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diff --git a/40240-8.txt b/40240-8.txt deleted file mode 100644 index 76e65f3..0000000 --- a/40240-8.txt +++ /dev/null @@ -1,14455 +0,0 @@ -The Project Gutenberg EBook of Letters on Astronomy, by Denison Olmsted - -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/license - - -Title: Letters on Astronomy - in which the Elements of the Science are Familiarly - Explained in Connection with Biographical Sketches of the - Most Eminent Astronomers - -Author: Denison Olmsted - -Release Date: July 15, 2012 [EBook #40240] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK LETTERS ON ASTRONOMY *** - - - - -Produced by David Starner, Mark Young and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - - - - -[Illustration PATH OF BIELA'S COMET.] - - - - -LETTERS - -ON - -ASTRONOMY, - - -IN WHICH THE - -ELEMENTS OF THE SCIENCE - -ARE - -FAMILIARLY EXPLAINED IN CONNECTION WITH BIOGRAPHICAL SKETCHES OF THE -MOST EMINENT ASTRONOMERS. - -WITH NUMEROUS ENGRAVINGS. - -BY DENISON OLMSTED, LL.D., - -PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE - -Revised Edition. - -INCLUDING THE LATEST DISCOVERIES. - -NEW YORK: HARPER & BROTHERS, PUBLISHERS, 329 & 331 PEARL STREET, -FRANKLIN SQUARE. - -1855. - - -Entered according to Act of Congress, in the year 1840, by - -MARSH, CAPEN, LYON, AND WEBB, - -in the Clerk's Office of the District Court of Massachusetts. - - - - -ADVERTISEMENT - -TO THE - -REVISED EDITION. - - -SINCE the first publication of these Letters, in 1840, the work has -passed through numerous editions, and received many tokens of public -favor, both as a class-book for schools and as a reading-book for the -family circle. The valuable discoveries made in the science within a few -years have suggested an additional Letter, which is accordingly annexed -to the series in the present revised form, giving a brief but -comprehensive notice of all the leading contributions with which -Astronomy has of late been enriched. - -The form of _Letters_ was chosen on account of the greater freedom it -admits, both of matter and of style, than a dress more purely -scientific. Thus the technical portion of the work, it was hoped, might -be relieved, and the whole rendered attractive to the youthful reader of -either sex by interspersing sketches of the master-builders who, in -successive ages, have reared the great temple of Astronomy, composing, -as they do, some of the most remarkable and interesting specimens of the -human race. - -The work was addressed to a female friend (now no more), who was a -distinguished ornament of her sex, and whose superior intellect and -refined taste required that the work should be free from every thing -superficial in matter or negligent in style; and it was deemed by the -writer no ordinary privilege that, in the composition of the work, an -image at once so exalted and so pure was continually present to his -mental vision. - - YALE COLLEGE, _January_, 1853. - - - - - CONTENTS. - - - PREFACE, 3 - - LETTER I. - - Introductory Observations, 9 - - LETTER II. - - Doctrine of the Sphere, 16 - - LETTER III. - - Astronomical Instruments.--Telescope, 29 - - LETTER IV. - - Telescope continued, 36 - - LETTER V. - - Observatories, 42 - - LETTER VI. - - Time and the Calendar, 59 - - LETTER VII. - - Figure of the Earth, 69 - - LETTER VIII. - - Diurnal Revolution, 81 - - LETTER IX. - - Parallax and Refraction, 89 - - LETTER X. - - The Sun, 101 - - LETTER XI. - - Annual Revolution.--Seasons, 111 - - LETTER XII. - - Laws of Motion, 126 - - LETTER XIII. - - Terrestrial Gravity, 134 - - LETTER XIV. - - Sir Isaac Newton.--Universal Gravitation.--Figure - of the Earth's Orbit.--Precession of the Equinoxes, 143 - - LETTER XV. - - The Moon, 157 - - LETTER XVI. - - The Moon.--Phases.--Harvest Moon.--Librations, 172 - - LETTER XVII. - - Moon's Orbit.--Her Irregularities, 180 - - LETTER XVIII. - - Eclipses, 195 - - LETTER XIX. - - Longitude.--Tides, 208 - - LETTER XX. - - Planets.--Mercury and Venus, 225 - - LETTER XXI. - - Superior Planets: Mars, Jupiter, Saturn, and Uranus, 243 - - LETTER XXII. - - Copernicus.--Galileo, 254 - - LETTER XXIII. - - Saturn.--Uranus.--Asteroids, 274 - - LETTER XXIV. - - The Planetary Motions.--Kepler's Laws.--Kepler, 291 - - LETTER XXV. - - Comets, 312 - - LETTER XXVI. - - Comets, 334 - - LETTER XXVII. - - Meteoric Showers, 346 - - LETTER XXVIII. - - Fixed Stars, 365 - - LETTER XXIX. - - Fixed Stars, 383 - - LETTER XXX. - - System of the World, 392 - - LETTER XXXI. - - Natural Theology, 406 - - LETTER XXXII. - - Recent Discoveries, 414 - - Index, 423 - - - - -LETTERS ON ASTRONOMY. - - - - -LETTER 1. - -INTRODUCTORY OBSERVATIONS. - - - "Ye sacred Muses, with whose beauty fired, - My soul is ravished, and my brain inspired, - Whose priest I am, whose holy fillets wear; - Would you your poet's first petition hear, - Give me the ways of wandering stars to know, - The depths of heaven above, and earth below; - Teach me the various labors of the moon, - And whence proceed th' eclipses of the sun; - Why flowing tides prevail upon the main, - And in what dark recess they shrink again; - What shakes the solid earth, what cause delays - The Summer nights, and shortens Winter days." - _Dryden's Virgil_ - -TO MRS. C---- M----. - -DEAR MADAM,--In the conversation we recently held on the study of -Astronomy, you expressed a strong desire to become better acquainted -with this noble science, but said you had always been repelled by the -air of severity which it exhibits, arrayed as it is in so many technical -terms, and such abstruse mathematical processes: or, if you had taken up -some smaller treatise, with the hope of avoiding these perplexities, you -had always found it so meager and superficial, as to afford you very -little satisfaction. You asked, if a work might not be prepared, which -would convey to the general reader some clear and adequate knowledge of -the great discoveries in astronomy, and yet require for its perusal no -greater preparation, than may be presumed of every well-educated English -scholar of either sex. - -You were pleased to add the request, that I would write such a work,--a -work which should combine, with a luminous exposition of the leading -truths of the science, some account of the interesting historical facts -with which it is said the records of astronomical discovery abound. -Having, moreover, heard much of the grand discoveries which, within the -last fifty years, have been made among the _fixed stars_, you expressed -a strong desire to learn more respecting these sublime researches. -Finally, you desired to see the argument for the existence and natural -attributes of the Deity, as furnished by astronomy, more fully and -clearly exhibited, than is done in any work which you have hitherto -perused. In the preparation of the proposed treatise, you urged me to -supply, either in the text or in notes, every _elementary principle_ -which would be essential to a perfect understanding of the work; for -although, while at school, you had paid some attention to geometry and -natural philosophy, yet so much time had since elapsed, that your memory -required to be refreshed on the most simple principles of these -elementary studies, and you preferred that I should consider you as -altogether unacquainted with them. - -Although, to satisfy a mind, so cultivated and inquisitive as yours, may -require a greater variety of powers and attainments than I possess, yet, -as you were pleased to urge me to the trial, I have resolved to make the -attempt, and will see how far I may be able to lead you into the -interior of this beautiful temple, without obliging you to force your -way through the "jargon of the schools." - -Astronomy, however, is a very difficult or a comparatively easy study, -according to the view we take of it. The investigation of the great laws -which govern the motions of the heavenly bodies has commanded the -highest efforts of the human mind; but profound truths, which it -required the mightiest efforts of the intellect to disclose, are often, -when once discovered, simple in their complexion, and may be expressed -in very simple terms. Thus, the creation of that element, on whose -mysterious agency depend all the forms of beauty and loveliness, is -enunciated in these few monosyllables, "And God said, let there be -light, and there was light;" and the doctrine of universal gravitation, -which is the key that unlocks the mysteries of the universe, is simply -this,--that every portion of matter in the universe tends towards every -other. The three great laws of motion, also, are, when stated, so plain, -that they seem hardly to assert any thing but what we knew before. That -all bodies, if at rest, will continue so, as is declared by the first -law of motion, until some force moves them; or, if in motion, will -continue so, until some force stops them, appears so much a matter of -course, that we can at first hardly see any good reason why it should be -dignified with the title of the first great law of motion; and yet it -contains a truth which it required profound sagacity to discover and -expound. - -It is, therefore, a pleasing consideration to those who have not either -the leisure of the ability to follow the astronomer through the -intricate and laborious processes, which conducted him to his great -discoveries, that they may fully avail themselves of the _results_ of -this vast toil, and easily understand truths which it required ages of -the severest labor to unfold. The descriptive parts of astronomy, or -what may be called the natural history of the heavens, is still more -easily understood than the laws of the celestial motions. The -revelations of the telescope, and the wonders it has disclosed in the -sun, in the moon, in the planets, and especially in the fixed stars, are -facts not difficult to be understood, although they may affect the mind -with astonishment. - -The great practical purpose of astronomy to the world is, enabling us -safely to navigate the ocean. There are indeed many other benefits which -it confers on man; but this is the most important. If, however, you ask, -what advantages the study of astronomy promises, as a branch of -education, I answer, that few subjects promise to the mind so much -profit and entertainment. It is agreed by writers on the human mind, -that the intellectual powers are enlarged and strengthened by the -habitual contemplation of great objects, while they are contracted and -weakened by being constantly employed upon little or trifling subjects. -The former elevate, the latter depress, the mind, to their own level. -Now, every thing in astronomy is great. The magnitudes, distances, and -motions, of the heavenly bodies; the amplitude of the firmament itself; -and the magnificence of the orbs with which it is lighted, supply -exhaustless materials for contemplation, and stimulate the mind to its -noblest efforts. The emotion felt by the astronomer is not that sudden -excitement or ecstasy, which wears out life, but it is a continued glow -of exalted feeling, which gives the sensation of breathing in a purer -atmosphere than others enjoy. We should at first imagine, that a study -which calls upon its votaries for the severest efforts of the human -intellect, which demands the undivided toil of years, and which robs the -night of its accustomed hours of repose, would abridge the period of -life; but it is a singular fact, that distinguished astronomers, as a -class, have been remarkable for longevity. I know not how to account for -this fact, unless we suppose that the study of astronomy itself has -something inherent in it, which sustains its votaries by a peculiar -aliment. - -It is the privilege of the student of this department of Nature, that -his cabinet is already collected, and is ever before him; and he is -exempted from the toil of collecting his materials of study and -illustration, by traversing land and sea, or by penetrating into the -depths of the earth. Nor are they in their nature frail and perishable. -No sooner is the veil of clouds removed, that occasionally conceals the -firmament by night, than his specimens are displayed to view, bright and -changeless. The renewed pleasure which he feels, at every new survey of -the constellations, grows into an affection for objects which have so -often ministered to his happiness. His imagination aids him in giving -them a personification, like that which the ancients gave to the -constellations; (as is evident from the names which they have -transmitted to us;) and he walks abroad, beneath the evening canopy, -with the conscious satisfaction and delight of being in the presence of -old friends. This emotion becomes stronger when he wanders far from -home. Other objects of his attachment desert him; the face of society -changes; the earth presents new features; but the same sun illumines the -day, the same moon adorns the night, and the same bright stars still -attend him. - -When, moreover, the student of the heavens can command the aid of -telescopes, of higher and higher powers, new acquaintances are made -every evening. The sight of each new member of the starry train, that -the telescope successively reveals to him, inspires a peculiar emotion -of pleasure; and he at length finds himself, whenever he sweeps his -telescope over the firmament, greeted by smiles, unperceived and unknown -to his fellow-mortals. The same personification is given to these -objects as to the constellations, and he seems to himself, at times, -when he has penetrated into the remotest depths of ether, to enjoy the -high prerogative of holding converse with the celestials. - -It is no small encouragement, to one who wishes to acquire a knowledge -of the heavens, that the subject is embarrassed with far less that is -technical than most other branches of natural history. Having first -learned a few definitions, and the principal circles into which, for -convenience, the sphere is divided, and receiving the great laws of -astronomy on the authority of the eminent persons who have investigated -them, you will find few hard terms, or technical distinctions, to repel -or perplex you; and you will, I hope, find that nothing but an -intelligent mind and fixed attention are requisite for perusing the -Letters which I propose to address to you. I shall indeed be greatly -disappointed, if the perusal does not inspire you with some portion of -that pleasure, which I have described as enjoyed by the astronomer -himself. - -The dignity of the study of the heavenly bodies, and its suitableness to -the most refined and cultivated mind, has been recognised in all ages. -Virgil celebrates it in the beautiful strains with which I have headed -this Letter, and similar sentiments have ever been cherished by the -greatest minds. - -As, in the course of these Letters, I propose to trace an outline of the -history of astronomy, from the earliest ages to the present time, you -may think this the most suitable place for introducing it; but the -successive discoveries in the science cannot be fully understood and -appreciated, until after an acquaintance has been formed with the -science itself. We must therefore reserve the details of this subject -for a future opportunity; but it may be stated, here, that astronomy was -cultivated the earliest of all the sciences; that great attention was -paid to it by several very ancient nations, as the Egyptians and -Chaldeans, and the people of India and China, before it took its rise in -Greece. More than six hundred years before the Christian era, however, -it began to be studied in this latter country. Thales and Pythagoras -were particularly distinguished for their devotion to this science; and -the celebrated school of Alexandria, in Egypt, which took its rise about -three hundred years before the Christian era, and flourished for several -hundred years, numbered among its disciples a succession of eminent -astronomers, among whom were Hipparchus, Eratosthenes, and Ptolemy. The -last of these composed a great work on astronomy, called the 'Almagest,' -in which is transmitted to us an account of all that was known of the -science by the Alexandrian school. The 'Almagest' was the principal -text-book in astronomy, for many centuries afterwards, and comparatively -few improvements were made until the age of Copernicus. Copernicus was -born at Thorn, in Prussia, in 1473. Previous to his time, the doctrine -was held, that the earth is at rest in the centre of the universe, and -that the sun, moon, and stars, revolve about it, every day, from east to -west; in short, that the _apparent_ motions of the heavenly bodies are -the same with their _real_ motions. But Copernicus expounded what is now -known to be the true theory of the celestial motions, in which the sun -is placed in the centre of the solar system, and the earth and all the -planets are made to revolve around him, from west to east, while the -apparent diurnal motion of the heavenly bodies, from east to west, is -explained by the revolution of the earth on its axis, in the same time, -from west to east; a motion of which we are unconscious, and which we -erroneously ascribe to external objects, as we imagine the shore is -receding from us, when we are unconscious of the motion of the ship that -carries us from it. - -Although many of the appearances, presented by the motions of the -heavenly bodies, may be explained on the former erroneous hypothesis, -yet, like other hypotheses founded in error, it was continually leading -its votaries into difficulties, and blinding their minds to the -perception of truth. They had advanced nearly as far as it was -practicable to go in the wrong road; and the great and sublime -discoveries of modern times are owing, in no small degree, to the fact, -that, since the days of Copernicus, astronomers have been pursuing the -plain and simple path of truth, instead of threading their way through -the mazes of error. - -Near the close of the sixteenth century, Tycho Brahe, a native of -Sweden, but a resident of Denmark, carried astronomical observations -(which constitute the basis of all that is valuable in astronomy) to a -far greater degree of perfection than had ever been done before. Kepler, -a native of Germany, one of the greatest geniuses the world has ever -seen, was contemporary with Tycho Brahe, and was associated with him in -a part of his labors. Galileo, an Italian astronomer of great eminence, -flourished only a little later than Tycho Brahe. He invented the -telescope, and, both by his discoveries and reasonings, contributed -greatly to establish the true system of the world. Soon after the -commencement of the seventeenth century, (1620,) Lord Bacon, a -celebrated English philosopher, pointed out the true method of -conducting all inquiries into the phenomena of Nature, and introduced -the _inductive method of philosophizing_. According to the inductive -method, we are to begin our inquiries into the causes of any events by -first examining and classifying all the _facts_ that relate to it, and, -from the comparison of these, to deduce our conclusions. - -But the greatest single discovery, that has ever been made in astronomy, -was the law of universal gravitation, a discovery made by Sir Isaac -Newton, in the latter part of the seventeenth century. The discovery of -this law made us acquainted with the hidden forces that move the great -machinery of the universe. It furnished the key which unlocks the inner -temple of Nature; and from this time we may regard astronomy as fixed on -a sure and immovable basis. I shall hereafter endeavor to explain to you -the leading principles of universal gravitation, when we come to the -proper place for inquiring into the causes of the celestial motions, as -exemplified in the motion of the earth around the sun. - - - - -LETTER II. - -DOCTRINE OF THE SPHERE. - - "All are but parts of one stupendous whole, - Whose body Nature is, and God the soul."--_Pope._ - - -LET us now consider what astronomy is, and into what great divisions it -is distributed; and then we will take a cursory view of the doctrine of -the sphere. This subject will probably be less interesting to you than -many that are to follow; but still, permit me to urge upon you the -necessity of studying it with attention, and reflecting upon each -definition, until you fully understand it; for, unless you fully and -clearly comprehend the circles of the sphere, and the use that is made -of them in astronomy, a mist will hang over every subsequent portion of -the science. I beg you, therefore, to pause upon every paragraph of this -Letter; and if there is any point in the whole which you cannot clearly -understand, I would advise you to mark it, and to recur to it -repeatedly; and, if you finally cannot obtain a clear idea of it -yourself, I would recommend to you to apply for aid to some of your -friends, who may be able to assist you. - -_Astronomy is that science which treats of the heavenly bodies._ More -particularly, its object is to teach what is known respecting the sun, -moon, planets, comets, and fixed stars; and also to explain the methods -by which this knowledge is acquired. Astronomy is sometimes divided into -descriptive, physical, and practical. Descriptive astronomy respects -_facts_; physical astronomy, _causes_; practical astronomy, the _means -of investigating the facts_, whether by instruments or by calculation. -It is the province of descriptive astronomy to observe, classify, and -record, all the phenomena of the heavenly bodies, whether pertaining to -those bodies individually, or resulting from their motions and mutual -relations. It is the part of physical astronomy to explain the causes of -these phenomena, by investigating the general laws on which they depend; -especially, by tracing out all the consequences of the law of universal -gravitation. Practical astronomy lends its aid to both the other -departments. - -The definitions of the different lines, points, and circles, which are -used in astronomy, and the propositions founded upon them, compose the -_doctrine of the sphere_. Before these definitions are given, I must -recall to your recollection a few particulars respecting the method of -measuring angles. (See Fig. 1, page 18.) - -A line drawn from the centre to the circumference of a circle is called -a _radius_, as C D, C B, or C K. - -Any part of the circumference of a circle is called an _arc_, as A B, or -B D. - -An angle is measured by an arc included between two radii. Thus, in -Fig. 1, the angle contained between the two radii, C A and C B, that is, -the angle A C B, is measured by the arc A B. Every circle, it will be -recollected, is divided into three hundred and sixty equal parts, called -degrees; and any arc, as A B, contains a certain number of degrees, -according to its length. Thus, if the arc A B contains forty degrees, -then the opposite angle A C B is said to be an angle of forty degrees, -and to be measured by A B. But this arc is the same part of the smaller -circle that E F is of the greater. The arc A B, therefore, contains the -same number of degrees as the arc E F, and either may be taken as the -measure of the angle A C B. As the whole circle contains three hundred -and sixty degrees, it is evident, that the quarter of a circle, or -_quadrant_, contains ninety degrees, and that the semicircle A B D G -contains one hundred and eighty degrees. - -[Illustration Fig. 1.] - -The _complement_ of an arc, or angle, is what it wants of ninety -degrees. Thus, since A D is an arc of ninety degrees, B D is the -complement of A B, and A B is the complement of B D. If A B denotes a -certain number of degrees of latitude, B D will be the complement of the -latitude, or the colatitude, as it is commonly written. - -The _supplement_ of an arc, or angle, is what it wants of one hundred -and eighty degrees. Thus, B A is the supplement of G D B, and G D B is -the supplement of B A. If B A were twenty degrees of longitude, G D B, -its supplement, would be one hundred and sixty degrees. An angle is said -to be _subtended_ by the side which is opposite to it. Thus, in the -triangle A C K, the angle at C is subtended by the side A K, the angle -at A by C K, and the angle at K by C A. In like manner, a side is said -to be subtended by an angle, as A K by the angle at C. - -Let us now proceed with the doctrine of the sphere. - -A section of a sphere, by a plane cutting it in any manner, is a circle. -_Great circles_ are those which pass through the centre of the sphere, -and divide it into two equal hemispheres. _Small circles_ are such as do -not pass through the centre, but divide the sphere into two unequal -parts. The _axis_ of a circle is a straight line passing through its -centre at right angles to its plane. The _pole_ of a great circle is the -point on the sphere where its axis cuts through the sphere. Every great -circle has two poles, each of which is every where ninety degrees from -the great circle. All great circles of the sphere cut each other in two -points diametrically opposite, and consequently their points of section -are one hundred and eighty degrees apart. A great circle, which passes -through the pole of another great circle, cuts the latter at right -angles. The great circle which passes through the pole of another great -circle, and is at right angles to it, is called a _secondary_ to that -circle. The angle made by two great circles on the surface of the sphere -is measured by an arc of another great circle, of which the angular -point is the pole, being the arc of that great circle intercepted -between those two circles. - -In order to fix the position of any place, either on the surface of the -earth or in the heavens, both the earth and the heavens are conceived to -be divided into separate portions, by circles, which are imagined to cut -through them, in various ways. The earth thus intersected is called the -_terrestrial_, and the heavens the _celestial_, sphere. We must bear in -mind, that these circles have no existence in Nature, but are mere -landmarks, artificially contrived for convenience of reference. On -account of the immense distances of the heavenly bodies, they appear to -us, wherever we are placed, to be fixed in the same concave surface, or -celestial vault. The great circles of the globe, extended every way to -meet the concave sphere of the heavens, become circles of the celestial -sphere. - -The _horizon_ is the great circle which divides the earth into upper and -lower hemispheres, and separates the visible heavens from the invisible. -This is the _rational_ horizon. The _sensible_ horizon is a circle -touching the earth at the place of the spectator, and is bounded by the -line in which the earth and skies seem to meet. The sensible horizon is -parallel to the rational, but is distant from it by the semidiameter of -the earth, or nearly four thousand miles. Still, so vast is the distance -of the starry sphere, that both these planes appear to cut the sphere in -the same line; so that we see the same hemisphere of stars that we -should see, if the upper half of the earth were removed, and we stood on -the rational horizon. - -The poles of the horizon are the zenith and nadir. The _zenith_ is the -point directly over our heads; and the _nadir_, that directly under our -feet. The plumb-line (such as is formed by suspending a bullet by a -string) is in the axis of the horizon, and consequently directed towards -its poles. Every place on the surface of the earth has its own horizon; -and the traveller has a new horizon at every step, always extending -ninety degrees from him, in all directions. - -_Vertical circles_ are those which pass through the poles of the -horizon, (the zenith and nadir,) perpendicular to it. - -The _meridian_ is that vertical circle which passes through the north -and south points. - -The _prime vertical_ is that vertical circle which passes through the -east and west points. - -The _altitude_ of a body is its elevation above the horizon, measured on -a vertical circle. - -The _azimuth_ of a body is its distance, measured on the horizon, from -the meridian to a vertical circle passing through that body. - -The _amplitude_ of a body is its distance, on the horizon, from the -prime vertical to a vertical circle passing through the body. - -Azimuth is reckoned ninety degrees from either the north or south point; -and amplitude ninety degrees from either the east or west point. Azimuth -and amplitude are mutually complements of each other, for one makes up -what the other wants of ninety degrees. When a point is _on_ the -horizon, it is only necessary to count the number of degrees of the -horizon between that point and the meridian, in order to find its -azimuth; but if the point is _above_ the horizon, then its azimuth is -estimated by passing a vertical circle through it, and reckoning the -azimuth from the point where this circle cuts the horizon. - -The _zenith distance_ of a body is measured on a vertical circle passing -through that body. It is the complement of the altitude. - -The _axis of the earth_ is the diameter on which the earth is conceived -to turn in its diurnal revolution. The same line, continued until it -meets the starry concave, constitutes the _axis of the celestial -sphere_. - -The _poles of the earth_ are the extremities of the earth's axis: the -_poles of the heavens_, the extremities of the celestial axis. - -The _equator_ is a great circle cutting the axis of the earth at right -angles. Hence, the axis of the earth is the axis of the equator, and its -poles are the poles of the equator. The intersection of the plane of the -equator with the surface of the earth constitutes the _terrestrial_, and -its intersection with the concave sphere of the heavens, the -_celestial_, equator. The latter, by way of distinction, is sometimes -denominated the _equinoctial_. - -The secondaries to the equator,--that is, the great circles passing -through the poles of the equator,--are called _meridians_, because that -secondary which passes through the zenith of any place is the meridian -of that place, and is at right angles both to the equator and the -horizon, passing, as it does, through the poles of both. These -secondaries are also called _hour circles_ because the arcs of the -equator intercepted between them are used as measures of time. - -The _latitude_ of a place on the earth is its distance from the equator -north or south. The _polar distance_, or angular distance from the -nearest pole, is the complement of the latitude. - -The _longitude_ of a place is its distance from some standard meridian, -either east or west, measured on the equator. The meridian, usually -taken as the standard, is that of the Observatory of Greenwich, in -London. If a place is directly _on_ the equator, we have only to -inquire, how many degrees of the equator there are between that place -and the point where the meridian of Greenwich cuts the equator. If the -place is north or south of the equator, then its longitude is the arc of -the equator intercepted between the meridian which passes through the -place and the meridian of Greenwich. - -The _ecliptic_ is a great circle, in which the earth performs its annual -revolutions around the sun. It passes through the centre of the earth -and the centre of the sun. It is found, by observation, that the earth -does not lie with its axis at right angles to the plane of the ecliptic, -so as to make the equator coincide with it, but that it is turned about -twenty-three and a half degrees out of a perpendicular direction, making -an angle with the plane itself of sixty-six and a half degrees. The -equator, therefore, must be turned the same distance out of a -coincidence with the ecliptic, the two circles making an angle with each -other of twenty-three and a half degrees. It is particularly important -that we should form correct ideas of the ecliptic, and of its relations -to the equator, since to these two circles a great number of -astronomical measurements and phenomena are referred. - -The _equinoctial points_, or _equinoxes_, are the intersections of the -ecliptic and equator. The time when the sun crosses the equator, in -going northward, is called the _vernal_, and in returning southward, the -_autumnal_, equinox. The vernal equinox occurs about the twenty-first of -March, and the autumnal, about the twenty-second of September. - -The _solstitial points_ are the two points of the ecliptic most distant -from the equator. The times when the sun comes to them are called -_solstices_. The Summer solstice occurs about the twenty-second of June, -and the Winter solstice about the twenty-second of December. The -ecliptic is divided into twelve equal parts, of thirty degrees each, -called _signs_, which, beginning at the vernal equinox, succeed each -other, in the following order: - - 1. Aries, [Zodiac: Aries] - 2. Taurus, [Zodiac: Taurus] - 3. Gemini, [Zodiac: Gemini] - 4. Cancer, [Zodiac: Cancer] - 5. Leo, [Zodiac: Leo] - 6. Virgo, [Zodiac: Virgo] - 7. Libra, [Zodiac: Libra] - 8. Scorpio, [Zodiac: Scorpio] - 9. Sagittarius, [Zodiac: Sagittarius] - 10. Capricornus, [Zodiac: Capricornus] - 11. Aquarius, [Zodiac: Aquarius] - 12. Pisces. [Zodiac: Pisces] - -The mode of reckoning on the ecliptic is by signs, degrees, minutes, and -seconds. The sign is denoted either by its name or its number. Thus, one -hundred degrees may be expressed either as the tenth degree of Cancer, -or as 3s 10°. It will be found an advantage to repeat the signs in their -proper order, until they are well fixed in the memory, and to be able to -recognise each sign by its appropriate character. - -Of the various meridians, two are distinguished by the name of -_colures_. The _equinoctial colure_ is the meridian which passes through -the equinoctial points. From this meridian, right ascension and -celestial longitude are reckoned, as longitude on the earth is reckoned -from the meridian of Greenwich. The _solstitial colure_ is the meridian -which passes through the solstitial points. - -The position of a celestial body is referred to the equator by its right -ascension and declination. _Right ascension_ is the angular distance -from the vernal equinox measured on the equator. If a star is situated -_on_ the equator, then its right ascension is the number of degrees of -the equator between the star and the vernal equinox. But if the star is -north or south of the equator, then its right ascension is the number of -degrees of the equator, intercepted between the vernal equinox and that -secondary to the equator which passes through the star. _Declination_ is -the distance of a body from the equator measured on a secondary to the -latter. Therefore, right ascension and declination correspond to -terrestrial longitude and latitude,--right ascension being reckoned from -the equinoctial colure, in the same manner as longitude is reckoned from -the meridian of Greenwich. On the other hand, celestial longitude and -latitude are referred, not to the equator, but to the ecliptic. -_Celestial longitude_ is the distance of a body from the vernal equinox -measured on the ecliptic. _Celestial latitude_ is the distance from the -ecliptic measured on a secondary to the latter. Or, more briefly, -longitude is distance _on_ the ecliptic: latitude, distance _from_ the -ecliptic. The _north polar distance_ of a star is the complement of its -declination. - -_Parallels of latitude_ are small circles parallel to the equator. They -constantly diminish in size, as we go from the equator to the pole. The -_tropics_ are the parallels of latitude which pass through the -solstices. The northern tropic is called the tropic of Cancer; the -southern, the tropic of Capricorn. The _polar circles_ are the parallels -of latitude that pass through the poles of the ecliptic, at the distance -of twenty-three and a half degrees from the poles of the earth. - -The _elevation of the pole_ of the heavens above the horizon of any -place is always equal to the latitude of the place. Thus, in forty -degrees of north latitude we see the north star forty degrees above the -northern horizon; whereas, if we should travel southward, its elevation -would grow less and less, until we reached the equator, where it would -appear _in_ the horizon. Or, if we should travel northwards, the north -star would rise continually higher and higher, until, if we could reach -the pole of the earth, that star would appear directly over head. The -_elevation of the equator_ above the horizon of any place is equal to -the complement of the latitude. Thus, at the latitude of forty degrees -north, the equator is elevated fifty degrees above the southern horizon. - -The earth is divided into five zones. That portion of the earth which -lies between the tropics is called the _torrid zone_; that between the -tropics and the polar circles, the _temperate zones_; and that between -the polar circles and the poles, the _frigid zones_. - -The _zodiac_ is the part of the celestial sphere which lies about eight -degrees on each side of the ecliptic. This portion of the heavens is -thus marked off by itself, because all the planets move within it. - -After endeavoring to form, from the definitions, as clear an idea as we -can of the various circles of the sphere, we may next resort to an -artificial globe, and see how they are severally represented there. I do -not advise to _begin_ learning the definitions from the globe; the mind -is more improved, and a power of conceiving clearly how things are in -Nature is more effectually acquired, by referring every thing, at first, -to the grand sphere of Nature itself, and afterwards resorting to -artificial representations to aid our conceptions. We can get but a very -imperfect idea of a man from a profile cut in paper, unless we know the -original. If we are acquainted with the individual, the profile will -assist us to recall his appearance more distinctly than we can do -without it. In like manner, orreries, globes, and other artificial aids, -will be found very useful, in assisting us to form distinct conceptions -of the relations existing between the different circles of the sphere, -and of the arrangements of the heavenly bodies; but, unless we have -already acquired some correct ideas of these things, by contemplating -them as they are in Nature, artificial globes, and especially orreries, -will be apt to mislead us. - -I trust you will be able to obtain the use of a globe,[1] to aid you in -the study of the foregoing definitions, or doctrine of the sphere; but -if not, I would recommend the following easy device. To represent the -earth, select a large _apple_, (a melon, when in season, will be found -still better.) The eye and the stem of the apple will indicate the -position of the two poles of the earth. Applying the thumb and finger of -the left hand to the poles, and holding the apple so that the poles may -be in a north and south line, turn this globe from west to east, and its -motion will correspond to the diurnal movement of the earth. Pass a wire -or a knitting needle through the poles, and it will represent the _axis_ -of the sphere. A circle cut around the apple, half way between the -poles, will be the _equator_; and several other circles cut between the -equator and the poles, parallel to the equator, will represent -_parallels of latitude_; of which, two, drawn twenty-three and a half -degrees from the equator, will be the _tropics_, and two others, at the -same distance from the poles, will be the _polar circles_. A great -circle cut through the poles, in a north and south direction, will form -the _meridian_, and several other great circles drawn through the poles, -and of course perpendicularly to the equator, will be secondaries to the -equator, constituting meridians, or _hour circles_. A great circle cut -through the centre of the earth, from one tropic to the other, would -represent the _plane_ of the ecliptic; and consequently a line cut round -the apple where such a section meets the surface, will be the -terrestrial _ecliptic_. The points where this circle meets the tropics -indicate the position of the _solstices_; and its intersection with the -equator, that of the _equinoctial points_. - -The _horizon_ is best represented by a circular piece of pasteboard, cut -so as to fit closely to the apple, being movable upon it. When this -horizon is passed through the poles, it becomes the horizon of the -equator; when it is so placed as to coincide with the earth's equator, -it becomes the horizon of the poles; and in every other situation it -represents the horizon of a place on the globe ninety degrees every way -from it. Suppose we are in latitude forty degrees; then let us place our -movable paper parallel to our own horizon, and elevate the pole forty -degrees above it, as near as we can judge by the eye. If we cut a circle -around the apple, passing through its highest part, and through the east -and west points, it will represent the _prime vertical_. - -Simple as the foregoing device is, if you will take the trouble to -construct one for yourself, it will lead you to more correct views of -the doctrine of the sphere, than you would be apt to obtain from the -most expensive artificial globes, although there are many other useful -purposes which such globes serve, for which the apple would be -inadequate. When you have thus made a sphere for yourself, or, with an -artificial globe before you, if you have access to one, proceed to point -out on it the various arcs of azimuth and altitude, right ascension and -declination, terrestrial and celestial latitude and longitude,--these -last being referred to the equator on the earth, and to the ecliptic in -the heavens. - -When the circles of the sphere are well learned, we may advantageously -employ projections of them in various illustrations. By the _projection -of the sphere_ is meant a representation of all its parts on a plane. -The plane itself is called the plane of projection. Let us take any -circular ring, as a wire bent into a circle, and hold it in different -positions before the eye. If we hold it parallel to the face, with the -whole breadth opposite to the eye, we see it as an entire circle. If we -turn it a little sideways, it appears oval, or as an ellipse; and, as we -continue to turn it more and more round, the ellipse grows narrower and -narrower, until, when the edge is presented to the eye, we see nothing -but a line. Now imagine the ring to be near a perpendicular wall, and -the eye to be removed at such a distance from it, as not to distinguish -any interval between the ring and the wall; then the several figures -under which the ring is seen will appear to be inscribed on the wall, -and we shall see the ring as a circle, when perpendicular to a straight -line joining the centre of the ring and the eye, or as an ellipse, when -oblique to this line, or as a straight line, when its edge is towards -us. - -[Illustration: Fig. 2.] - -It is in this manner that the circles of the sphere are projected, as -represented in the following diagram, Fig. 2. Here, various circles are -represented as projected on the meridian, which is supposed to be -situated directly before the eye, at some distance from it. The horizon -H O, being perpendicular to the meridian, is seen edgewise, and -consequently is projected into a straight line. The same is the case -with the prime vertical Z N, with the equator E Q, and the several small -circles parallel to the equator, which represent the two tropics and the -two polar circles. In fact, all circles whatsoever, which are -perpendicular to the plane of projection, will be represented by -straight lines. But every circle which is perpendicular to the horizon, -except the prime vertical, being seen obliquely, as Z M N, will be -projected into an ellipse, one half only of which is seen,--the other -half being on the other side of the plane of projection. In the same -manner, P R P, an hour circle, is represented by an ellipse on the plane -of projection. - -FOOTNOTE: - -[1] A small pair of globes, that will answer every purpose required by -the readers of these Letters, may be had of the publishers of this Work, -at a price not exceeding ten dollars; or half that sum for a celestial -globe, which will serve alone for studying astronomy. - - - - -LETTER III. - -ASTRONOMICAL INSTRUMENTS.----TELESCOPE. - - "Here truths sublime, and sacred science charm, - Creative arts new faculties supply, - Mechanic powers give more than giant's arm, - And piercing optics more than eagle's eye; - Eyes that explore creation's wondrous laws, - And teach us to adore the great Designing Cause."--_Beattie_. - - -If, as I trust, you have gained a clear and familiar knowledge of the -circles and divisions of the sphere, and of the mode of estimating the -position of a heavenly body by its azimuth and altitude, or by its right -ascension and declination, or by its longitude and latitude, you will -now enter with advantage upon an account of those _instruments_, by -means of which our knowledge of astronomy has been greatly promoted and -perfected. - -The most ancient astronomers employed no instruments of observation, but -acquired their knowledge of the heavenly bodies by long-continued and -most attentive inspection with the naked eye. Instruments for measuring -angles were first used in the Alexandrian school, about three hundred -years before the Christian era. - -Wherever we are situated on the earth, we appear to be in the centre of -a vast sphere, on the concave surface of which all celestial objects are -inscribed. If we take any two points on the surface of the sphere, as -two stars, for example, and imagine straight lines to be drawn to them -from the eye, the angle included between these lines will be measured by -the arc of the sky contained between the two points. Thus, if D B H, -Fig. 3, page 30, represents the concave surface of the sphere, A, B, two -points on it, as two stars, and C A, C B, straight lines drawn from the -spectator to those points, then the angular distance between them is -measured by the arc A B, or the angle A C B. But this angle may be -measured on a much smaller circle, having the same centre, as G F K, -since the arc E F will have the same number of degrees as the arc A B. -The simplest mode of taking an angle between two stars is by means of an -arm opening at a joint like the blade of a penknife, the end of the arm -moving like C E upon the graduated circle K F G. In fact, an instrument -constructed on this principle, resembling a carpenter's rule with a -folding joint, with a semicircle attached, constituted the first rude -apparatus for measuring the angular distance between two points on the -celestial sphere. Thus the sun's elevation above the horizon might be -ascertained, by placing one arm of the rule on a level with the horizon, -and bringing the edge of the other into a line with the sun's centre. - -[Illustration Fig. 3.] - -The common surveyor's compass affords a simple example of angular -measurement. Here, the needle lies in a north and south line, while the -circular rim of the compass, when the instrument is level, corresponds -to the horizon. Hence the compass shows the azimuth of an object, or how -many degrees it lies east or west of the meridian. - -It is obvious, that the larger the graduated circle is, the more -minutely its limb may be divided. If the circle is one foot in diameter, -each degree will occupy one tenth of an inch. If the circle is twenty -feet in diameter, a degree will occupy the space of two inches, and -could be easily divided into minutes, since each minute would cover a -space one thirtieth of an inch. Refined astronomical circles are now -divided with very great skill and accuracy, the spaces between the -divisions being, when read off, magnified by a microscope; but in former -times, astronomers had no mode of measuring small angles but by -employing very large circles. But the telescope and microscope enable us -at present to measure celestial arcs much more accurately than was done -by the older astronomers. In the best instruments, the measurements -extend to a single second of space, or one thirty-six hundredth part of -a degree,--a space, on a circle twelve feet in diameter, no greater than -one fifty-seven hundredth part of an inch. To divide, or _graduate_, -astronomical instruments, to such a degree of nicety, requires the -highest efforts of mechanical skill. Indeed, the whole art of -instrument-making is regarded as the most difficult and refined of all -the mechanical arts; and a few eminent artists, who have produced -instruments of peculiar power and accuracy, take rank with astronomers -of the highest celebrity. - -I will endeavor to make you acquainted with several of the principal -instruments employed in astronomical observations, but especially with -the telescope, which is the most important and interesting of them all. -I think I shall consult your wishes, as well as your improvement, by -giving you a clear insight into the principles of this prince of -instruments, and by reciting a few particulars, at least, respecting its -invention and subsequent history. - -The _Telescope_, as its name implies, is an instrument employed for -viewing distant objects.