nu        n
+
+    [X]  [x]            Xi        x
+
+    [O]  [o]            Omicron   [)o]
+
+    [P]  [p]            Pi        p
+
+    [R]  [r]            Rho       r
+
+    [S]  [s] or [s]     Sigma     s
+
+    [T]  [t]            Tau       t
+
+    [Y]  [y]            Upsilon   u
+
+    [Ph]  [ph]          Phi       ph
+
+    [Ch]  [ch]          Chi       ch
+
+    [Ps]  [ps]          Psi       ps
+
+    [Ō]  [ō]            Omega     [=o]
+
+
+POPULAR LITERATURE OF ASTRONOMY
+
+The following brief bibliography, while making no pretense at
+completeness, may serve as a useful guide to supplementary reading:
+
+
+_General Treatises_
+
+YOUNG. _General Astronomy._ An admirable general survey of the entire
+field.
+
+NEWCOMB. _Popular Astronomy._ The second edition of a German translation
+of this work by Engelmann and Vogel is especially valuable.
+
+BALL. _Story of the Heavens._ Somewhat easier reading than either of the
+preceding.
+
+CHAMBERS. _Descriptive Astronomy._ An elaborate but elementary work in
+three volumes.
+
+LANGLEY. _The New Astronomy._ Treats mainly of the physical condition of
+the celestial bodies.
+
+PROCTOR and RANYARD. _Old and New Astronomy._
+
+
+_Special Treatises_
+
+PROCTOR. _The Moon._ A general treatment of the subject.
+
+NASMYTH and CARPENTER. _The Moon._ An admirably illustrated but
+expensive work dealing mainly with the topography and physical
+conditions of the moon. There is a cheaper and very good edition in
+German.
+
+YOUNG. _The Sun._ International Scientific Series. The most recent and
+authoritative treatise on this subject.
+
+PROCTOR. _Other Worlds than Ours._ An account of planets, comets, etc.
+
+NEWTON. _Meteor._ Encyclopędia Britannica.
+
+AIRY. _Gravitation._ A non-mathematical exposition of the laws of
+planetary motion.
+
+STOKES. _On Light as a Means of Investigation._ Burnett Lectures. II.
+The basis of spectrum analysis.
+
+SCHELLEN. _Spectrum Analysis._
+
+THOMSON (Sir W., Lord KELVIN), _Popular Lectures, etc._ Lectures on the
+Tides, The Sun's Heat, etc.
+
+BALL. _Time and Tide._ An exposition of the researches of G. H. Darwin
+upon tidal friction.
+
+GORE. _The Visible Universe._ Deals with a class of problems
+inadequately treated in most popular astronomies.
+
+DARWIN. _The Tides._ An admirable elementary exposition.
+
+CLERKE. _The System of the Stars._ Stellar astronomy.
+
+NEWCOMB. Chapters on the Stars, in _Popular Science Monthly_ for 1900.
+
+CLERKE. _History of Astronomy during the Nineteenth Century._ An
+admirable work.
+
+WOLF. _Geschichte der Astronomie._ München, 1877. An excellent German
+work.
+
+
+A LIST OF STARS FOR TIME OBSERVATIONS
+
+See § 20.
+
+ ------------------+---------------+------------------+-------------+
+ NAME.             |  Magnitude.   | Right Ascension. | Declination.|
+ ------------------+---------------+------------------+-------------+
+                   |               |                  |             |
+                   |               |     h. m.        |      °      |
+ [b] Ceti          |       2       |     0 38.6       |    - 18.5   |
+ [ź] Ceti          |       3       |     1  3.6       |    - 10.7   |
+ [a] Ceti          |       3       |     2 57.1       |    +  3.7   |
+ [g] Eridani       |       3       |     3 53.4       |    - 13.8   |
+ _Aldebaran_       |       1       |     4 30.2       |    + 16.3   |
+                   |               |                  |             |
+ _Rigel_           |       0       |     5  9.7       |    -  8.3   |
+ [k] Orionis       |       2       |     5 43.0       |    -  9.7   |
+ [b] Canis Majoris |       2       |     6 18.3       |    - 17.9   |
+ _Sirius_          |      -1       |     6 40.7       |    - 16.6   |
+ _Procyon_         |       0       |     7 34.1       |    +  5.5   |
+                   |               |                  |             |
+ [a] Hydrę         |       2       |     9 22.7       |    -  8.2   |
+ _Regulus_         |       1       |    10  3.0       |    + 12.5   |
+ [n] Hydrę         |       3       |    10 44.7       |    - 15.7   |
+ [e] Corvi         |       3       |    12  5.0       |    - 22.1   |
+ [g] Corvi         |       3       |    12 10.7       |    - 17.0   |
+                   |               |                  |             |
+ _Spica_           |       1       |    13 19.9       |    - 10.6   |
+ [z] Virginis      |       3       |    13 29.6       |    -  0.1   |
+ [a] Librę         |       3       |    14 45.3       |    - 15.6   |
+ [b] Librę         |       3       |    15 11.6       |    -  9.0   |
+ _Antares_         |       1       |    16 23.3       |    - 26.2   |
+                   |               |                  |             |
+ [a] Ophiuchi      |       2       |    17 30.3       |    + 12.6   |
+ [e] Sagittarii    |       2       |    18 17.5       |    - 34.4   |
+ [d] Aquilę        |       3       |    19 20.5       |    +  2.9   |
+ _Altair_          |       1       |    19 45.9       |    +  8.6   |
+ [b] Aquarii       |       3       |    21 26.3       |    -  6.0   |
+                   |               |                  |             |
+ [a] Aquarii       |       3       |    22  0.6       |    -  0.8   |
+ _Fomalhaut_       |       1       |    22 52.1       |    - 30.2   |
+ ------------------+---------------+------------------+-------------+
+
+
+
+
+INDEX
+
+
+The references are to section numbers.