[2] It aids the eye in two ways; first, by -enlarging the visual angle under which objects are seen, and, secondly, -by collecting and conveying to the eye a much larger amount of the light -that emanates from the object, than would enter the naked pupil. A -complete knowledge of the telescope cannot be acquired, without an -acquaintance with the science of optics; but one unacquainted with that -science may obtain some idea of the leading principles of this noble -instrument. Its main principle is as follows: _By means of the -telescope, we first form an image of a distant object,--as the moon, for -example,--and then magnify that image by a microscope._ - -[Illustration Fig. 4.] - -Let us first see how the image is formed. This may be done either by a -convex lens, or by a concave mirror. A convex lens is a flat piece of -glass, having its two faces convex, or spherical, as is seen in a common -sun-glass, or a pair of spectacles. Every one who has seen a sun-glass, -knows, that, when held towards the sun, it collects the solar rays into -a small bright circle in the focus. This is in fact a small _image_ of -the sun. In the same manner, the image of any distant object, as a star, -may be formed, as is represented in the following diagram. Let A B C D, -Fig. 4, represent the tube of the telescope. At the front end, or at the -end which is directed towards the object, (which we will suppose to be -the moon,) is inserted a convex lens, L, which receives the rays of -light from the moon, and collects them into the focus at _a_, forming an -image of the moon. This image is viewed by a magnifier attached to the -end B C. The lens, L, is called the _object-glass_, and the microscope -in B C, the _eyeglass_. We apply a microscope to this image just as we -would to any object; and, by greatly enlarging its dimensions, we may -render its various parts far more distinct than they would otherwise be; -while, at the same time, the lens collects and conveys to the eye a much -greater quantity of light than would proceed directly from the body -under examination. A very few rays of light only, from a distant object, -as a star, can enter the eye directly; but a lens one foot in diameter -will collect a beam of light of the same dimensions, and convey it to -the eye. By these means, many obscure celestial objects become -distinctly visible, which would otherwise be either too minute, or not -sufficiently luminous, to be seen by us. - -But the image may also be formed by means of a _concave mirror_, which, -as well as the concave lens, has the property of collecting the rays of -light which proceed from any luminous body, and of forming an image of -that body. The image formed by a concave mirror is magnified by a -microscope, in the same manner as when formed by the concave lens. When -the lens is used to form an image, the instrument is called a -_refracting telescope_; when a concave mirror is used, it is called a -_reflecting telescope_. - -The office of the object-glass is simply _to collect_ the light, and to -form an _image_ of the object, but not to magnify it: the magnifying -power is wholly in the eyeglass. Hence the principle of the telescope is -as follows: _By means of the object-glass_, (in the refracting -telescope,) _or by the concave mirror_, (in the reflecting telescope,) -_we form an image of the object_, _and magnify that image by a -microscope_. - -The invention of this noble instrument is generally ascribed to the -great philosopher of Florence, Galileo. He had heard that a spectacle -maker of Holland had accidentally hit upon a discovery, by which distant -objects might be brought apparently nearer; and, without further -information, he pursued the inquiry, in order to ascertain what forms -and combinations of glasses would produce such a result. By a very -philosophical process of reasoning, he was led to the discovery of that -peculiar form of the telescope which bears his name. - -Although the telescopes made by Galileo were no larger than a common -spyglass of the kind now used on board of ships, yet, as they gave new -views of the heavenly bodies, revealing the mountains and valleys of -the moon, the satellites of Jupiter, and multitudes of stars which are -invisible to the naked eye, it was regarded with infinite delight and -astonishment. - -_Reflecting_ telescopes were first constructed by Sir Isaac Newton, -although the use of a concave reflector, instead of an object-glass, to -form the image, had been previously suggested by Gregory, an eminent -Scotch astronomer. The first telescope made by Newton was only six -inches long. Its reflector, too, was only a little more than an inch. -Notwithstanding its small dimensions, it performed so well, as to -encourage further efforts; and this illustrious philosopher afterwards -constructed much larger instruments, one of which, made with his own -hands, was presented to the Royal Society of London, and is now -carefully preserved in their library. - -Newton was induced to undertake the construction of reflecting -telescopes, from the belief that refracting telescopes were necessarily -limited to a very small size, with only moderate illuminating powers, -whereas the dimensions and powers of the former admitted of being -indefinitely increased. Considerable _magnifying_ powers might, indeed, -be obtained from refractors, by making them very long; but the -_brightness_ with which telescopic objects are seen, depends greatly on -the dimensions of the beam of light which is collected by the -object-glass, or by the mirror, and conveyed to the eye; and therefore, -small object-glasses cannot have a very high illuminating power. Now, -the experiments of Newton on colors led him to believe, that it would be -impossible to employ large lenses in the construction of telescopes, -since such glasses would give to the images, they formed, the colors of -the rainbow. But later opticians have found means of correcting these -imperfections, so that we are now able to use object-glasses a foot or -more in diameter, which give very clear and bright images. Such -instruments are called _achromatic_ telescopes,--a name implying the -absence of prismatic or rainbow colors in the image. It is, however, far -more difficult to construct large achromatic than large reflecting -telescopes. Very large pieces of glass can seldom be found, that are -sufficiently pure for the purpose; since every inequality in the glass, -such as waves, tears, threads, and the like, spoils it for optical -purposes, as it distorts the light, and produces nothing but confused -images. - -The achromatic telescope (that is, the refracting telescope, having such -an object-glass as to give a colorless image) was invented by Dollond, a -distinguished English artist, about the year 1757. He had in his -possession a quantity of glass of a remarkably fine quality, which -enabled him to carry his invention at once to a high degree of -perfection. It has ever since been, with the manufacturers of -telescopes, a matter of the greatest difficulty to find pieces of glass, -of a suitable quality for object-glasses, more than two or three inches -in diameter. Hence, large achromatic telescopes are very expensive, -being valued in proportion to the _cubes_ of their diameters; that is, -if a telescope whose aperture (as the breadth of the object-glass is -technically called) is two inches, cost one hundred dollars, one whose -aperture is eight inches would cost six thousand four hundred dollars. - -Since it is so much easier to make large reflecting than large -refracting telescopes, you may ask, why the latter are ever attempted, -and why reflectors are not exclusively employed? I answer, that the -achromatic telescope, when large and well constructed, is a more perfect -and more durable instrument than the reflecting telescope. Much more of -the light that falls on the mirror is absorbed than is lost in passing -through the object-glass of a refractor; and hence the larger achromatic -telescopes afford a stronger light than the reflecting, unless the -latter are made of an enormous and unwieldy size. Moreover, the mirror -is very liable to tarnish, and will never retain its full lustre for -many years together; and it is no easy matter to restore the lustre, -when once impaired. - -In my next Letter, I will give you an account of some of the most -celebrated telescopes that have ever been constructed, and point out the -method of using this excellent instrument, so as to obtain with it the -finest views of the heavenly bodies. - -FOOTNOTE: - -[2] From two Greek words, =tźle=, (_tele_,) _far_, and =schopeō=, -(_skopeo_,) _to see_. - - - - -LETTER IV - -TELESCOPE CONTINUED. - - ----"the broad circumference - Hung on his shoulders like the moon, whose orb - Through _optic glass_ the Tuscan artist views - At evening, from the top of Fesolé - Or in Valdarno, to descry new lands, - Rivers or mountains, in her spotted globe."--_Milton._ - - -The two most celebrated telescopes, hitherto made, are Herschel's -_forty-feet reflector_, and the _great Dorpat refractor_. Herschel was a -Hanoverian by birth, but settled in England in the younger part of his -life. As early as 1774, he began to make telescopes for his own use; -and, during his life, he made more than four hundred, of various sizes -and powers. Under the patronage of George the Third, he completed, in -1789, his great telescope, having a tube of iron, forty feet long, and a -speculum, forty-nine and a half inches or more than four feet in -diameter. Let us endeavor to form a just conception of this gigantic -instrument, which we can do only by dwelling on its dimensions, and -comparing them with those of other objects with which we are familiar, -as the length or height of a house, and the breadth of a hogshead or -cistern, of known dimensions. The reflector alone weighed nearly a ton. -So large and ponderous an instrument must require a vast deal of -machinery to work it, and to keep it steady; and, accordingly, the -framework surrounding it was formed of heavy timbers, and resembled the -frame of a large building. When one of the largest of the fixed stars, -as Sirius, is entering the field of this telescope, its approach is -announced by a bright dawn, like that which precedes the rising sun; and -when the star itself enters the field, the light is insupportable to the -naked eye. The planets are expanded into brilliant luminaries, like the -moon; and innumerable multitudes of stars are scattered like glittering -dust over the celestial vault. - -The great Dorpat telescope is of more recent construction. It was made -by Fraunhofer, a German optician of the greatest eminence, at Munich, in -Bavaria, and takes its name from its being attached to the observatory -at Dorpat, in Russia. It is of much smaller dimensions than the great -telescope of Herschel. Its object-glass is nine and a half inches in -diameter, and its length, fourteen feet. Although the price of this -instrument was nearly five thousand dollars, yet it is said that this -sum barely covered the actual expenses. It weighs five thousand pounds, -and yet is turned with the finger. In facility of management, it has -greatly the advantage of Herschel's telescope. Moreover, the sky of -England is so much of the time unfavorable for astronomical observation, -that _one hundred_ good hours (or those in which the higher powers can -be used) are all that can be obtained in a whole year. On this account, -and on account of the difficulty of shifting the position of the -instrument, Herschel estimated that it would take about six hundred -years to obtain with it even a momentary glimpse of every part of the -heavens. This remark shows that such great telescopes are unsuited to -the common purposes of astronomical observation. Indeed, most of -Herschel's discoveries were made with his small telescopes; and -although, for certain rare purposes, powers were applied which magnified -seven thousand times, yet, in most of his observations, powers -magnifying only two or three hundred times were employed. The highest -power of the Dorpat telescope is only seven hundred, and yet the -director of this instrument, Professor Struve, is of the opinion, that -it is nearly or quite equal in quality, all things considered, to -Herschel's forty-feet reflector. - -It is not generally understood in what way greatness of size in a -telescope increases its powers; and it conveys but an imperfect idea of -the excellence of a telescope, to tell how much it magnifies. In the -same instrument, an increase of magnifying power is always attended with -a diminution of the light and of the field of view. Hence, the lower -powers generally afford the most agreeable views, because they give the -clearest light, and take in the largest space. The several circumstances -which influence the qualities of a telescope are, illuminating power, -distinctness, field of view, and magnifying power. Large mirrors and -large object-glasses are superior to smaller ones, because they collect -a larger beam of light, and transmit it to the eye. Stars which are -invisible to the naked eye are rendered visible by the telescope, -because this instrument collects and conveys to the eye a large beam of -the few rays which emanate from the stars; whereas a beam of these rays -of only the diameter of the pupil of the eye, would afford too little -light for distinct vision. In this particular, large telescopes have -great advantages over small ones. The great mirror of Herschel's -forty-feet reflector collects and conveys to the eye a beam more than -four feet in diameter. The Dorpat telescope also transmits to the eye a -beam nine and one half inches in diameter. This seems small, in -comparison with the reflector; but much less of the light is lost on -passing through the glass than is absorbed by the mirror, and the mirror -is very liable to be clouded or tarnished; so that there is not so great -a difference in the two instruments, in regard to illuminating power, as -might be supposed from the difference of size. - -_Distinctness of view_ is all-important to the performance of an -instrument. The object may be sufficiently bright, yet, if the image is -distorted, or ill-defined, the illumination is of little consequence. -This property depends mainly on the skill with which all the -imperfections of figure and color in the glass or mirror are corrected, -and can exist in perfection only when the image is rendered completely -achromatic, and when all the rays that proceed from each point in the -object are collected into corresponding points of the image, -unaccompanied by any other rays. Distinctness is very much affected by -the _steadiness_ of the instrument. Every one knows how indistinct a -page becomes, when a book is passed rapidly backwards and forwards -before the eyes, and how difficult it is to read in a carriage in rapid -motion on a rough road. - -_Field of view_ is another important consideration. The finest -instruments exhibit the moon, for example, not only bright and distinct, -in all its parts, but they take in the whole disk at once; whereas, the -inferior instruments, when the higher powers, especially, are applied, -permit us to see only a small part of the moon at once. - -I hope, my friend, that, when you have perused these Letters, or rather, -while you are perusing them, you will have frequent opportunities of -looking through a good telescope. I even anticipate that you will -acquire such a taste for viewing the heavenly bodies with the aid of a -good glass, that you will deem a telescope a most suitable appendage to -your library, and as certainly not less an ornament to it than the more -expensive statues with which some people of fortune adorn theirs. I will -therefore, before concluding this letter, offer you a few _directions -for using the telescope_. - -Some states of weather, even when the sky is clear, are far more -favorable for astronomical observation than others. After sudden changes -of temperature in the atmosphere, the medium is usually very unsteady. -If the sun shines out warm after a cloudy season, the ground first -becomes heated, and the air that is nearest to it is expanded, and -rises, while the colder air descends, and thus ascending and descending -currents of air, mingling together, create a confused and wavy medium. -The same cause operates when a current of hot air rises from a chimney; -and hence the state of the atmosphere in cities and large towns is very -unfavorable to the astronomer, on this account, as well as on account -of the smoky condition in which it is usually found. After a long season -of dry weather, also, the air becomes smoky, and unfit for observation. -Indeed, foggy, misty, or smoky, air is so prevalent in some countries, -that only a very few times in the whole year can be found, which are -entirely suited to observation, especially with the higher powers; for -we must recollect, that these inequalities and imperfections are -magnified by telescopes, as well as the objects themselves. Thus, as I -have already mentioned, not more than one hundred good hours in a year -could be obtained for observation with Herschel's great telescope. By -_good_ hours, Herschel means that the sky must be very clear, the moon -absent, no twilight, no haziness, no violent wind, and no sudden change -of temperature. As a general fact, the warmer climates enjoy a much -finer sky for the astronomer than the colder, having many more clear -evenings, a short twilight, and less change of temperature. The watery -vapor of the atmosphere, also, is more perfectly dissolved in hot than -in cold air, and the more water air contains, provided it is in a state -of perfect solution, the clearer it is. - -A _certain preparation of the observer himself_ is also requisite for -the nicest observations with the telescope. He must be free from all -agitation, and the eye must not recently have been exposed to a strong -light, which contracts the pupil of the eye. Indeed, for delicate -observations, the observer should remain for some time beforehand in a -dark room, to let the pupil of the eye dilate. By this means, it will be -enabled to admit a larger number of the rays of light. In ascending the -stairs of an observatory, visitors frequently get out of breath, and -having perhaps recently emerged from a strongly-lighted apartment, the -eye is not in a favorable state for observation. Under these -disadvantages, they take a hasty look into the telescope, and it is no -wonder that disappointment usually follows. - -Want of steadiness is a great difficulty attending the use of the -highest magnifiers; for the motions of the instrument are magnified as -well as the object. Hence, in the structure of observatories, the -greatest pains is requisite, to avoid all tremor, and to give to the -instruments all possible steadiness; and the same care is to be -exercised by observers. In the more refined observations, only one or -two persons ought to be near the instrument. - -In general, _low powers_ afford better views of the heavenly bodies than -very high magnifiers. It may be thought absurd, to recommend the use of -low powers, in respect to large instruments especially, since it is -commonly supposed that the advantage of large instruments is, that they -will bear high magnifying powers. But this is not their only, nor even -their principal, advantage. A good light and large field are qualities, -for most purposes, more important than great magnifying power; and it -must be borne in mind, that, as we increase the magnifying power in a -given instrument, we diminish both the illumination and the field of -view. Still, different objects require different magnifying powers; and -a telescope is usually furnished with several varieties of powers, one -of which is best fitted for viewing the moon, another for Jupiter, and a -still higher power for Saturn. Comets require only the lowest -magnifiers; for here, our object is to command as much light, and as -large a field, as possible, while it avails little to increase the -dimensions of the object. On the other hand, for certain double stars, -(stars which appear single to the naked eye, but double to the -telescope,) we require very high magnifiers, in order to separate these -minute objects so far from each other, that the interval can be -distinctly seen. Whenever we exhibit celestial objects to inexperienced -observers, it is useful to precede the view with good _drawings_ of the -objects, accompanied by an explanation of what each appearance, -exhibited in the telescope, indicates. The novice is told, that -mountains and valleys can be seen in the moon by the aid of the -telescope; but, on looking, he sees a confused mass of light and shade, -and nothing which looks to him like either mountains or valleys. Had his -attention been previously directed to a plain drawing of the moon, and -each particular appearance interpreted to him, he would then have looked -through the telescope with intelligence and satisfaction. - - - - -LETTER V. - -OBSERVATORIES. - - "We, though from heaven remote, to heaven will move, - With strength of mind, and tread the abyss above; - And penetrate, with an interior light, - Those upper depths which Nature hid from sight. - Pleased we will be, to walk along the sphere - Of shining stars, and travel with the year."--_Ovid._ - - -An observatory is a structure fitted up expressly for astronomical -observations, and furnished with suitable instruments for that purpose. - -The two most celebrated observatories, hitherto built, are that of Tycho -Brahe, and that of Greenwich, near London. The observatory of Tycho -Brahe, Fig. 5, was constructed at the expense of the King of Denmark, in -a style of royal magnificence, and cost no less than two hundred -thousand crowns. It was situated on the island of Huenna, at the -entrance of the Baltic, and was called Uraniburg, or the palace of the -skies. - -Before I give you an account of Tycho's observatory, I will recite a few -particulars respecting this great astronomer himself. - -Tycho Brahe was of Swedish descent, and of noble family; but having -received his education at the University of Copenhagen, and spent a -large part of his life in Denmark, he is usually considered as a Dane, -and quoted as a Danish astronomer. He was born in the year 1546. When he -was about fourteen years old, there happened a great eclipse of the sun, -which awakened in him a high interest, especially when he saw how -[Illustration Fig. 5.] accurately all the circumstances of it answered -to the prediction with which he had been before made acquainted. He was -immediately seized with an irresistible passion to acquire a knowledge -of the science which could so successfully lift the veil of futurity. -His friends had destined him for the profession of law, and, from the -superior talents of which he gave early promise, and with the advantage -of powerful family connexions, they had marked out for him a -distinguished career in public life. They therefore endeavored to -discourage him from pursuing a path which they deemed so much less -glorious than that, and vainly sought, by various means, to extinguish -the zeal for astronomy which was kindled in his youthful bosom. -Despising all the attractions of a court, he contracted an alliance with -a peasant girl, and, in the peaceful retirement of domestic life, -desired no happier lot than to peruse the grand volume which the -nocturnal heavens displayed to his enthusiastic imagination. He soon -established his fame as one of the greatest astronomers of the age, and -monarchs did homage to his genius. The King of Denmark became his -munificent patron, and James the First, King of England, when he went to -Denmark to complete his marriage with a Danish Princess, passed eight -days with Tycho in his observatory, and, at his departure, addressed to -the astronomer a Latin ode, accompanied with a magnificent present. He -gave him also his royal license to print his works in England, and added -to it the following complimentary letter: "Nor am I acquainted with -these things on the relation of others, or from a mere perusal of your -works, but I have seen them with my own eyes, and heard them with my own -ears, in your residence at Uraniburg, during the various learned and -agreeable conversations which I there held with you, which even now -affect my mind to such a degree, that it is difficult to decide, whether -I recollect them with greater pleasure or admiration." Admiring -disciples also crowded to this sanctuary of the sciences, to acquire a -knowledge of the heavens. - -The observatory consisted of a main building, which was square, each -side being sixty feet, and of large wings in the form of round towers. -The whole was executed in a style of great magnificence, and Tycho, who -was a nobleman by descent, gratified his taste for splendor and -ornament, by giving to every part of the structure an air of the most -finished elegance. Nor were the instruments with which it was furnished -less magnificent than the buildings. They were vastly larger than had -before been employed in the survey of the heavens, and many of them were -adorned with costly ornaments. The cut on page 46, Fig. 6, represents -one of Tycho's large and splendid instruments, (an astronomical -quadrant,) on one side of which was figured a representation of the -astronomer and his assistants, in the midst of their instruments, and -intently engaged in making and recording observations. It conveys to us -a striking idea of the magnificence of his arrangements, and of the -extent of his operations. - -Here Tycho sat in state, clad in the robes of nobility, and supported -throughout his establishment the etiquette due to his rank. His -observations were more numerous than all that had ever been made before, -and they were carried to a degree of accuracy that is astonishing, when -we consider that they were made without the use of the telescope, which -was not yet invented. - -Tycho carried on his observations at Uraniburg for about twenty years, -during which time he accumulated an immense store of accurate and -valuable _facts_, which afforded the groundwork of the discovery of the -great laws of the solar system established by Kepler, of whom I shall -tell you more hereafter. - -But the high marks of distinction which Tycho enjoyed, not only from his -own Sovereign, but also from foreign potentates, provoked the envy of -the courtiers of his royal patron. They did not indeed venture to make -their attacks upon him while his generous patron was living; but the -King was no sooner dead, and succeeded by a young monarch, who did not -feel the same [Illustration Fig. 6.] interest in protecting and -encouraging this great ornament of the kingdom, than his envious foes -carried into execution their long-meditated plot for his ruin. They -represented to the young King, that the treasury was exhausted, and that -it was necessary to retrench a number of pensions, which had been -granted for useless purposes, and in particular that of Tycho, which, -they maintained, ought to be conferred upon some person capable of -rendering greater services to the state. By these means, they succeeded -in depriving him of his support, and he was compelled to retreat under -the hospitable mansion of a friend in Germany. Here he became known to -the Emperor, who invited him to Prague, where, with an ample stipend, he -resumed his labors. But, though surrounded with affectionate friends and -admiring disciples, he was still an exile in a foreign land. Although -his country had been base in its ingratitude, it was yet the land which -he loved; the scene of his earliest affection; the theatre of his -scientific glory. These feelings continually preyed upon his mind, and -his unsettled spirit was ever hovering among his native mountains. In -this condition he was attacked by a disease of the most painful kind, -and, though its agonizing paroxysms had lengthened intermissions, yet he -saw that death was approaching. He implored his pupils to persevere in -their scientific labors; he conversed with Kepler on some of the -profoundest points of astronomy; and with these secular occupations he -mingled frequent acts of piety and devotion. In this happy condition he -expired, without pain, at the age of fifty-five.[3] - -The observatory at Greenwich was not built until a hundred years after -that of Tycho Brahe, namely, in 1676. The great interests of the British -nation, which are involved in navigation, constituted the ruling motive -with the government to lend their aid in erecting and maintaining this -observatory. - -The site of the observatory at Greenwich is on a commanding eminence -facing the River Thames, five miles east of the central parts of London. -Being part of a royal park, the neighboring grounds are in no danger of -being occupied by buildings, so as to obstruct the view. It is also in -full view of the shipping on the Thames; and, according to a standing -regulation of the observatory, at the instant of one o'clock, every day, -a huge ball is dropped from over the house, as a signal to the -commanders of vessels for regulating their chronometers. - -The buildings comprise a series of rooms, of sufficient number and -extent to accommodate the different instruments, the inmates of the -establishment, and the library; and on the top is a celebrated camera -obscura, exhibiting a most distinct and perfect picture of the grand and -unrivalled scenery which this eminence commands. - -This establishment, by the accuracy and extent of its observations, has -contributed more than all other institutions to perfect the science of -astronomy. - -To preside over and direct this great institution, a man of the highest -eminence in the science is appointed by the government, with the title -of _Astronomer Royal_. He is paid an ample salary, with the -understanding that he is to devote himself exclusively to the business -of the observatory. The astronomers royal of the Greenwich observatory, -from the time of its first establishment, in 1676, to the present time, -have constituted a series of the proudest names of which British science -can boast. A more detailed sketch of their interesting history will be -given towards the close of these Letters. - -Six assistants, besides inferior laborers, are constantly in attendance; -and the business of making and recording observations is conducted with -the utmost system and order. - -The great objects to be attained in the construction of an observatory -are, a commanding and unobstructed view of the heavens; freedom from -causes that affect the transparency and uniform state of the -atmosphere, such as fires, smoke, or marshy grounds; mechanical -facilities for the management of instruments, and, especially, every -precaution that is necessary to secure perfect steadiness. This last -consideration is one of the greatest importance, particularly in the use -of very large magnifiers; for we must recollect, that any motion in the -instrument is magnified by the full power of the glass, and gives a -proportional unsteadiness to the object. A situation is therefore -selected as remote as possible from public roads, (for even the passing -of carriages would give a tremulous motion to the ground, which would be -sensible in large instruments,) and structures of solid masonry are -commenced deep enough in the ground to be unaffected by frost, and built -up to the height required, without any connexion with the other parts of -the building. Many observatories are furnished with a movable dome for a -roof, capable of revolving on rollers, so that instruments penetrating -through the roof may be easily brought to bear upon any point at or near -the zenith. - -You will not perhaps desire me to go into a minute description of all -the various instruments that are used in a well-constructed observatory. -Nor is this necessary, since a very large proportion of all astronomical -observations are taken on the meridian, by means of the transit -instrument and clock. When a body, in its diurnal revolution, comes to -the meridian, it is at its highest point above the horizon, and is then -least affected by refraction and parallax. This, then, is the most -favorable position for taking observations upon it. Moreover, it is -peculiarly easy to take observations on a body when in this situation. -Hence the transit instrument and clock are the most important members of -an astronomical observatory. You will, therefore, expect me to give you -some account of these instruments. - -[Illustration Fig. 7.] - -The _transit instrument_ is a telescope which is fixed permanently in -the meridian, and moves only in that plane. The accompanying diagram, -Fig. 7, represents a side view of a portable transit instrument, -exhibiting the telescope supported on a firm horizontal axis, on which -it turns in the plane of the meridian, from the south point of the -horizon through the zenith to the north point. It can therefore be so -directed as to observe the passage of a star across the meridian at any -altitude. The accompanying graduated circle enables the observer to set -the instrument at any required altitude, corresponding to the known -altitude at which the body to be observed crosses the meridian. Or it -may be used to measure the altitude of a body, or its zenith distance, -at the time of its meridian passage. Near the circle may be seen a -spirit-level, which serves to show when the axis is exactly on a level -with the horizon. The framework is made of solid metal, (usually brass,) -every thing being arranged with reference to keeping the instrument -perfectly steady. It stands on screws, which not only afford a steady -support, but are useful for adjusting the instrument to a perfect -level. The transit instrument is sometimes fixed immovably to a solid -foundation, as a pillar of stone, which is built up from a depth in the -ground below the reach of frost. When enclosed in a building, as in an -observatory, the stone pillar is carried up separate from the walls and -floors of the building, so as to be entirely free from the agitations to -which they are liable. - -The use of the transit instrument is to show the precise instant when a -heavenly body is on the meridian, or to measure the time it occupies in -crossing the meridian. The _astronomical clock_ is the constant -companion of the transit instrument. This clock is so regulated as to -keep exact pace with the stars, and of course with the revolution of the -earth on its axis; that is, it is regulated to _sidereal_ time. It -measures the progress of a star, indicating an hour for every fifteen -degrees, and twenty-four hours for the whole period of the revolution of -the star. Sidereal time commences when the vernal equinox is on the -meridian, just as solar time commences when the sun is on the meridian. -Hence the hour by the sidereal clock has no correspondence with the hour -of the day, but simply indicates how long it is since the equinoctial -point crossed the meridian. For example, the clock of an observatory -points to three hours and twenty minutes; this may be in the morning, at -noon, or any other time of the day,--for it merely shows that it is -three hours and twenty minutes since the equinox was on the meridian. -Hence, when a star is on the meridian, the clock itself shows its right -ascension, which you will recollect is the angular distance measured on -the equinoctial, from the point of intersection of the ecliptic and -equinoctial, called the vernal equinox, reckoning fifteen degrees for -every hour, and a proportional number of degrees and minutes for a less -period. I have before remarked, that a very large portion of all -astronomical observations are taken when the bodies are on the meridian, -by means of the transit instrument and clock. - -Having now described these instruments, I will next explain the manner -of using them for different observations. Any thing becomes a measure of -time, which divides duration equally. The equinoctial, therefore, is -peculiarly adapted to this purpose, since, in the daily revolution of -the heavens, equal portions of the equinoctial pass under the meridian -in equal times. The only difficulty is, to ascertain the amount of these -portions for given intervals. Now, the clock shows us exactly this -amount; for, when regulated to sidereal time, (as it easily may be,) the -hour-hand keeps exact pace with the equator, revolving once on the -dial-plate of the clock while the equator turns once by the revolution -of the earth. The same is true, also, of all the small circles of -diurnal revolution; they all turn exactly at the same rate as the -equinoctial, and a star situated any where between the equator and the -pole will move in its diurnal circle along with the clock, in the same -manner as though it were in the equinoctial. Hence, if we note the -interval of time between the passage of any two stars, as shown by the -clock, we have a measure of the number of degrees by which they are -distant from each other in right ascension. Hence we see how easy it is -to take arcs of right ascension: the transit instrument shows us when a -body is on the meridian; the clock indicates how long it is since the -vernal equinox passed it, which is the right ascension itself; or it -tells us the difference of right ascension between any two bodies, -simply by indicating the difference in time between their periods of -passing the meridian. Again, it is easy to take the _declination_ of a -body when on the meridian. By declination, you will recollect, is meant -the distance of a heavenly body from the equinoctial; the same, indeed, -as latitude on the earth. When a star is passing the meridian, if, on -the instant of crossing the meridian wire of the telescope, we take its -distance from the north pole, (which may readily be done, because the -position of the pole is always known, being equal to the latitude of the -place,) and subtract this distance from ninety degrees, the remainder -will be the distance from the equator, which is the declination. You -will ask, why we take this indirect method of finding the declination? -Why we do not rather take the distance of the star from the equinoctial, -at once? I answer, that it is easy to point an instrument to the north -pole, and to ascertain its exact position, and of course to measure any -distance from it on the meridian, while, as there is nothing to mark the -exact situation of the equinoctial, it is not so easy to take direct -measurements from it. When we have thus determined the situation of a -heavenly body, with respect to two great circles at right angles with -each other, as in the present case, the distance of a body from the -equator and from the equinoctial colure, or that meridian which passes -though the vernal equinox, we know its relative position in the heavens; -and when we have thus determined the relative positions of all the -stars, we may lay them down on a map or a globe, exactly as we do places -on the earth, by means of their latitude and longitude. - -The foregoing is only a _specimen_ of the various uses of the transit -instrument, in finding the relative places of the heavenly bodies. -Another use of this excellent instrument is, to regulate our clocks and -watches. By an observation with the transit instrument, we find when the -sun's centre is on the meridian. This is the exact time of _apparent_ -noon. But watches and clocks usually keep _mean_ time, and therefore, in -order to set our timepiece by the transit instrument, we must apply to -the apparent time of noon the equation of time, as will be explained in -my next Letter. - -A _noon-mark_ may easily be made by the aid of the transit instrument. A -window sill is frequently selected as a suitable place for the mark, -advantage being taken of the shadow projected upon it by the -perpendicular casing of the window. Let an assistant stand, with a rule -laid on the line of shadow, and with a knife ready to make the mark, the -instant when the observer at the transit instrument announces that the -centre of the sun is on the meridian. By a concerted signal, as the -stroke of a bell, the inhabitants of a town may all fix a noon-mark from -the same observation. If the signal be given on one of the days when -apparent time and mean time become equal to each other, as on the -twenty-fourth of December, no equation of time is required. - -As a noon-mark is convenient for regulating timepieces, I will point out -a method of making one, which may be practised without the aid of the -telescope. Upon a smooth, level plane, freely exposed to the sun, with a -pair of compasses describe a circle. In the centre, where the leg of the -compasses stood, erect a perpendicular wire of such a length, that the -termination of its shadow shall fall upon the circumference of the -circle at some hour before noon, as about ten o'clock. Make a small dot -at the point where the end of the shadow falls upon the circle, and do -the same where it falls upon it again in the afternoon. Take a point -half-way between these two points, and from it draw a line to the -centre, and it will be a true meridian line. The direction of this line -would be the same, whether it were made in the Summer or in the Winter; -but it is expedient to draw it about the fifteenth of June, for then the -shadow alters its length most rapidly, and the moment of its crossing -the wire will be more definite, than in the Winter. At this time of -year, also, the sun and clock agree, or are together, as will be more -fully explained in my next Letter; whereas, at other times of the year, -the time of noon, as indicated by a common clock, would not agree with -that indicated by the sun. If the upper end of the wire is flattened, -and a small hole is made in it, through which the sun may shine, the -instant when this bright spot falls upon the circle will be better -defined than the termination of the shadow. - -Another important instrument of the observatory is the _mural circle_. -It is a graduated circle, usually of very large size, fixed permanently -in the plane of the meridian, and attached firmly to a perpendicular -wall; and on its centre is a telescope, which revolves along with it, -and is easily brought to bear on any object in any point in the -meridian. It is made of large size, sometimes twenty feet in diameter, -in order that very small angles may be measured on its limb; for it is -obvious that a small angle, as one second, will be a larger space on the -limb of an instrument, in proportion as the instrument itself is larger. -The vertical circle usually connected with the transit instrument, as in -Fig. 7, may indeed be employed for the same purposes as the mural -circle, namely, to measure arcs of the meridian, as meridian altitudes, -zenith distances, north polar distances, and declinations; but as that -circle must necessarily be small, and therefore incapable of measuring -very minute angles, the mural circle is particularly useful in measuring -these important arcs. It is very difficult to keep so large an -instrument perfectly steady; and therefore it is attached to a massive -wall of solid masonry, and is hence called a _mural_ circle, from a -Latin word, (_murus_,) which signifies a wall. - -The diagram, Fig. 8, page 56, represents a mural circle fixed to its -wall, and ready for observations. It will be seen, that every expedient -is employed to give the instrument firmness of parts and steadiness of -position. The circle is of solid metal, usually of brass, and it is -strengthened by numerous radii, which keep it from warping or bending; -and these are made in the form of hollow cones, because that is the -figure which unites in the highest degree lightness and strength. On the -rim of the instrument, at A, you may observe a microscope. This is -attached to a micrometer,--a delicate piece of apparatus, used for -reading the minute subdivisions of angles; for, after dividing the limb -of the instrument as minutely as possible, it will then be necessary to -magnify those divisions with the microscope, and subdivide each of these -parts with the micrometer. Thus, if we have a mural circle twenty feet -in diameter, and of course nearly sixty-three feet in circumference, -since there are twenty-one thousand and six hundred minutes in the -whole circle, we shall find, by calculation, that one minute would -occupy, on the limb of such an instrument, only about one thirtieth of -an inch, and a second, only one eighteen hundredth of an inch. We could -not, therefore, hope to carry the actual divisions to a greater degree -of minuteness than minutes; but each of these spaces may again be -subdivided into seconds by the micrometer. - -[Illustration Fig. 8.] - -From these statements, you will acquire some faint idea of the extreme -difficulty of making perfect astronomical instruments, especially where -they are intended to measure such minute angles as one second. Indeed, -the art of constructing astronomical instruments is one which requires -such refined mechanical genius,--so superior a mind to devise, and so -delicate a hand to execute,--that the most celebrated instrument-makers -take rank with the most distinguished astronomers; supplying, as they -do, the means by which only the latter are enabled to make these great -discoveries. Astronomers have sometimes made their own telescopes; but -they have seldom, if ever, possessed the refined manual skill which is -requisite for graduating delicate instruments. - -The _sextant_ is also one of the most valuable instruments for taking -celestial arcs, or the distance between any two points on the celestial -sphere, being applicable to a much greater number of purposes than the -instruments already described. It is particularly valuable for measuring -celestial arcs at sea, because it is not, like most astronomical -instruments, affected by the motion of the ship. The principle of the -sextant may be briefly described, as follows: it gives the angular -distance between any two bodies on the celestial sphere, by reflecting -the image of one of the bodies so as to coincide with the other body, as -seen directly. The arc through which the reflector is turned, to bring -the reflected body to coincide with the other body, becomes a measure of -the angular distance between them. By keeping this principle in view, -you will be able to understand the use of the several parts of the -instrument, as they are exhibited in the diagram, Fig. 9, page 58. - -It is, you observe, of a triangular shape, and it is made strong and -firm by metallic cross-bars. It has two reflectors, I and H, called, -respectively, the index glass and the horizon glass, both of which are -firmly fixed perpendicular to the plane of the instrument. The index -glass is attached to the movable arm, ID, and turns as this is moved -along the graduated limb, EF. This arm also carries a _vernier_, at D, a -contrivance which, like the micrometer, enables us to take off minute -parts of the spaces into which the limb is divided. The horizon glass, -H, consists of two parts; the upper part being transparent or open, so -that the eye, looking through the telescope, T, can see through it a -distant body, as a star at S, while the lower part is a reflector. - -[Illustration Fig. 9.] - -Suppose it were required to measure the angular distance between the -moon and a certain star,--the moon being at M, and the star at S. The -instrument is held firmly in the hand, so that the eye, looking through -the telescope, sees the star, S, through the transparent part of the -horizon glass. Then the movable arm, ID, is moved from F towards E, -until the image of M is reflected down to S, when the number of degrees -and parts of a degree reckoned on the limb, from F to the index at D, -will show the angular distance between the two bodies. - -FOOTNOTE: - -[3] Brewster's Life of Newton - - - - -LETTER VI. - -TIME AND THE CALENDAR. - - "From old Eternity's mysterious orb - Was Time cut off, and cast beneath the skies."--_Young._ - - -HAVING hitherto been conversant only with the many fine and sentimental -things which the poets have sung respecting Old Time, perhaps you will -find some difficulty in bringing down your mind to the calmer -consideration of what time really is, and according to what different -standards it is measured for different purposes. You will not, however, -I think, find the subject even in our matter-of-fact and unpoetical way -of treating it, altogether uninteresting. What, then, is time? _Time is -a measured portion of indefinite duration._ It consists of equal -portions cut off from eternity, as a line on the surface of the earth is -separated from its contiguous portions that constitute a great circle of -the sphere, by applying to it a two-foot scale; or as a few yards of -cloth are measured off from a piece of unknown or indefinite extent. - -Any thing, or any event which takes place at equal intervals, may become -a measure of time. Thus, the pulsations of the wrist, the flowing of a -given quantity of sand from one vessel to another, as in the hourglass, -the beating of a pendulum, and the revolution of a star, have been -severally employed as measures of time. But the great standard of time -is the period of the revolution of the earth on its axis, which, by the -most exact observations, is found to be always the same. I have -anticipated a little of this subject, in giving an account of the -transit instrument and clock, but I propose, in this letter, to enter -into it more at large. - -The time of the earth's revolution on its axis, as already explained, is -called a sidereal day, and is determined by the revolution of a star in -the heavens. This interval is divided into twenty-four _sidereal_ -hours. Observations taken on numerous stars, in different ages of the -world, show that they all perform their diurnal revolution in the same -time, and that their motion, during any part of the revolution, is -always uniform. Here, then, we have an exact measure of time, probably -more exact than any thing which can be devised by art. _Solar time_ is -reckoned by the apparent revolution of the sun from the meridian round -to the meridian again. Were the sun stationary in the heavens, like a -fixed star, the time of its apparent revolution would be equal to the -revolution of the earth on its axis, and the solar and the sidereal days -would be equal. But, since the sun passes from west to east, through -three hundred and sixty degrees, in three hundred and sixty-five and one -fourth days, it moves eastward nearly one degree a day. While, -therefore, the earth is turning round on its axis, the sun is moving in -the same direction, so that, when we have come round under the same -celestial meridian from which we started, we do not find the sun there, -but he has moved eastward nearly a degree, and the earth must perform so -much more than one complete revolution, before we come under the sun -again. Now, since we move, in the diurnal revolution, fifteen degrees in -sixty minutes, we must pass over one degree in four minutes. It takes, -therefore, four minutes for us to _catch up_ with the sun, after we have -made one complete revolution. Hence the solar day is about four minutes -longer than the sidereal; and if we were to reckon the sidereal day -twenty-four hours, we should reckon the solar day twenty-four hours four -minutes. To suit the purposes of society at large, however, it is found -more convenient to reckon the solar days twenty-four hours, and throw -the fraction into the sidereal day. Then, - - 24h. 4m. : 24h. :: 24h. : 23h. 56m. 4s. - -That is, when we reduce twenty-four hours and four minutes to -twenty-four hours, the same proportion will require that we reduce the -sidereal day from twenty-four hours to twenty-three hours fifty-six -minutes four seconds; or, in other words, a sidereal day is such a part -of a solar day. The solar days, however, do not always differ from the -sidereal by precisely the same fraction, since they are not constantly -of the same length. Time, as measured by the sun, is called _apparent -time_, and a clock so regulated as always to keep exactly with the sun, -is said to keep apparent time. _Mean time_ is time reckoned by the -_average_ length of all the solar days throughout the year. This is the -period which constitutes the _civil_ day of twenty-four hours, beginning -when the sun is on the lower meridian, namely, at twelve o'clock at -night, and counted by twelve hours from the lower to the upper meridian, -and from the upper to the lower. The _astronomical_ day is the apparent -solar day counted through the whole twenty-four hours, (instead of by -periods of twelve hours each, as in the civil day,) and begins at noon. -Thus it is now the tenth of June, at nine o'clock, A.M., according to -civil time; but we have not yet reached the tenth of June by -astronomical time, nor shall we, until noon to-day; consequently, it is -now June ninth, twenty-first hour of astronomical time. Astronomers, -since so many of their observations are taken on the meridian, are -always supposed to look towards the south. Geographers, having formerly -been conversant only with the northern hemisphere, are always understood -to be looking towards the north. Hence, left and right, when applied to -the astronomer, mean east and west, respectively; but to the geographer -the right is east, and the left, west. - -Clocks are usually regulated so as to indicate mean solar time; yet, as -this is an artificial period not marked off, like the sidereal day, by -any natural event, it is necessary to know how much is to be added to, -or subtracted from, the apparent solar time, in order to give the -corresponding mean time. The interval, by which apparent time differs -from mean time, is called the _equation of time_. If one clock is so -constructed as to keep exactly with the sun, going faster or slower, -according as the lengths of the solar days vary, and another clock is -regulated to mean time, then the difference of the two clocks, at any -period, would be the equation of time for that moment. If the apparent -clock were _faster_ than the mean, then the equation of time must be -subtracted; but if the apparent clock were slower than the mean, then -the equation of time must be added, to give the mean time. The two -clocks would differ most about the third of November, when the apparent -time is sixteen and one fourth minutes greater than the mean. But since -apparent time is sometimes greater and sometimes less than mean time, -the two must obviously be sometimes equal to each other. This is, in -fact, the case four times a year, namely, April fifteenth, June -fifteenth, September first, and December twenty-fourth. - -Astronomical clocks are made of the best workmanship, with every -advantage that can promote their regularity. Although they are brought -to an astonishing degree of accuracy, yet they are not as regular in -their movements as the stars are, and their accuracy requires to be -frequently tested. The transit instrument itself, when once accurately -placed in the meridian, affords the means of testing the correctness of -the clock, since one revolution of a star, from the meridian to the -meridian again, ought to correspond exactly to twenty-four hours by the -clock, and to continue the same, from day to day; and the right -ascensions of various stars, as they cross the meridian, ought to be -such by the clock, as they are given in the tables, where they are -stated according to the accurate determinations of astronomers. Or, by -taking the difference of any two stars, on successive days, it will be -seen whether the going of the clock is uniform for that part of the day; -and by taking the right ascensions of different pairs of stars, we may -learn the rate of the clock at various parts of the day. We thus learn, -not only whether the clock accurately measures the length of the -sidereal day, but also whether it goes uniformly from hour to hour. - -Although astronomical clocks have been brought to a great degree of -perfection, so as hardly to vary a second for many months, yet none are -absolutely perfect, and most are so far from it, as to require to be -corrected by means of the transit instrument, every few days. Indeed, -for the nicest observations, it is usual not to attempt to bring the -clock to a state of absolute correctness, but, after bringing it as near -to such a state as can conveniently be done, to ascertain how much it -gains or loses in a day; that is, to ascertain the _rate_ of its going, -and to make allowance accordingly. - -Having considered the manner in which the smaller divisions of time are -measured, let us now take a hasty glance at the larger periods which -compose the calendar. - -As a _day_ is the period of the revolution of the earth on its axis, so -a _year_ is the period of the revolution of the earth around the sun. -This time, which constitutes the _astronomical year_, has been -ascertained with great exactness, and found to be three hundred and -sixty-five days five hours forty-eight minutes and fifty-one seconds. -The most ancient nations determined the number of days in the year by -means of the _stylus_, a perpendicular rod which casts its shadow on a -smooth plane bearing a meridian line. The time when the shadow was -shortest, would indicate the day of the Summer solstice; and the number -of days which elapsed, until the shadow returned to the same length -again, would show the number of days in the year. This was found to be -three hundred and sixty-five whole days, and accordingly, this period -was adopted for the civil year. Such a difference, however, between the -civil and astronomical years, at length threw all dates into confusion. -For if, at first, the Summer solstice happened on the twenty-first of -June, at the end of four years, the sun would not have reached the -solstice until the twenty-second of June; that is, it would have been -behind its time. At the end of the next four years, the solstice would -fall on the twenty-third; and in process of time, it would fall -successively on every day of the year. The same would be true of any -other fixed date. - -Julius Cęsar, who was distinguished alike for the variety and extent of -his knowledge, and his skill in arms, first attempted to make the -calendar conform to the motions of the sun. - - "Amidst the hurry of tumultuous war, - The stars, the gods, the heavens, were still his care." - -Aided by Sosigenes, an Egyptian astronomer, he made the first correction -of the calendar, by introducing an additional day every fourth year, -making February to consist of twenty-nine instead of twenty-eight days, -and of course the whole year to consist of three hundred and sixty-six -days. This fourth year was denominated _Bissextile_, because the sixth -day before the Kalends of March was reckoned twice. It is also called -Leap Year. - -The Julian year was introduced into all the civilized nations that -submitted to the Roman power, and continued in general use until the -year 1582. But the true correction was not six hours, but five hours -forty-nine minutes; hence the addition was too great by eleven minutes. -This small fraction would amount in one hundred years to three fourths -of a day, and in one thousand years to more than seven days. From the -year 325 to the year 1582, it had, in fact, amounted to more than ten -days; for it was known that, in 325, the vernal equinox fell on the -twenty-first of March, whereas, in 1582, it fell on the eleventh. It was -ordered by the Council of Nice, a celebrated ecclesiastical council, -held in the year 325, that Easter should be celebrated upon the first -Sunday after the first full moon, next following the vernal equinox; and -as certain other festivals of the Romish Church were appointed at -particular seasons of the year, confusion would result from such a want -of constancy between any fixed date and a particular season of the year. -Suppose, for example, a festival accompanied by numerous religious -ceremonies, was decreed by the Church to be held at the time when the -sun crossed the equator in the Spring, (an event hailed with great joy, -as the harbinger of the return of Summer,) and that, in the year 325, -March twenty-first was designated as the time for holding the festival, -since, at that period, it was on the twenty-first of March when the sun -reached the equinox; the next year, the sun would reach the equinox a -little sooner than the twenty-first of March, only eleven minutes, -indeed, but still amounting in twelve hundred years to ten days; that -is, in 1582, the sun reached the equinox on the eleventh of March. If, -therefore, they should continue to observe the twenty-first as a -religious festival in honor of this event, they would commit the -absurdity of celebrating it ten days after it had passed by. Pope -Gregory the Thirteenth, who was then at the head of the Roman See, was a -man of science, and undertook to reform the calendar, so that fixed -dates would always correspond to the same seasons of the year. He first -decreed, that the year should be brought forward ten days, by reckoning -the fifth of October the fifteenth; and, in order to prevent the -calendar from falling into confusion afterwards, he prescribed the -following rule: _Every year whose number is not divisible by four, -without a remainder, consists of three hundred and sixty-five days; -every year which is so divisible, but is not divisible by one hundred, -of three hundred and sixty-six; every year divisible by one hundred, but -not by four hundred, again, of three hundred and sixty-five; and every -year divisible by four hundred, of three hundred and sixty-six._ - -Thus the year 1838, not being divisible by four, contains three hundred -and sixty-five days, while 1836 and 1840 are leap years. Yet, to make -every fourth year consist of three hundred and sixty-six days would -increase it too much, by about three fourths of a day in a century; -therefore every hundredth year has only three hundred and sixty-five -days. Thus 1800, although divisible by four, was not a leap year, but a -common year. But we have allowed a _whole_ day in a hundred years, -whereas we ought to have allowed only _three fourths_ of a day. Hence, -in four hundred years, we should allow a day too much, and therefore, we -let the four hundredth remain a leap year. This rule involves an error -of less than a day in four thousand two hundred and thirty-seven years. - -The Pope, who, you will recollect, at that age assumed authority over -all secular princes, issued his decree to the reigning sovereigns of -Christendom, commanding the observance of the calendar as reformed by -him. The decree met with great opposition among the Protestant States, -as they recognised in it a new exercise of ecclesiastical tyranny; and -some of them, when they received it, made it expressly understood, that -their acquiescence should not be construed as a submission to the Papal -authority. - -In 1752, the Gregorian year, or _New Style_, was established in Great -Britain by act of Parliament; and the dates of all deeds, and other -legal papers, were to be made according to it. As above a century had -then passed since the first introduction of the new style, eleven days -were suppressed, the third of September being called the fourteenth. By -the same act, the beginning of the year was changed from March -twenty-fifth to January first. A few persons born previously to 1752 -have come down to our day, and we frequently see inscriptions on -tombstones of those whose time of birth is recorded in old style. In -order to make this correspond to our present mode of reckoning, we must -add eleven days to the date. Thus the same event would be June twelfth -of old style, or June twenty-third of new style; and if an event -occurred between January first and March twenty-fifth, the date of the -year would be advanced one, since February 1st, 1740, O.S. would be -February 1st, 1741, N.S. Thus, General Washington was born February -11th, 1731, O.S., or February 22d, 1732, N.S. If we inquire how any -present event may be made to correspond in date to the old style, we -must subtract twelve days, and put the year back one, if the event lies -between January first and March twenty-fifth. Thus, June tenth, N.S. -corresponds to May twenty-ninth, O.S.; and March 20th, 1840, to March -8th, 1839. France, being a Roman Catholic country, adopted the new style -soon after it was decreed by the Pope; but Protestant countries, as we -have seen, were much slower in adopting it; and Russia, and the Greek -Church generally, still adhere to the old style. In order, therefore, to -make the Russian dates correspond to ours, we must add to them twelve -days. - -It may seem to you very remarkable, that so much pains should have been -bestowed upon this subject; but without a correct and uniform standard -of time, the dates of deeds, commissions, and all legal papers; of fasts -and festivals, appointed by ecclesiastical authority; the returns of -seasons, and the records of history,--must all fall into inextricable -confusion. To change the observance of certain religious feasts, which -have been long fixed to particular days, is looked upon as an impious -innovation; and though the times of the events, upon which these -ceremonies depend, are utterly unknown, it is still insisted upon by -certain classes in England, that the Glastenbury thorn blooms on -Christmas day. - -Although the ancient Grecian calendar was extremely defective, yet the -common people were entirely averse to its reformation. Their -superstitious adherence to these errors was satirized by Aristophanes, -in his comedy of the Clouds. An actor, who had just come from Athens, -recounts that he met with Diana, or the moon, and found her extremely -incensed, that they did not regulate her course better. She complained, -that the order of Nature was changed, and every thing turned topsyturvy. -The gods no longer knew what belonged to them; but, after paying their -visits on certain feast-days, and expecting to meet with good cheer, as -usual, they were under the disagreeable necessity of returning back to -heaven without their suppers. - -Among the Greeks, and other ancient nations, the length of the year was -generally regulated by the course of the moon. This planet, on account -of the different appearances which she exhibits at her full, change, -and quarters, was considered by them as best adapted of any of the -celestial bodies for this purpose. As one lunation, or revolution of the -moon around the earth, was found to be completed in about twenty-nine -and one half days, and twelve of these periods being supposed equal to -one revolution of the sun, their months were made to consist of -twenty-nine and thirty days alternately, and their year of three hundred -and fifty-four days. But this disagreed with the annual revolution of -the sun, which must evidently govern the seasons of the year, more than -eleven days. The irregularities, which such a mode of reckoning would -occasion, must have been too obvious not to have been observed. For, -supposing it to have been settled, at any particular time, that the -beginning of the year should be in the Spring; in about sixteen years -afterwards, the beginning would have been in Autumn; and in thirty-three -or thirty-four years, it would have gone backwards through all the -seasons, to Spring again. This defect they attempted to rectify, by -introducing a number of days, at certain times, into the calendar, as -occasion required, and putting the beginning of the year forwards, in -order to make it agree with the course of the sun. But as these -additions, or _intercalations_, as they were called, were generally -consigned to the care of the priests, who, from motives of interest or -superstition, frequently omitted them, the year was made long or short -at pleasure. - -The _week_ is another division of time, of the highest antiquity, which, -in almost all countries, has been made to consist of seven days; a -period supposed by some to have been traditionally derived from the -creation of the world; while others imagine it to have been regulated by -the phases of the moon. The names, Saturday, Sunday, and Monday, are -obviously derived from Saturn, the Sun, and the Moon; while Tuesday, -Wednesday, Thursday, and Friday, are the days of Tuisco, Woden, Thor, -and Friga, which are Saxon names for Mars, Mercury, Jupiter, and -Venus.[4] - -The common year begins and ends on the same day of the week; but leap -year ends one day later than it began. Fifty-two weeks contain three -hundred and sixty-four days; if, therefore, the year begins on Tuesday, -for example, we should complete fifty-two weeks on Monday, leaving one -day, (Tuesday,) to complete the year, and the following year would begin -on Wednesday. Hence, any day of the month is one day later in the week, -than the corresponding day of the preceding year. Thus, if the sixteenth -of November, 1838, falls on Friday, the sixteenth of November, 1837, -fell on Thursday, and will fall, in 1839, on Saturday. But if leap year -begins on Sunday, it ends on Monday, and the following year begins on -Tuesday; while any given day of the month is two days later in the week -than the corresponding date of the preceding year. - -FOOTNOTE: - -[4] Bonnycastle's Astronomy. - - - - -LETTER VII. - -FIGURE OF THE EARTH. - - "He took the golden compasses, prepared - In God's eternal store, to circumscribe - This universe, and all created things; - One foot he centred, and the other turned - Round through the vast profundity obscure, - And said, 'Thus far extend, thus far thy bounds, - This be thy just circumference, O World!'"--_Milton._ - - -IN the earliest ages, the earth was regarded as one continued plane; -but, at a comparatively remote period, as five hundred years before the -Christian era, astronomers began to entertain the opinion that the earth -is round. We are able now to adduce various arguments which severally -prove this truth. First, when a ship is coming in from sea, we first -observe only the very highest parts of the ship, while the lower -portions come successively into view. Were the earth a continued plane, -the lower parts of the ship would be visible as soon as the higher, as -is evident from Fig. 10, page 70. - -[Illustration Fig. 10.] - -[Illustration Fig. 11.] - -Since light comes to the eye in straight lines, by which objects become -visible, it is evident, that no reason exists why the parts of the ship -near the water should not be seen as soon as the upper parts. But if the -earth be a sphere, then the line of sight would pass above the deck of -the ship, as is represented in Fig. 11; and as the ship drew nearer to -land, the lower parts would successively rise above this line and come -into view exactly in the manner known to observation. Secondly, in a -lunar eclipse, which is occasioned by the moon's passing through the -earth's shadow, the figure of the shadow is seen to be spherical, which -could not be the case unless the earth itself were round. Thirdly, -navigators, by steering continually in one direction, as east or west, -have in fact come round to the point from which they started, and thus -confirmed the fact of the earth's rotundity beyond all question. One may -also reach a given place on the earth, by taking directly opposite -courses. Thus, he may reach Canton in China, by a westerly route around -Cape Horn, or by an easterly route around the Cape of Good Hope. All -these arguments severally prove that the earth is round. - -But I propose, in this Letter, to give you some account of the unwearied -labors which have been performed to ascertain the _exact_ figure of the -earth; for although the earth is properly described in general language -as round, yet it is not an exact sphere. Were it so, all its diameters -would be equal; but it is known that a diameter drawn through the -equator exceeds one drawn from pole to pole, giving to the earth the -form of a _spheroid_,--a figure resembling an orange, where the ends are -flattened a little and the central parts are swelled out. - -Although it would be a matter of very rational curiosity, to investigate -the precise shape of the planet on which Heaven has fixed our abode, yet -the immense pains which has been bestowed on this subject has not all -arisen from mere curiosity. No accurate measurements can be taken of the -distances and magnitudes of the heavenly bodies, nor any exact -determinations made of their motions, without a knowledge of the exact -figure of the earth; and hence is derived a powerful motive for -ascertaining this element with all possible precision. - -The first satisfactory evidence that was obtained of the exact figure of -the earth was derived from reasoning on the effects of the earth's -_centrifugal force_, occasioned by its rapid revolution on its own axis. -When water is whirled in a pail, we see it recede from the centre and -accumulate upon the sides of the vessel; and when a millstone is whirled -rapidly, since the portions of the stone furthest from the centre -revolve much more rapidly than those near to it, their greater tendency -to recede sometimes makes them fly off with a violent explosion. A case, -which comes still nearer to that of the earth, is exhibited by a mass of -clay revolving on a potter's wheel, as seen in the process of making -earthen vessels. The mass swells out in the middle, in consequence of -the centrifugal force exerted upon it by a rapid motion. Now, in the -diurnal revolution, the equatorial parts of the earth move at the rate -of about one thousand miles per hour, while the poles do not move at -all; and since, as we take points at successive distances from the -equator towards the pole, the rate at which these points move grows -constantly less and less; and since, in revolving bodies, the -centrifugal force is proportioned to the velocity, consequently, those -parts which move with the greatest rapidity will be more affected by -this force than those which move more slowly. Hence, the equatorial -regions must be higher from the centre than the polar regions; for, were -not this the case, the waters on the surface of the earth would be -thrown towards the equator, and be piled up there, just as water is -accumulated on the sides of a pail when made to revolve rapidly. - -Huyghens, an eminent astronomer of Holland, who investigated the laws of -centrifugal forces, was the first to infer that such must be the actual -shape of the earth; but to Sir Isaac Newton we owe the full developement -of this doctrine. By combining the reasoning derived from the known laws -of the centrifugal force with arguments derived from the principles of -universal gravitation, he concluded that the distance through the earth, -in the direction of the equator, is greater than that in the direction -of the poles. He estimated the difference to be about thirty-four miles. - -But it was soon afterwards determined by the astronomers of France, to -ascertain the figure of the earth by actual measurements, specially -instituted for that purpose. Let us see how this could be effected. If -we set out at the equator and travel towards the pole, it is easy to see -when we have advanced one degree of latitude, for this will be indicated -by the rising of the north star, which appears in the horizon when the -spectator stands on the equator, but rises in the same proportion as he -recedes from the equator, until, on reaching the pole, the north star -would be seen directly over head. Now, were the earth a perfect sphere, -the meridian of the earth would be a perfect circle, and the distance -between any two places, differing one degree in latitude, would be -exactly equal to the distance between any other two places, differing in -latitude to the same amount. But if the earth be a spheroid, flattened -at the poles, then a line encompassing the earth from north to south, -constituting the terrestrial meridian, would not be a perfect circle, -but an ellipse or oval, having its longer diameter through the equator, -and its shorter through the poles. The part of this curve included -between two radii, drawn from the centre of the earth to the celestial -meridian, at angles one degree asunder, would be greater in the polar -than in the equatorial region; that is, the degrees of the meridian -would lengthen towards the poles. - -The French astronomers, therefore, undertook to ascertain by actual -measurements of arcs of the meridian, in different latitudes, whether -the degrees of the meridian are of uniform length, or, if not, in what -manner they differ from each other. After several indecisive -measurements of an arc of the meridian in France, it was determined to -effect simultaneous measurements of arcs of the meridian near the -equator, and as near as possible to the north pole, presuming that if -degrees of the meridian, in different latitudes, are really of different -lengths, they will differ most in points most distant from each other. -Accordingly, in 1735, the French Academy, aided by the government, sent -out two expeditions, one to Peru and the other to Lapland. Three -distinguished mathematicians, Bouguer, La Condamine, and Godin, were -despatched to the former place, and four others, Maupertius, Camus, -Clairault, and Lemonier, were sent to the part of Swedish Lapland which -lies at the head of the Gulf of Tornea, the northern arm of the Baltic. -This commission completed its operations several years sooner than the -other, which met with greater difficulties in the way of their -enterprise. Still, the northern detachment had great obstacles to -contend with, arising particularly from the extreme length and severity -of their Winters. The measurements, however, were conducted with care -and skill, and the result, when compared with that obtained for the -length of a degree in France, plainly indicated, by its greater amount, -a compression of the earth towards the poles. - -Mean-while, Bouguer and his party were prosecuting a similar work in -Peru, under extraordinary difficulties. These were caused, partly by the -localities, and partly by the ill-will and indolence of the inhabitants. -The place selected for their operations was in an elevated valley -between two principal chains of the Andes. The lowest point of their arc -was at an elevation of a mile and a half above the level of the sea; -and, in some instances, the heights of two neighboring signals differed -more than a mile. Encamped upon lofty mountains, they had to struggle -against storms, cold, and privations of every description, while the -invincible indifference of the Indians, they were forced to employ, was -not to be shaken by the fear of punishment or the hope of reward. Yet, -by patience and ingenuity, they overcame all obstacles, and executed -with great accuracy one of the most important operations, of this -nature, ever undertaken. To accomplish this, however, took them nine -years; of which, three were occupied in determining the latitudes -alone.[5] - -I have recited the foregoing facts, in order to give you some idea of -the unwearied pains which astronomers have taken to ascertain the exact -figure of the earth. You will find, indeed, that all their labors are -characterized by the same love of accuracy. Years of toilsome watchings, -and incredible labor of computation, have been undergone, for the sake -of arriving only a few seconds nearer to the truth. - -The length of a degree of the meridian, as measured in Peru, was less -than that before determined in France, and of course less than that of -Lapland; so that the spheroidal figure of the earth appeared now to be -ascertained by actual measurement. Still, these measures were too few in -number, and covered too small a portion of the whole quadrant from the -equator to the pole, to enable astronomers to ascertain the exact law of -curvature of the meridian, and therefore similar measurements have since -been prosecuted with great zeal by different nations, particularly by -the French and English. In 1764, two English mathematicians of great -eminence, Mason and Dixon, undertook the measurement of an arc in -Pennsylvania, extending more than one hundred miles. - -[Illustration Fig. 12.] - -[Illustration Fig. 13.] - -These operations are carried on by what is called a system of -_triangulation_. Without some knowledge of trigonometry, you will not be -able fully to understand this process; but, as it is in its nature -somewhat curious, and is applied to various other geographical -measurements, as well as to the determination of arcs of the meridian, I -am desirous that you should understand its general principles. Let us -reflect, then, that it must be a matter of the greatest difficulty, to -execute with exactness the measurement of a line of any great length in -one continued direction on the earth's surface. Even if we select a -level and open country, more or less inequalities of surface will occur; -rivers must be crossed, morasses must be traversed, thickets must be -penetrated, and innumerable other obstacles must be surmounted; and -finally, every time we apply an artificial measure, as a rod, for -example, we obtain a result not absolutely perfect. Each error may -indeed be very small, but small errors, often repeated, may produce a -formidable aggregate. Now, one unacquainted with trigonometry can easily -understand the fact, that, when we know certain parts of a triangle, we -can find the other parts by calculation; as, in the rule of three in -arithmetic, we can obtain the fourth term of a proportion, from having -the first three terms given. Thus, in the triangle A B C, Fig. 12, if we -know the side A B, and the angles at A and B, we can find by -computation, the other sides, A C and B C, and the remaining angle at C. -Suppose, then, that in measuring an arc of the meridian through any -country, the line were to pass directly through A B, but the ground was -so obstructed between A and B, that we could not possibly carry our -measurement through it. We might then measure another line, as A C, -which was accessible, and with a compass take the bearing of B from the -points A and C, by which means we should learn the value of the angles -at A and C. From these data we might calculate, by the rules of -trigonometry, the exact length of the line A B. Perhaps the ground might -be so situated, that we could not reach the point B, by any route; -still, if it could be seen from A and C, it would be all we should want. -Thus, in conducting a trigonometrical survey of any country, conspicuous -signals are placed on elevated points, and the bearings of these are -taken from the extremities of a known line, called the base, and thus -the relative situation of various places is accurately determined. Were -we to undertake to run an exact north and south line through any -country, as New England, we should select, near one extremity, a spot of -ground favorable for actual measurement, as a level, unobstructed plain; -we should provide a measure whose length in feet and inches was -determined with the greatest possible precision, and should apply it -with the utmost care. We should thus obtain a _base line_. From the -extremities of this line, we should take (with some appropriate -instrument) the bearing of some signal at a greater or less distance, -and thus we should obtain one side and two angles of a triangle, from -which we could find, by the rules of trigonometry, either of the unknown -sides. Taking this as a new base, we might take the bearing of another -signal, still further on our way, and thus proceed to run the required -north and south line, without actually measuring any thing more than the -first, or base line. Thus, in Fig. 13, we wish to measure the distance -between the two points A and O, which are both on the same meridian, as -is known by their having the same longitude; but, on account of various -obstacles, it would be found very inconvenient to measure this line -directly, with a rod or chain, and even if we could do it, we could not -by this method obtain nearly so accurate a result, as we could by a -series of triangles, where, after the base line was measured, we should -have nothing else to measure except angles, which can be determined, by -observation, to a greater degree of exactness, than lines. We therefore, -in the first place, measure the base line, A B, with the utmost -precision. Then, taking the bearing of some signal at C from A and B, we -obtain the means of calculating the side B C, as has been already -explained. Taking B C as a new base, we proceed, in like manner, to -determine successively the sides C D, D E, and E F, and also A C, and C -E. Although A C is not in the direction of the meridian, but -considerably to the east of it, yet it is easy to find the corresponding -distance on the meridian, A M; and in the same manner we can find the -portions of the meridian M N and N O, corresponding respectively to C E -and E F. Adding these several parts of the meridian together, we obtain -the length of the arc from A to O, in miles; and by observations on the -north star, at each extremity of the arc, namely, at A and at O, we -could determine the difference of latitude between these two points. -Suppose, for example, that the distance between A and O is exactly five -degrees, and that the length of the intervening line is three hundred -and forty-seven miles; then, dividing the latter by the former number, -we find the length of a degree to be sixty-nine miles and four tenths. -To take, however, a few of the results actually obtained, they are as -follows: - - Places of observation. Latitude. Length of a deg. - in miles. - Peru, 00° 00' 00" 68.732 - Pennsylvania, 39 12 00 68.896 - France, 46 12 00 69.054 - England, 51 29 54-1/2 69.146 - Sweden, 66 20 10 69.292 - -This comparison shows, that the length of a degree gradually increases, -as we proceed from the equator towards the pole. Combining the results -of various estimates, the dimensions of the terrestrial spheroid are -found to be as follows: - - Equatorial diameter, 7925.648 miles. - Polar diameter, 7899.170 " - Average diameter, 7912.409 " - -The difference between the greatest and the least is about twenty-six -and one half miles, which is about one two hundred and ninety-ninth part -of the greatest. This fraction is denominated the _ellipticity_ of the -earth,--being the excess of the equatorial over the polar diameter. - -The operations, undertaken for the purpose of determining the figure of -the earth, have been conducted with the most refined exactness. At any -stage of the process, the length of the last side, as obtained by -calculation, may be actually measured in the same manner as the base -from which the series of triangles commenced. When thus measured, it is -called the _base of verification_. In some surveys, the base of -verification, when taken at a distance of four hundred miles from the -starting point, has not differed more than one foot from the same line, -as determined by calculation. - -Another method of arriving at the exact figure of the earth is, by -observations with the _pendulum_. If a pendulum, like that of a clock, -be suspended, and the number of its vibrations per hour be counted, they -will be found to be different in different latitudes. A pendulum that -vibrates thirty-six hundred times per hour, at the equator, will vibrate -thirty-six hundred and five and two thirds times, at London, and a still -greater number of times nearer the north pole. Now, the vibrations of -the pendulum are produced by the force of gravity. Hence their -comparative number at different places is a measure of the relative -forces of gravity at those places. But when we know the relative forces -of gravity at different places, we know their relative distances from -the centre of the earth; because the nearer a place is to the centre of -the earth, the greater is the force of gravity. Suppose, for example, we -should count the number of vibrations of a pendulum at the equator, and -then carry it to the north pole, and count the number of vibrations made -there in the same time,--we should be able, from these two observations, -to estimate the relative forces of gravity at these two points; and, -having the relative forces of gravity, we can thence deduce their -relative distances from the centre of the earth, and thus obtain the -polar and equatorial diameters. Observations of this kind have been -taken with the greatest accuracy, in many places on the surface of the -earth, at various distances from each other, and they lead to the same -conclusions respecting the figure of the earth, as those derived from -measuring arcs of the meridian. It is pleasing thus to see a great -truth, and one apparently beyond the pale of human investigation, -reached by two routes entirely independent of each other. Nor, indeed, -are these the only proofs which have been discovered of the spheroidal -figure of the earth. In consequence of the accumulation of matter above -the equatorial regions of the earth, a body weighs less there than -towards the poles, being further removed from the centre of the earth. -The same accumulation of matter, by the force of attraction which it -exerts, causes slight inequalities in the motions of the moon; and since -the amount of these becomes a measure of the force which produces them, -astronomers are able, from these inequalities, to calculate the exact -quantity of the matter thus accumulated, and hence to determine the -figure of the earth. The result is not essentially different from that -obtained by the other methods. Finally, the shape of the earth's shadow -is altered, by its spheroidal figure,--a circumstance which affects the -time and duration of a lunar eclipse. All these different and -independent phenomena afford a pleasing example of the harmony of truth. -The known effects of the centrifugal force upon a body revolving on its -axis, like the earth, lead us to infer that the earth is of a spheroidal -figure; but if this be the fact, the pendulum ought to vibrate faster -near the pole than at the equator, because it would there be nearer the -centre of the earth. On trial, such is found to be the case. If, again, -there be such an accumulation of matter about the equatorial regions, -its effects ought to be visible in the motions of the moon, which it -would influence by its gravity; and there, also, its effects are traced. -At length, we apply our measures to the surface of the earth itself, and -find the same fact, which had thus been searched out among the hidden -things of Nature, here palpably exhibited before our eyes. Finally, on -estimating from these different sources, what the exact amount of the -compression at the poles must be, all bring out nearly one and the same -result. This truth, so harmonious in itself, takes along with it, and -establishes, a thousand other truths on which it rests. - -FOOTNOTE: - -[5] Library of Useful Knowledge: History of Astronomy, page 95. - - - - -LETTER VIII. - -DIURNAL REVOLUTIONS. - - "To some she taught the fabric of the sphere, - The changeful moon, the circuit of the stars, - The golden zones of heaven."--_Akenside._ - - -WITH the elementary knowledge already acquired, you will now be able to -enter with pleasure and profit on the various interesting phenomena -dependent on the revolution of the earth on its axis and around the sun. -The apparent diurnal revolution of the heavenly bodies, from east to -west, is owing to the actual revolution of the earth on its own axis, -from west to east. If we conceive of a radius of the earth's equator -extended until it meets the concave sphere of the heavens, then, as the -earth revolves, the extremity of this line would trace out a curve on -the face of the sky; namely, the celestial equator. In curves parallel -to this, called the _circles of diurnal revolution_, the heavenly bodies -actually _appear_ to move, every star having its own peculiar circle. -After you have first rendered familiar the real motion of the earth from -west to east, you may then, without danger of misapprehension, adopt the -common language, that all the heavenly bodies revolve around the earth -once a day, from east to west, in circles parallel to the equator and to -each other. - -I must remind you, that the time occupied by a star, in passing from any -point in the meridian until it comes round to the same point again, is -called a _sidereal day_, and measures the period of the earth's -revolution on its axis. If we watch the returns of the same star from -day to day, we shall find the intervals exactly equal to each other; -that is, _the sidereal days are all equal_. Whatever star we select for -the observation, the same result will be obtained. The stars, therefore, -always keep the same relative position, and have a common movement -round the earth,--a consequence that naturally flows from the hypothesis -that their _apparent_ motion is all produced by a single _real_ motion; -namely, that of the earth. The sun, moon, and planets, as well as the -fixed stars, revolve in like manner; but their returns to the meridian -are not, like those of the fixed stars, at exactly equal intervals. - -The _appearances_ of the diurnal motions of the heavenly bodies are -different in different parts of the earth,--since every place has its -own horizon, and different horizons are variously inclined to each -other. Nothing in astronomy is more apt to mislead us, than the -obstinate habit of considering the horizon as a fixed and immutable -plane, and of referring every thing to it. We should contemplate the -earth as a huge globe, occupying a small portion of space, and encircled -on all sides, at an immense distance, by the starry sphere. We should -free our minds from their habitual proneness to consider one part of -space as naturally _up_ and another _down_, and view ourselves as -subject to a force (gravity) which binds us to the earth as truly as -though we were fastened to it by some invisible cords or wires, as the -needle attaches itself to all sides of a spherical loadstone. We should -dwell on this point, until it appears to us as truly up, in the -direction B B, C C, D D, when one is at B, C, D, respectively, as in the -direction A A, when he is at A, Fig. 14. - -Let us now suppose the spectator viewing the diurnal revolutions from -several different positions on the earth. On the _equator_, his horizon -would pass through both poles; for the horizon cuts the celestial vault -at ninety degrees in every direction from the zenith of the spectator; -but the pole is likewise ninety degrees from his zenith, when he stands -on the equator; and consequently, the pole must be in the horizon. Here, -also, the celestial equator would coincide with the prime vertical, -being a great circle passing through the east and west points. Since all -the diurnal circles are parallel to the equator, consequently, they -would all, like the equator be perpendicular to the horizon. Such a -view of the heavenly bodies is called a right sphere, which may be thus -defined: _a right sphere is one in which all the daily revolutions of -the stars are in circles perpendicular to the horizon_. - -[Illustration Fig. 14.] - -A right sphere is seen only at the equator. Any star situated in the -celestial equator would appear to rise directly in the east, at midnight -to be in the zenith of the spectator, and to set directly in the west. -In proportion as stars are at a greater distance from the equator -towards the pole, they describe smaller and smaller circles, until, near -the pole, their motion is hardly perceptible. - -If the spectator advances one degree from the equator towards the north -pole, his horizon reaches one degree beyond the pole of the earth, and -cuts the starry sphere one degree below the pole of the heavens, or -below the north star, if that be taken as the place of the pole. As he -moves onward towards the pole, his horizon continually reaches further -and further beyond it, until, when he comes to the pole of the earth, -and under the pole of the heavens, his horizon reaches on all sides to -the equator, and coincides with it. Moreover, since all the circles of -daily motion are parallel to the equator, they become, to the spectator -at the pole, parallel to the horizon. Or, _a parallel sphere is that in -which all the circles of daily motion are parallel to the horizon_. - -To render this view of the heavens familiar, I would advise you to -follow round in mind a number of separate stars, in their diurnal -revolution, one near the horizon, one a few degrees above it, and a -third near the zenith. To one who stood upon the north pole, the stars -of the northern hemisphere would all be perpetually in view when not -obscured by clouds, or lost in the sun's light, and none of those of the -southern hemisphere would ever be seen. The sun would be constantly -above the horizon for six months in the year, and the remaining six -continually out of sight. That is, at the pole, the days and nights are -each six months long. The appearances at the south pole are similar to -those at the north. - -A perfect parallel sphere can never be seen, except at one of the -poles,--a point which has never been actually reached by man; yet the -British discovery ships penetrated within a few degrees of the north -pole, and of course enjoyed the view of a sphere nearly parallel. - -As the circles of daily motion are parallel to the horizon of the pole, -and perpendicular to that of the equator, so at all places between the -two, the diurnal motions are oblique to the horizon. This aspect of the -heavens constitutes an oblique sphere, which is thus defined: _an -oblique sphere is that in which the circles of daily motion are oblique -to the horizon_. - -Suppose, for example, that the spectator is at the latitude of fifty -degrees. His horizon reaches fifty degrees beyond the pole of the earth, -and gives the same apparent elevation to the pole of the heavens. It -cuts the equator and all the circles of daily motion, at an angle of -forty degrees,--being always equal to what the altitude of the pole -lacks of ninety degrees: that is, it is always equal to the co-altitude -of the pole. Thus, let H O, Fig. 15, represent the horizon, E Q the -equator, and P P“ the axis of the earth. Also, _l l, m m, n n_, -parallels of latitude. Then the horizon of a spectator at Z, in latitude -fifty degrees, reaches to fifty degrees beyond the pole; and the angle E -C H, which the equator makes with the horizon, is forty degrees,--the -complement of the latitude. As we advance still further north, the -elevation of the diurnal circle above the horizon grows less and less, -and consequently, the motions of the heavenly bodies more and more -oblique to the horizon, until finally, at the pole, where the latitude -is ninety degrees, the angle of elevation of the equator vanishes, and -the horizon and the equator coincide with each other, as before stated. - -[Illustration Fig. 15.] - -_The circle of perpetual apparition is the boundary of that space around -the elevated pole, where the stars never set._ Its distance from the -pole is equal to the latitude of the place. For, since the altitude of -the pole is equal to the latitude, a star, whose polar distance is just -equal to the latitude, will, when at its lowest point, only just reach -the horizon; and all the stars nearer the pole than this will evidently -not descend so far as the horizon. Thus _m m_, Fig. 15, is the circle of -perpetual apparition, between which and the north pole, the stars never -set, and its distance from the pole, O P, is evidently equal to the -elevation of the pole, and of course to the latitude. - -In the opposite hemisphere, a similar part of the sphere adjacent to the -depressed pole never rises. Hence, _the circle of perpetual occultation -is the boundary of that space around the depressed pole, within which -the stars never rise._ - -Thus _m“ m“_, Fig. 15, is the circle of perpetual occultation, between -which and the south pole, the stars never rise. - -In an oblique sphere, the horizon cuts the circles of daily motion -unequally. Towards the elevated pole, more than half the circle is above -the horizon, and a greater and greater portion, as the distance from the -equator is increased, until finally, within the circle of perpetual -apparition, the whole circle is above the horizon. Just the opposite -takes place in the hemisphere next the depressed pole. Accordingly, when -the sun is in the equator, as the equator and horizon, like all other -great circles of the sphere, bisect each other, the days and nights are -equal all over the globe. But when the sun is north of the equator, the -days become longer than the nights, but shorter, when the sun is south -of the equator. Moreover, the higher the latitude, the greater is the -inequality in the lengths of the days and nights. By examining Fig. 15, -you will easily see how each of these cases must hold good. - -Most of the appearances of the diurnal revolution can be explained, -either on the supposition that the celestial sphere actually turns -around the earth once in twenty-four hours, or that this motion of the -heavens is merely apparent, arising from the revolution of the earth on -its axis, in the opposite direction,--a motion of which we are -insensible, as we sometimes lose the consciousness of our own motion in -a ship or steam-boat, and observe all external objects to be receding -from us, with a common motion. Proofs, entirely conclusive and -satisfactory, establish the fact, that it is the earth, and not the -celestial sphere, that turns; but these proofs are drawn from various -sources, and one is not prepared to appreciate their value, or even to -understand some of them, until he has made considerable proficiency in -the study of astronomy, and become familiar with a great variety of -astronomical phenomena. To such a period we will therefore postpone the -discussion of the earth's rotation on its axis. - -While we retain the same place on the earth, the diurnal revolution -occasions no change in our horizon, but our horizon goes round, as well -as ourselves. Let us first take our station on the equator, at sunrise; -our horizon now passes through both the poles and through the sun, which -we are to conceive of as at a great distance from the earth, and -therefore as cut, not by the terrestrial, but by the celestial, horizon. -As the earth turns, the horizon dips more and more below the sun, at the -rate of fifteen degrees for every hour; and, as in the case of the polar -star, the sun appears to rise at the same rate. In six hours, therefore, -it is depressed ninety degrees below the sun, bringing us directly under -the sun, which, for our present purpose, we may consider as having all -the while maintained the same fixed position in space. The earth -continues to turn, and in six hours more, it completely reverses the -position of our horizon, so that the western part of the horizon, which -at sunrise was diametrically opposite to the sun, now cuts the sun, and -soon afterwards it rises above the level of the sun, and the sun sets. -During the next twelve hours, the sun continues on the invisible side of -the sphere, until the horizon returns to the position from which it set -out, and a new day begins. - -Let us next contemplate the similar phenomena at the _poles_. Here the -horizon, coinciding, as it does, with the equator, would cut the sun -through its centre and the sun would appear to revolve along the surface -of the sea, one half above and the other half below the horizon. This -supposes the sun in its annual revolution to be at one of the equinoxes. -When the sun is north of the equator, it revolves continually round in a -circle, which, during a single revolution, appears parallel to the -equator, and it is constantly day; and when the sun is south of the -equator, it is, for the same reason, continual night. - -When we have gained a clear idea of the appearances of the diurnal -revolutions, as exhibited to a spectator at the equator and at the pole, -that is, in a right and in a parallel sphere, there will be little -difficulty in imagining how they must be in the intermediate latitudes, -which have an oblique sphere. - -The appearances of the sun and stars, presented to the inhabitants of -different countries, are such as correspond to the sphere in which they -live. Thus, in the fervid climates of India, Africa, and South America, -the sun mounts up to the highest regions of the heavens, and descends -directly downwards, suddenly plunging beneath the horizon. His rays, -darting almost vertically upon the heads of the inhabitants, strike with -a force unknown to the people of the colder climates; while in places -remote from the equator, as in the north of Europe, the sun, in Summer, -rises very far in the north, takes a long circuit towards the south, and -sets as far northward in the west as the point where it rose on the -other side of the meridian. As we go still further north, to the -northern parts of Norway and Sweden, for example, to the confines of the -frigid zone, the Summer's sun just grazes the northern horizon, and at -noon appears only twenty-three and one half degrees above the southern. -On the other hand, in mid-winter, in the north of Europe, as at St. -Petersburgh, the day dwindles almost to nothing,--lasting only while the -sun describes a very short arc in the extreme south. In some parts of -Siberia and Iceland, the only day consists of a little glimmering of the -sun on the verge of the southern horizon, at noon. - - - - -LETTER IX. - -PARALLAX AND REFRACTION. - - "Go, wondrous creature! mount where science guides, - Go measure earth, weigh air, and state the tides; - Instruct the planets in what orbs to run, - Correct old Time, and regulate the sun."