+
+
+  Absorption of starlight, 225.
+
+  Absorption spectra, 87.
+
+  Accelerating force, 35.
+
+  Adjustment of observations, 2.
+
+  Albedo of moon, 97.
+    of Venus, 148.
+
+  Algol, 205.
+
+  Altitudes, 4, 21.
+
+  Andromeda nebula, 214.
+
+  Angles, measurement of, 2.
+
+  Angular diameter, 7.
+
+  Annular eclipse, 64.
+
+  Asteroids, 156.
+
+  Atmosphere of the earth, 49.
+    of the moon, 103.
+    of Jupiter, 139.
+    of Mars, 153.
+
+  Aurora, 51.
+
+  Azimuth, 5, 21.
+
+
+  Biela's comet, 181.
+
+  Bode's law, 134, 232.
+
+  Bredichin's theory of comet tails, 180.
+
+
+  Calendar, O. S. and N. S., 61.
+
+  Capture of comets and meteors, 176.
+
+  Canals of Mars, 154.
+
+  Celestial mechanics, 32.
+
+  Changes upon the moon, 108.
+
+  Chemical constitution of sun, 116.
+    of stars, 210.
+
+  Chromosphere, the sun's, 124.
+
+  Chronology, 59.
+
+  Classification of stars, 212.
+
+  Clocks and watches, 74.
+    sidereal clock, 12.
+
+  Collisions with comets, 183.
+
+  Colors of stars, 209.
+
+  Comets, general characteristics, 158-164.
+    development of, 179, 181.
+    groups, 177.
+    orbits, 161.
+    periodic, 176.
+    spectra, 182.
+    tails, 180.
+
+  Comets and meteors, relation of, 175.
+
+  Conic sections, 38.
+
+  Constellations, 184.
+
+  Corona, the sun's, 123.
+
+  Craters, lunar, 105.
+
+
+  Dark stars, 201.
+
+  Day, 52, 62.
+
+  Declination, 21.
+
+  Development of comet, 179.
+    of moon, 241.
+    of nebulę, 245.
+    of stars, 242, 244.
+    of sun, 228.
+  of universe, 226.
+
+  Distribution of stars and nebulę, 220.
+
+  Diurnal motion, 10, 15.
+
+  Doppler principle, 89.
+
+  Double nebulę, 215.
+
+  Double stars, 198.
+    development of, 244.
+
+  Driving clock, 80.
+
+
+  Earth, atmosphere, 48.
+    mass, 45.
+    size and shape, 44.
+    warming of the earth, 47.
+
+  Eclipses, nature of, 63.
+    annular eclipse, 64.
+    eclipse limits, 68.
+    eclipse maps, 70, 71.
+    number of, in a year, 69.
+    partial eclipse, 64.
+    prediction of, 70, 71.
+    recurrence of, 72.
+    shadow cone, 64, 66.
+    total eclipse, 64.
+    uses of, 73.
+
+  Eclipses of Jupiter's satellites, 141.
+
+  Eclipse theory of variable stars, 205.
+
+  Ecliptic, 26.
+    obliquity of, 25.
+
+  Ellipse, 33.
+
+  Epochs for planetary motion, 30.
+
+  Energy, radiant, 75.
+    condensation of, 76.
+
+  Epicycle, 32.
+
+  Equation of time, 53.
+
+  Equator, 16, 21.
+
+  Equatorial mounting, 80.