--_Pope._ - - -I THINK you must have felt some astonishment, that astronomers are able -to calculate the exact distances and magnitudes of the sun, moon, and -planets. We should, at the first thought, imagine that such knowledge as -this must be beyond the reach of the human faculties, and we might be -inclined to suspect that astronomers practise some deception in this -matter, for the purpose of exciting the admiration of the unlearned. I -will therefore, in the present Letter, endeavor to give you some clear -and correct views respecting the manner in which astronomers acquire -this knowledge. - -In our childhood, we all probably adopt the notion that the sky is a -real dome of definite surface, in which the heavenly bodies are fixed. -When any objects are beyond a certain distance from the eye, we lose all -power of distinguishing, by our sight alone, between different -distances, and cannot tell whether a given object is one million or a -thousand millions of miles off. Although the bodies seen in the sky are -in fact at distances extremely various,--some, as the clouds, only a few -miles off; others, as the moon, but a few thousand miles; and others, as -the fixed stars, innumerable millions of miles from us,--yet, as our eye -cannot distinguish these different distances, we acquire the habit of -referring all objects beyond a moderate height to one and the same -surface, namely, an imaginary spherical surface, denominated the -celestial vault. Thus, the various objects represented in the diagram on -next page, though differing very much in shape and diameter, would all -be _projected_ upon the sky alike, and compose a part, indeed, of the -imaginary vault itself. The place which each object occupies is -determined by lines drawn from the eye of the spectator through the -extremities of the body, to meet the imaginary concave sphere. Thus, to -a spectator at O, Fig 16, the several lines A B, C D, and E F, would all -be projected into arches on the face of the sky, and be seen as parts of -the sky itself, as represented by the lines A“ B“, C“ D“, and E“ F“. And -were a body actually to move in the several directions indicated by -these lines, they would appear to the spectator to describe portions of -the celestial vault. Thus, even when moving through the crooked line, -from _a_ to _b_, a body would appear to be moving along the face of the -sky, and of course in a regular curve line, from _c_ to _d_. - -[Illustration Fig. 16.] - -But, although all objects, beyond a certain moderate height, are -projected on the imaginary surface of the sky, yet different spectators -will project the same object on _different parts_ of the sky. Thus, a -spectator at A, Fig. 17, would see a body, C, at M, while a spectator at -B would see the same body at N. This change of place in a body, as seen -from different points, is called parallax, which is thus defined: -_parallax is the apparent change of place which bodies undergo by being -viewed from different points_. [Illustration Fig. 17.] - -The arc M N is called the _parallactic arc_, and the angle A C B, the -_parallactic angle_. - -It is plain, from the figure, that near objects are much more affected -by parallax than distant ones. Thus, the body C, Fig. 17, makes a much -greater parallax than the more distant body D,--the former being -measured by the arc M N, and the latter by the arc O P. We may easily -imagine bodies to be so distant, that they would appear projected at -very nearly the same point of the heavens, when viewed from places very -remote from each other. Indeed, the fixed stars, as we shall see more -fully hereafter, are so distant, that spectators, a hundred millions of -miles apart, see each star in one and the same place in the heavens. - -It is by means of parallax, that astronomers find the distances and -magnitudes of the heavenly bodies. In order fully to understand this -subject, one requires to know something of trigonometry, which science -enables us to find certain unknown parts of a triangle from certain -other parts which are known. Although you may not be acquainted with the -principles of trigonometry, yet you will readily understand, from your -knowledge of arithmetic, that from certain things given in a problem -others may be found. Every triangle has of course three sides and three -angles; and, if we know two of the angles and one of the sides, we can -find all the other parts, namely, the remaining angle and the two -unknown sides. Thus, in the triangle A B C, Fig. 18, if we know the -length of the side A B, and how many degrees each of the angles A B C -and B C A contains, we can find the length of the side B C, or of the -side A C, and the remaining angle at A. Now, let us apply these -principles to the measurements of some of the heavenly bodies. - -[Illustration Fig. 18.] - -[Illustration Fig. 19.] - -In Fig. 19, let A represent the earth, C H the horizon, and H Z a -quadrant of a great circle of the heavens, extending from the horizon to -the zenith; and let E, F, G, O, be successive positions of the moon, at -different elevations, from the horizon to the meridian. Now, a spectator -on the surface of the earth, at A, would refer the moon, when at E, to -_h_, on the face of the sky, whereas, if seen from the centre of the -earth, it would appear at H. So, when the moon was at F, a spectator at -A would see it at _p_, while, if seen from the centre, it would have -appeared at P. The parallactic arcs, H _h_, P _p_, R _r_, grow -continually smaller and smaller, as a body is situated higher above the -horizon; and when the body is in the zenith, then the parallax vanishes -altogether, for at O the moon would be seen at Z, whether viewed from A -or C. - -Since, then, a heavenly body is liable to be referred to different -points on the celestial vault, when seen from different parts of the -earth, and thus some confusion be occasioned in the determination of -points on the celestial sphere, astronomers have agreed to consider the -true place of a celestial object to be that where it would appear, if -seen from the centre of the earth; and the doctrine of parallax teaches -how to reduce observations made at any place on the surface of the -earth, to such as they would be, if made from the centre. - -When the moon, or any heavenly body, is seen in the horizon, as at E, -the change of place is called the horizontal parallax. Thus, the angle A -E C, measures the horizontal parallax of the moon. Were a spectator to -view the earth from the centre of the moon, he would see the -semidiameter of the earth under this same angle; hence, _the horizontal -parallax of any body is the angle subtended by the semidiameter of the -earth, as seen from the body_. Please to remember this fact. - -It is evident from the figure, that the effect of parallax upon the -place of a celestial body is to _depress_ it. Thus, in consequence of -parallax, E is depressed by the arc H _h_; F, by the arc P _p_; G, by -the arc R _r_; while O sustains no change. Hence, in all calculations -respecting the altitude of the sun, moon, or planets, the amount of -parallax is to be added: the stars, as we shall see hereafter, have no -sensible parallax. - -It is now very easy to see how, when the parallax of a body is known, we -may find its distance from the centre of the earth. Thus, in the -triangle A C E, Fig. 19, the side A C is known, being the semidiameter -of the earth; the angle C A E, being a right angle, is also known; and -the parallactic angle, A E C, is found from observation; and it is a -well-known principle of trigonometry, that when we have any two angles -of a triangle, we may find the remaining angle by subtracting the sum of -these two from one hundred and eighty degrees. Consequently, in the -triangle A E C, we know all the angles and one side, namely, the side A -C; hence, we have the means of finding the side C E, which is the -distance from the centre of the earth to the centre of the moon. - -[Illustration Fig. 20.] - -When the distance of a heavenly body is known, and we can measure, with -instruments, its angular breadth, we can easily determine its -_magnitude_. Thus, if we have the distance of the moon, E S, Fig. 20, -and half the breadth of its disk S C, (which is measured by the angle S -E C,) we can find the length of the line, S C, in miles. Twice this line -is the diameter of the body; and when we know the diameter of a sphere, -we can, by well-known rules, find the contents of the surface, and its -solidity. - -You will perhaps be curious to know, _how the moon's horizontal parallax -is found_; for it must have been previously ascertained, before we could -apply this method to finding the distance of the moon from the earth. -Suppose that two astronomers take their stations on the same meridian, -but one south of the equator, as at the Cape of Good Hope, and another -north of the equator, as at Berlin, in Prussia, which two places lie -nearly on the same meridian. The observers would severally refer the -moon to different points on the face of the sky,--the southern observer -carrying it further north, and the northern observer further south, -than its true place, as seen from the centre of the earth. This will be -plain from the diagram, Fig. 21. If A and B represent the positions of -the spectators, M the moon, and C D an arc of the sky, then it is -evident, that C D would be the parallactic arc. - -[Illustration Fig. 21.] - -These observations furnish materials for calculating, by the aid of -trigonometry, the moon's horizontal parallax, and we have before seen -how, when we know the parallax of a heavenly body, we can find both its -distance from the earth and its magnitude. - -Beside the change of place which these heavenly bodies undergo, in -consequence of parallax, there is another, of an opposite kind, arising -from the effect of the atmosphere, called _refraction_. Refraction -elevates the apparent place of a body, while parallax depresses it. It -affects alike the most distant as well as nearer bodies. - -In order to understand the nature of refraction, we must consider, that -an object always appears in the direction in which the _last_ ray of -light comes to the eye. If the light which comes from a star were bent -into fifty directions before it reached the eye, the star would -nevertheless appear in the line described by the ray nearest the eye. -The operation of this principle is seen when an oar, or any stick, is -thrust into water. As the rays of light by which the oar is seen have -their direction changed as they pass out of water into air, the apparent -direction in which the body is seen is changed in the same degree, -giving it a bent appearance,--the part below the water having apparently -a different direction from the part above. Thus, in Fig. 22, page 96, if -S _a x_ be the oar, S _a b_ will be the bent appearance, as affected by -refraction. The transparent substance through which any ray of light -passes is called a _medium_. It is a general fact in optics, that, when -light passes out of a rarer into a denser medium, as out of air into -water, or out of space into air, it is turned _towards_ a perpendicular -to the surface of the medium; and when it passes out of a denser into a -rarer medium, as out of water into air, it is turned _from_ the -perpendicular. In the above case, the light, passing out of space into -air, is turned towards the radius of the earth, this being perpendicular -to the surface of the atmosphere; and it is turned more and more towards -that radius the nearer it approaches to the earth, because the density -of the air rapidly increases near the earth. - -[Illustration Fig. 22.] - -Let us now conceive of the atmosphere as made up of a great number of -parallel strata, as A A, B B, C C, and D D, increasing rapidly in -density (as is known to be the fact) in approaching near to the surface -of the earth. Let S be a star, from which a ray of light, S _a_, enters -the atmosphere at _a_, where, being much turned towards the radius of -the convex surface, it would change its direction into the line _a b_, -and again into _b c_, and _c_ O, reaching the eye at O. Now, since an -object always appears in the direction in which the light finally -strikes the eye, the star would be seen in the direction O _c_, and, -consequently, the star would apparently change its place, by -refraction, from S to S“, being elevated out of its true position. -Moreover, since, on account of the continual increase of density in -descending through the atmosphere, the light would be continually turned -out of its course more and more, it would therefore move, not in the -polygon represented in the figure, but in a corresponding curve line, -whose curvature is rapidly increased near the surface of the earth. - -When a body is in the zenith, since a ray of light from it enters the -atmosphere at right angles to the refracting medium, it suffers no -refraction. Consequently, the position of the heavenly bodies, when in -the zenith, is not changed by refraction, while, near the horizon, where -a ray of light strikes the medium very obliquely, and traverses the -atmosphere through its densest part, the refraction is greatest. The -whole amount of refraction, when a body is in the horizon, is -thirty-four minutes; while, at only an elevation of one degree, the -refraction is but twenty-four minutes; and at forty-five degrees, it is -scarcely a single minute. Hence it is always important to make our -observations on the heavenly bodies when they are at as great an -elevation as possible above the horizon, being then less affected by -refraction than at lower altitudes. - -Since the whole amount of refraction near the horizon exceeds -thirty-three minutes, and the diameters of the sun and moon are -severally less than this, these luminaries are in view both before they -have actually risen and after they have set. - -The rapid increase of refraction near the horizon is strikingly evinced -by the _oval_ figure which the sun assumes when near the horizon, and -which is seen to the greatest advantage when light clouds enable us to -view the solar disk. Were all parts of the sun equally raised by -refraction, there would be no change of figure; but, since the lower -side is more refracted than the upper, the effect is to shorten the -vertical diameter, and thus to give the disk an oval form. This effect -is particularly remarkable when the sun, at his rising or setting, is -observed from the top of a mountain, or at an elevation near the -seashore; for in such situations, the rays of light make a greater angle -than ordinary with a perpendicular to the refracting medium, and the -amount of refraction is proportionally greater. In some cases of this -kind, the shortening of the vertical diameter of the sun has been -observed to amount to six minutes, or about one fifth of the whole. - -The apparent enlargement of the sun and moon, when near the horizon, -arises from an optical illusion. These bodies, in fact, are not seen -under so great an angle when in the horizon as when on the meridian, for -they are nearer to us in the latter case than in the former. The -distance of the sun, indeed, is so great, that it makes very little -difference in his apparent diameter whether he is viewed in the horizon -or on the meridian; but with the moon, the case is otherwise; its -angular diameter, when measured with instruments, is perceptibly larger -when at its culmination, or highest elevation above the horizon. Why, -then, do the sun and moon appear so much larger when near the horizon? -It is owing to a habit of the mind, by which we judge of the magnitudes -of distant objects, not merely by the angle they subtend at the eye, but -also by our impressions respecting their distance, allowing, under a -given angle, a greater magnitude as we imagine the distance of a body to -be greater. Now, on account of the numerous objects usually in sight -between us and the sun, when he is near the horizon, he appears much -further removed from us than when on the meridian; and we unconsciously -assign to him a proportionally greater magnitude. If we view the sun, in -the two positions, through a smoked glass, no such difference of size is -observed; for here no objects are seen but the sun himself. - -_Twilight_ is another phenomenon depending on the agency of the earth's -atmosphere. It is that illumination of the sky which takes place just -before sunrise and which continues after sunset. It is owing partly to -refraction, and partly to reflection, but mostly to the latter. While -the sun is within eighteen degrees of the horizon, before it rises or -after it sets, some portion of its light is conveyed to us, by means of -numerous reflections from the atmosphere. At the equator, where the -circles of daily motion are perpendicular to the horizon, the sun -descends through eighteen degrees in an hour and twelve minutes. The -light of day, therefore, declines rapidly, and as rapidly advances after -daybreak in the morning. At the pole, a constant twilight is enjoyed -while the sun is within eighteen degrees of the horizon, occupying -nearly two thirds of the half year when the direct light of the sun is -withdrawn, so that the progress from continual day to constant night is -exceedingly gradual. To an inhabitant of an oblique sphere, the twilight -is longer in proportion as the place is nearer the elevated pole. - -Were it not for the power the atmosphere has of dispersing the solar -light, and scattering it in various directions, no objects would be -visible to us out of direct sunshine; every shadow of a passing cloud -would involve us in midnight darkness; the stars would be visible all -day; and every apartment into which the sun had not direct admission -would be involved in the obscurity of night. This scattering action of -the atmosphere on the solar light is greatly increased by the -irregularity of temperature caused by the sun, which throws the -atmosphere into a constant state of undulation; and by thus bringing -together masses of air of different temperatures, produces partial -reflections and refractions at their common boundaries, by which means -much light is turned aside from a direct course, and diverted to the -purposes of general illumination.[6] In the upper regions of the -atmosphere, as on the tops of very high mountains, where the air is too -much rarefied to reflect much light, the sky assumes a black appearance, -and stars become visible in the day time. - -Although the atmosphere is usually so transparent, that it is invisible -to us, yet we as truly move and live in a fluid as fishes that swim in -the sea. Considered in comparison with the whole earth, the atmosphere -is to be regarded as a thin layer investing the surface, like a film of -water covering the surface of an orange. Its actual height, however, is -over a hundred miles, though we cannot assign its precise boundaries. -Being perfectly elastic, the lower portions, bearing as they do, the -weight of all the mass above them, are greatly compressed, while the -upper portions having little to oppose the natural tendency of air to -expand, diffuse themselves widely. The consequence is, that the -atmosphere undergoes a rapid diminution of density, as we ascend from -the earth, and soon becomes exceedingly rare. At so moderate a height as -seven miles, it is four times rarer than at the surface, and continues -to grow rare in the same proportion, namely, being four times less for -every seven miles of ascent. It is only, therefore, within a few miles -of the earth, that the atmosphere is sufficiently dense to sustain -clouds and vapors, which seldom rise so high as eight miles, and are -usually much nearer to the earth than this. So rare does the air become -on the top of Mount Chimborazo, in South America, that it is incompetent -to support most of the birds that fly near the level of the sea. The -condor, a bird which has remarkably long wings, and a light body, is the -only bird seen towering above this lofty summit. The transparency of the -atmosphere,--a quality so essential to fine views of the starry -heavens,--is much increased by containing a large proportion of water, -provided it is perfectly dissolved, or in a state of invisible vapor. A -country at once hot and humid, like some portions of the torrid zone, -presents a much brighter and more beautiful view of the moon and stars, -than is seen in cold climates. Before a copious rain, especially in hot -weather, when the atmosphere is unusually humid, we sometimes observe -the sky to be remarkably resplendent, even in our own latitude. -Accordingly, this unusual clearness of the sky, when the stars shine -with unwonted brilliancy, is regarded as a sign of approaching rain; and -when, after the rain is apparently over, the air is remarkably -transparent, and distant objects on the earth are seen with uncommon -distinctness, while the sky exhibits an unusually deep azure, we may -conclude that the serenity is only temporary, and that the rain will -probably soon return. - -FOOTNOTE: - -[6] Sir J. Herschel. - - - - -LETTER X. - -THE SUN. - - "Great source of day! best image here below - Of thy Creator, ever pouring wide, - From world to world, the vital ocean round, - On Nature write, with every beam, His praise."--_Thomson._ - - -THE subjects which have occupied the preceding Letters are by no means -the most interesting parts of our science. They constitute, indeed, -little more than an introduction to our main subject, but comprise such -matters as are very necessary to be clearly understood, before one is -prepared to enter with profit and delight upon the more sublime and -interesting field which now opens before us. - -We will begin our survey of the heavenly bodies with the SUN, which -first claims our homage, as the natural monarch of the skies. The moon -will next occupy our attention; then the other bodies which compose the -solar system, namely, the planets and comets; and, finally, we shall -leave behind this little province in the great empire of Nature, and -wing a bolder flight to the fixed stars. - -The _distance_ of the sun from the earth is about ninety-five millions -of miles. It may perhaps seem incredible to you, that astronomers should -be able to determine this fact with any degree of certainty. Some, -indeed, not so well informed as yourself, have looked upon the -marvellous things that are told respecting the distances, magnitudes, -and velocities, of the heavenly bodies, as attempts of astronomers to -impose on the credulity of the world at large; but the certainty and -exactness with which the predictions of astronomers are fulfilled, as an -eclipse, for example, ought to inspire full confidence in their -statements. I can assure you, my dear friend, that the evidence on which -these statements are founded is perfectly satisfactory to those whose -attainments in the sciences qualify them to understand them; and, so far -are astronomers from wishing to impose on the unlearned, by announcing -such wonderful discoveries as they have made among the heavenly bodies, -no class of men have ever shown a stricter regard and zeal than they for -the exact truth, wherever it is attainable. - -Ninety-five millions of miles is indeed a vast distance. No human mind -is adequate to comprehend it fully; but the nearest approaches we can -make towards it are gained by successive efforts of the mind to conceive -of great distances, beginning with such as are clearly within our grasp. -Let us, then, first take so small a distance as that of the breadth of -the Atlantic ocean, and follow, in mind, a ship, as she leaves the port -of New York, and, after twenty days' steady sail, reaches Liverpool. -Having formed the best idea we are able of this distance, we may then -reflect, that it would take a ship, moving constantly at the rate of ten -miles per hour, more than a thousand years to reach the sun. - -The diameter of the sun is towards a million of miles; or, more exactly, -it is eight hundred and eighty-five thousand miles. One hundred and -twelve bodies as large as the earth, lying side by side, would be -required to reach across the solar disk; and our ship, sailing at the -same rate as before, would be ten years in passing over the same space. -Immense as is the sun, we can readily understand why it appears no -larger than it does, when we reflect, that its distance is still more -vast. Even large objects on the earth, when seen on a distant eminence, -or over a wide expanse of water, dwindle almost to a point. Could we -approach nearer and nearer to the sun, it would constantly expand its -volume, until finally it would fill the whole vault of heaven. We could, -however, approach but little nearer to the sun without being consumed by -the intensity of his heat. Whenever we come nearer to any fire, the heat -rapidly increases, being four times as great at half the distance, and -one hundred times as great at one tenth the distance. This fact is -expressed by saying, that the heat increases as the square of the -distance decreases. Our globe is situated at such a distance from the -sun, as exactly suits the animal and vegetable kingdoms. Were it either -much nearer or much more remote, they could not exist, constituted as -they are. The intensity of the solar light also follows the same law. -Consequently, were we nearer to the sun than we are, its blaze would be -insufferable; or, were we much further off, the light would be too dim -to serve all the purposes of vision. - -The sun is one million four hundred thousand times as large as the -earth; but its matter is not more than about one fourth as dense as that -of the earth, being only a little heavier than water, while the average -density of the earth is more than five times that of water. Still, on -account of the immense magnitude of the sun, its entire quantity of -matter is three hundred and fifty thousand times as great as that of the -earth. Now, the force of gravity in a body is greater, in proportion as -its quantity of matter is greater. Consequently, we might suppose, that -the weight of a body (weight being nothing else than the measure of the -force of gravity) would be increased in the same proportion; or, that a -body, which weighs only one pound at the surface of the earth, would -weigh three hundred and fifty thousand pounds at the sun. But we must -consider, that the attraction exerted by any body is the same as though -all the matter were concentrated in the centre. Thus, the attraction -exerted by the earth and by the sun is the same as though the entire -matter of each body were in its centre. Hence, on account of the vast -dimensions of the sun, its surface is one hundred and twelve times -further from its centre than the surface of the earth is from its -centre; and, since the force of gravity diminishes as the square of the -distance increases, that of the sun, exerted on bodies at its surface, -is (so far as this cause operates) the square of one hundred and twelve, -or twelve thousand five hundred and forty-four times less than that of -the earth. If, therefore, we increase the weight of a body three hundred -and fifty-four thousand times, in consequence of the greater amount of -matter in the sun, and diminish it twelve thousand five hundred and -forty-four times, in consequence of the force acting at a greater -distance from the body, we shall find that the body would weigh about -twenty-eight times more on the sun than on the earth. Hence, a man -weighing three hundred pounds would, if conveyed to the surface of the -sun, weigh eight thousand four hundred pounds, or nearly three tons and -three quarters. A limb of our bodies, weighing forty pounds, would -require to lift it a force of one thousand one hundred and twenty -pounds, which would be beyond the ordinary power of the muscles. At the -surface of the earth, a body falls from rest by the force of gravity, in -one second, sixteen and one twelfth feet; but at the surface of the sun, -a body would, in the same time, fall through four hundred and -forty-eight and seven tenths feet. - -The sun turns on his own axis once in a little more than twenty-five -days. This fact is known by observing certain dark places seen by the -telescope on the sun's disk, called _solar spots_. These are very -variable in size and number. Sometimes, the sun's disk, when viewed with -a telescope, is quite free from spots, while at other times we may see a -dozen or more distinct clusters, each containing a great number of -spots, some large and some very minute. Occasionally, a single spot is -so large as to be visible to the naked eye, especially when the sun is -near the horizon, and the glare of his light is taken off. One measured -by Dr. Herschel was no less than fifty thousand miles in diameter. A -solar spot usually consists of two parts, the _nucleus_ and the _umbra_. -The nucleus is black, of a very irregular shape, and is subject to great -and sudden changes, both in form and size. Spots have sometimes seemed -to burst asunder, and to project fragments in different directions. The -umbra is a wide margin, of lighter shade, and is often of greater extent -than the nucleus. The spots are usually confined to a zone extending -across the central regions of the sun, not exceeding sixty degrees in -breadth. Fig. 23 exhibits the appearance of the solar spots. As these -spots have all a common motion from day to day, across the sun's disk; -as they go off at one limb, and, after a certain interval, sometimes -come on again on the opposite limb, it is inferred that this apparent -motion is imparted to them by an actual revolution of the sun on his own -axis. We know that the spots must be in contact, or very nearly so, at -least, with the body of the sun, and cannot be bodies revolving around -it, which are projected on the solar disk when they are between us and -the sun; for, in that case, they would not be so long in view as out of -view, as will be evident from inspecting the following diagram. Let S, -Fig. 24, page 106, represent the sun, and _b_ a body revolving round it -in the orbit _a b c_; and let E represent the earth, where, of course, -the spectator is situated. The body would be seen projected on the sun -only while passing from _b_ to _c_, while, throughout the remainder of -its orbit, it would be out of view, whereas no such inequality exists in -respect to the two periods. - -[Illustration Fig. 23.] - -[Illustration Fig. 24.] - -If you ask, what is the _cause_ of the solar spots, I can only tell you -what different astronomers have supposed respecting them. They attracted -the notice of Galileo soon after the invention of the telescope, and he -formed an hypothesis respecting their nature. Supposing the sun to -consist of a solid body embosomed in a sea of liquid fire, he believed -that the spots are composed of black cinders, formed in the interior of -the sun by volcanic action, which rise and float on the surface of the -fiery sea. The chief objections to this hypothesis are, first, the _vast -extent_ of some of the spots, covering, as they do, two thousand -millions of square miles, or more,--a space which it is incredible -should be filled by lava in so short a time as that in which the spots -are sometimes formed; and, secondly, the _sudden disappearance_ which -the spots sometimes undergo, a fact which can hardly be accounted for by -supposing, as Galileo did, that such a vast accumulation of matter all -at once sunk beneath the fiery flood. Moreover, we have many reasons for -believing that the spots are _depressions_ below the general surface. - -La Lande, an eminent French astronomer of the last century, held that -the sun is a solid, opaque body, having its exterior diversified with -high mountains and deep valleys, and covered all over with a burning sea -of liquid matter. The spots he supposed to be produced by the flux and -reflux of this fiery sea, retreating occasionally from the mountains, -and exposing to view a portion of the dark body of the sun. But it is -inconsistent with the nature of fluids, that a liquid, like the sea -supposed, should depart so far from its equilibrium and remain so long -fixed, as to lay bare the immense spaces occupied by some of the solar -spots. - -Dr. Herschel's views respecting the nature and constitution of the sun, -embracing an explanation of the solar spots, have, of late years, been -very generally received by the astronomical world. This great -astronomer, after attentively viewing the surface of the sun, for a long -time, with his large telescopes, came to the following conclusions -respecting the nature of this luminary. He supposes the sun to be a -planetary body like our earth, diversified with mountains and valleys, -to which, on account of the magnitude of the sun, he assigns a -prodigious extent, some of the mountains being six hundred miles high, -and the valleys proportionally deep. He employs in his explanation no -volcanic fires, but supposes two separate regions of dense clouds -floating in the solar atmosphere, at different distances from the sun. -The exterior stratum of clouds he considers as the depository of the -sun's light and heat, while the inferior stratum serves as an awning or -screen to the body of the sun itself, which thus becomes fitted to be -the residence of animals. The proofs offered in support of this -hypothesis are chiefly the following: first, that the appearances, as -presented to the telescope, are such as accord better with the idea that -the fluctuations arise from the motions of clouds, than that they are -owing to the agitations of a liquid, which could not depart far enough -from its general level to enable us to see its waves at so great a -distance, where a line forty miles in length would subtend an angle at -the eye of only the tenth part of a second; secondly, that, since clouds -are easily dispersed to any extent, the great dimensions which the solar -spots occasionally exhibit are more consistent with this than with any -other hypothesis; and, finally, that a lower stratum of clouds, similar -to those of our atmosphere, was frequently seen by the Doctor, far below -the luminous clouds which are the fountains of light and heat. - -Such are the views of one who had, it must be acknowledged, great -powers of observation, and means of observation in higher perfection -than have ever been enjoyed by any other individual; but, with all -deference to such authority, I am compelled to think that the hypothesis -is encumbered with very serious objections. Clouds analogous to those of -our atmosphere (and the Doctor expressly asserts that his lower stratum -of clouds are analogous to ours, and reasons respecting the upper -stratum according to the same analogy) cannot exist in hot air; they are -tenants only of cold regions. How can they be supposed to exist in the -immediate vicinity of a fire so intense, that they are even dissipated -by it at the distance of ninety-five millions of miles? Much less can -they be supposed to be the depositories of such devouring fire, when any -thing in the form of clouds, floating in our atmosphere, is at once -scattered and dissolved by the accession of only a few degrees of heat. -Nothing, moreover, can be imagined more unfavorable for radiating heat -to such a distance, than the light, inconstant matter of which clouds -are composed, floating loosely in the solar atmosphere. There is a -logical difficulty in the case: it is ascribing to things properties -which they are not known to possess; nay, more, which they are known not -to possess. From variations of light and shade in objects seen at -moderate distances on the earth, we are often deceived in regard to -their appearances; and we must distrust the power of an astronomer to -decide upon the nature of matter seen at the distance of ninety-five -millions of miles. - -I think, therefore, we must confess our ignorance of the nature and -constitution of the sun; nor can we, as astronomers, obtain much more -satisfactory knowledge respecting it than the common apprehension, -namely, that it is an immense globe of fire. We have not yet learned -what causes are in operation to maintain its undecaying fires; but our -confidence in the Divine wisdom and goodness leads us to believe, that -those causes are such as will preserve those fires from extinction, and -at a nearly uniform degree of intensity. Any material change in this -respect would jeopardize the safety of the animal and vegetable -kingdoms, which could not exist without the enlivening influence of the -solar heat, nor, indeed, were that heat any more or less intense than it -is at present. - -If we inquire whether the surface of the sun is in a state of actual -combustion, like burning fuel, or merely in a state of intense ignition, -like a stone heated to redness in a furnace, we shall find it most -reasonable to conclude that it is in a state of ignition. If the body of -the sun were composed of combustible matter and were actually on fire, -the material of the sun would be continually wasting away, while the -products of combustion would fill all the vast surrounding regions, and -obscure the solar light. But solid bodies may attain a very intense -state of ignition, and glow with the most fervent heat, while none of -their material is consumed, and no clouds or fumes rise to obscure their -brightness, or to impede their further emission of heat. An ignited -surface, moreover, is far better adapted than flame to the radiation of -heat. Flame, when made to act in contact with the surfaces of solid -bodies, heats them rapidly and powerfully; but it sends forth, or -_radiates_, very little heat, compared with solid matter in a high state -of ignition. These various considerations render it highly probable to -my mind, that the body of the sun is not in a state of actual -combustion, but merely in a state of high ignition. - -The solar beam consists of a mixture of several different sorts of rays. -First, there are the _calorific_ rays, which afford heat, and are -entirely distinct from those which afford light, and may be separated -from them. Secondly, there are the _colorific_ rays, which give light, -consisting of rays of seven distinct colors, namely, violet, indigo, -blue, green, yellow, orange, red. These, when separated, as they may be -by a glass prism, compose the _prismatic spectrum_. They appear also in -the rainbow. When united again, in due proportions, they constitute -white light, as seen in the light of the sun. Thirdly, there are found -in the solar beam a class of rays which afford neither heat nor light, -but which produce chemical changes in certain bodies exposed to their -influence, and hence are called _chemical_ rays. Fourthly, there is -still another class, called _magnetizing_ rays, because they are capable -of imparting magnetic properties to steel. These different sorts of rays -are sent forth from the sun, to the remotest regions of the planetary -worlds, invigorating all things by their life-giving influence, and -dispelling the darkness that naturally fills all space. - -But it was not alone to give heat and light, that the sun was placed in -the firmament. By his power of attraction, also, he serves as the great -regulator of the planetary motions, bending them continually from the -straight line in which they tend to move, and compelling them to -circulate around him, each at nearly a uniform distance, and all in -perfect harmony. I will hereafter explain to you the manner in which the -gravity of the sun thus acts, to control the planetary motions. For the -present, let us content ourselves with reflecting upon the wonderful -force which the sun must put forth, in order to bend out of their -courses, into circular orbits, such a number of planets, some of which -are more than a thousand times as large as the earth. Were a ship of war -under full sail, and it should be required to turn her aside from her -course by a rope attached to her bow, we can easily imagine that it -would take a great force to do it, especially were it required that the -force should remain stationary and the ship be so constantly diverted -from her course, as to be made to go round the force as round a centre. -Somewhat similar to this is the action which the sun exerts on each of -the planets by some invisible influence, called gravitation. The bodies -which he thus turns out of their course, and bends into a circular orbit -around himself, are, however, many millions of times as ponderous as the -ship, and are moving many thousand times as swiftly. - - - - -LETTER XI. - -ANNUAL REVOLUTION.--SEASONS - - "These, as they change, Almighty Father, these - Are but the varied God. The rolling year - Is full of Thee."--_Thomson._ - - -WE have seen that the apparent revolution of the heavenly bodies, from -east to west, every twenty-four hours, is owing to a real revolution of -the earth on its own axis, in the opposite direction. This motion is -very easily understood, resembling, as it does, the spinning of a top. -We must, however, conceive of the top as turning without any visible -support, and not as resting in the usual manner on a plane. The annual -motion of the earth around the sun, which gives rise to an apparent -motion of the sun around the earth once a year, and occasions the change -of seasons, is somewhat more difficult to understand; and it may cost -you some reflection, before you will settle all the points respecting -the changes of the seasons clearly in your mind. We sometimes see these -two motions exemplified in a top. When, as the string is pulled, the top -is thrown forwards on the floor, we may see it move forward (sometimes -in a circle) at the same time that it spins on its axis. Let a candle be -placed on a table, to represent the sun, and let these two motions be -imagined to be given to a top around it, and we shall have a case -somewhat resembling the actual motions of the earth around the sun. - -When bodies are at such a distance from each other as the earth and the -sun, a spectator on either would project the other body upon the concave -sphere of the heavens, always seeing it on the opposite side of a great -circle one hundred and eighty degrees from himself. - -Recollect that the path in which the earth moves round the sun is -called the ecliptic. We are not to conceive of this, or of any other -celestial circle, as having any real, palpable existence, any more than -the path of a bird through the sky. You will perhaps think it quite -superfluous for me to remind you of this; but, from the habit of seeing -the orbits of the heavenly bodies represented in diagrams and orreries, -by palpable lines and circles, we are apt inadvertently to acquire the -notion, that the orbits of the planets, and other representations of the -artificial sphere, have a real, palpable existence in Nature; whereas, -they denote the places where mere geometrical or imaginary lines run. -You might have expected to see an orrery, exhibiting a view of the sun -and planets, with their various motions, particularly described in my -Letter on astronomical instruments and apparatus. I must acknowledge, -that I entertain a very low opinion of the utility of even the best -orreries, and I cannot recommend them as auxiliaries in the study of -astronomy. The numerous appendages usually connected with them, some to -support them in a proper position, and some to communicate to them the -requisite motions, enter into the ideas which the learner forms -respecting the machinery of the heavens; and it costs much labor -afterwards to divest the mind of such erroneous impressions. Astronomy -can be exhibited much more clearly and beautifully to the mental eye -than to the visual organ. It is much easier to conceive of the sun -existing in boundless space, and of the earth as moving around him at a -great distance, the mind having nothing in view but simply these two -bodies, than it is, in an orrery, to contemplate the motion of a ball -representing the earth, carried by a complicated apparatus of wheels -around another ball, supported by a cylinder or wire, to represent the -sun. I would advise you, whenever it is practicable, to think how things -are in Nature, rather than how they are represented by art. The -machinery of the heavens is much simpler than that of an orrery. - -In endeavoring to obtain a clear idea of the revolution of the earth -around the sun, imagine to yourself a plane (a geometrical plane, having -merely length and breadth, but no thickness) passing through the centres -of the sun and the earth, and extended far beyond the earth till it -reaches the firmament of stars. Although, indeed, no such dome actually -exists as that under which we figure to ourselves the vault of the sky, -yet, as the fixed stars appear to be set in such a dome, we may imagine -that the circles of the sphere, when indefinitely enlarged, finally -reach such an imaginary vault. All that is essential is, that we should -imagine this to exist far beyond the bounds of the solar system, the -various bodies that compose the latter being situated close around the -sun, at the centre. - -Along the line where this great circle meets the starry vault, are -situated a series of constellations,--Aries, Taurus, Gemini, &c.,--which -occupy successively this portion of the heavens. When bodies are at such -a distance from each other as the sun and the earth, I have said that a -spectator on either would project the other body upon the concave sphere -of the heavens, always seeing it on the opposite side of a great circle -one hundred and eighty degrees from himself. The place of a body, when -viewed from any point, is denoted by the position it occupies among the -stars. Thus, in the diagram, Fig. 25, page 114, when the earth arrives -at E, it is said to be in Aries, because, if viewed from the sun, it -would be projected on that part of the heavens; and, for the same -reason, to a spectator at E, the sun would be in Libra. When the earth -shifts its position from Aries to Taurus, as we are unconscious of our -own motion, the sun it is that appears to move from Libra to Scorpio, in -the opposite part of the heavens. Hence, as we go forward, in the order -of the signs, on one side of the ecliptic, the sun seems to be moving -forward at the same rate on the opposite side of the same great circle; -and therefore, although we are unconscious of our own motion, we can -read it, from day to day, in the motions of the sun. If we could see -the stars at the same time with the sun, we could actually observe, from -day to day, the sun's progress through them, as we observe the progress -of the moon at night; only the sun's rate of motion would be nearly -fourteen times slower than that of the moon. Although we do not see the -stars when the sun is present, we can observe that it makes daily -progress eastward, as is apparent from the constellations of the zodiac -occupying, successively, the western sky immediately after sunset, -proving that either all the stars have a common motion westward, -independent of their diurnal motion, or that the sun has a motion past -them from west to east. We shall see, hereafter, abundant evidence to -prove, that this change in the relative position of the sun and stars, -is owing to a change in the apparent place of the sun, and not to any -change in the stars. - -[Illustration Fig. 25.] - -To form a clear idea of the two motions of the earth, imagine yourself -standing on a circular platform which turns slowly round its centre. -While you are carried slowly round the entire of the circuit of the -heavens, along with the platform, you may turn round upon your heel the -same way three hundred and sixty-five times. The former is analogous to -our annual motion with the earth around the sun; the latter, to our -diurnal revolution in common with the earth around its own axis. - -Although the apparent revolution of the sun is in a direction opposite -to the real motion of the earth, as regards absolute space, yet both are -nevertheless from west to east, since these terms do not refer to any -directions in absolute space, but to the order in which certain -constellations (the constellations of the Zodiac) succeed one another. -The earth itself, on opposite sides of its orbit, does in fact move -towards directly opposite points of space; but it is all the while -pursuing its course in the order of the signs. In the same manner, -although the earth turns on its axis from west to east, yet any place on -the surface of the earth is moving in a direction in space exactly -opposite to its direction twelve hours before. If the sun left a visible -trace on the face of the sky, the ecliptic would of course be distinctly -marked on the celestial sphere, as it is on an artificial globe; and -were the equator delineated in a similar manner, we should then see, at -a glance, the relative position of these two circles,--the points where -they intersect one another, constituting the equinoxes; the points where -they are at the greatest distance asunder, that is, the solstices; and -various other particulars, which, for want of such visible traces, we -are now obliged to search for by indirect and circuitous methods. It -will aid you, to have constantly before your mental vision an imaginary -delineation of these two important circles on the face of the sky. - -The equator makes an angle with the ecliptic of twenty-three degrees and -twenty-eight minutes. This is called the obliquity of the ecliptic. As -the sun and earth are both always in the ecliptic, and as the motion of -the earth in one part of it makes the sun appear to move in the -opposite part, at the same rate, the sun apparently descends, in Winter, -twenty-three degrees and twenty-eight minutes to the south of the -equator, and ascends, in Summer, the same number of degrees north of it. -We must keep in mind, that the celestial equator and celestial ecliptic -are here understood, and we may imagine them to be two great circles -delineated on the face of the sky. On comparing observations made at -different periods, for more than two thousand years, it is found, that -the obliquity of the ecliptic is not constant, but that it undergoes a -slight diminution, from age to age, amounting to fifty-two seconds in a -century, or about half a second annually. We might apprehend that, by -successive approaches to each other, the equator and ecliptic would -finally coincide; but astronomers have discovered, by a most profound -investigation, based on the principles of universal gravitation, that -this irregularity is confined within certain narrow limits; and that the -obliquity, after diminishing for some thousands of years, will then -increase for a similar period, and will thus vibrate forever about a -mean value. - -As the earth traverses every part of her orbit in the course of a year, -she will be once at each solstice, and once at each equinox. The best -way of obtaining a correct idea of her two motions is, to conceive of -her as standing still for a single day, at some point in her orbit, -until she has turned once on her axis, then moving about a degree, and -halting again, until another diurnal revolution is completed. Let us -suppose the earth at the Autumnal equinox, the sun, of course, being at -the Vernal equinox,--for we must always think of these two bodies as -diametrically opposite to each other. Suppose the earth to stand still -in its orbit for twenty-four hours. The revolution of the earth on its -axis, from west to east, will make the sun appear to describe a great -circle of the heavens from east to west, coinciding with the equator. At -the end of this period, suppose the sun to move northward one degree, -and to remain there for twenty-four hours; in which time, the -revolution of the earth, will make the sun appear to describe another -circle, from east to west, parallel to the equator, but one degree north -of it. Thus, we may conceive of the sun as moving one degree north, -every day, for about three months, when it will reach the point of the -ecliptic furthest from the equator, which point is called the _tropic_, -from a Greek word, signifying _to turn_; because, after the sun has -passed this point, his motion in his orbit carries him continually -towards the equator, and therefore he seems to turn about. The same -point is also called the _solstice_, from a Latin word, signifying to -_stand still_; since, when the sun has reached its greatest northern or -southern limit, while its declination is at the point where it ceases to -increase, but begins to decrease, there the sun seems for a short time -stationary, with regard to the equator, appearing for several days to -describe the same parallel of latitude. - -When the sun is at the northern tropic, which happens about the -twenty-first of June, his elevation above the southern horizon at noon -is the greatest in the year; and when he is at the southern tropic, -about the twenty-first of December, his elevation at noon is the least -in the year. The difference between these two meridian altitudes will -give the whole distance from one tropic to the other, and consequently, -twice the distance from each tropic to the equator. By this means, we -find how far the tropic is from the equator, and that gives us the angle -which the equator and ecliptic make with each other; for the greatest -distance between any two great circles on the sphere is always equal to -the angle which they make with each other. Thus, the ancient astronomers -were able to determine the obliquity of the ecliptic with a great degree -of accuracy. It was easy to find the situation of the zenith, because -the direction of a plumb-line shows us where that is; and it was easy to -find the distances from the zenith where the sun was at the greatest and -least distances; respectively. The difference of these two arcs is the -angular distance from one tropic to the other; and half this arc is the -distance of either tropic from the equator, and of course, equal to the -obliquity of the ecliptic. All this will be very easily understood from -the annexed diagram, Fig. 26. Let Z be the zenith of a spectator -situated at C; Z _n_ the least, and Z _s_ the greatest distance of the -sun from the zenith. From Z _s_ subtract Z _n_, and then _s n_, the -difference, divided by two, will give the obliquity of the ecliptic. - -[Illustration Fig. 26.] - -The motion of the earth in its orbit is nearly seventy times as great as -its greatest motion around its axis. In its revolution around the sun, -the earth moves no less than one million six hundred and forty thousand -miles per day, sixty-eight thousand miles per hour, eleven hundred miles -per minute, and nearly nineteen miles every second; a velocity nearly -sixty times as great as the greatest velocity of a cannon ball. Places -on the earth turn with very different degrees of velocity in different -latitudes. Those near the equator are carried round on the circumference -of a large circle; those towards the poles, on the circumference of a -small circle; while one standing on the pole itself would not turn at -all. Those who live on the equator are carried about one thousand miles -an hour. In our latitude, (forty-one degrees and eighteen minutes,) the -diurnal velocity is about seven hundred and fifty miles per hour. It -would seem, at first view, quite incredible, that we should be whirled -round at so rapid a rate, and yet be entirely insensible of any motion; -and much more, that we could be going so swiftly through space, in our -circuit around the sun, while all things, when unaffected by local -causes, appear to be in such a state of quiescence. Yet we have the most -unquestionable evidence of the fact; nor is it difficult to account for -it, in consistency with the general state of repose among bodies on the -earth, when we reflect that their relative motions, with respect to each -other, are not in the least disturbed by any motions which they may have -in common. When we are on board a steam-boat, we move about in the same -manner when the boat is in rapid motion, as when it is lying still; and -such would be the case, if it moved steadily a hundred times faster than -it does. Were the earth, however, suddenly to stop its diurnal -revolution, all movable bodies on its surface would be thrown off in -tangents to the surface with velocities proportional to that of their -diurnal motion; and were the earth suddenly to halt in its orbit, we -should be hurled forward into space with inconceivable rapidity. - -I will next endeavor to explain to you the phenomena of the _Seasons_. -These depend on two causes; first, the inclination of the earth's axis -to the plane of its orbit; and, secondly, to the circumstance, that the -axis always remains parallel to itself. Imagine to yourself a candle -placed in the centre of a ring, to represent the sun in the centre of -the earth's orbit, and an apple with a knittingneedle running through it -in the direction of the stem. Run a knife around the central part of the -apple, to mark the situation of the equator. The circumference of the -ring represents the earth's orbit in the plane of the ecliptic. Place -the apple so that the equator shall coincide with the wire; then the -axis will lie directly across the plane of the ecliptic; that is, at -right angles to it. Let the apple be carried quite round the ring, -constantly preserving the axis parallel to itself, and the equator all -the while coinciding with the wire that represents the orbit. Now, since -the sun enlightens half the globe at once, so the candle, which here -represents the sun, will shine on the half of the apple that is turned -towards it; and the circle which divides the enlightened from the -unenlightened side of the apple, called the _terminator_, will pass -through both the poles. If the apple be turned slowly round on its axis, -the terminator will successively pass over all places on the earth, -giving the appearance of sunrise to places at which it arrives, and of -sunset to places from which it departs. If, therefore, the equator had -coincided with the ecliptic, as would have been the case, had the -earth's axis been perpendicular to the plane of its orbit, the diurnal -motion of the sun would always have been in the equator, and the days -and nights would have been equal all over the globe. To the inhabitants -of the equatorial parts of the earth, the sun would always have appeared -to move in the prime vertical, rising directly in the east, passing -through the zenith at noon, and setting in the west. In the polar -regions, the sun would always have appeared to revolve in the horizon; -while, at any place between the equator and the pole, the course of the -sun would have been oblique to the horizon, but always oblique in the -same degree. There would have been nothing of those agreeable -vicissitudes of the seasons which we now enjoy; but some regions of the -earth would have been crowned with perpetual spring, others would have -been scorched with the unremitting fervor of a vertical sun, while -extensive regions towards either pole would have been consigned to -everlasting frost and sterility. - -To understand, then, clearly, the causes of the change of seasons, use -the same apparatus as before; but, instead of placing the axis of the -earth at right angles to the plane of its orbit, turn it out of a -perpendicular position a little, (twenty-three degrees and twenty-eight -minutes,) then the equator will be turned just the same number of -degrees out of a coincidence with the ecliptic. Let the apple be carried -around the ring, always holding the axis inclined at the same angle to -the plane of the ring, and always parallel to itself. You will find that -there will be two points in the circuit where the plane of the equator, -that you had marked around the centre of the apple, will pass through -the centre of the sun; these will be the points where the celestial -equator and the ecliptic cut one another, or the equinoxes. When the -earth is at either of these points, the sun shines on both poles alike; -and, if we conceive of the earth, while in this situation, as turning -once round on its axis, the apparent diurnal motion of the sun will be -the same as it would be, were the earth's axis perpendicular to the -plane of the equator. For that day, the sun would revolve in the -equator, and the days and nights would be equal all over the globe. If -the apple were carried round in the manner supposed, then, at the -distance of ninety degrees from the equinoxes, the same pole would be -turned from the sun on one side, just as much as it was turned towards -him on the other. In the former case, the sun's light would fall short -of the pole twenty-three and one half degrees, and in the other case, it -would reach beyond it the same number of degrees. I would recommend to -you to obtain as clear an idea as you can of the cause of the change of -seasons, by thinking over the foregoing illustration. You may then clear -up any remaining difficulties, by studying the diagram, Fig. 27, on page -122. - -[Illustration Fig. 27.] - -Let A B C D represent the earth's place in different parts of its orbit, -having the sun in the centre. Let A, C, be the positions of the earth at -the equinoxes, and B, D, its positions at the tropics,--the axis _n s_ -being always parallel to itself. It is difficult to represent things of -this kind correctly, all on the same plane; but you will readily see, -that the figure of the earth, here, answers to the apple in the former -illustration; that the hemisphere towards _n_ is above, and that towards -_s_ is below, the plane of the paper. When the earth is at A and C, the -Vernal and Autumnal equinoxes, the sun, you will perceive, shines on -both the poles _n_ and _s_; and, if you conceive of the globe, while in -this position, as turned round on its axis, as it is in the diurnal -revolution, you will readily understand, that the sun would describe the -celestial equator. This may not at first appear so obvious, by -inspecting the figure; but if you consider the point _n_ as raised above -the plane of the paper, and the point _s_ as depressed below it, you -will readily see how the plane of the equator would pass through the -centre of the sun. Again, at B, when the earth is at the southern -tropic, the sun shines twenty-three and a half degrees beyond the north -pole, _n_, and falls the same distance short of the south pole, _s_. The -case is exactly reversed when the earth is at the northern tropic, and -the sun at the southern. While the earth is at one of the tropics, at B, -for example, let us conceive of it as turning on its axis, and we shall -readily see, that all that part of the earth which lies within the north -polar circle will enjoy continual day, while that within the south polar -circle will have continual night; and that all other places will have -their days longer as they are nearer to the enlightened pole, and -shorter as they are nearer to the unenlightened pole. This figure -likewise shows the successive positions of the earth, at different -periods of the year, with respect to the signs, and what months -correspond to particular signs. Thus, the earth enters Libra, and the -sun Aries, on the twenty-first of March, and on the twenty-first of -June, the earth is just entering Capricorn, and the sun, Cancer. You -will call to mind what is meant by this phraseology,--that by saying the -earth enters Libra, we mean that a spectator placed on the sun would see -the earth in that part of the celestial ecliptic, which is occupied by -the sign Libra; and that a spectator on the earth sees the sun at the -same time projected on the opposite part of the heavens, occupied by the -sign Cancer. - -Had the axis of the earth been perpendicular to the plane of the -ecliptic, then the sun would always have appeared to move in the -equator, the days would every where have been equal to the nights, and -there could have been no change of seasons. On the other hand, had the -inclination of the ecliptic to the equator been much greater than it is, -the vicissitudes of the seasons would have been proportionally greater, -than at present. Suppose, for instance, the equator had been at right -angles to the ecliptic, in which case, the poles of the earth would have -been situated in the ecliptic itself; then, in different parts of the -earth, the appearances would have been as follows: To a spectator on the -_equator_, (where all the circles of diurnal revolution are -perpendicular to the horizon,) the sun, as he left the vernal equinox, -would every day perform his diurnal revolution in a smaller and smaller -circle, until he reached the north pole, when he would halt for a -moment, and then wheel about and return to the equator, in a reverse -order. The progress of the sun through the southern signs, to the south -pole, would be similar to that already described. Such would be the -appearances to an inhabitant of the equatorial regions. To a spectator -living in an _oblique_ sphere, in our own latitude, for example, the -sun, while north of the equator, would advance continually northward, -making his diurnal circuit in parallels further and further distant from -the equator, until he reached the circle of perpetual apparition; after -which, he would climb, by a spiral course, to the north star, and then -as rapidly return to the equator. By a similar progress southward, the -sun would at length pass the circle of perpetual occultation, and for -some time (which would be longer or shorter, according to the latitude -of the place of observation) there would be continual night. To a -spectator on the _pole_ of the earth and under the pole of the heaven, -during the long day of six months, the sun would wind its way to a point -directly over head, pouring down upon the earth beneath not merely the -heat of the torrid zone, but the heat of a torrid noon, accumulating -without intermission. - -The great vicissitudes of heat and cold, which would attend these -several movements of the sun, would be wholly incompatible with the -existence of either the animal or the vegetable kingdom, and all -terrestrial Nature would be doomed to perpetual sterility and -desolation. The happy provision which the Creator has made against such -extreme vicissitudes, by confining the changes of the seasons within -such narrow bounds, conspires with many other express arrangements in -the economy of Nature, to secure the safety and comfort of the human -race. - -Perhaps you have never reflected upon all the reasons, why the several -changes of position, with respect to the horizon, which the sun -undergoes in the course of the year, occasion such a difference in the -amount of heat received from him. Two causes contribute to increase the -heat of Summer and the cold of Winter. The higher the sun ascends above -the horizon, the more directly his rays fall upon the earth; and their -heating power is rapidly augmented, as they approach a perpendicular -direction. When the sun is nearly over head, his rays strike us with far -greater force than when they meet us obliquely; and the earth absorbs a -far greater number of those rays of heat which strike it -perpendicularly, than of those which meet it in a slanting direction. -When the sun is near the horizon, his rays merely glance along the -ground, and many of them, before they reach it, are absorbed and -dispersed in passing through the atmosphere. Those who have felt only -the oblique solar rays, as they fall upon objects in the high latitudes, -have a very inadequate idea of the power of a vertical, noonday sun, as -felt in the region of the equator. - -The increased length of the day in Summer is another cause of the heat -of this season of the year. This cause more sensibly affects places far -removed from the equator, because at such places the days are longer and -the nights shorter than in the torrid zone. By the operation of this -cause, the solar heat accumulates there so much, during the longest days -of Summer, that the temperature rises to a higher degree than is often -known in the torrid climates. - -But the temperature of a place is influenced very much by several other -causes, as well as by the force and duration of the sun's heat. First, -the _elevation_ of a country above the level of the sea has a great -influence upon its climate. Elevated districts of country, even in the -torrid zone, often enjoy the most agreeable climate in the world. The -cold of the upper regions of the atmosphere modifies and tempers the -solar heat, so as to give a most delightful softness, while the -uniformity of temperature excludes those sudden and excessive changes -which are often experienced in less favored climes. In ascending certain -high mountains situated within the torrid zone, the traveller passes, in -a short time, through every variety of climate, from the most oppressive -and sultry heat, to the soft and balmy air of Spring, which again is -succeeded by the cooler breezes of Autumn, and then by the severest -frosts of Winter. A corresponding difference is seen in the products of -the vegetable kingdom. While Winter reigns on the summit of the -mountain, its central regions may be encircled with the verdure of -Spring, and its base with the flowers and fruits of Summer. Secondly, -the proximity of the _ocean_ also has a great effect to equalize the -temperature of a place. As the ocean changes its temperature during the -year much less than the land, it becomes a source of warmth to -contiguous countries in Winter, and a fountain of cool breezes in -Summer. Thirdly, the relative _humidity_ or _dryness_ of the atmosphere -of a place is of great importance, in regard to its effects on the -animal system. A dry air of ninety degrees is not so insupportable as a -humid air of eighty degrees; and it may be asserted as a general -principle, that a hot and humid atmosphere is unhealthy, although a hot -air, when dry, may be very salubrious. In a warm atmosphere which is -dry, the evaporation of moisture from the surface of the body is rapid, -and its cooling influence affords a most striking relief to an intense -heat without; but when the surrounding atmosphere is already filled with -moisture, no such evaporation takes place from the surface of the skin, -and no such refreshing effects are experienced from this cause. Moisture -collects on the skin; a sultry, oppressive sensation is felt; and chills -and fevers are usually in the train. - - - - -LETTER XII. - -LAWS OF MOTION. - - "What though in solemn silence, all - Move round this dark, terrestrial ball! - In reason's ear they all rejoice, - And utter forth a glorious voice; - For ever singing, as they shine, - 'The hand that made us is divine.'"--_Addison._ - - -HOWEVER incredible it may seem, no fact is more certain, than that the -earth is constantly on the wing, flying around the sun with a velocity -so prodigious, that, for every breath we draw, we advance on our way -forty or fifty miles. If, when passing across the waters in a -steam-boat, we can wake, after a night's repose, and find ourselves -conducted on our voyage a hundred miles, we exult in the triumphs of -art, which could have moved so ponderous a body as a steam-ship over -such a space in so short a time, and so quietly, too, as not to disturb -our slumbers; but, with a motion vastly more quiet and uniform, we have, -in the same interval, been carried along with the earth in its orbit -more than half a million of miles. In the case of the steam-ship, -however perfect the machinery may be, we still, in our waking hours at -least, are made sensible of the action of the forces by which the motion -is maintained,--as the roaring of the fire, the beating of the piston, -and the dashing of the paddle-wheels; but in the more perfect machinery -which carries the earth forward on her grander voyage, no sound is -heard, nor the least intimation afforded of the stupendous forces by -which this motion is achieved. To the pious observer of Nature it might -seem sufficient, without any inquiry into second causes, to ascribe the -motions of the spheres to the direct agency of the Supreme Being. If, -however, we can succeed in finding the secret springs and cords, by -which the motions of the heavenly bodies are immediately produced and -controlled, it will detract nothing from our just admiration of the -Great First Cause of all things. We may therefore now enter upon the -inquiry into the nature or laws of the forces by which the earth is made -to revolve on her axis and in her orbit; and having learned what it is, -that causes and maintains the motions of the earth, you will then -acquire, at the same time, a knowledge of all the celestial machinery. -The subject will involve an explanation of the laws of motion, and of -the principles of universal gravitation. - -It was once supposed, that we could never reason respecting the laws -that govern the heavenly bodies from what we observe in bodies around -us, but that motion is one thing on the earth and quite another thing in -the skies; and hence, that it is impossible for us, by any inquiries -into the laws of terrestrial Nature, to ascertain how things take place -among the heavenly bodies. Galileo and Newton, however, proceeded on the -contrary supposition, that Nature is uniform in all her works; that the -same Almighty arm rules over all; and that He works by the same fixed -laws through all parts of His boundless realm. The certainty with which -all the predictions of astronomers, made on these suppositions, are -fulfilled, attests the soundness of the hypothesis. Accordingly, those -laws, which all experience, endlessly multiplied and varied, proves to -be the laws of terrestrial motion, are held to be the laws that govern -also the motions of the most distant planets and stars, and to prevail -throughout the universe of matter. Let us, then, briefly review these -great laws of motion, which are three in number. The FIRST LAW is as -follows: _every body perseveres in a state of rest, or of uniform motion -in a straight line, unless compelled by some force to change its state_. -By _force_ is meant any thing which produces motion. - -The foregoing law has been fully established by experiment, and is -conformable to all experience. It embraces several particulars. First, a -body, when at rest, remains so, unless some force puts it in motion; and -hence it is inferred, when a body is found in motion, that some force -must have been applied to it sufficient to have caused its motion. Thus, -the fact, that the earth is in motion around the sun and around its own -axis, is to be accounted for by assigning to each of these motions a -force adequate, both in quantity and direction, to produce these -motions, respectively. - -Secondly, when a body is once in motion, it will continue to move for -ever, unless something stops it. When a ball is struck on the surface of -the earth, the friction of the earth and the resistance of the air soon -stop its motion; when struck on smooth ice, it will go much further -before it comes to a state of rest, because the ice opposes much less -resistance than the ground; and, were there no impediment to its -motion, it would, when once set in motion, continue to move without -end. The heavenly bodies are actually in this condition: they continue -to move, not because any new forces are applied to them; but, having -been once set in motion, they continue in motion because there is -nothing to stop them. This property in bodies to persevere in the state -they are actually in,--if at rest, to remain at rest, or, if in motion, -to continue in motion,--is called _inertia_. The inertia of a body -(which is measured by the force required to overcome it) is proportioned -to the quantity of matter it contains. A steam-boat manifests its -inertia, on first starting it, by the enormous expenditure of force -required to bring it to a given rate of motion; and it again manifests -its inertia, when in rapid motion, by the great difficulty of stopping -it. The heavenly bodies, having been once put in motion, and meeting -with nothing to stop them, move on by their own inertia. A top affords a -beautiful illustration of inertia, continuing, as it does, to spin after -the moving force is withdrawn. - -Thirdly, the motion to which a body naturally tends is _uniform_; that -is, the body moves just as far the second minute as it did the first, -and as far the third as the second; and passes over equal spaces in -equal times. I do not assert that the motion of all moving bodies is _in -fact_ uniform, but that such is their _tendency_. If it is otherwise -than uniform, there is some cause operating to disturb the uniformity to -which it is naturally prone. - -Fourthly, a body in motion will move in a _straight line_, unless -diverted out of that line by some external force; and the body will -resume its straight-forward motion, whenever the force that turns it -aside is withdrawn. Every body that is revolving in an orbit, like the -moon around the earth, or the earth around the sun, _tends_ to move in a -straight line which is a tangent[7] to its orbit. Thus, if A B C, Fig. -28, represents the orbit of the moon around the earth, were it not for -the constant action of some force that draws her towards the earth, she -would move off in a straight line. If the force that carries her towards -the earth were suspended at A, she would immediately desert the circular -motion, and proceed in the direction A D. In the same manner, a boy -whirls a stone around his head in a sling, and then letting go one of -the strings, and releasing the force that binds it to the circle, it -flies off in a straight line which is a tangent to that part of the -circle where it was released. This tendency which a body revolving in an -orbit exhibits, to recede from the centre and to fly off in a tangent, -is called the _centrifugal force_. We see it manifested when a pail of -water is whirled. The water rises on the sides of the vessel, leaving a -hollow in the central parts. We see an example of the effects of -centrifugal action, when a horse turns swiftly round a corner, and the -rider is thrown outwards; also, when a wheel passes rapidly through a -small collection of water, and portions of the water are thrown off from -the top of the wheel in straight lines which are tangents to the wheel. - -[Illustration Fig. 28.] - -The centrifugal force is increased as the velocity is increased. Thus, -the parts of a millstone most remote from the centre sometimes acquire a -centrifugal force so much greater than the central parts, which move -much slower, that the stone is divided, and the exterior portions are -projected with great violence. In like manner, as the equatorial parts -of the earth, in the diurnal revolution, revolve much faster than the -parts towards the poles, so the centrifugal force is felt most at the -equator, and becomes strikingly manifest by the diminished weight of -bodies, since it acts in opposition to the force of gravity. - -Although the foregoing law of motion, when first presented to the mind, -appears to convey no new truth, but only to enunciate in a formal manner -what we knew before; yet a just understanding of this law, in all its -bearings, leads us to a clear comprehension of no small share of all the -phenomena of motion. The second and third laws may be explained in fewer -terms. - -The SECOND LAW of motion is as follows: _motion is proportioned to the -force impressed, and in the direction of that force_. - -The meaning of this law is, that every force that is applied to a body -produces its full effect, proportioned to its intensity, either in -causing or in preventing motion. Let there be ever so many blows applied -at once to a ball, each will produce its own effect in its own -direction, and the ball will move off, not indeed in the zigzag, complex -lines corresponding to the directions of the several forces, but in a -single line expressing the united effect of all. If you place a ball at -the corner of a table, and give it an impulse, at the same instant, with -the thumb and finger of each hand, one impelling it in the direction of -one side of the table, and the other in the direction of the other side, -the ball will move diagonally across the table. If the blows be exactly -proportioned each to the length of the side of the table on which it is -directed, the ball will run exactly from corner to corner, and in the -same time that it would have passed over each side by the blow given in -the direction of that side. This principle is expressed by saying, that -a body impelled by two forces, acting respectively in the directions of -the two sides of a parallelogram, and proportioned in intensity to the -lengths of the sides, will describe the diagonal of the parallelogram in -the same time in which it would have described the sides by the forces -acting separately. - -The converse of this proposition is also true, namely, that any single -motion may be considered as the _resultant_ of two others,--the motion -itself being represented by the diagonal, while the two _components_ are -represented by the sides, of a parallelogram. This reduction of a motion -to the individual motions that produce it, is called the _resolution of -motion_, or the _resolution of forces_. Nor can a given motion be -resolved into _two_ components, merely. These, again, may be resolved -into others, varying indefinitely, in direction and intensity, from all -which the given motion may be considered as having resulted. This -composition and resolution of motion or forces is often of great use, in -inquiries into the motions of the heavenly bodies. The composition often -enables us to substitute a single force for a great number of others, -whose individual operations would be too complicated to be followed. By -this means, the investigation is greatly simplified. On the other hand, -it is frequently very convenient to resolve a given motion into two or -more others, some of which may be thrown out of the account, as not -influencing the particular point which we are inquiring about, while -others are far more easily understood and managed than the single force -would have been. It is characteristic of great minds, to simplify these -inquiries. They gain an insight into complicated and difficult subjects, -not so much by any extraordinary faculty of seeing in the dark, as by -the power of removing from the object all incidental causes of -obscurity, until it shines in its own clear and simple light. - -If every force, when applied to a body, produces its full and legitimate -effect, how many other forces soever may act upon it, impelling it -different ways, then it must follow, that the smallest force ought to -move the largest body; and such is in fact the case. A snap of a finger -upon a seventy-four under full sail, if applied in the direction of its -motion, would actually increase its speed, although the effect might be -too small to be visible. Still it is something, and may be truly -expressed by a fraction. Thus, suppose a globe, weighing a million of -pounds, were suspended from the ceiling by a string, and we should apply -to it the snap of a finger,--it is granted that the motion would be -quite insensible. Let us then divide the body into a million equal -parts, each weighing one pound; then the same impulse, applied to each -one separately, would produce a sensible effect, moving it, say one -inch. It will be found, on trial, that the same impulse given to a mass -of two pounds will move it half an inch; and hence it is inferred, that, -if applied to a mass weighing a million of pounds, it would move it the -millionth part of an inch. - -It is one of the curious results of the second law of motion, that an -unlimited number of motions may exist together in the same body. Thus, -at the same moment, we may be walking around a post in the cabin of a -steam-boat, accompanying the boat in its passage around an island, -revolving with the earth on its axis, flying through space in our annual -circuit around the sun, and possibly wheeling, along with the sun and -his whole retinue of planets, around some centre in common with the -starry worlds. - -The THIRD LAW of motion is this: _action and reaction are equal, and in -contrary directions_. - -Whenever I give a blow, the body struck exerts an equal force on the -striking body. If I strike the water with an oar, the water communicates -an equal impulse to the oar, which, being communicated to the boat, -drives it forward in the opposite direction. If a magnet attracts a -piece of iron, the iron attracts the magnet just as much, in the -opposite direction; and, in short, every portion of matter in the -universe attracts and is attracted by every other, equally, in an -opposite direction. This brings us to the doctrine of universal -gravitation, which is the very key that unlocks all the secrets of the -skies. This will form the subject of my next Letter. - -FOOTNOTE: - -[7] A tangent is a straight line touching a circle, as A D, in Fig. 28 - - - - -LETTER XIII. - -TERRESTRIAL GRAVITY. - - - "To Him no high, no low, no great, no small, - He fills, He bounds, connects, and equals all."--_Pope._ - -WE discover in Nature a tendency of every portion of matter towards -every other. This tendency is called _gravitation_. In obedience to this -power, a stone falls to the ground, and a planet revolves around the -sun. We may contemplate this subject as it relates either to phenomena -that take place near the surface of the earth, or in the celestial -regions. The former, _gravity_, is exemplified by falling bodies; the -latter, _universal gravitation_, by the motions of the heavenly bodies. -The laws of terrestrial gravity were first investigated by Galileo; -those of universal gravitation, by Sir Isaac Newton. Terrestrial gravity -is only an individual example of universal gravitation; being the -tendency of bodies towards the centre of the earth. We are so much -accustomed, from our earliest years, to see bodies fall to the earth, -that we imagine bodies must of necessity fall "downwards;" but when we -reflect that the earth is round, and that bodies fall towards the centre -on all sides of it, and that of course bodies on opposite sides of the -earth fall in precisely opposite directions, and towards each other, we -perceive that there must be some force acting to produce this effect; -nor is it enough to say, as the ancients did, that bodies "naturally" -fall to the earth. Every motion implies some force which produces it; -and the fact that bodies fall towards the earth, on all sides of it, -leads us to infer that that force, whatever it is, resides in the earth -itself. We therefore call it _attraction_. We do not, however, say what -attraction _is_, but what it _does_. We must bear in mind, also, that, -according to the third law of motion, this attraction is mutual; that -when a stone falls towards the earth, it exerts the same force on the -earth that the earth exerts on the stone; but the motion of the earth -towards the stone is as much less than that of the stone towards the -earth, as its quantity of matter is greater; and therefore its motion is -quite insensible. - -But although we are compelled to acknowledge the _existence_ of such a -force as gravity, causing a tendency in all bodies towards each other, -yet we know nothing of its _nature_, nor can we conceive by what medium -bodies at such a distance as the moon and the earth exercise this -influence on each other. Still, we may trace the modes in which this -force acts; that is, its _laws_; for the laws of Nature are nothing else -than the modes in which the powers of Nature act. - -We owe chiefly to the great Galileo the first investigation of the laws -of terrestrial gravity, as exemplified in falling bodies; and I will -avail myself of this opportunity to make you better acquainted with one -of the most interesting of men and greatest of philosophers. - -Galileo was born at Pisa, in Italy, in the year 1564. He was the son of -a Florentine nobleman, and was destined by his father for the medical -profession, and to this his earlier studies were devoted. But a fondness -and a genius for mechanical inventions had developed itself, at a very -early age, in the construction of his toys, and a love of drawing; and -as he grew older, a passion for mathematics, and for experimental -research, predominated over his zeal for the study of medicine, and he -fortunately abandoned that for the more congenial pursuits of natural -philosophy and astronomy. In the twenty-fifth year of his age, he was -appointed, by the Grand Duke of Tuscany, professor of mathematics in the -University of Pisa. At that period, there prevailed in all the schools a -most extraordinary reverence for the writings of Aristotle, the -preceptor of Alexander the Great,--a philosopher who flourished in -Greece, about three hundred years before the Christian era. Aristotle, -by his great genius and learning, gained a wonderful ascendency over the -minds of men, and became the oracle of the whole reading world for -twenty centuries. It was held, on the one hand, that all truths worth -knowing were contained in the writings of Aristotle; and, on the other, -that an assertion which contradicted any thing in Aristotle could not be -true. But Galileo had a greatness of mind which soared above the -prejudices of the age in which he lived, and dared to interrogate Nature -by the two great and only successful methods of discovering her -secrets,--experiment and observation. Galileo was indeed the first -philosopher that ever fully employed experiments as the means of -learning the laws of Nature, by imitating on a small what she performs -on a great scale, and thus detecting her modes of operation. Archimedes, -the great Sicilian philosopher, had in ancient times introduced -mathematical or geometrical reasoning into natural philosophy; but it -was reserved for Galileo to unite the advantages of both mathematical -and experimental reasonings in the study of Nature,--both sure and the -only sure guides to truth, in this department of knowledge, at least. -Experiment and observation furnish materials upon which geometry builds -her reasonings, and from which she derives many truths that either lie -for ever hidden from the eye of observation, or which it would require -ages to unfold. - -This method, of interrogating Nature by experiment and observation, was -matured into a system by Lord Bacon, a celebrated English philosopher, -early in the seventeenth century,--indeed, during the life of Galileo. -Previous to that time, the inquirers into Nature did not open their eyes -to see how the facts really _are_; but, by metaphysical processes, in -imitation of Aristotle, determined how they _ought to be_, and hastily -concluded that they were so. Thus, they did not study into the laws of -motion, by observing how motion actually takes place, under various -circumstances, but first, in their closets, constructed a definition of -motion, and thence inferred all its properties. The system of reasoning -respecting the phenomena of Nature, introduced by Lord Bacon, was this: -in the first place, to examine all the facts of the case, and then from -these to determine the laws of Nature. To derive general conclusions -from the comparison of a great number of individual instances -constitutes the peculiarity of the Baconian philosophy. It is called the -_inductive_ system, because its conclusions were built on the induction, -or comparison, of a great many single facts. Previous to the time of -Lord Bacon, hardly any insight had been gained into the causes of -natural phenomena, and hardly one of the laws of Nature had been clearly -established, because all the inquirers into Nature were upon a wrong -road, groping their way through the labyrinth of error. Bacon pointed -out to them the true path, and held before them the torch-light of -experiment and observation, under whose guidance all successful students -of Nature have since walked, and by whose illumination they have gained -so wonderful an insight into the mysteries of the natural world. - -It is a remarkable fact, that two such characters as Bacon and Galileo -should appear on the stage at the same time, who, without any -communication with each other, or perhaps without any personal knowledge -of each other's existence, should have each developed the true method of -investigating the laws of Nature. Galileo practised what Bacon only -taught; and some, therefore, with much reason, consider Galileo as a -greater philosopher than Bacon. "Bacon," says Hume, "pointed out, at a -great distance, the road to philosophy; Galileo both pointed it out to -others, and made, himself, considerable advances in it. The Englishman -was ignorant of geometry; the Florentine revived that science, excelled -in it, and was the first who applied it, together with experiment, to -natural philosophy. The former rejected, with the most positive disdain, -the system of Copernicus; the latter fortified it with new proofs, -derived both from reason and the senses." - -When we reflect that geometry is a science built upon self-evident -truths, and that all its conclusions are the result of pure -demonstration, and can admit of no controversy; when we further reflect, -that experimental evidence rests on the testimony of the senses, and we -infer a thing to be true because we actually see it to be so; it shows -us the extreme bigotry, the darkness visible, that beclouded the human -intellect, when it not only refused to admit conclusions first -established by pure geometrical reasoning, and afterwards confirmed by -experiments exhibited in the light of day, but instituted the most cruel -persecutions against the great philosopher who first proclaimed these -truths. Galileo was hated and persecuted by two distinct bodies of men, -both possessing great influence in their respective spheres,--the one -consisting of the learned doctors of philosophy, who did nothing more, -from age to age, than reiterate the doctrines of Aristotle, and were -consequently alarmed at the promulgation of principles subversive of -those doctrines; the other consisting of the Romish priesthood, -comprising the terrible Inquisition, who denounced the truths taught by -Galileo, as inconsistent with certain declarations of the Holy -Scriptures. We shall see, as we advance, what a fearful warfare he had -to wage against these combined powers of darkness. - -Aristotle had asserted, that, if two different weights of the same -material were let fall from the same height, the heavier one would reach -the ground sooner than the other, in proportion as it was more weighty. -For example: if a ten-pound leaden weight and a one-pound were let fall -from a given height at the same instant, the former would reach the -ground ten times as soon as the latter. No one thought of making the -trial, but it was deemed sufficient that Aristotle had said so; and -accordingly this assertion had long been received as an axiom in the -science of motion. Galileo ventured to appeal from the authority of -Aristotle to that of his own senses, and maintained, that both weights -would fall in the same time. The learned doctors ridiculed the idea. -Galileo tried the experiment in their presence, by letting fall, at the -same instant, large and small weights from the top of the celebrated -leaning tower of Pisa. Yet, with the sound of the two weights clicking -upon the pavement at the same moment, they still maintained that the -ten-pound weight would reach the ground in one tenth part of the time of -the other, because they could quote the chapter and verse of Aristotle -where the fact was asserted. Wearied and disgusted with the malice and -folly of these Aristotelian philosophers, Galileo, at the age of -twenty-eight, resigned his situation in the university of Pisa, and -removed to Padua, in the university of which place he was elected -professor of mathematics. Up to this period, Galileo had devoted himself -chiefly to the studies of the laws of motion, and the other branches of -mechanical philosophy. Soon afterwards, he began to publish his -writings, in rapid succession, and became at once among the most -conspicuous of his age,--a rank which he afterwards well sustained and -greatly exalted, by the invention of the telescope, and by his numerous -astronomical discoveries. I will reserve an account of these great -achievements until we come to that part of astronomy to which they were -more immediately related, and proceed, now, to explain to you the -leading principles of _terrestrial gravity_, as exemplified in falling -bodies. - -First, _all bodies near the earth's surface fall in straight lines -towards the centre of the earth_. We are not to infer from this fact, -that there resides at the centre any peculiar force, as a great -loadstone, for example, which attracts bodies towards itself; but bodies -fall towards the centre of the sphere, because the combined attractions -of all the particles of matter in the earth, each exerting its proper -force upon the body, would carry it towards the centre. This may be -easily illustrated by a diagram. Let B, Fig. 29, page 140, be the -centre of the earth, and A a body without it. Every portion of matter in -the earth exerts some force on A, to draw it down to the earth. But -since there is just as much matter on one side of the line A B, as on -the other side, each half exerts an equal force to draw the body towards -itself; therefore it falls in the direction of the diagonal between the -two forces. Thus, if we compare the effects of any two particles of -matter at equal distances from the line A B, but on opposite sides of -it, as _a_, _b_, while the force of the particle at _a_ would tend to -draw A in the direction of A _a_, that of _b_ would draw it in the -direction of A _b_, and it would fall in the line A B, half way between -the two. The same would hold true of any other two corresponding -particles of matter on different sides of the earth, in respect to a -body situated in any place without it. - -[Illustration Fig. 29.] - -Secondly, _all bodies fall towards the earth, from the same height, with -equal velocities_. A musket-ball, and the finest particle of down, if -let fall from a certain height towards the earth, tend to descend -towards it at the same rate, and would proceed with equal speed, were it -not for the resistance of the air, which retards the down more than it -does the ball, and finally stops it. If, however, the air be removed out -of the way, as it may be by means of the air-pump, the two bodies keep -side by side in falling from the greatest height at which we can try the -experiment. - -Thirdly, _bodies, in falling towards the earth, have their rate of -motion continually accelerated_. Suppose we let fall a musket-ball from -the top of a high tower, and watch its progress, disregarding the -resistance of the air: the first second, it will pass over sixteen feet -and one inch, but its speed will be constantly increased, being all the -while urged onward by the same force, and retaining all that it has -already acquired; so that the longer it is in falling, the swifter its -motion becomes. Consequently, when bodies fall from a great height, they -acquire an immense velocity before they reach the earth. Thus, a man -falling from a balloon, or from the mast-head of a ship, is broken in -pieces; and those meteoric stones, which sometimes fall from the sky, -bury themselves deep in the earth. On measuring the spaces through which -a body falls, it is found, that it will fall four times as far in two -seconds as in one, and one hundred times as far in ten seconds as in -one; and universally, the space described by a falling body is -proportioned to the time multiplied into itself; that is, to the square -of the time. - -Fourthly, _gravity is proportioned to the quantity of matter_. A body -which has twice as much matter as another exerts a force of attraction -twice as great, and also receives twice as much from the same body as it -would do, if it were only just as heavy as that body. Thus the earth, -containing, as it does, forty times as much matter as the moon, exerts -upon the moon forty times as much force as it would do, were its mass -the same with that of the moon; but it is also capable of _receiving_ -forty times as much gravity from the moon as it would do, were its mass -the same as the moon's; so that the power of attracting and that of -being attracted are reciprocal; and it is therefore correct to say, that -the moon attracts the earth _just as much_ as the earth attracts the -moon; and the same may be said of any two bodies, however different in -quantity of matter. - -Fifthly, _gravity, when acting at a distance from the earth, is not as -intense as it is near the earth_. At such a distance as we are -accustomed to ascend above the general level of the earth, no great -difference is observed. On the tops of high mountains, we find bodies -falling towards the earth, with nearly the same speed as they do from -the smallest elevations. It is found, nevertheless, that there is a real -difference; so that, in fact, the weight of a body (which is nothing -more than the measure of its force of gravity) is not quite so great on -the tops of high mountains as at the general level of the sea. Thus, a -thousand pounds' weight, on the top of a mountain half a mile high, -would weigh a quarter of a pound less than at the level of the sea; and -if elevated four thousand miles above the earth,--that is, _twice_ as -far from the centre of the earth as the surface is from the centre,--it -would weigh only one fourth as much as before; if _three times_ as far, -it would weigh only one ninth as much. So that the force of gravity -decreases, as we recede from the earth, in the same proportion as the -square of the distance increases. This fact is generalized by saying, -that _the force of gravity, at different distances from the earth, is -inversely as the square of the distance_. - -Were a body to fall from a great distance,--suppose a thousand times -that of the radius of the earth,--the force of gravity being one million -times less than that at the surface of the earth, the motion of the body -would be exceedingly slow, carrying it over only the sixth part of an -inch in a day. It would be a long time, therefore, in making any -sensible approaches towards the earth; but at length, as it drew near to -the earth it would acquire a very great velocity, and would finally rush -towards it with prodigious violence. Falling so far, and being -continually accelerated on the way, we might suppose that it would at -length attain a velocity infinitely great; but it can be demonstrated, -that, if a body were to fall from an infinite distance, attracted to the -earth only by gravity, it could never acquire a velocity greater than -about seven miles per second. This, however, is a speed inconceivably -great, being about eighteen times the greatest velocity that can be -given to a cannon-ball, and more than twenty-five thousand miles per -hour. - -But the phenomena of falling bodies must have long been observed, and -their laws had been fully investigated by Galileo and others, before the -cause of their falling was understood, or any such principle as -gravity, inherent in the earth and in all bodies, was applied to them. -The developement of this great principle was the work of Sir Isaac -Newton; and I will give you, in my next Letter, some particulars -respecting the life and discoveries of this wonderful man. - - - - -LETTER XIV. - -SIR ISAAC NEWTON.