+
+  Equinoxes, 25.
+
+  Ether, 75.
+
+  Evening star, 31.
+
+
+  Faculę, 122.
+
+  Falling bodies, law of, 35.
+
+  Finding the stars, 14.
+
+  Fraunhofer lines, 87.
+
+
+  Galaxy, 219.
+
+  Geography of the sky, 16.
+
+  Graphical representation, 6.
+
+  Grating, diffraction, 84.
+
+  Gravitation, law of, 37.
+
+
+  Harvest moon, 93.
+
+  Heat of the sun, 118, 126.
+
+  Helmholtz, contraction theory of the sun, 126, 228.
+
+  Horizon, 4, 21.
+
+  Hour angle, 21.
+
+  Hour circle, 21.
+
+  Hyperbola, 38.
+
+
+  Japetus, satellite of Saturn, 145.
+
+  Jupiter, 136.
+    atmosphere, 139.
+    belts, 137.
+    invisible from fixed stars, 197.
+    orbit of, 29.
+    physical condition, 139.
+    rotation and flattening, 138.
+    satellites, 140.
+    surface markings, 137.
+
+
+  Kepler's laws, 33, 111.
+
+
+  Latitude, determination of, 18.
+
+  Leap year, 61.
+
+  Lenses, 77.
+
+  Leonid meteor shower, 172.
+    perturbations of, 174.
+
+  Librations of moon, 98.
+
+  Life upon the planets, 157.
+
+  Light curves, 205.
+
+  Light, nature of, 75.
+
+  Light year, 190.
+
+  Limits of eclipses, 68.
+
+  Longitude, 56.
+    determination of, 58.
+
+  Lunation, 60.
+
+
+  Magnifying power of telescope, 79.
+
+  Magnitude, stellar, 9, 186.
+
+  Mars, atmosphere, temperature, 150.
+    canals, 154.
+    orbit, 30.
+    polar caps, 152.
+    rotation, 151.
+    satellites, 155.
+    surface markings, 150.
+
+  Mass, determination of, 37.
+    of comets, 164.
+    of double stars, 200.
+    of moon, 94.
+    of planets, 40, 133.
+
+  Measurements, accurate, 1.
+
+  Mercury, 149.
+    motion of its perihelion, 43.
+    orbit of, 30.
+
+  Meridian, 19, 21.
+
+  Meteors, nature of, 165, 169.
+    number of, 167.
+    velocity, 170.
+
+  Meteors and comets, relation of, 175.
+
+  Meteor showers, radiant, 171.
+    Leonids, capture of, 172, 173.
+    perturbations, 174.
+
+  Milky Way, 219.
+
+  Mira, [o] Ceti, 204.
+
+  Mirrors, 77.
+
+  Month, 60.
+
+  Moon, 91.
+    albedo, 97.
+    atmosphere, 103.
+    changes in, 108.
+    density, surface gravity, 95.
+    development of, 241.
+    harvest moon, 93.
+    influence upon the earth, 109, 233.
+    librations, 98.
+    map of, 101.
+    mass and size, 94.
+    motion, 24, 92.
+    mountains and craters, 104.
+    phases, 91, 92.
+    physical condition, 100, 107.
+
+  Month, 60.
+
+  Morning star, 31.
+
+  Motion in line of sight, 89, 193.
+
+  Multiple stars, 202.
+
+
+  Names of stars, 8.
+
+  Nebulę, 214.
+    density, 217.
+    development of, 245.
+    motion, 218.
+    spectra, 216.
+    types and classes of, 215.
+
+  Nebular hypothesis, 230.
+    objections to, 231.
+
+  Neptune, 146.
+    discovery of, 41.
+
+  Newton's laws of motion, 34.
+    law of gravitation, 37, 43.
+
+  Nodes, 39.
+    relation to eclipses, 67, 71.
+
+  Nucleus, of comet, 160.
+
+
+  Objective, of telescope, 78.
+
+  Obliquity of ecliptic, 25.
+
+  Observations, of stars, 10.
+
+  Occultation of stars, 103.
+
+  Orbits, of comets, 161.
+    of double stars, 199.
+    of moon, 92.
+    of planets, 28.
+
+  Orion nebula, 215.
+
+
+  Parabola, 35, 38, 161.
+
+  Parabolic velocity, 38.
+
+  Parallax, 114, 188.
+
+  Penumbra, 64, 121.
+
+  Perihelion, 38.
+
+  Periodic comets, 176.
+
+  Personal equation, 82.
+
+  Perturbations, 39.
+    of meteors, 174.
+
+  Phases, of the moon, 91, 92.
+
+  Photography, 81.
+    of stars, 13.