--UNIVERSAL GRAVITATION.--FIGURE OF THE EARTH'S -ORBIT.--PRECESSION OF THE EQUINOXES. - - "The heavens are all his own; from the wild rule - Of whirling vortices, and circling spheres, - To their first great simplicity restored. - The schools astonished stood; but found it vain - To combat long with demonstration clear, - And, unawakened, dream beneath the blaze - Of truth. At once their pleasing visions fled, - With the light shadows of the morning mixed, - When Newton rose, our philosophic sun."--_Thomson's Elegy._ - - -SIR ISAAC NEWTON was born in Lincolnshire, England, in 1642, just one -year after the death of Galileo. His father died before he was born, and -he was a helpless infant, of a diminutive size, and so feeble a frame, -that his attendants hardly expected his life for a single hour. The -family dwelling was of humble architecture, situated in a retired but -beautiful valley, and was surrounded by a small farm, which afforded but -a scanty living to the widowed mother and her precious charge. The cut -on page 144, Fig 30, represents the modest mansion, and the emblems of -rustic life that first met the eyes of this pride of the British nation, -and ornament of human nature. It will probably be found, that genius has -oftener emanated from the cottage than from the palace. - -[Illustration Fig. 30.] - -The boyhood of Newton was distinguished chiefly for his ingenious -mechanical contrivances. Among other pieces of mechanism, he constructed -a windmill so curious and complete in its workmanship, as to excite -universal admiration. After carrying it a while by the force of the -wind, he resolved to substitute animal power, and for this purpose he -inclosed in it a mouse, which he called the miller, and which kept the -mill a-going by acting on a tread-wheel. The power of the mouse was -brought into action by unavailing attempts to reach a portion of corn -placed above the wheel. A water-clock, a four-wheeled carriage propelled -by the rider himself, and kites of superior workmanship, were among the -productions of the mechanical genius of this gifted boy. At a little -later period, he began to turn his attention to the motions of the -heavenly bodies, and constructed several sun-dials on the walls of the -house where he lived. All this was before he had reached his fifteenth -year. At this age, he was sent by his mother, in company with an old -family servant, to a neighboring market-town, to dispose of products of -their farm, and to buy articles of merchandise for their family use; but -the young philosopher left all these negotiations to his worthy partner, -occupying himself, mean-while, with a collection of old books, which he -had found in a garret. At other times, he stopped on the road, and took -shelter with his book under a hedge, until the servant returned. They -endeavored to educate him as a farmer; but the perusal of a book, the -construction of a water-mill, or some other mechanical or scientific -amusement, absorbed all his thoughts, when the sheep were going astray, -and the cattle were devouring or treading down the corn. One of his -uncles having found him one day under a hedge, with a book in his hand, -and entirely absorbed in meditation, took it from him, and found that it -was a mathematical problem which so engrossed his attention. His -friends, therefore, wisely resolved to favor the bent of his genius, and -removed him from the farm to the school, to prepare for the university. -In the eighteenth year of his age, Newton was admitted into Trinity -College, Cambridge. He made rapid and extraordinary advances in the -mathematics, and soon afforded unequivocal presages of that greatness -which afterwards placed him at the head of the human intellect. In 1669, -at the age of twenty-seven, he became professor of mathematics at -Cambridge, a post which he occupied for many years afterwards. During -the four or five years previous to this he had, in fact, made most of -those great discoveries which have immortalized his name. We are at -present chiefly interested in one of these, namely, that of _universal -gravitation_; and let us see by what steps he was conducted to this -greatest of scientific discoveries. - -In the year 1666, when Newton was about twenty-four years of age, the -plague was prevailing at Cambridge, and he retired into the country. One -day, while he sat in a garden, musing on the phenomena of Nature around -him, an apple chanced to fall to the ground. Reflecting on the -mysterious power that makes all bodies near the earth fall towards its -centre, and considering that this power remains unimpaired at -considerable heights above the earth, as on the tops of trees and -mountains, he asked himself,--"May not the same force extend its -influence to a great distance from the earth, even as far as the moon? -Indeed, may not this be the very reason, why the moon is drawn away -continually from the straight line in which every body tends to move, -and is thus made to circulate around the earth?" You will recollect that -it was mentioned, in my Letter which contained an account of the first -law of motion, that if a body is put in motion by any force, it will -always move forward in a straight line, unless some other force compels -it to turn aside from such a direction; and that, when we see a body -moving in a curve, as a circular orbit, we are authorized to conclude -that there is some force existing within the circle, which continually -draws the body away from the direction in which it tends to move. -Accordingly, it was a very natural suggestion, to one so well acquainted -with the laws of motion as Newton, that the moon should constantly bend -towards the earth, from a tendency to fall towards it, as any other -heavy body would do, if carried to such a distance from the earth. -Newton had already proved, that if such a power as gravity extends from -the earth to distant bodies, it must decrease, as the square of the -distance from the centre of the earth increases; that is, at double the -distance, it would be four times less; at ten times the distance, one -hundred times less; and so on. Now, it was known that the moon is about -sixty times as far from the centre of the earth as the surface of the -earth is from the centre, and consequently, the force of attraction at -the moon must be the square of sixty, or thirty-six hundred times less -than it is at the earth; so that a body at the distance of the moon -would fall towards the earth very slowly, only one thirty-six hundredth -part as far in a given time, as at the earth. Does the moon actually -fall towards the earth at this rate; or, what is the same thing, does -she depart at this rate continually from the straight line in which she -tends to move, and in which she would move, if no external force -diverted her from it? On making the calculation, such was found to be -the fact. Hence gravity, and no other force than gravity, acts upon the -moon, and compels her to revolve around the earth. By reasonings equally -conclusive, it was afterwards proved, that a similar force compels all -the planets to circulate around the sun; and now, we may ascend from the -contemplation of this force, as we have seen it exemplified in falling -bodies, to that of a universal power whose influence extends to all the -material creation. It is in this sense that we recognise the principle -of universal gravitation, the law of which may be thus enunciated; _all -bodies in the universe, whether great or small, attract each other, with -forces proportioned to their respective quantities of matter, and -inversely as the squares of their distances from each other_. - -This law asserts, first, that attraction reigns throughout the material -world, affecting alike the smallest particle of matter and the greatest -body; secondly, that it acts upon every mass of matter, precisely in -proportion to its quantity; and, thirdly, that its intensity is -diminished as the square of the distance is increased. - -Observation has fully confirmed the prevalence of this law throughout -the solar system; and recent discoveries among the fixed stars, to be -more fully detailed hereafter, indicate that the same law prevails -there. The law of universal gravitation is therefore held to be the -grand principle which governs all the celestial motions. Not only is it -consistent with all the observed motions of the heavenly bodies, even -the most irregular of those motions, but, when followed out into all its -consequences, it would be competent to assert that such irregularities -must take place, even if they had never been observed. - -Newton first published the doctrine of universal gravitation in the -'Principia,' in 1687. The name implies that the work contains the -fundamental principles of natural philosophy and astronomy. Being -founded upon the immutable basis of mathematics, its conclusions must of -course be true and unalterable, and thenceforth we may regard the great -laws of the universe as traced to their remotest principle. The greatest -astronomers and mathematicians have since occupied themselves in -following out the plan which Newton began, by applying the principles of -universal gravitation to all the subordinate as well as to the grand -movements of the spheres. This great labor has been especially achieved -by La Place, a French mathematician of the highest eminence, in his -profound work, the 'Mecanique Celeste.' Of this work, our distinguished -countryman, Dr. Bowditch, has given a magnificent translation, and -accompanied it with a commentary, which both illustrates the original, -and adds a great amount of matter hardly less profound than that. - -[Illustration Fig. 31.] - -We have thus far taken the earth's orbit around the sun as a great -circle, such being its projection on the sphere constituting the -celestial ecliptic. The real path of the earth around the sun is -learned, as I before explained to you, by the apparent path of the sun -around the earth once a year. Now, when a body revolves about the earth -at a great distance from us, as is the case with the sun and moon, we -cannot certainly infer that it moves in a circle because it appears to -describe a circle on the face of the sky, for such might be the -appearance of its orbit, were it ever so irregular a curve. Thus, if E, -Fig. 31, represents the earth, and ACB, the irregular path of a body -revolving about it, since we should refer the body continually to some -place on the celestial sphere, XYZ, determined by lines drawn from the -eye to the concave sphere through the body, the body, while moving from -A to B through C, would appear to move from X to Z, through Y. Hence, we -must determine from other circumstances than the actual appearance, what -is the true figure of the orbit. - -[Illustration Fig. 32.] - -Were the earth's path a circle, having the sun in the centre, the sun -would always appear to be at the same distance from us; that is, the -radius of the orbit, or _radius vector_, (the name given to a line drawn -from the centre of the sun to the orbit of any planet,) would always be -of the same length. But the earth's distance from the sun is constantly -varying, which shows that its orbit is not a circle. We learn the true -figure of the orbit, by ascertaining the _relative distances_ of the -earth from the sun, at various periods of the year. These distances all -being laid down in a diagram, according to their respective lengths, the -extremities, on being connected, give us our first idea of the shape of -the orbit, which appears of an oval form, and at least resembles an -ellipse; and, on further trial, we find that it has the properties of an -ellipse. Thus, let E, Fig. 32, be the place of the earth, and _a_, _b_, -_c_, &c., successive positions of the sun; the _relative_ lengths of the -lines E _a_, E _b_, &c., being known, on connecting the points _a_, -_b_, _c_, &c., the resulting figure indicates the true figure of the -earth's orbit. - -These relative distances are found in two different ways; first, _by -changes in the sun's apparent diameter_, and, secondly, _by variations -in his angular velocity_. The same object appears to us smaller in -proportion as it is more distant; and if we see a heavenly body varying -in size, at different times, we infer that it is at different distances -from us; that when largest, it is nearest to us, and when smallest, -furthest off. Now, when the sun's diameter is accurately measured by -instruments, it is found to vary from day to day; being, when greatest, -more than thirty-two minutes and a half, and when smallest, only -thirty-one minutes and a half,--differing, in all, about seventy-five -seconds. When the diameter is greatest, which happens in January, we -know that the sun is nearest to us; and when the diameter is least, -which occurs in July, we infer that the sun is at the greatest distance -from us. The point where the earth, or any planet, in its revolution, is -nearest the sun, is called its _perihelion_; the point where it is -furthest from the sun, its _aphelion_. Suppose, then, that, about the -first of January, when the diameter of the sun is greatest, we draw a -line, E _a_, Fig. 32, to represent it, and afterwards, every ten days, -draw other lines, E _b_, E _c_, &c.; increasing in the same ratio as the -apparent diameters of the sun decrease. These lines must be drawn at -such a distance from each other, that the triangles, E _a b_, E _b c_, -&c., shall be all equal to each other, for a reason that will be -explained hereafter. On connecting the extremities of these lines, we -shall obtain the figure of the earth's orbit. - -Similar conclusions may be drawn from observations on the sun's _angular -velocity_. A body appears to move most rapidly when nearest to us. -Indeed, the apparent velocity increases rapidly, as it approaches us, -and as rapidly diminishes, when it recedes from us. If it comes twice as -near as before, it appears to move not merely twice as swiftly, but four -times as swiftly; if it comes ten times nearer, its apparent velocity -is one hundred times as great as before. We say, therefore, that the -velocity varies inversely as the square of the distance; for, as the -distance is diminished ten times, the velocity is increased the square -of ten; that is, one hundred times. Now, by noting the time it takes the -sun, from day to day, to cross the central wire of the -transit-instrument, we learn the comparative velocities with which it -moves at different times; and from these we derive the comparative -distances of the sun at the corresponding times; and laying down these -relative distances in a diagram, as before, we get our first notions of -the actual figure of the earth's orbit, or the path which it describes -in its annual revolution around the sun. - -Having now learned the fact, that the earth moves around the sun, not in -a circular but in an elliptical orbit, you will desire to know by what -forces it is impelled, to make it describe this figure, with such -uniformity and constancy, from age to age. It is commonly said, that -gravity causes the earth and the planets to circulate around the sun; -and it is true that it is gravity which turns them aside from the -straight line in which, by the first law of motion, they tend to move, -and thus causes them to revolve around the sun. But what force is that -which gave to them this original impulse, and impressed upon them such a -tendency to move forward in a straight line? The name _projectile_ force -is given to it, because it is the same _as though_ the earth were -originally projected into space, when first created; and therefore its -motion is the result of two forces, the projectile force, which would -cause it to move forward in a straight line which is a tangent to its -orbit, and gravitation, which bends it towards the sun. But before you -can clearly understand the nature of this motion, and the action of the -two forces that produce it, I must explain to you a few elementary -principles upon which this and all the other planetary motions depend. - -You have already learned, that when a body is acted on by two forces, in -different directions, it moves in the direction of neither, but in some -direction between them. If I throw a stone horizontally, the attraction -of the earth will continually draw it downward, out of the line of -direction in which it was thrown, and make it descend to the earth in a -curve. The particular form of the curve will depend on the velocity with -which it is thrown. It will always _begin_ to move in the line of -direction in which it is projected; but it will soon be turned from that -line towards the earth. It will, however, continue nearer to the line of -projection in proportion as the velocity of projection is greater. Thus, -let A C, Fig. 33, be perpendicular to the horizon, and A B parallel to -it, and let a stone be thrown from A, in the direction of A B. It will, -in every case, commence its motion in the line A B, which will therefore -be a tangent to the curve it describes; but, if it is thrown with a -small velocity, it will soon depart from the tangent, describing the -line A D; with a greater velocity, it will describe a curve nearer the -tangent, as A E; and with a still greater velocity, it will describe the -curve A F. - -[Illustration Fig. 33.] - -As an example of a body revolving in an orbit under the influence of two -forces, suppose a body placed at any point, P, Fig. 34, above the -surface of the earth, and let P A be the direction of the earth's -centre; that is, a line perpendicular to the horizon. If the body were -allowed to move, without receiving any impulse, it would descend to the -earth in the direction P A with an accelerated motion. But suppose that, -at the moment of its departure from P, it receives a blow in the -direction P B, which would carry it to B in the time the body would fall -from P to A; then, under the influence of both forces, it would descend -along the curve P D. If a stronger blow were given to it in the -direction P B, it would describe a larger curve, P E; or, finally, if -the impulse were sufficiently strong, it would circulate quite around -the earth, and return again to P, describing the circle P F G. With a -velocity of projection still greater, it would describe an ellipse, P I -K; and if the velocity be increased to a certain degree, the figure -becomes a parabola, L P M,--a curve which never returns into itself. - -[Illustration Fig. 34.] - -In Fig. 35, page 154, suppose the planet to have passed the point C, at -the aphelion, with so small a velocity, that the attraction of the sun -bends its path very much, and causes it immediately to begin to approach -towards the sun. The sun's attraction will increase its velocity, as it -moves through D, E, and F, for the sun's attractive force on the planet, -when at D, is acting in the direction D S; and, on account of the small -angle made between D E and D S, the force acting in the line D S helps -the planet forward in the path D E, and thus increases its velocity. In -like manner, the velocity of the planet will be continually increasing -as it passes through D, E, and F; and though the attractive force, on -account of the planet's nearness, is so much increased, and tends, -therefore, to make the orbit more curved, yet the velocity is also so -much increased, that the orbit is not more curved than before; for the -same increase of velocity, occasioned by the planet's approach to the -sun, produces a greater increase of centrifugal force, which carries it -off again. We may see, also, the reason why, when the planet has reached -the most distant parts of its orbit, it does not entirely fly off, and -never return to the sun; for, when the planet passes along H, K, A, the -sun's attraction retards the planet, just as gravity retards a ball -rolled up hill; and when it has reached C, its velocity is very small, -and the attraction to the centre of force causes a great deflection from -the tangent, sufficient to give its orbit a great curvature, and the -planet wheels about, returns to the sun, and goes over the same orbit -again. As the planet recedes from the sun, its centrifugal force -diminishes faster than the force of gravity, so that the latter finally -preponderates. - -[Illustration Fig. 35.] - -I shall conclude what I have to say at present, respecting the motion of -the earth around the sun, by adding a few words respecting the -precession of the equinoxes. - -The _precession of the equinoxes_ is a slow but continual shifting of -the equinoctial points, from east to west. Suppose that we mark the -exact place in the heavens where, during the present year, the sun -crosses the equator, and that this point is close to a certain star; -next year, the sun will cross the equator a little way westward of that -star, and so every year, a little further westward, until, in a long -course of ages, the place of the equinox will occupy successively every -part of the ecliptic, until we come round to the same star again. As, -therefore, the sun revolving from west to east, in his apparent orbit, -comes round to the point where it left the equinox, it meets the equinox -before it reaches that point. The appearance is as though the equinox -_goes forward_ to meet the sun, and hence the phenomenon is called the -_precession_ of the equinoxes; and the fact is expressed by saying, that -the equinoxes retrograde on the ecliptic, until the line of the -equinoxes (a straight line drawn from one equinox to the other) makes a -complete revolution, from east to west. This is of course a retrograde -motion, since it is contrary to the order of the signs. The equator is -conceived as _sliding_ westward on the ecliptic, always preserving the -same inclination to it, as a ring, placed at a small angle with another -of nearly the same size which remains fixed, may be slid quite around -it, giving a corresponding motion to the two points of intersection. It -must be observed, however, that this mode of conceiving of the -precession of the equinoxes is purely imaginary, and is employed merely -for the convenience of representation. - -The amount of precession annually is fifty seconds and one tenth; -whence, since there are thirty-six hundred seconds in a degree, and -three hundred and sixty degrees in the whole circumference of the -ecliptic, and consequently one million two hundred and ninety-six -thousand seconds, this sum, divided by fifty seconds and one tenth, -gives twenty-five thousand eight hundred and sixty-eight years for the -period of a complete revolution of the equinoxes. - -Suppose we now fix to the centre of each of the two rings, before -mentioned, a wire representing its axis, one corresponding to the axis -of the ecliptic, the other to that of the equator, the extremity of each -being the pole of its circle. As the ring denoting the equator turns -round on the ecliptic, which, with its axis, remains fixed, it is easy -to conceive that the axis of the equator revolves around that of the -ecliptic, and the pole of the equator around the pole of the ecliptic, -and constantly at a distance equal to the inclination of the two -circles. To transfer our conceptions to the celestial sphere, we may -easily see that the axis of the diurnal sphere (that of the earth -produced) would not have its pole constantly in the same place among the -stars, but that this pole would perform a slow revolution around the -pole of the ecliptic, from east to west, completing the circuit in about -twenty-six thousand years. Hence the star which we now call the -pole-star has not always enjoyed that distinction, nor will it always -enjoy it, hereafter. When the earliest catalogues of the stars were -made, this star was twelve degrees from the pole. It is now one degree -twenty-four minutes, and will approach still nearer; or, to speak more -accurately, the pole will come still nearer to this star, after which it -will leave it, and successively pass by others. In about thirteen -thousand years, the bright star Lyra (which lies near the circle in -which the pole of the equator revolves about the pole of the ecliptic, -on the side opposite to the present pole-star) will be within five -degrees of the pole, and will constitute the pole-star. As Lyra now -passes near our zenith, you might suppose that the change of position of -the pole among the stars would be attended with a change of altitude of -the north pole above the horizon. This mistaken idea is one of the many -misapprehensions which result from the habit of considering the horizon -as a fixed circle in space. However the pole might shift its position in -space, we should still be at the same distance from it, and our horizon -would always reach the same distance beyond it. - -The time occupied by the sun, in passing from the equinoctial point -round to the same point again, is called the _tropical year_. As the sun -does not perform a complete revolution in this interval, but falls short -of it fifty seconds and one tenth, the tropical year is shorter than the -sidereal by twenty minutes and twenty seconds, in mean solar time, this -being the time of describing an arc of fifty seconds and one tenth, in -the annual revolution. - -The changes produced by the precession of the equinoxes, in the apparent -places of the circumpolar stars, have led to some interesting results in -_chronology_. In consequence of the retrograde motion of the equinoctial -points, the _signs_ of the ecliptic do not correspond, at present, to -the _constellations_ which bear the same names, but lie about one sign, -or thirty degrees, westward of them. Thus, that division of the ecliptic -which is called the sign Taurus lies in the constellation Aries, and the -sign Gemini, in the constellation Taurus. Undoubtedly, however, when the -ecliptic was thus first divided, and the divisions named, the several -constellations lay in the respective divisions which bear their names. - - - - -LETTER XV. - -THE MOON. - - "Soon as the evening shades prevail - The Moon takes up the wondrous tale, - And nightly to the listening earth - Repeats the story of her birth."--_Addison._ - - -HAVING now learned so much of astronomy as relates to the earth and the -sun, and the mutual relations which exist between them, you are prepared -to enter with advantage upon the survey of the other bodies that compose -the solar system. This being done, we shall then have still before us -the boundless range of the fixed stars. - -The moon, which next claims our notice, has been studied by astronomers -with greater attention than any other of the heavenly bodies, since her -comparative nearness to the earth brings her peculiarly within the range -of our telescopes, and her periodical changes and very irregular -motions, afford curious subjects, both for observation and speculation. -The mild light of the moon also invites our gaze, while her varying -aspects serve barbarous tribes, especially, for a kind of dial-plate -inscribed on the face of the sky, for weeks, and months, and times, and -seasons. - -The moon is distant from the earth about two hundred and forty thousand -miles; or, more exactly, two hundred and thirty-eight thousand five -hundred and forty-five miles. Her angular or apparent diameter is about -half a degree, and her real diameter, two thousand one hundred and sixty -miles. She is a companion, or satellite, to the earth, revolving around -it every month, and accompanying us in our annual revolution around the -sun. Although her nearness to us makes her appear as a large and -conspicuous object in the heavens, yet, in comparison with most of the -other celestial bodies, she is in fact very small, being only one -forty-ninth part as large as the earth, and only about one seventy -millionth part as large as the sun. - -The moon shines by light borrowed from the sun, being itself an opaque -body, like the earth. When the disk, or any portion of it, is -illuminated, we can plainly discern, even with the naked eye, varieties -of light and shade, indicating inequalities of surface which we imagine -to be land and water. I believe it is the common impression, that the -darker portions are land and the lighter portions water; but if either -part is water, it must be the darker regions. A smooth polished surface, -like water, would reflect the sun's light like a mirror. It would, like -a convex mirror, form a diminished image of the sun, but would not -itself appear luminous like an uneven surface, which multiplies the -light by numerous reflections within itself. Thus, from this cause, high -broken mountainous districts appear more luminous than extensive plains. - -[Illustration Figures 36, 37. TELESCOPIC VIEWS OF THE MOON.] - -By the aid of the telescope, we may see undoubted indications of -mountains and valleys. Indeed, with a good glass, we can discover the -most decisive evidence that the surface of the moon is exceedingly -varied,--one part ascending in lofty peaks, another clustering in -huge mountain groups, or long ranges, and another bearing all the marks -of deep caverns or valleys. You will not, indeed, at the first sight of -the moon through a telescope, recognise all these different objects. If -you look at the moon when half her disk is enlightened, (which is the -best time for seeing her varieties of surface,) you will, at the first -glance, observe a motley appearance, particularly along the line called -the _terminator_, which separates the enlightened from the unenlightened -part of the disk. (Fig. 37.) On one side of the terminator, within the -dark part of the disk, you will see illuminated points, and short, -crooked lines, like rude characters marked with chalk on a black ground. -On the other side of the terminator you will see a succession of little -circular groups, appearing like numerous bubbles of oil on the surface -of water. The further you carry your eye from the terminator, on the -same side of it, the more indistinctly formed these bubbles appear, -until towards the edge of the moon they assume quite a different aspect. - -Some persons, when they look into a telescope for the first time, having -heard that mountains and valleys are to be seen, and discovering nothing -but these unmeaning figures, break off in disappointment, and have their -faith in these things rather diminished than increased. I would advise -you, therefore, before you take even your first view of the moon through -a telescope, to form as clear an idea as you can, how mountains, and -valleys, and caverns, situated at such a distance from the eye, ought to -look, and by what marks they may be recognised. Seize, if possible, the -most favorable period, (about the time of the first quarter,) and -previously learn from drawings and explanations, how to interpret every -thing you see. - -What, then, ought to be the respective appearances of mountains, -valleys, and deep craters, or caverns, in the moon? The sun shines on -the moon in the same way as it shines on the earth; and let, us reflect, -then, upon the manner in which it strikes similar objects here. One -half the globe is constantly enlightened; and, by the revolution of the -earth on its axis, the terminator, or the line which separates the -enlightened from the unenlightened part of the earth, travels along from -east to west, over different places, as we see the moon's terminator -travel over her disk from new to full moon; although, in the case of the -earth, the motion is more rapid, and depends on a different cause. In -the morning, the sun's light first strikes upon the tops of the -mountains, and, if they are very high, they may be brightly illuminated -while it is yet night in the valleys below. By degrees, as the sun -rises, the circle of illumination travels down the mountain, until at -length it reaches the bottom of the valleys; and these in turn enjoy the -full light of day. Again, a mountain casts a shadow opposite to the sun, -which is very long when the sun first rises, and shortens continually as -the sun ascends, its length at a given time, however, being proportioned -to the height of the mountain; so that, if the shadow be still very long -when the sun is far above the horizon, we infer that the mountain is -very lofty. We may, moreover, form some judgment of the shape of a -mountain, by observing that of its shadow. - -Now, the moon is so distant that we could not easily distinguish places -simply by their elevations, since they would be projected into the same -imaginary plane which constitutes the apparent disk of the moon; but the -foregoing considerations would enable us to infer their existence. Thus, -when you view the moon at any time within her first quarter, but better -near the end of that period, you will observe, on the side of the -terminator within the dark part of the disk, the tops of mountains which -the light of the sun is just striking, as the morning sun strikes the -tops of mountains on the earth. These you will recognise by those white -specks and little crooked lines, before mentioned, as is represented in -Fig. 37. These bright points and lines you will see altering their -figure, every hour, as they come more and more into the sun's light; -and, mean-while, other bright points, very minute at first, will start -into view, which also in turn grow larger as the terminator approaches -them, until they fall into the enlightened part of the disk. As they -fall further and further within this part, you will have additional -proofs that they are mountains, from the shadows which they cast on the -plain, always in a direction opposite to the sun. The mountain itself -may entirely disappear, or become confounded with the other enlightened -portions of the surface; but its position and its shape may still be -recognised by the dark line which it projects on the plane. This line -will correspond in shape to that of the mountain, presenting at one time -a long serpentine stripe of black, denoting that the mountain is a -continued range; at another time exhibiting a conical figure tapering to -a point, or a series of such sharp points; or a serrated, uneven -termination, indicating, in each case respectively, a conical mountain, -or a group of peaks, or a range with lofty cliffs. All these appearances -will indeed be seen in miniature; but a little familiarity with them -will enable you to give them, in imagination, their proper dimensions, -as you give to the pictures of known animals their due sizes, although -drawn on a scale far below that of real life. - -In the next place, let us see how valleys and deep craters in the moon -might be expected to appear. We could not expect to see depressions any -more than elevations, since both would alike be projected on the same -imaginary disk. But we may recognise such depressions, from the manner -in which the light of the sun shines into them. When we hold a china -tea-cup at some distance from a candle, in the night, the candle being -elevated but little above the level of the top of the cup, a luminous -crescent will be formed on the side of the cup opposite to the candle, -while the side next to the candle will be covered by a deep shadow. As -we gradually elevate the candle, the crescent enlarges and travels down -the side of the cup, until finally the whole interior becomes -illuminated. We observe similar appearances in the moon, which we -recognise as deep depressions. They are those circular spots near the -terminator before spoken of, which look like bubbles of oil floating on -water. They are nothing else than circular craters or deep valleys. When -they are so situated that the light of the sun is just beginning to -shine into them, you may see, as in the tea-cup, a luminous crescent -around the side furthest from the sun, while a deep black shadow is cast -on the side next to the sun. As the cavity is turned more and more -towards the light, the crescent enlarges, until at length the whole -interior is illuminated. If the tea-cup be placed on a table, and a -candle be held at some distance from it, nearly on a level with the top, -but a little above it, the cup itself will cast a shadow on the table, -like any other elevated object. In like manner, many of these circular -spots on the moon cast deep shadows behind them, indicating that the -tops of the craters are elevated far above the general level of the -moon. The regularity of some of these circular spots is very remarkable. -The circle, in some instances, appears as well formed as could be -described by a pair of compasses, while in the centre there not -unfrequently is seen a conical mountain casting its pointed shadow on -the bottom of the crater. I hope you will enjoy repeated opportunities -to view the moon through a telescope. Allow me to recommend to you, not -to rest satisfied with a hasty or even with a single view, but to verify -the preceding remarks by repeated and careful inspection of the lunar -disk, at different ages of the moon. - -The various places on the moon's disk have received appropriate names. -The dusky regions being formerly supposed to be seas, were named -accordingly; and other remarkable places have each two names, one -derived from some well-known spot on the earth, and the other from some -distinguished personage. Thus, the same bright spot on the surface of -the moon is called _Mount Sinai_ or _Tycho_, and another, _Mount Etna_ -or _Copernicus_. The names of individuals, however, are more used than -the others. The diagram, Fig. 36, (see page 159,) represents rudely, the -telescopic appearance of the full moon. The reality is far more -beautiful. A few of the most remarkable points have the following names -corresponding to the numbers and letters on the map. - - 1. Tycho, 6. Eratosthenes, - 2. Kepler, 7. Plato, - 3. Copernicus, 8. Archimedes, - 4. Aristarchus, 9. Eudoxus, - 5. Helicon, 10. Aristotle. - - A. Mare Humorum, _Sea of Humors_, - B. Mare Nubium, _Sea of Clouds_, - C. Mare Imbrium, _Sea of Rains_, - D. Mare Nectaris, _Sea of Nectar_, - E. Mare Tranquillitatis, _Sea of Tranquillity_, - F. Mare Serenitatis, _Sea of Serenity_, - G. Mare Fecunditatis, _Sea of Plenty_, - H. Mare Crisium, _Crisian Sea_. - -The heights of the lunar mountains, and the depths of the valleys, can -be estimated with a considerable degree of accuracy. Some of the -mountains are as high as five miles, and the valleys, in some instances, -are four miles deep. Hence it is inferred, that the surface of the moon -is more broken and irregular than that of the earth, its mountains being -higher and its valleys deeper, in proportion to its magnitude, than -those of the earth. - -The varieties of surface in the moon, as seen by the aid of large -telescopes, have been well described by Dr. Dick, in his 'Celestial -Scenery,' and I cannot give you a better idea of them, than to add a few -extracts from his work. The lunar mountains in general exhibit an -arrangement and an aspect very different from the mountain scenery of -our globe. They may be arranged under the four following varieties: - -First, _insulated mountains_, which rise from plains nearly level, -shaped like a sugar loaf, which may be supposed to present an appearance -somewhat similar to Mount Etna, or the Peak of Teneriffe. The shadows -of these mountains, in certain phases of the moon, are as distinctly -perceived as the shadow of an upright staff, when placed opposite to the -sun; and these heights can be calculated from the length of their -shadows. Some of these mountains being elevated in the midst of -extensive plains, would present to a spectator on their summits -magnificent views of the surrounding regions. - -Secondly, _mountain ranges_, extending in length two or three hundred -miles. These ranges bear a distant resemblance to our Alps, Apennines, -and Andes; but they are much less in extent. Some of them appear very -rugged and precipitous; and the highest ranges are in some places more -than four miles in perpendicular altitude. In some instances, they are -nearly in a straight line from northeast to southwest, as in the range -called the _Apennines_; in other cases, they assume the form of a -semicircle, or crescent. - -Thirdly, _circular ranges_, which appear on almost every part of the -moon's surface, particularly in its southern regions. This is one grand -peculiarity of the lunar ranges, to which we have nothing similar on the -earth. A plain, and sometimes a large cavity, is surrounded with a -circular ridge of mountains, which encompasses it like a mighty rampart. -These annular ridges and plains are of all dimensions, from a mile to -forty or fifty miles in diameter, and are to be seen in great numbers -over every region of the moon's surface; they are most conspicuous, -however, near the upper and lower limbs, about the time of the half -moon. - -The mountains which form these circular ridges are of different -elevations, from one fifth of a mile to three miles and a half, and -their shadows cover one half of the plain at the base. These plains are -sometimes on a level with the general surface of the moon, and in other -cases they are sunk a mile or more below the level of the ground which -surrounds the exterior circle of the mountains. - -Fourthly, _central mountains_, or those which are placed in the middle -of circular plains. In many of the plains and cavities surrounded by -circular ranges of mountains there stands a single insulated mountain, -which rises from the centre of the plain, and whose shadow sometimes -extends, in the form of a pyramid, half across the plain to the opposite -ridges. These central mountains are generally from half a mile to a mile -and a half in perpendicular altitude. In some instances, they have two, -and sometimes three, different tops, whose shadows can be easily -distinguished from each other. Sometimes they are situated towards one -side of the plain, or cavity; but in the great majority of instances -their position is nearly or exactly central. The lengths of their bases -vary from five to about fifteen or sixteen miles. - -The _lunar caverns_ form a very peculiar and prominent feature of the -moon's surface, and are to be seen throughout almost every region, but -are most numerous in the southwest part of the moon. Nearly a hundred of -them, great and small, may be distinguished in that quarter. They are -all nearly of a circular shape, and appear like a very shallow egg-cup. -The smaller cavities appear, within, almost like a hollow cone, with the -sides tapering towards the centre; but the larger ones have, for the -most part, flat bottoms, from the centre of which there frequently rises -a small, steep, conical hill, which gives them a resemblance to the -circular ridges and central mountains before described. In some -instances, their margins are level with the general surface of the moon; -but, in most cases, they are encircled with a high annular ridge of -mountains, marked with lofty peaks. Some of the larger of these cavities -contain smaller cavities of the same kind and form, particularly in -their sides. The mountainous ridges which surround these cavities -reflect the greatest quantity of light; and hence that region of the -moon in which they abound appears brighter than any other. From their -lying in every possible direction, they appear, at and near the time of -full moon, like a number of brilliant streaks, or radiations. These -radiations appear to converge towards a large brilliant spot, -surrounded by a faint shade, near the lower part of the moon, which is -named Tycho,--a spot easily distinguished even by a small telescope. The -spots named Kepler and Copernicus are each composed of a central spot -with luminous radiations.[8] - -The broken surface and apparent geological structure of the moon has -suggested the opinion, that the moon has been subject to powerful -_volcanic_ action. This opinion receives support from certain actual -appearances of volcanic fires, which have at different times been -observed. In a total eclipse of the sun, the moon comes directly between -us and that luminary, and presents her dark side towards us under -circumstances very favorable for observation. At such times, several -astronomers, at different periods, have noticed bright spots, which they -took to be volcanoes. It must evidently require a large fire to be -visible at all, at such a distance; and even a burning spark, or point -but just visible in a large telescope, might be in fact a volcano raging -like Etna or Vesuvius. Still, as fires might be supposed to exist in the -moon from different causes, we should require some marks peculiar to -volcanic fires, to assure us that such was their origin in a given case. -Dr. Herschel examined this point with great attention, and with better -means of observation than any of his predecessors enjoyed, and fully -embraced the opinion that what he saw were volcanoes. In April, 1787, he -records his observations as follows: "I perceive three volcanoes in -different places in the dark part of the moon. Two of them are already -nearly extinct, or otherwise in a state of going to break out; the third -shows an eruption of fire or luminous matter." On the next night, he -says: "The volcano burns with greater violence than last night; its -diameter cannot be less than three seconds; and hence the shining or -burning matter must be above three miles in diameter. The appearance -resembles a small piece of burning charcoal, when it is covered with a -very thin coat of white ashes; and it has a degree of brightness about -as strong as that with which such a coal would be seen to glow in faint -daylight." That these were really volcanic fires, he considered further -evident from the fact, that where a fire, supposed to have been -volcanic, had been burning, there was seen, after its extinction, an -accumulation of matter, such as would arise from the production of a -great quantity of lava, sufficient to form a mountain. - -It is probable that the moon has an _atmosphere_, although it is -difficult to obtain perfectly satisfactory evidence of its existence; -for granting the existence of an atmosphere bearing the same proportion -to that planet as our atmosphere bears to the earth, its dimensions and -its density would be so small, that we could detect its presence only by -the most refined observations. As our twilight is owing to the agency of -our atmosphere, so, could we discern any appearance of twilight in the -moon, we should regard that fact as indicating that she is surrounded by -an atmosphere. Or, when the moon covers the sun in a solar eclipse, -could we see around her circumference a faint luminous ring, indicating -that the sunlight shone through an aerial medium, we might likewise -infer the existence of such a medium. Such a faint ring of light has -sometimes, as is supposed, been observed. Schroeter, a German -astronomer, distinguished for the acuteness of his vision and his powers -of observation in general, was very confident of having obtained, from -different sources, clear evidence of a lunar atmosphere. He concluded, -that the inferior or more dense part of the moon's atmosphere is not -more than fifteen hundred feet high, and that the entire height, at -least to the limit where it would be too rare to produce any of the -phenomena which are relied on as proofs of its existence, is not more -than a mile. - -It has been a question, much agitated among astronomers, whether there -is _water_ in the moon. Analogy strongly inclines us to reply in the -affirmative. But the analogy between the earth and the moon, as derived -from all the particulars in which we can compare the two bodies, is too -feeble to warrant such a conclusion, and we must have recourse to other -evidence, before we can decide the point. In the first place, then, -there is no positive evidence in favor of the existence of water in the -moon. Those extensive level regions, before spoken of, and denominated -seas in the geography of this planet, have no other signs of being -water, except that they are level and dark. But both these particulars -would characterize an earthly plain, like the deserts of Arabia and -Africa. In the second place, were those dark regions composed of water, -the terminator would be entirely smooth where it passed over these -oceans or seas. It is indeed indented by few inequalities, compared with -those which it exhibits where it passes over the mountainous regions; -but still, the inequalities are too considerable to permit the -conclusion, that these level spots are such perfect levels as water -would form. They do not appear to be more perfect levels than many plain -countries on the globe. The deep caverns, moreover, seen in those dusky -spots which were supposed to be seas, are unfavorable to the supposition -that those regions are covered by water. In the third place, the face of -the moon, when illuminated by the sun and not obscured by the state of -our own atmosphere, is always serene, and therefore free from clouds. -Clouds are objects of great extent; they frequently intercept light, -like solid bodies; and did they exist about the moon, we should -certainly see them, and should lose sight of certain parts of the lunar -disk which they covered. But neither position is true; we neither see -any clouds about the moon, with our best telescopes, nor do we, by the -intervention of clouds, ever lose sight of any portion of the moon when -our own atmosphere is clear. But the want of clouds in the lunar -atmosphere almost necessarily implies the absence of water in the moon. -This planet is at the same distance from the sun as our own, and has, in -this respect, an equal opportunity to feel the influence of his rays. -Its days are also twenty-seven times as long as ours, a circumstance -which would augment the solar heat. When the pressure of the atmosphere -is diminished on the surface of water, its tendency to pass into the -state of vapor is increased. Were the whole pressure of the atmosphere -removed from the surface of a lake, in a Summer's day, when the -temperature was no higher than seventy-two degrees, the water would -begin to boil. Now it is well ascertained, that if there be any -atmosphere about the moon, it is much lighter than ours, and presses on -the surface of that body with a proportionally small force. This -circumstance, therefore, would conspire with the other causes mentioned, -to convert all the water of the moon into vapor, if we could suppose it -to have existed at any given time. - -But those, who are anxious to furnish the moon and other planets with -all the accommodations which they find in our own, have a subterfuge in -readiness, to which they invariably resort in all cases like the -foregoing. "There may be," say they, "some means, unknown to us, -provided for retaining water on the surface of the moon, and for -preventing its being wasted by evaporation: perhaps it remains unaltered -in quantity, imparting to the lunar regions perpetual verdure and -fertility." To this I reply, that the bare possibility of a thing is but -slight evidence of its reality; nor is such a condition possible, except -by miracle. If they grant that the laws of Nature are the same in the -moon as in the earth, then, according to the foregoing reasoning, there -cannot be water in the moon; but if they say that the laws of Nature are -not the same there as here, then we cannot reason at all respecting -them. One who resorts to a subterfuge of this kind ruins his own cause. -He argues the existence of water in the moon, from the analogy of that -planet to this. But if the laws of Nature are not the same there as -here, what becomes of his analogy? A liquid substance which would not -evaporate by such a degree of solar heat as falls on the moon, which -would not evaporate the faster, in consequence of the diminished -atmospheric pressure which prevails there, could not be water, for it -would not have the properties of water, and things are known by their -properties. Whenever we desert the cardinal principle of the Newtonian -philosophy,--that the laws of Nature are uniform throughout all her -realms,--we wander in a labyrinth; all analogies are made void; all -physical reasonings cease; and imaginary possibilities or direct -miracles take the place of legitimate natural causes. - -On the supposition that the moon is inhabited, the question has often -been raised, whether we may hope that our telescopes will ever be so -much improved, and our other means of observation so much augmented, -that we shall be able to discover either the lunar inhabitants or any of -their works. - -The improbability of our ever identifying _artificial structures_ in the -moon may be inferred from the fact, that a space a mile in diameter is -the least space that could be distinctly seen. Extensive works of art, -as large cities, or the clearing up of large tracts of country for -settlement or tillage, might indeed afford some varieties of surface; -but they would be merely varieties of light and shade, and the -individual objects that occasioned them would probably never be -recognised by their distinctive characters. Thus, a building equal to -the great pyramid of Egypt, which covers a space less than the fifth of -a mile in diameter, would not be distinguished by its figure; indeed, it -would be a mere point. Still less is it probable that we shall ever -discover any inhabitants in the moon. Were we to view the moon with a -telescope that magnifies ten thousand times, it would bring the moon -apparently ten thousand times nearer, and present it to the eye like a -body twenty-four miles off. But even this is a distance too great for us -to see the works of man with distinctness. Moreover, from the nature of -the telescope itself, we can never hope to apply a magnifying power so -high as that here supposed. As I explained to you, when speaking of the -telescope, whenever we increase the magnifying power of this instrument -we diminish its field of view, so that with very high magnifiers we can -see nothing but a point, such as a fixed star. We at the same time, -also, magnify the vapors and smoke of the atmosphere, and all the -imperfections of the medium, which greatly obscures the object, and -prevents our seeing it distinctly. Hence it is generally most -satisfactory to view the moon with low powers, which afford a large -field of view and give a clear light. With Clark's telescope, belonging -to Yale College, we seldom gain any thing by applying to the moon a -higher power than one hundred and eighty, although the instrument admits -of magnifiers as high as four hundred and fifty. - -Some writers, however, suppose that possibly we may trace indications of -lunar inhabitants in their works, and that they may in like manner -recognise the existence of the inhabitants of our planet. An author, who -has reflected much on subjects of this kind, reasons as follows: "A -navigator who approaches within a certain distance of a small island, -although he perceives no human being upon it, can judge with certainty -that it is inhabited, if he perceives human habitations, villages, -corn-fields, or other traces of cultivation. In like manner, if we could -perceive changes or operations in the moon, which could be traced to the -agency of intelligent beings, we should then obtain satisfactory -evidence that such beings exist on that planet; and it is thought -possible that such operations may be traced. A telescope which magnifies -twelve hundred times will enable us to perceive, as a visible point on -the surface of the moon, an object whose diameter is only about three -hundred feet. Such an object is not larger than many of our public -edifices; and therefore, were any such edifices rearing in the moon, or -were a town or city extending its boundaries, or were operations of this -description carrying on, in a district where no such edifices had -previously been erected, such objects and operations might probably be -detected by a minute inspection. Were a multitude of living creatures -moving from place to place, in a body, or were they even encamping in an -extensive plain, like a large army, or like a tribe of Arabs in the -desert, and afterwards removing, it is possible such changes might be -traced by the difference of shade or color, which such movements would -produce. In order to detect such minute objects and operations, it would -be requisite that the surface of the moon should be distributed among at -least a hundred astronomers, each having a spot or two allotted to him, -as the object of his more particular investigation, and that the -observations be continued for a period of at least thirty or forty -years, during which time certain changes would probably be perceived, -arising either from physical causes, or from the operations of living -agents."[9] - -FOOTNOTE: - -[8] Dick's 'Celestial Scenery,' Chapter IV - - - - -LETTER XVI. - -THE MOON.--PHASES.--HARVEST MOON.--LIBRATIONS. - - "First to the neighboring Moon this mighty key - Of nature he applied. Behold! it turned - The secret wards, it opened wide the course - And various aspects of the queen of night: - Whether she wanes into a scanty orb, - Or, waxing broad, with her pale shadowy light, - In a soft deluge overflows the sky."--_Thomson's Elegy._ - - -LET us now inquire into the revolutions of the moon around the earth, -and the various changes she undergoes every month, called her _phases_, -which depend on the different positions she assumes, with respect to the -earth and the sun, in the course of her revolution. - -The moon revolves about the earth from west to east. Her apparent orbit, -as traced out on the face of the sky, is a great circle; but this fact -would not certainly prove that the orbit is really a circle, since, if -it were an ellipse, or even a more irregular curve, the projection of -it on the face of the sky would be a circle, as explained to you before. -(See page 148.) The moon is comparatively so near to the earth, that her -apparent movements are very rapid, so that, by attentively watching her -progress in a clear night, we may see her move from star to star, -changing her place perceptibly, every few hours. The interval during -which she goes through the entire circuit of the heavens, from any star -until she comes round to the same star again, is called a _sidereal -month_, and consists of about twenty-seven and one fourth days. The time -which intervenes between one new moon and another is called a _synodical -month_, and consists of nearly twenty-nine and a half days. A new moon -occurs when the sun and moon meet in the same part of the heavens; but -the sun as well as the moon is apparently travelling eastward, and -nearly at the rate of one degree a day, and consequently, during the -twenty-seven days while the moon has been going round the earth, the sun -has been going forward about the same number of degrees in the same -direction. Hence, when the moon comes round to the part of the heavens -where she passed the sun last, she does not find him there, but must go -on more than two days, before she comes up with him again. - -The moon does not pursue precisely the same track around the earth as -the sun does, in his apparent annual motion, though she never deviates -far from that track. The inclination of her orbit to the ecliptic is -only about five degrees, and of course the moon is never seen further -from the ecliptic than about that distance, and she is commonly much -nearer to the ecliptic than five degrees. We may therefore see nearly -what is the situation of the ecliptic in our evening sky at any -particular time of year, just by watching the path which the moon -pursues, from night to night, from new to full moon. - -The two points where the moon's orbit crosses the ecliptic are called -her _nodes_. They are the intersections of the lunar and solar orbits, -as the equinoxes are the intersections of the equinoctial and ecliptic, -and, like the latter, are one hundred and eighty degrees apart. - -The changes of the moon, commonly called her _phases_, arise from -different portions of her illuminated side being turned towards the -earth at different times. When the moon is first seen after the setting -sun, her form is that of a bright crescent, on the side of the disk next -to the sun, while the other portions of the disk shine with a feeble -light, reflected to the moon from the earth. Every night, we observe the -moon to be further and further eastward of the sun, until, when she has -reached an elongation from the sun of ninety degrees, half her visible -disk is enlightened, and she is said to be in her _first quarter_. The -terminator, or line which separates the illuminated from the dark part -of the moon, is convex towards the sun from the new to the first -quarter, and the moon is said to be _horned_. The extremities of the -crescent are called _cusps_. At the first quarter, the terminator -becomes a straight line, coinciding with the diameter of the disk; but -after passing this point, the terminator becomes concave towards the -sun, bounding that side of the moon by an elliptical curve, when the -moon is said to be _gibbous_. When the moon arrives at the distance of -one hundred and eighty degrees from the sun, the entire circle is -illuminated, and the moon is _full_. She is then _in opposition_ to the -sun, rising about the time the sun sets. For a week after the full, the -moon appears gibbous again, until, having arrived within ninety degrees -of the sun, she resumes the same form as at the first quarter, being -then at her _third quarter_. From this time until new moon, she exhibits -again the form of a crescent before the rising sun, until, approaching -her _conjunction_ with the sun, her narrow thread of light is lost in -the solar blaze; and finally, at the moment of passing the sun, the dark -side is wholly turned towards us, and for some time we lose sight of the -moon. - -By inspecting Fig. 38, (where T represents the earth, A, B, C, &c., the -moon in her orbit, and _a_, _b_, _c_, &c., her phases, as seen in the -heavens,) we shall easily see how all these changes occur. - -[Illustration Fig. 38.] - -You have doubtless observed, that the moon appears much further in the -south at one time than at another, when of the same age. This is owing -to the fact that the ecliptic, and of course the moon's path, which is -always very near it, is differently situated with respect to the -_horizon_, at a given time of night, at different seasons of the year. -This you will see at once, by turning to an artificial globe, and -observing how the ecliptic stands with respect to the horizon, at -different periods of the revolution. Thus, if we place the two -equinoctial points in the eastern and western horizon, Libra being in -the west, it will represent the position of the ecliptic at sunset in -the month of September, when the sun is crossing the equator; and at -that season of the year, the moon's path through our evening sky, one -evening after another, from new to full, will be nearly along the same -route, crossing the meridian nearly at right angles. But if we place the -Winter solstice, or first degree of Capricorn, in the western horizon, -and the first degree of Cancer in the eastern, then the position of the -ecliptic will be very oblique to the meridian, the Winter solstice being -very far in the southwest, and the Summer solstice very far in the -northeast; and the course of the moon from new to full will be nearly -along this track. Keeping these things in mind, we may easily see why -the moon runs sometimes high and sometimes low. Recollect, also, that -the new moon is always in the same part of the heavens with the sun, and -that the full moon is in the opposite part of the heavens from the sun. -Now, when the sun is at the Winter solstice, it sets far in the -southwest, and accordingly the new moon runs very low; but the full -moon, being in the opposite tropic, which rises far in the northeast, -runs very high, as is known to be the case in mid-winter. But now take -the position of the ecliptic in mid-summer. Then, at sunset, the tropic -of Cancer is in the northwest, and the tropic of Capricorn in the -southeast; consequently, the new moons run high and the full moons low. - -It is a natural consequence of this arrangement, to render the moon's -light the most beneficial to us, by giving it to us in greatest -abundance, when we have least of the sun's light, and giving it to us -most sparingly, when the sun's light is greatest. Thus, during the long -nights of Winter, the full moon runs high, and continues a very long -time above the horizon; while in mid-summer, the full moon runs low, and -is above the horizon for a much shorter period. This arrangement -operates very favorably to the inhabitants of the polar regions. At the -season when the sun is absent, and they have constant night, then the -moon, during the second and third quarters, embracing the season of full -moon, is continually above the horizon, compensating in no small degree -for the absence of the sun; while, during the Summer months, when the -sun is constantly above the horizon, and the light of the moon is not -needed, then she is above the horizon during the first and last -quarters, when her light is least, affording at that time her greatest -light to the inhabitants of the other hemisphere, from whom the sun is -withdrawn. - -About the time of the Autumnal equinox, the moon, when near her full, -rises about sunset a number of nights in succession. This occasions a -remarkable number of brilliant moonlight evenings; and as this is, in -England, the period of harvest, the phenomenon is called the _harvest -moon_. Its return is celebrated, particularly among the peasantry, by -festive dances, and kept as a festival, called the _harvest home_,--an -occasion often alluded to by the British poets. Thus Henry Kirke White: - - "Moon of harvest, herald mild - Of plenty, rustic labor's child, - Hail, O hail! I greet thy beam, - As soft it trembles o'er the stream, - And gilds the straw-thatch'd hamlet wide, - Where innocence and peace reside; - 'Tis thou that glad'st with joy the rustic throng, - Promptest the tripping dance, th' exhilarating song." - -To understand the reason of the harvest moon, we will, as before, -consider the moon's orbit as coinciding with the ecliptic, because we -may then take the ecliptic, as it is drawn on the artificial globe, to -represent that orbit. We will also bear in mind, (what has been fully -illustrated under the last head,) that, since the ecliptic cuts the -meridian obliquely, while all the circles of diurnal revolution cut it -perpendicularly, different portions of the ecliptic will cut the horizon -at different angles. Thus, when the equinoxes are in the horizon, the -ecliptic makes a very small angle with the horizon; whereas, when the -solstitial points are in the horizon, the same angle is far greater. In -the former case, a body moving eastward in the ecliptic, and being at -the eastern horizon at sunset, would descend but a little way below the -horizon in moving over many degrees of the ecliptic. Now, this is just -the case of the moon at the time of the harvest home, about the time of -the Autumnal equinox. The sun being then in Libra, and the moon, when -full, being of course opposite to the sun, or in Aries; and moving -eastward, in or near the ecliptic, at the rate of about thirteen degrees -per day, would descend but a small distance below the horizon for five -or six days in succession; that is for two or three days before, and the -same number of days after, the full; and would consequently rise during -all these evenings nearly at the same time, namely, a little before, or -a little after, sunset, so as to afford a remarkable succession of fine -moonlight evenings. - -The moon _turns on her axis_ in the same time in which she revolves -around the earth. This is known by the moon's always keeping nearly the -same face towards us, as is indicated by the telescope, which could not -happen unless her revolution on her axis kept pace with her motion in -her orbit. Take an apple, to represent the moon; stick a knittingneedle -through it, in the direction of the stem, to represent the axis, in -which case the two eyes of the apple will aptly represent the poles. -Through the poles cut a line around the apple, dividing it into two -hemispheres, and mark them, so as to be readily distinguished from each -other. Now place a candle on the table, to represent the earth, and -holding the apple by the knittingneedle, carry it round the candle, and -you will see that, unless you make the apple turn round on the axis as -you carry it about the candle, it will present different sides towards -the candle; and that, in order to make it always present the same side, -it will be necessary to make it revolve exactly once on its axis, while -it is going round the circle,--the revolution on its axis always keeping -exact pace with the motion in its orbit. The same thing will be -observed, if you walk around a tree, always keeping your face towards -the tree. If you have your face towards the tree when you set out, and -walk round without turning, when you have reached the opposite side of -the tree, your back will be towards it, and you will find that, in order -to keep your face constantly towards the tree, it will be necessary to -turn yourself round on your heel at the same rate as you go forward. - -Since, however, the motion of the moon on its axis is uniform, while the -motion in its orbit is unequal, the moon does in fact reveal to us a -little sometimes of one side and sometimes of the other. Thus if, while -carrying the apple round the candle, you carry it forward a little -faster than the rate at which it turns on its axis, a portion of the -hemisphere usually out of sight is brought into view on one side; or if -the apple is moved forward slower than it is turned on its axis, a -portion of the same hemisphere comes into view on the other side. These -appearances are called the moon's _librations in longitude_. The moon -has also a _libration in latitude_;--so called, because in one part of -her revolution more of the region around one of the poles comes into -view, and, in another part of the revolution, more of the region around -the other pole, which gives the appearance of a tilting motion to the -moon's axis. This is owing to the fact, that the moon's axis is inclined -to the plane of her orbit. If, in the experiment with the apple, you -hold the knittingneedle parallel to the candle, (in which case the axis -will be perpendicular to the plane of revolution,) the candle will shine -upon both poles during the whole circuit, and an eye situated where the -candle is would constantly see both poles; but now incline the needle -towards the plane of revolution, and carry it round, always keeping it -parallel to itself, and you will observe that the two poles will be -alternately in and out of sight. - -The moon exhibits another appearance of this kind, called her _diurnal -libration_, depending on the daily rotation of the spectator. She turns -the same face towards the _centre_ of the earth only, whereas we view -her from the surface. When she is on the meridian, we view her disk -nearly as though we viewed it from the centre of the earth, and hence, -in this situation, it is subject to little change; but when she is near -the horizon, our circle of vision takes in more of the upper limb than -would be presented to a spectator at the centre of the earth. Hence, -from this cause, we see a portion of one limb while the moon is rising, -which is gradually lost sight of, and we see a portion of the opposite -limb, as the moon declines to the west. You will remark that neither of -the foregoing changes implies any actual motion in the moon, but that -each arises from a change of position in the spectator. Since the -succession of day and night depends on the revolution of a planet on its -own axis, and it takes the moon twenty-nine and a half days to perform -this revolution, so that the sun shall go from the meridian of any place -and return to the same meridian again, of course the lunar day occupies -this long period. So protracted an exposure to the sun's rays, -especially in the equatorial regions of the moon, must occasion an -excessive accumulation of heat; and so long an absence of the sun must -occasion a corresponding degree of cold. A spectator on the side of the -moon which is opposite to us would never see the earth, but one on the -side next to us would see the earth constantly in his firmament, -undergoing a gradual succession of changes, corresponding to those which -the moon exhibits to the earth, but in the reverse order. Thus, when it -is full moon to us, the earth, as seen from the moon, is then in -conjunction with the sun, and of course presents her dark side to the -moon. - -Soon after this, an inhabitant of the moon would see a crescent, -resembling our new moon, which would in like manner increase and go -through all the changes, from new to full, and from full to new, as we -see them in the moon. There are, however, in the two cases, several -striking points of difference. In the first place, instead of -twenty-nine and a half days, all these changes occur in one lunar day -and night. During the first and last quarters, the changes would occur -in the day-time; but during the second and third quarters, during the -night. By this arrangement, the lunarians would enjoy the greatest -possible benefit from the light afforded by the earth, since in the half -of her revolution where she appears to them as full, she would be -present while the sun was absent, and would afford her least light while -the sun was present. In the second place, the earth would appear -thirteen times as large to a spectator on the moon as the moon appears -to us, and would afford nearly the same proportion of light, so that -their long nights must be continually cheered by an extraordinary degree -of light derived from this source; and if the full moon is hailed by our -poets as "refulgent lamp of night,"[10] with how much more reason might -a lunarian exult thus, in view of the splendid orb that adorns his -nocturnal sky! In the third place, the earth, as viewed from any -particular place on the moon, would occupy invariably the same part of -the heavens. For while the rotation of the moon on her axis from west to -east would appear to make the earth (as the moon does to us) revolve -from east to west, the corresponding progress of the moon in her orbit -would make the earth appear to revolve from west to east; and as these -two motions are equal, their united effect would be to keep the moon -apparently stationary in the sky. Thus, a spectator at E, Fig. 38, page -175, in the middle of the disk that is turned towards the earth, would -have the earth constantly on his meridian, and at E, the conjunction of -the earth and sun would occur at mid-day; but when the moon arrived at -G, the same place would be on the margin of the circle of illumination, -and will have the sun in the horizon; but the earth would still be on -his meridian and in quadrature. In like manner, a place situated on the -margin of the circle of illumination, when the moon is at E, would have -the earth in the horizon; and the same place would always see the earth -in the horizon, except the slight variations that would occur from the -librations of the moon. In the fourth place, the earth would present to -a spectator on the moon none of that uniformity of aspect which the moon -presents to us, but would exhibit an appearance exceedingly diversified. -The comparatively rapid rotation of the earth, repeated fifteen times -during a lunar night, would present, in rapid succession, a view of our -seas, oceans, continents, and mountains, all diversified by our clouds, -storms, and volcanoes. - -FOOTNOTES: - -[9] Dick's 'Celestial Scenery.' - -[10] - - "As when the moon, refulgent lamp of night, - O'er heaven's clear azure sheds her sacred light, - When not a breath disturbs the deep serene, - And not a cloud o'ercasts the solemn scene, - Around her throne the vivid planets roll, - And stars unnumbered gild the glowing pole; - O'er the dark trees a yellower verdure shed, - And tip with silver every mountain's head; - Then shine the vales, the rocks in prospect rise, - A flood of glory bursts from all the skies; - The conscious swains, rejoicing in the sight, - Eye the blue vault, and bless the useful light." - - _Pope's Homer._ - - - - -LETTER XVII. - -MOON'S ORBIT.--HER IRREGULARITIES. - - "Some say the zodiac constellations - Have long since left their antique stations, - Above a sign, and prove the same - In Taurus now, once in the Ram; - That in twelve hundred years and odd, - The sun has left his ancient road, - And nearer to the earth is come, - 'Bove fifty thousand miles from home."--_Hudibras._ - - -WE have thus far contemplated the revolution of the moon around the -earth as though the earth were at rest. But in order to have just ideas -respecting the moon's motions, we must recollect that the moon likewise -revolves along with the earth around the sun. It is sometimes said that -the earth _carries_ the moon along with her, in her annual revolution. -This language may convey an erroneous idea; for the moon, as well as the -earth, revolves around the sun under the influence of two forces, which -are independent of the earth, and would continue her motion around the -sun, were the earth removed out of the way. Indeed, the moon is -attracted towards the sun two and one fifth times more than towards the -earth, and would abandon the earth, were not the latter also carried -along with her by the same forces. So far as the sun acts equally on -both bodies, the motion with respect to each other would not be -disturbed. Because the gravity of the moon towards the sun is found to -be greater, at the conjunction, than her gravity towards the earth, some -have apprehended that, if the doctrine of universal gravitation is true, -the moon ought necessarily to abandon the earth. In order to understand -the reason why it does not do thus, we must reflect, that, when a body -is revolving in its orbit under the influence of the projectile force -and gravity, whatever diminishes the force of gravity, while that of -projection remains the same, causes the body to approach nearer to the -tangent of her orbit, and of course to recede from the centre; and -whatever increases the amount of gravity, carries the body towards the -centre. Thus, in Fig. 33, page 152, if, with a certain force of -projection acting in the direction A B, and of attraction, in the -direction A C, the attraction which caused a body to move in the line A -D were diminished, it would move nearer to the tangent, as in A E, or A -F. Now, when the moon is in conjunction, her gravity towards the earth -acts in opposition to that towards the sun, (see Fig. 38, page 175,) -while her velocity remains too great to carry her with what force -remains, in a circle about the sun, and she therefore recedes from the -sun, and commences her revolution around the earth. On arriving at the -opposition, the gravity of the earth conspires with that of the sun, and -the moon's projectile force being less than that required to make her -revolve in a circular orbit, when attracted towards the sun by the sum -of these forces, she accordingly begins to approach the sun, and -descends again to the conjunction. - -The attraction of the sun, however, being every where greater than that -of the earth, the actual path of the moon around the sun is every where -concave towards the latter. Still, the elliptical path of the moon -around the earth is to be conceived of, in the same way as though both -bodies were at rest with respect to the sun. Thus, while a steam-boat is -passing _swiftly_ around an island, and a man is walking _slowly_ around -a post in the cabin, the line which he describes in space between the -forward motion of the boat and his circular motion around the post, may -be every where concave towards the island, while his path around the -post will still be the same as though both were at rest. A nail in the -rim of a coach-wheel will turn around the axis of the wheel, when the -coach has a forward motion, in the same manner as when the coach is at -rest, although the line actually described by the nail will be the -resultant of both motions, and very different from either. - -We have hitherto regarded the moon as describing a great circle on the -face of the sky, such being the visible orbit, as seen by projection. -But, on a more exact investigation, it is found that her orbit is not a -circle, and that her motions are subject to very numerous -irregularities. These will be best understood in connexion with the -causes on which they depend. The law of universal gravitation has been -applied with wonderful success to their developement, and its results -have conspired with those of long-continued observation, to furnish the -means of ascertaining with great exactness the place of the moon in the -heavens, at any given instant of time, past or future, and thus to -enable astronomers to determine longitudes, to calculate eclipses, and -to solve other problems of the highest interest. The whole number of -irregularities to which the moon is subject is not less than sixty, but -the greater part are so small as to be hardly deserving of attention; -but as many as thirty require to be estimated and allowed for, before we -can ascertain the exact place of the moon at any given time. You will be -able to understand something of the cause of these irregularities, if -you first gain a distinct idea of the mutual actions of the sun, the -moon, and the earth. The irregularities in the moon's motions are due -chiefly to the disturbing influence of the sun, which operates in two -ways; first, by acting unequally on the earth and moon; and secondly, by -acting obliquely on the moon, on account of the inclination of her orbit -to the ecliptic. If the sun acted equally on the earth and moon, and -always in parallel lines, this action would serve only to restrain them -in their annual motions around the sun, and would not affect their -actions on each other, or their motions about their common centre of -gravity. In that case, if they were allowed to fall towards the sun, -they would fall equally, and their respective situations would not be -affected by their descending equally towards it. But, because the moon -is nearer the sun in one half of her orbit than the earth is, and in the -other half of her orbit is at a greater distance than the earth from the -sun, while the power of gravity is always greater at a less distance; it -follows, that in one half of her orbit the moon is more attracted than -the earth towards the sun, and, in the other half, less attracted than -the earth. - -To see the effects of this process, let us suppose that the projectile -motions of the earth and moon were destroyed, and that they were allowed -to fall freely towards the sun. (See Fig. 38, page 175.) If the moon was -in conjunction with the sun, or in that part of her orbit which is -nearest to him, the moon would be more attracted than the earth, and -fall with greater velocity towards the sun; so that the distance of the -moon from the earth would be increased by the fall. If the moon was in -opposition, or in the part of her orbit which is furthest from the sun, -she would be less attracted than the earth by the sun, and would fall -with a less velocity, and be left behind; so that the distance of the -moon from the earth would be increased in this case, also. If the moon -was in one of the quarters, then the earth and the moon being both -attracted towards the centre of the sun, they would both descend -directly towards that centre, and, by approaching it, they would -necessarily at the same time approach each other, and in this case their -distance from each other would be diminished. Now, whenever the action -of the sun would increase their distance, if they were allowed to fall -towards the sun, then the sun's action, by endeavoring to separate them, -diminishes their gravity to each other; whenever the sun's action would -diminish the distance, then it increases their mutual gravitation. -Hence, in the conjunction and opposition, their gravity towards each -other is diminished by the action of the sun, while in the quadratures -it is increased. But it must be remembered, that it is not the total -action of the sun on them that disturbs their motions, but only that -part of it which tends at one time to separate them, and at another time -to bring them nearer together. The other and far greater part has no -other effect than to retain them in their annual course around the sun. - -The cause of the lunar irregularities was first investigated by Sir -Isaac Newton, in conformity with his doctrine of universal gravitation, -and the explanation was first published in the 'Principia;' but, as it -was given in a mathematical dress, there were at that age very few -persons capable of reading or understanding it. Several eminent -individuals, therefore, undertook to give a popular explanation of these -difficult points. Among Newton's contemporaries, the best commentator -was M'Laurin, a Scottish astronomer, who published a large work entitled -'M'Laurin's Account of Sir Isaac Newton's Discoveries.' No writer of his -own day, and, in my opinion, no later commentator, has equalled -M'Laurin, in reducing to common apprehension the leading principles of -the doctrine of gravitation, and the explanation it affords of the -motions of the heavenly bodies. To this writer I am indebted for the -preceding easy explanation of the irregularities of the moon's motions, -as well as for several other illustrations of the same sublime doctrine. - -The figure of the moon's orbit is an ellipse. We have before seen, that -the earth's orbit around the sun is of the same figure; and we shall -hereafter see this to be true of all the planetary orbits. The path of -the earth, however, departs very little from a circle; that of the moon -differs materially from a circle, being considerably longer one way than -the other. Were the orbit a circle having the earth in the centre, then -the radius vector, or line drawn from the centre of the moon to the -centre of the earth, would always be of the same length; but it is found -that the length of the radius vector is only fifty-six times the radius -of the earth when the moon is nearest to us, while it is sixty-four -times that radius when the moon is furthest from us. The point in the -moon's orbit nearest the earth is called her _perigee_; the point -furthest from the earth, her _apogee_. We always know when the moon is -at one of these points, by her apparent diameter or apparent velocity; -for, when at the perigee, her diameter is greater than at any time, and -her motion most rapid; and, on the other hand, her diameter is least, -and her motion slowest, when she is at her apogee. - -The moon's nodes constantly shift their positions in the ecliptic, from -east to west, at the rate of about nineteen and a half degrees every -year, returning to the same points once in eighteen and a half years. In -order to understand what is meant by this backward motion of the nodes, -you must have very distinctly in mind the meaning of the terms -themselves; and if, at any time, you should be at a loss about the -signification of any word that is used in expressing an astronomical -proposition, I would advise you to turn back to the previous definition -of that term, and revive its meaning clearly in the mind, before you -proceed any further. In the present case, you will recollect that the -moon's nodes are the two points where her orbit cuts the plane of the -ecliptic. Suppose the great circle of the ecliptic marked out on the -face of the sky in a distinct line, and let us observe, at any given -time, the exact moment when the moon crosses this line, which we will -suppose to be close to a certain star; then, on its next return to that -part of the heavens, we shall find that it crosses the ecliptic sensibly -to the westward of that star, and so on, further and further to the -westward, every time it crosses the ecliptic at either node. This fact -is expressed by saying that _the nodes retrograde on the ecliptic_; -since any motion from east to west, being contrary to the order of the -signs, is called retrograde. The line which joins these two points, or -the line of the nodes, is also said to have a retrograde motion, or to -revolve from east to west once in eighteen and a half years. - -The _line of the apsides_ of the moon's orbit revolves from west to -east, through her whole course, in about nine years. You will recollect -that the apsides of an elliptical orbit are the two extremities of the -longer axis of the ellipse; corresponding to the perihelion and aphelion -of bodies revolving about the sun, or to the perigee and apogee of a -body revolving about the earth. If, in any revolution of the moon, we -should accurately mark the place in the heavens where the moon is -nearest the earth, (which may be known by the moon's apparent diameter -being then greatest,) we should find that, at the next revolution, it -would come to its perigee a little further eastward than before, and so -on, at every revolution, until, after nine years, it would come to its -perigee nearly at the same point as at first. This fact is expressed by -saying, that the perigee, and of course the apogee, revolves, and that -the line which joins these two points, or the line of the apsides, also -revolves. - -These are only a few of the irregularities that attend the motions of -the moon. These and a few others were first discovered by actual -observation and have been long known; but a far greater number of lunar -irregularities have been made known by following out all the -consequences of the law of universal gravitation. - -The moon may be regarded as a body endeavoring to make its way around -the earth, but as subject to be continually impeded, or diverted from -its main course, by the action of the sun and of the earth; sometimes -acting in concert and sometimes in opposition to each other. Now, by -exactly estimating the amount of these respective forces, and -ascertaining their resultant or combined effect, in any given case, the -direction and velocity of the moon's motion may be accurately -determined. But to do this has required the highest powers of the human -mind, aided by all the wonderful resources of mathematics. Yet, so -consistent is truth with itself, that, where some minute inequality in -the moon's motions is developed at the end of a long and intricate -mathematical process, it invariably happens, that, on pointing the -telescope to the moon, and watching its progress through the skies, we -may actually see her commit the same irregularities, unless (as is the -case with many of them) they are too minute to be matters of -observation, being beyond the powers of our vision, even when aided by -the best telescopes. But the truth of the law of gravitation, and of the -results it gives, when followed out by a chain of mathematical -reasoning, is fully confirmed, even in these minutest matters, by the -fact that the moon's place in the heavens, when thus determined, always -corresponds, with wonderful exactness, to the place which she is -actually observed to occupy at that time. - -The mind, that was first able to elicit from the operations of Nature -the law of universal gravitation, and afterwards to apply it to the -complete explanation of all the irregular wanderings of the moon, must -have given evidence of intellectual powers far elevated above those of -the majority of the human race. We need not wonder, therefore, that such -homage is now paid to the genius of Newton,--an admiration which has -been continually increasing, as new discoveries have been made by -tracing out new consequences of the law of universal gravitation. - -The chief object of astronomical _tables_ is to give the amount of all -the irregularities that attend the motions of the heavenly bodies, by -estimating the separate value of each, under all the different -circumstances in which a body can be placed. Thus, with respect to the -moon, before we can determine accurately the distance of the moon from -the vernal equinox, that is, her longitude at any given moment, we must -be able to make exact allowances for all her irregularities which would -affect her longitude. These are in all no less than sixty, though most -of them are so exceedingly minute, that it is not common to take into -the account more than twenty-eight or thirty. The values of these are -all given in the lunar tables; and in finding the moon's place, at any -given time, we proceed as follows: We first find what her place would be -on the supposition that she moves uniformly in a circle. This gives her -_mean_ place. We next apply the various corrections for her irregular -motions; that is, we apply the _equations_, subtracting some and adding -others, and thus we find her _true_ place. - -The astronomical tables have been carried to such an astonishing degree -of accuracy, that it is said, by the highest authority, that an -astronomer could now predict, for a thousand years to come, the precise -moment of the passage of any one of the stars over the meridian wire of -the telescope of his transit-instrument, with such a degree of accuracy, -that the error would not be so great as to remove the object through an -angular space corresponding to the semidiameter of the finest wire that -could be made; and a body which, by the tables, ought to appear in the -transit-instrument in the middle of that wire, would in no case be -removed to its outer edge. The astronomer, the mathematician, and the -artist, have united their powers to produce this great result. The -astronomer has collected the data, by long-continued and most accurate -observations on the actual motions of the heavenly bodies, from night to -night, and from year to year; the mathematician has taken these data, -and applied to them the boundless resources of geometry and the -calculus; and, finally, the instrument-maker has furnished the means, -not only of verifying these conclusions, but of discovering new truths, -as the foundation of future reasonings. - -Since the points where the moon crosses the ecliptic, or the moon's -nodes, constantly shift their positions about nineteen and a half -degrees to the westward, every year, the sun, in his annual progress in -the ecliptic, will go from the node round to the same node again in less -time than a year, since the node goes to meet him nineteen and a half -degrees to the west of the point where they met before. It would have -taken the sun about nineteen days to have passed over this arc; and -consequently, the interval between two successive conjunctions between -the sun and the moon's node is about nineteen days shorter than the -solar year of three hundred and sixty-five days; that is, it is about -three hundred and forty-six days; or, more exactly, it is 346.619851 -days. The time from one new moon to another is 29.5305887 days. Now, -nineteen of the former periods are almost exactly equal to two hundred -and twenty-three of the latter: - - For 346.619851 × 19=6585.78 days=18 y. 10 d. - And 29.5305887 × 223=6585.32 " = " " " " - -Hence, if the sun and moon were to leave the moon's node together, after -the sun had been round to the same node nineteen times, the moon would -have made very nearly two hundred and twenty-three conjunctions with the -sun. If, therefore, she was in conjunction with the sun at the beginning -of this period, she would be in conjunction again at the end of it; and -all things relating to the sun, the moon, and the node, would be -restored to the same relative situation as before, and the sun and moon -would start again, to repeat the same phenomena, arising out of these -relations, as occurred in the preceding period, and in the same order. -Now, when the sun and moon meet at the moon's node, an eclipse of the -sun happens; and during the entire period of eighteen and a half years -eclipses will happen, nearly in the same manner as they did at -corresponding times in the preceding period. Thus, if there was a great -eclipse of the sun on the fifth year of one of these periods, a similar -eclipse (usually differing somewhat in magnitude) might be expected on -the fifth year of the next period. Hence this period, consisting of -about eighteen years and ten days, under the name of the _Saros_, was -used by the Chaldeans, and other ancient nations, in predicting -eclipses. It was probably by this means that Thales, a Grecian -astronomer who flourished six hundred years before the Christian era, -predicted an eclipse of the sun. Herodotus, the old historian of Greece, -relates that the day was suddenly changed into night, and that Thales of -Miletus had foretold that a great eclipse was to happen _this year_. It -was therefore, at that age, considered as a distinguished feat to -predict even the year in which an eclipse was to happen. This eclipse is -memorable in ancient history, from its having terminated the war between -the Lydians and the Medes, both parties being smitten with such -indications of the wrath of the gods. - -The _Metonic Cycle_ has sometimes been confounded with the Saros, but it -is not the same with it, nor was the period used, like the Saros, for -foretelling eclipses, but for ascertaining the _age_ of the moon at any -given period. It consisted of nineteen tropical years, during which time -there are exactly two hundred and thirty-five new moons; so that, at the -end of this period, the new moons will recur at seasons of the year -corresponding exactly to those of the preceding cycle. If, for example, -a new moon fell at the time of the vernal equinox, in one cycle, -nineteen years afterwards it would occur again at the same equinox; or, -if it had happened ten days after the equinox, in one cycle, it would -also happen ten days after the equinox, nineteen years afterwards. By -registering, therefore, the exact days of any cycle at which the new or -full moons occurred, such a calendar would show on what days these -events would occur in any other cycle; and, since the regulation of -games, feasts, and fasts, has been made very extensively, both in -ancient and modern times, according to new or full moons, such a -calendar becomes very convenient for finding the day on which the new or -full moon required takes place. Suppose, for example, it were decreed -that a festival should be held on the day of the first full moon after -the Vernal equinox. Then, to find on what day that would happen, in any -given year, we have only to see what year it is of the lunar cycle; for -the day will be the same as it was in the corresponding year of the -calendar which records all the full moons of the cycle for each year, -and the respective days on which they happen. - -The Athenians adopted the metonic cycle four hundred and thirty-three -years before the Christian era, for the regulation of their calendars, -and had it inscribed in letters of gold on the walls of the temple of -Minerva. Hence the term _golden number_, still found in our almanacs, -which denotes the year of the lunar cycle. Thus, fourteen was the golden -number for 1837, being the fourteenth year of the lunar cycle. - -The inequalities of the moon's motions are divided into periodical and -secular. _Periodical_ inequalities are those which are completed in -comparatively short periods. _Secular_ inequalities are those which are -completed only in very long periods, such as centuries or ages. Hence -the corresponding terms _periodical equations_ and _secular equations_. -As an example of a secular inequality, we may mention the acceleration -of the _moon's mean motion_. It is discovered that the moon actually -revolves around the earth in a less period now than she did in ancient -times. The difference, however, is exceedingly small, being only about -ten seconds in a century. In a lunar eclipse, the moon's longitude -differs from that of the sun, at the middle of the eclipse, by exactly -one hundred and eighty degrees; and since the sun's longitude at any -given time of the year is known, if we can learn the day and hour when -an eclipse occurred at any period of the world, we of course know the -longitude of the sun and moon at that period. Now, in the year 721, -before the Christian era, Ptolemy records a lunar eclipse to have -happened, and to have been observed by the Chaldeans. The moon's -longitude, therefore, for that time, is known; and as we know the mean -motions of the moon, at present, starting from that epoch, and -computing, as may easily be done, the place which the moon ought to -occupy at present, at any given time, she is found to be actually nearly -a degree and a half in advance of that place. Moreover, the same -conclusion is derived from a comparison of the Chaldean observations -with those made by an Arabian astronomer of the tenth century. - -This phenomenon at first led astronomers to apprehend that the moon -encountered a resisting medium, which, by destroying at every revolution -a small portion of her projectile force, would have the effect to bring -her nearer and nearer to the earth, and thus to augment her velocity. -But, in 1786, La Place demonstrated that this acceleration is one of the -legitimate effects of the sun's disturbing force, and is so connected -with changes in the eccentricity of the earth's orbit, that the moon -will continue to be accelerated while that eccentricity diminishes; but -when the eccentricity has reached its minimum, or lowest point, (as it -will do, after many ages,) and begins to increase, then the moon's -motions will begin to be retarded, and thus her mean motions will -oscillate for ever about a mean value. - - - - -LETTER XVIII. - -ECLIPSES. - - ----"As when the sun, new risen, - Looks through the horizontal misty air, - Shorn of his beams, or from behind the moon, - In dim eclipse, disastrous twilight sheds - On half the nations, and with fear of change - Perplexes monarchs: darkened so, yet shone, - Above them all, the Archangel."