+
+  Photosphere, of sun, 121.
+
+  Planets, 26, 133.
+    distances from the sun, 134.
+    how to find, 29.
+    mass, density, size, 133.
+    motion of, 27, 38.
+    periodic times of, 30.
+
+  Planetary nebulę, 215.
+
+  Pleiades, 16, 215.
+
+  Plumb-line apparatus, 11, 18.
+
+  Poles, 21.
+
+  Precession, 46.
+
+  Prisms, 84.
+
+  Problem of three bodies, 39.
+
+  Prominences, solar, 125.
+
+  Proper motions, 191.
+
+  Protractor, 2.
+
+  Ptolemaic system, 32.
+
+
+  Radiant energy, 75.
+
+  Radiant, of meteor shower, 171.
+
+  Radius victor, 33.
+
+  Reference lines and circles, 17.
+
+  Refraction, 50.
+
+  Right ascension, 16, 20, 21.
+
+  Roche's limit, 239.
+
+  Rotation, of earth, 55.
+    of Mars, 151.
+    of moon, 99.
+    of Jupiter, 138.
+    of Saturn, 144.
+    of sun, 120, 132.
+
+
+  Saros, 72.
+
+  Satellites, of Jupiter, 136, 140.
+    of Mars, 155.
+    of Saturn, 145.
+
+  Saturn, 142.
+    ball of, 144.
+    orbit, 29.
+    rings, 142.
+    rotation, 144.
+    satellites, 145.
+
+  Seasons, on the earth, 47.
+    on Mars, 151.
+
+  Shadow cone, 64, 66.
+
+  Sidereal time, 20, 54.
+
+  Shooting stars, 158. (See Meteor.)
+
+  Spectroscope, 84.
+
+  Spectroscopic binaries, 203.
+
+  Spectrum, 84, 87.
+    of comets, 182.
+    of nebulę, 216.
+    of stars, 211.
+    types of, 88.
+
+  Spectrum analysis, 85.
+
+  Spiral nebulę, 215.
+
+  Standard time, 57.
+
+  Stars, 8, 184.
+    classes of, 212.
+    clusters, 213.
+    colors, 209.
+    dark stars, 201.
+    development of, 242.
+    distances from the sun, 188, 196.
+    distribution of, 220.
+    double stars, 198, 203.
+    drift, 194.
+    magnitudes, 9, 196.
+    number of, 185.
+    spectra, 211.
+    temporary, 208.
+    variable, 204.
+
+  Starlight, absorption of, 225.
+
+  Star maps, construction of, 23.
+
+  Stellar system, extent of, 223.
+
+  Sun's apparent motion, 25.
+    real motion, 195.
+
+  Sun, 110.
+    chemical composition, 116.
+    chromosphere, 124.
+    corona, 123.
+    distance from the earth, 111.
+    faculę, 119, 122.
+    gaseous constitution, 127.
+    heat of, 117.
+    mechanism of, 126.
+    physical properties, 115-120.
+    prominences, 125.
+    rotation, 120, 132.
+    surface of, 119.
+    temperature, 118.
+
+  Sun spots, 119, 121.
+    period, 129, 131.
+    zones, 130.
+
+
+  Telescopes, 78.
+    equatorial mounting for, 80.
+    magnifying power of, 79.
+
+  Temperature of Jupiter, 139.
+    of Mars, 152.
+    of Mercury, 149.
+    of moon, 107.
+    of sun, 118.
+
+  Temporary stars, 208.
+
+  Terminator, 91.
+
+  Tenth meter, 75.
+
+  Tidal friction, 233-238.
+
+  Tides, 42.
+
+  Time, sidereal, 20, 54.
+    solar, 52.
+    determination of, 20.
+    equation of, 53.
+    standard, 57.
+
+  Triangulation, 3.
+
+  Trifid nebula, 215.
+
+  Twilight, 51.
+
+  Twinkling, of stars, 48.
+
+
+  Universe, development of, 226.
+    stability of, 247.
+
+  Uranus, 146.
+
+
+  Variable stars, 204.
+
+  Velocity, its relation to orbital motion, 38.
+
+  Venus, 148.
+    orbit of, 30.
+
+  Vernal equinox, 21, 25.
+
+  Vertical circle, 21.
+
+
+  Wave front, 76.
+
+  Wave lengths, 75, 86.
+
+
+  Year, 25.
+    leap year, 61.
+    sidereal year, 59.
+    tropical year, 60.
+
+
+  Zenith, 21.
+
+  Zodiac, 26.
+
+  Zodiacal light, 168.
+
+
+
+
+THE END
+
+
+
+
+
+
+
+End of Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock
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