--_Milton._ - - -HAVING now learned various particulars respecting the earth, the sun, -and the moon, you are prepared to understand the explanation of solar -and lunar eclipses, which have in all ages excited a high degree of -interest. Indeed, what is more admirable, than that astronomers should -be able to tell us, years beforehand, the exact instant of the -commencement and termination of an eclipse, and describe all the -attendant circumstances with the greatest fidelity. You have doubtless, -my dear friend, participated in this admiration, and felt a strong -desire to learn how it is that astronomers are able to look so far into -futurity. I will endeavor, in this Letter, to explain to you the leading -principles of the calculation of eclipses, with as much plainness as -possible. - -An _eclipse of the moon_ happens when the moon, in its revolution around -the earth, falls into the earth's shadow. An _eclipse of the sun_ -happens when the moon, coming between the earth and the sun, covers -either a part or the whole of the solar disk. - -The earth and the moon being both opaque, globular bodies, exposed to -the sun's light, they cast shadows opposite to the sun, like any other -bodies on which the sun shines. Were the sun of the same size with the -earth and the moon, then the lines drawn touching the surface of the sun -and the surface of the earth or moon (which lines form the boundaries of -the shadow) would be parallel to each other, and the shadow would be a -cylinder infinite in length; and were the sun less than the earth or -the moon, the shadow would be an increasing cone, its narrower end -resting on the earth; but as the sun is vastly greater than either of -these bodies, the shadow of each is a cone whose base rests on the body -itself, and which comes to a point, or vertex, at a certain distance -behind the body. These several cases are represented in the following -diagrams, Figs. 39, 40, 41. - -[Illustration Figs. 39, 40, 41.] - -It is found, by calculation, that the length of the moon's shadow, on an -average, is just about sufficient to reach to the earth; but the moon is -sometimes further from the earth than at others, and when she is nearer -than usual, the shadow reaches considerably beyond the surface of the -earth. Also, the moon, as well as the earth, is at different distances -from the sun at different times, and its shadow is longest when it is -furthest from the sun. Now, when both these circumstances conspire, that -is, when the moon is in her perigee and along with the earth in her -aphelion, her shadow extends nearly fifteen thousand miles beyond the -centre of the earth, and covers a space on the surface one hundred and -seventy miles broad. The earth's shadow is nearly a million of miles in -length, and consequently more than three and a half times as long as the -distance of the earth from the moon; and it is also, at the distance of -the moon, three times as broad as the moon itself. - -An eclipse of the sun can take place only at new moon, when the sun and -moon meet in the same part of the heavens, for then only can the moon -come between us and the sun; and an eclipse of the moon can occur only -when the sun and moon are in opposite parts of the heavens, or at full -moon; for then only can the moon fall into the shadow of the earth. - -[Illustration Fig. 42.] - -The nature of eclipses will be clearly understood from the following -representation. The diagram, Fig. 42, exhibits the relative position of -the sun, the earth, and the moon, both in a solar and in a lunar -eclipse. Here, the moon is first represented, while revolving round the -earth, as passing between the earth and the sun, and casting its shadow -on the earth. As the moon is here supposed to be at her average distance -from the earth, the shadow but just reaches the earth's surface. Were -the moon (as is sometimes the case) nearer the earth her shadow would -not terminate in a point, as is represented in the figure, but at a -greater or less distance nearer the base of the cone, so as to cover a -considerable space, which, as I have already mentioned, sometimes -extends to one hundred and seventy miles in breadth, but is commonly -much less than this. On the other side of the earth, the moon is -represented as traversing the earth's shadow, as is the case in a lunar -eclipse. As the moon is sometimes nearer the earth and sometimes further -off, it is evident that it will traverse the shadow at a broader or a -narrower part, accordingly. The figure, however, represents the moon as -passing the shadow further from the earth than is ever actually the -case, since the distance from the earth is never so much as one third of -the whole length of the shadow. - -It is evident from the figure, that if a spectator were situated where -the moon's shadow strikes the earth, the moon would cut off from him the -view of the sun, or the sun would be totally eclipsed. Or, if he were -within a certain distance of the shadow on either side, the moon would -be partly between him and the sun, and would intercept from him more or -less of the sun's light, according as he was nearer to the shadow or -further from it. If he were at _c_ or _d_, he would just see the moon -entering upon the sun's disk; if he were nearer the shadow than either -of these points, he would have a portion of this light cut off from his -view, and more, in proportion as he drew nearer the shadow; and the -moment he entered the shadow, he would lose sight of the sun. To all -places between _a_ or _b_ and the shadow, the sun would cast a partial -shadow of the moon, growing deeper and deeper, as it approached the true -shadow. This partial shadow is called the moon's _penumbra_. In like -manner, as the moon approaches the earth's shadow, in a lunar eclipse, -as soon as she arrives at _a_, the earth begins to intercept from her a -portion of the sun's light, or she falls in the earth's penumbra. She -continues to lose more and more of the sun's light, as she draws near to -the shadow, and hence her disk becomes gradually obscured, until it -enters the shadow, when the sun's light is entirely lost. - -As the sun and earth are both situated in the plane of the ecliptic, if -the moon also revolved around the earth in this plane, we should have a -solar eclipse at every new moon, and a lunar eclipse at every full moon; -for, in the former case, the moon would come directly between us and -the sun, and in the latter case, the earth would come directly between -the sun and the moon. But the moon is inclined to the ecliptic about -five degrees, and the centre of the moon may be all this distance from -the centre of the sun at new moon, and the same distance from the centre -of the earth's shadow at full moon. It is true, the moon extends across -her path, one half her breadth lying on each side of it, and the sun -likewise reaches from the ecliptic a distance equal to half his breadth. -But these luminaries together make but little more than a degree, and -consequently, their two semidiameters would occupy only about half a -degree of the five degrees from one orbit to the other where they are -furthest apart. Also, the earth's shadow, where the moon crosses it, -extends from the ecliptic less than three fourths of a degree, so that -the semidiameter of the moon and of the earth's shadow would together -reach but little way across the space that may, in certain cases, -separate the two luminaries from each other when they are in opposition. -Thus, suppose we could take hold of the circle in the figure that -represents the moon's orbit, (Fig. 42, page 197,) and lift the moon up -five degrees above the plane of the paper, it is evident that the moon, -as seen from the earth, would appear in the heavens five degrees above -the sun, and of course would cut off none of his light; and it is also -plain that the moon, at the full, would pass the shadow of the earth -five degrees below it, and would suffer no eclipse. But in the course of -the sun's apparent revolution round the earth once a year he is -successively in every part of the ecliptic; consequently, the -conjunctions and oppositions of the sun and moon may occur at any part -of the ecliptic, and of course at the two points where the moon's orbit -crosses the ecliptic,--that is, at the nodes; for the sun must -necessarily come to each of these nodes once a year. If, then, the moon -overtakes the sun just as she is crossing his path, she will hide more -or less of his disk from us. Since, also, the earth's shadow is always -directly opposite to the sun, if the sun is at one of the nodes, the -shadow must extend in the direction of the other node, so as to lie -directly across the moon's path; and if the moon overtakes it there, she -will pass through it, and be eclipsed. Thus, in Fig. 43, let BN -represent the sun's path, and AN, the moon's,--N being the place of the -node; then it is evident, that if the two luminaries at new moon be so -far from the node, that the distances between their centres is greater -than their semidiameters, no eclipse can happen; but if that distance is -less than this sum, as at E, F, then an eclipse will take place; but if -the position be as at C, D, the two bodies will just touch one another. -If A denotes the earth's shadow, instead of the sun, the same -illustration will apply to an eclipse of the moon. - -[Illustration Fig. 43.] - -Since bodies are defined to be in conjunction when they are in the -_same_ part of the heavens, and to be in opposition when they are in -_opposite_ parts of the heavens, it may not appear how the sun and moon -can be in conjunction, as at A and B, when they are still at some -distance from each other. But it must be recollected that bodies are in -conjunction when they have the same longitude, in which case they are -situated in the same great circle perpendicular to the ecliptic,--that -is, in the same secondary to the ecliptic. One of these bodies may be -much further from the ecliptic than the other; still, if the same -secondary to the ecliptic passes through them both, they will be in -conjunction or opposition. - -In a total eclipse of the moon, its disk is still visible, shining with -a dull, red light. This light cannot be derived directly from the sun, -since the view of the sun is completely hidden from the moon; nor by -reflection from the earth, since the illuminated side of the earth is -wholly turned from the moon; but it is owing to refraction from the -earth's atmosphere, by which a few scattered rays of the sun are bent -round into the earth's shadow and conveyed to the moon, sufficient in -number to afford the feeble light in question. - -It is impossible fully to understand the _method of calculating -eclipses_, without a knowledge of trigonometry; still it is not -difficult to form some general notion of the process. It may be readily -conceived that, by long-continued observations on the sun and moon, the -laws of their revolution may be so well understood, that the exact -places which they will occupy in the heavens at any future times may be -foreseen and laid down in tables of the sun and moon's motions; that we -may thus ascertain, by inspecting the tables, the instant when these two -bodies will be together in the heavens, or be in conjunction, and when -they will be one hundred and eighty degrees apart, or in opposition. -Moreover, since the exact place of the moon's node among the stars at -any particular time is known to astronomers, it cannot be difficult to -determine when the new or full moon occurs in the same part of the -heavens as that where the node is projected, as seen from the earth. In -short, as astronomers can easily determine what will be the relative -position of the sun, the moon, and the moon's nodes, for any given time, -they can tell when these luminaries will meet so near the node as to -produce an eclipse of the sun, or when they will be in opposition so -near the node as to produce an eclipse of the moon. - -A little reflection will enable you to form a clear idea of the -situation of the sun, the moon, and the earth, at the time of a solar -eclipse. First, suppose the conjunction to take place at the node; that -is, imagine the moon to come _directly_ between the earth and the sun, -as she will of course do, if she comes between the earth and the sun the -moment she is crossing the ecliptic; for then the three bodies will all -lie in one and the same straight line. But when the moon is in the -ecliptic, her shadow, or at least the axis, or central line, of the -shadow, must coincide with the line that joins the centres of the sun -and earth, and reach along the plane of the ecliptic towards the earth. -The moon's shadow, at her average distance from the earth, is just about -long enough to reach the surface of the earth; but when the moon, at the -new, is in her apogee, or at her greatest distance from the earth, the -shadow is not long enough to reach the earth. On the contrary, when the -moon is nearer to us than her average distance, her shadow is long -enough to reach beyond the earth, extending, when the moon is in her -perigee, more than fourteen thousand miles beyond the centre of the -earth. Now, as during the eclipse the moon moves nearly in the plane of -the ecliptic, her shadow which accompanies her must also move nearly in -the same plane, and must therefore traverse the earth across its central -regions, along the terrestrial ecliptic, since this is nothing more than -the intersection of the plane of the celestial ecliptic with the earth's -surface. The motion of the earth, too, on its axis, in the same -direction, will carry a place along with the shadow, though with a less -velocity by more than one half; so that the actual velocity of the -shadow, in respect to places over which it passes on the earth, will -only equal the difference between its own rate and that of the places, -as they are carried forward in the diurnal revolution. - -We have thus far supposed that the moon comes to her conjunction -precisely at the node, or at the moment when she is crossing the -ecliptic. But, secondly, suppose she is on the north side of the -ecliptic at the time of conjunction, and moving towards her descending -node, and that the conjunction takes place as far from the node as an -eclipse can happen. The shadow will not fall in the plane of the -ecliptic, but a little northward of it, so as just to graze the earth -near the pole of the ecliptic. The nearer the conjunction comes to the -node, the further the shadow will fall from the polar towards the -equatorial regions. - -In a solar eclipse, the shadow of the moon travels over a portion of the -earth, as the shadow of a small cloud, seen from an eminence in a clear -day, rides along over hills and plains. Let us imagine ourselves -standing on the moon; then we shall see the earth partially eclipsed by -the moon's shadow, in the same manner as we now see the moon eclipsed by -the shadow of the earth; and we might calculate the various -circumstances of the eclipse,--its commencement, duration, and -quantity,--in the same manner as we calculate these elements in an -eclipse of the moon, as seen from the earth. But although the general -characters of a solar eclipse might be investigated on these principles, -so far as respects the earth at large, yet, as the appearances of the -same eclipse of the sun are very different at different places on the -earth's surface, it is necessary to calculate its peculiar aspects for -each place separately, a circumstance which makes the calculation of a -solar eclipse much more complicated and tedious than that of an eclipse -of the moon. The moon, when she enters the shadow of the earth, is -deprived of the light of the part immersed, and the effect upon its -appearance is the same as though that part were painted black, in which -case it would be black alike to all places where the moon was above the -horizon. But it not so with a solar eclipse. We do not see this by the -shadow cast on the earth, as we should do, if we stood on the moon, but -by the interposition of the moon between us and the sun; and the sun may -be hidden from one observer, while he is in full view of another only a -few miles distant. Thus, a small insulated cloud sailing in a clear sky -will, for a few moments, hide the sun from us, and from a certain space -near us, while all the region around is illuminated. But although the -analogy between the motions of the shadow of a small cloud and of the -moon in a solar eclipse holds good in many particulars, yet the velocity -of the lunar shadow is far greater than that of the cloud, being no less -than two thousand two hundred and eighty miles per hour. - -The moon's shadow can never cover a space on the earth more than one -hundred and seventy miles broad, and the space actually covered commonly -falls much short of that. The portion of the earth's surface ever -covered by the moon's penumbra is about four thousand three hundred and -ninety-three miles. - -The apparent diameter of the moon varies materially at different times, -being greatest when the moon is nearest to us, and least when she is -furthest off; while the sun's apparent dimensions remain nearly the -same. When the moon is at her average distance from the earth, she is -just about large enough to cover the sun's disk; consequently, if, in a -central eclipse of the sun, the moon is at her mean distance, she covers -the sun but for an instant, producing only a momentary eclipse. If she -is nearer than her average distance, then the eclipse may continue total -some time, though never more than eight minutes, and seldom so long as -that; but if she is further off than usual, or towards her apogee, then -she is not large enough to cover the whole solar disk, but we see a ring -of the sun encircling the moon, constituting an _annular eclipse_, as -seen in Fig. 44. Even the elevation of the moon above the horizon will -sometimes sensibly affect the dimensions of the eclipse. You will -recollect that the moon is nearer to us when on the meridian than when -in the horizon by nearly four thousand miles, or by nearly the radius of -the earth; and consequently, her apparent diameter is largest when on -the meridian. The difference is so considerable, that the same eclipse -will appear total to a spectator who views it near his meridian, while, -at the same moment, it appears annular to one who has the moon near his -horizon. An annular eclipse may last, at most, twelve minutes and -twenty-four seconds. - -[Illustration Fig. 44.] - -Eclipses of the sun are more frequent than those of the moon. Yet lunar -eclipses being visible to every part of the terrestrial hemisphere -opposite to the sun, while those of the sun are visible only to a small -portion of the hemisphere on which the moon's shadow falls, it happens -that, for any particular place on the earth, lunar eclipses are more -frequently visible than solar. In any year, the number of eclipses of -both luminaries cannot be less than two nor more than seven: the most -usual number is four, and it is very rare to have more than six. A total -eclipse of the moon frequently happens at the next full moon after an -eclipse of the sun. For since, in a solar eclipse, the sun is at or near -one of the moon's nodes,--that is, is projected to the place in the sky -where the moon crosses the ecliptic,--the earth's shadow, which is of -course directly opposite to the sun, must be at or near the other node, -and may not have passed too far from the node before the moon comes -round to the opposition and overtakes it. In total eclipses of the sun, -there has sometimes been observed a remarkable radiation of light from -the margin of the sun, which is thought to be owing to the zodiacal -light, which is of such dimensions as to extend far beyond the solar -orb. A striking appearance of this kind was exhibited in the total -eclipse of the sun which occurred in June, 1806. - -A total eclipse of the sun is one of the most sublime and impressive -phenomena of Nature. Among barbarous tribes it is ever contemplated with -fear and astonishment, and as strongly indicative of the displeasure of -the gods. Two ancient nations, the Lydians and Medes, alluded to before, -who were engaged in a bloody war, about six hundred years before Christ, -were smitten with such awe, on the appearance of a total eclipse of the -sun, just on the eve of a battle, that they threw down their arms, and -made peace. When Columbus first discovered America, and was in danger of -hostility from the Natives, he awed them into submission by telling them -that the sun would be darkened on a certain day, in token of the anger -of the gods at them, for their treatment of him. - -Among cultivated nations, a total eclipse of the sun is recognised, from -the exactness with which the time of occurrence and the various -appearances answer to the prediction, as affording one of the proudest -triumphs of astronomy. By astronomers themselves, it is of course viewed -with the highest interest, not only as verifying their calculations, but -as contributing to establish, beyond all doubt, the certainty of those -grand laws, the truth of which is involved in the result. I had the good -fortune to witness the total eclipse of the sun of June, 1806, which was -one of the most remarkable on record. To the wondering gaze of childhood -it presented a spectacle that can never be forgotten. A bright and -beautiful morning inspired universal joy, for the sky was entirely -cloudless. Every one was busily occupied in preparing smoked glass, in -readiness for the great sight, which was to be first seen about ten -o'clock. A thrill of mingled wonder and delight struck every mind when, -at the appointed moment, a little black indentation appeared on the limb -of the sun. This gradually expanded, covering more and more of the solar -disk, until an increasing gloom was spread over the face of Nature; and -when the sun was wholly lost, near mid-day, a feeling of horror pervaded -almost every beholder. The darkness was wholly unlike that of twilight -or night. A thick curtain, very different from clouds, hung upon the -face of the sky, producing a strange and indescribably gloomy -appearance, which was reflected from all things on the earth, in hues -equally strange and unnatural. Some of the planets, and the largest of -the fixed stars, shone out through the gloom, yet with their usual -brightness. The temperature of the air rapidly declined, and so sudden a -chill came over the earth, that many persons caught severe colds from -their exposure. Even the animal tribes exhibited tokens of fear and -agitation. Birds, especially, fluttered and flew swiftly about, and -domestic fowls went to rest. - -Indeed, the word _eclipse_ is derived from a Greek word, (= ekleipsis=, -_ekleipsis_,) which signifies to fail, to faint or swoon away; since the -moon, at the period of her greatest brightness, falling into the shadow -of the earth, was imagined by the ancients to sicken and swoon, as if -she were going to die. By some very ancient nations she was supposed, at -such times, to be in pain; and, in order to relieve her fancied -distress, they lifted torches high in the atmosphere, blew horns and -trumpets, beat upon brazen vessels, and even, after the eclipse was -over, they offered sacrifices to the moon. The opinion also extensively -prevailed, that it was in the power of witches, by their spells and -charms, not only to darken the moon, but to bring her down from her -orbit, and to compel her to shed her baleful influences upon the earth. -In solar eclipses, also, especially when total, the sun was supposed to -turn away his face in abhorrence of some atrocious crime, that either -had been perpetrated or was about to be perpetrated, and to threaten -mankind with everlasting night, and the destruction of the world. To -such superstitions Milton alludes, in the passage which I have taken for -the motto of this Letter. - -The Chinese, who, from a very high period of antiquity, have been great -observers of eclipses, although they did not take much notice of those -of the moon, regarded eclipses of the sun in general as unfortunate, but -especially such as occurred on the first day of the year. These were -thought to forebode the greatest calamities to the emperor, who on such -occasions did not receive the usual compliments of the season. When, -from the predictions of their astronomers, an eclipse of the sun was -expected, they made great preparation at court for observing it; and as -soon as it commenced, a blind man beat a drum, a great concourse -assembled, and the mandarins, or nobility, appeared in state. - - - - -LETTER XIX. - -LONGITUDE.--TIDES. - - "First in his east, the glorious lamp was seen, - Regent of day, and all the horizon round - Invested with bright rays, jocund to run - His _longitude_ through heaven's high road; the gray - Dawn and the Pleiades before him danced, - Shedding sweet influence."--_Milton._ - - -THE ancients studied astronomy chiefly as subsidiary to astrology, with -the vain hope of thus penetrating the veil of futurity, and reading -their destinies among the stars. The moderns, on the other hand, have in -view, as the great practical object of this study, the perfecting of the -art of navigation. When we reflect on the vast interests embarked on the -ocean, both of property and life, and upon the immense benefits that -accrue to society from a safe and speedy intercourse between the -different nations of the earth, we cannot but see that whatever tends to -enable the mariner to find his way on the pathless ocean, and to secure -him against its multiplied dangers, must confer a signal benefit on -society. - -In ancient times, to venture out of sight of land was deemed an act of -extreme audacity; and Horace, the Roman poet, pronounces him who first -ventured to trust his frail bark to the stormy ocean, endued with a -heart of oak, and girt with triple folds of brass. But now, the -navigator who fully avails himself of all the resources of science, and -especially of astronomy, may launch fearlessly on the deep, and almost -bid defiance to rocks and tempests. By enabling the navigator to find -his place on the ocean with almost absolute precision, however he may -have been driven about by the winds, and however long he may have been -out of sight of land, astronomers must be held as great benefactors to -all who commit either their lives or their fortunes to the sea. Nor -have they secured to the art of navigation such benefits without -incredible study and toil, in watching the motions of the heavenly -bodies, in investigating the laws by which their movements are governed, -and in reducing all their discoveries to a form easily available to the -navigator, so that, by some simple observation on one or two of the -heavenly bodies, with instruments which the astronomer has invented, and -prepared for his use, and by looking out a few numbers in tables which -have been compiled for him, with immense labor, he may ascertain the -exact place he occupies on the surface of the globe, thousands of miles -from land. - -The situation of any place is known by its latitude and longitude. As -charts of every ocean and sea are furnished to the sailor, in which are -laid down the latitudes and longitudes of every point of land, whether -on the shores of islands or the main, he has, therefore, only to -ascertain his latitude and longitude at any particular place on the -ocean, in order to find where he is, with respect to the nearest point -of land, although this may be, and may always have been, entirely out of -sight to him. - -To determine the _latitude_ of a place is comparatively an easy matter, -whenever we can see either the sun or the stars. The distance of the sun -from the zenith, when on the meridian, on a given day of the year, -(which distance we may easily take with the sextant,) enables us, with -the aid of the tables, to find the latitude of the place; or, by taking -the altitude of the north star, we at once obtain the latitude. - -The _longitude_ of a place may be found by any method, by which we may -ascertain how much its time of day differs from that of Greenwich at the -same moment. A place that lies eastward of another comes to the meridian -an hour earlier for every fifteen degrees of longitude, and of course -has the hour of the day so much in advance of the other, so that it -counts one o'clock when the other place counts twelve. On the other -hand, a place lying westward of another comes to the meridian later by -one hour for every fifteen degrees, so that it counts only eleven -o'clock when the other place counts twelve. Keeping these principles in -view, it is easy to see that a comparison of the difference of time -between two places at the same moment, allowing fifteen degrees for an -hour, sixty minutes for every four minutes of time, and sixty seconds -for every four seconds of time, affords us an accurate mode of finding -the difference of longitude between the two places. This comparison may -be made by means of a chronometer, or from solar or lunar eclipses, or -by what is called the lunar method of finding the longitude. - -_Chronometers_ are distinguished from clocks, by being regulated by -means of a balance-wheel instead of a pendulum. A watch, therefore, -comes under the general definition of a chronometer; but the name is -more commonly applied to larger timepieces, too large to be carried -about the person, and constructed with the greatest possible accuracy, -with special reference to finding the longitude. Suppose, then, we are -furnished with a chronometer set to Greenwich time. We arrive at New -York, for example, and compare it with the time there. We find it is -five hours in advance of the New-York time, indicating five o'clock, -P.M., when it is noon at New York. Hence we find that the longitude of -New York is 5×15=75 degrees.[11] The time at New York, or any individual -place, can be known by observations with the transit-instrument, which -gives us the precise moment when the sun is on the meridian. - -It would not be necessary to resort to Greenwich, for the purpose of -setting our chronometer to Greenwich time, as it might be set at any -place whose longitude is known, having been previously determined. Thus, -if we know that the longitude of a certain place is exactly sixty -degrees east of Greenwich, we have only to set our chronometer four -hours behind the time at that place, and it will be regulated to -Greenwich time. Hence it is a matter of the greatest importance to -navigation, that the longitude of numerous ports, in different parts of -the earth, should be accurately determined, so that when a ship arrives -at any such port, it may have the means of setting or verifying its -chronometer. - -This method of taking the longitude seems so easy, that you will perhaps -ask, why it is not sufficient for all purposes, and accordingly, why it -does not supersede the move complicated and laborious methods? why every -sailor does not provide himself with a chronometer, instead of finding -his longitude at sea by tedious and oft-repeated calculations, as he is -in the habit of doing? I answer, it is only in a few extraordinary cases -that chronometers have been constructed of such accuracy as to afford -results as exact as those obtained by the other methods, to be described -shortly; and instruments of such perfection are too expensive for -general use among sailors. Indeed, the more common chronometers cost too -much to come within the means of a great majority of sea-faring men. -Moreover, by being transported from place to place, chronometers are -liable to change their _rate_. By the rate of any timepiece is meant its -deviation from perfect accuracy. Thus, if a clock should gain one second -per day, one day with another, and we should find it impossible to bring -it nearer to the truth, we may reckon this as its rate, and allow for it -in our estimate of the time of any particular observation. If the error -was not uniform, but sometimes greater and sometimes less than one -second per day, then the amount of such deviation is called its -"variation from its mean rate." I introduce these minute statements, -(which are more precise than I usually deem necessary,) to show you to -what an astonishing degree of accuracy chronometers have in some -instances been brought. They have been carried from London to Baffin's -Bay, and brought back, after a three years' voyage, and found to have -varied from their mean rate, during the whole time, only a second or -two, while the extreme variation of several chronometers, tried at the -Royal Observatory at Greenwich, never exceeded a second and a half. -Could chronometers always be depended on to such a degree of accuracy as -this, we should hardly desire any thing better for determining the -longitude of different places on the earth. A recent determination of -the longitude of the City Hall in New York, by means of three -chronometers, sent out from London expressly for that purpose, did not -differ from the longitude as found by a solar eclipse (which is one of -the best methods) but a second and a quarter. - -_Eclipses of the sun and moon_ furnish the means of ascertaining the -longitude of a place, because the entrance of the moon into the earth's -shadow in a lunar eclipse, and the entrance of the moon upon the disk of -the sun in a solar eclipse, are severally examples of one of those -instantaneous occurrences in the heavens, which afford the means of -comparing the times of different places, and of thus determining their -differences of longitude. Thus, if the commencement of a lunar eclipse -was seen at one place an hour sooner than at another, the two places -would be fifteen degrees apart, in longitude; and if the longitude of -one of the places was known, that of the other would become known also. -The exact instant of the moon's entering into the shadow of the earth, -however, cannot be determined with very great precision, since the moon, -in passing through the earth's penumbra, loses its light gradually, so -that the moment when it leaves the penumbra and enters into the shadow -cannot be very accurately defined. The first contact of the moon with -the sun's disk, in a solar eclipse, or the moment of leaving it,--that -is, the beginning and end of the eclipse,--are instants that can be -determined with much precision, and accordingly they are much relied on -for an accurate determination of the longitude. But, on account of the -complicated and laborious nature of the calculation of the longitude -from an eclipse of the sun, (since the beginning and end are not seen at -different places, at the same moment,) this method of finding the -longitude is not adapted to common use, nor available at sea. It is -useful, however, for determining the longitude of fixed observatories. -The _lunar method of finding the longitude_ is the most refined and -accurate of all the modes practised at sea. The motion of the moon -through the heavens is so rapid, that she perceptibly alters her -distance from any star every minute; consequently, the moment when that -distance is a certain number of degrees and minutes is one of those -instantaneous events, which may be taken advantage of for comparing the -times of different places, and thus determining their difference of -longitude. Now, in a work called the 'Nautical Almanac,' printed in -London, annually, for the use of navigators, the distance of the moon -from the sun by day, or from known fixed stars by night, for every day -and night in the year, is calculated beforehand. If, therefore, a sailor -wishes to ascertain his longitude, he may take with his sextant the -distance of the moon from one of these stars at any time,--suppose nine -o'clock, at night,--and then turn to the 'Nautical Almanac,' and see -_what time it was at Greenwich_ when the distance between the moon and -that star was the same. Let it be twelve o'clock, or three hours in -advance of his time: his longitude, of course, is forty-five degrees -west. - -This method requires more skill and accuracy than are possessed by the -majority of seafaring men; but, when practised with the requisite degree -of skill, its results are very satisfactory. Captain Basil Hall, one of -the most scientific commanders in the British navy, relates the -following incident, to show the excellence of this method. He sailed -from San Blas, on the west coast of Mexico, and, after a voyage of eight -thousand miles, occupying eighty-nine days, arrived off Rio de Janeiro, -having, in this interval, passed through the Pacific Ocean, rounded Cape -Horn, and crossed the South Atlantic, without making any land, or even -seeing a single sail, with the exception of an American whaler off Cape -Horn. When within a week's sail of Rio, he set seriously about -determining, by lunar observations, the precise line of the ship's -course, and its situation at a determinate moment; and having -ascertained this within from five to ten miles, ran the rest of the way -by those more ready and compendious methods, known to navigators, which -can be safely employed for short trips between one known point and -another, but which cannot be trusted in long voyages, where the moon is -the only sure guide. They steered towards Rio Janeiro for some days -after taking the lunars, and, having arrived within fifteen or twenty -miles of the coast, they hove to, at four in the morning, till the day -should break, and then bore up, proceeding cautiously, on account of a -thick fog which enveloped them. As this cleared away, they had the -satisfaction of seeing the great Sugar-Loaf Rock, which stands on one -side of the harbor's mouth, so nearly right ahead, that they had not to -alter their course above a point, in order to hit the entrance of the -harbor. This was the first land they had seen for three months, after -crossing so many seas, and being set backwards and forwards by -innumerable currents and foul winds. The effect on all on board was -electric; and the admiration of the sailors was unbounded. Indeed, what -could be more admirable than that a man on the deck of a vessel, by -measuring the distance between the moon and a star, with a little -instrument which he held in his hand, could determine his exact place on -the earth's surface in the midst of a vast ocean, after having traversed -it in all directions, for three months, crossing his track many times, -and all the while out of sight of land? - -The lunar method of finding the longitude could never have been -susceptible of sufficient accuracy, had not the motions of the moon, -with all their irregularities, been studied and investigated by the most -laborious and profound researches. Hence Newton, while wrapt in those -meditations which, to superficial minds, would perhaps have appeared -rather curious than useful, inasmuch as they respected distant bodies of -the universe which seemed to have little connexion with the affairs of -this world, was laboring night and day for the benefit of the sailor and -the merchant. He was guiding the vessel of the one, and securing the -merchandise of the other; and thus he contributed a large share to -promote the happiness of his fellow-men, not only in exalting the powers -of the human intellect, but also in preserving the lives and fortunes of -those engaged in navigation and commerce. Principles in science are -rules in art; and the philosopher who is engaged in the investigation of -these principles, although his pursuits may be thought less practically -useful than those of the artisan who carries out those principles into -real life, yet, without the knowledge of the principles, the rules would -have never been known. Studies, therefore, the most abstruse, are, when -viewed as furnishing rules to act, often productive of the highest -practical utility. - -Since the _tides_ are occasioned by the influence of the sun and moon, I -will conclude this Letter with a few remarks on this curious phenomenon. -By the tides are meant the alternate rising and falling of the waters of -the ocean. Its greatest and least elevations are called _high and low -water_; its rising and falling are called _flood and ebb_; and the -extraordinary high and low tides that occur twice every month are called -_spring and neap tides_. It is high or low tide on opposite sides of the -globe at the same time. If, for example, we have high water at noon, it -is also high water to those who live on the meridian below us, where it -is midnight. In like manner, low water occurs simultaneously on opposite -sides of the meridian. The average amount of the tides for the whole -globe is about two and a half feet; but their actual height at different -places is very various, sometimes being scarcely perceptible, and -sometimes rising to sixty or seventy feet. At the same place, also, the -phenomena of the tides are very different at different times. In the Bay -of Fundy, where the tide rises seventy feet, it comes in a mighty wave, -seen thirty miles off, and roaring with a loud noise. At the mouth of -the Severn, in England, the flood comes up in one head about ten feet -high, bringing certain destruction to any small craft that has been -unfortunately left by the ebbing waters on the flats and as it passes -the mouth of the Avon, it sends up that small river a vast body of -water, rising, at Bristol, forty or fifty feet. - -Tides are caused by the unequal attractions of the sun and moon upon -different parts of the earth. Suppose the projectile force by which the -earth is carried forward in her orbit to be suspended, and the earth to -fall towards one of these bodies,--the moon, for example,--in -consequence of their mutual attraction. Then, if all parts of the earth -fell equally towards the moon, no derangement of its different parts -would result, any more than of the particles of a drop of water, in its -descent to the ground. But if one part fell faster than another, the -different portions would evidently be separated from each other. Now, -this is precisely what takes place with respect to the earth, in its -fall towards the moon. The portions of the earth in the hemisphere next -to the moon, on account of being nearer to the centre of attraction, -fall faster than those in the opposite hemisphere, and consequently -leave them behind. The solid earth, on account of its cohesion, cannot -obey this impulse, since all its different portions constitute one mass, -which is acted on in the same manner as though it were all collected in -the centre; but the waters on the surface, moving freely under this -impulse, endeavor to desert the solid mass and fall towards the moon. -For a similar reason, the waters in the opposite hemisphere, falling -less towards the moon than the solid earth does, are left behind, or -appear to rise. - -[Illustration Fig. 46.] - -But if the moon draws the waters of the earth into an oval form towards -herself, raising them simultaneously on the opposite sides of the earth, -they must obviously be drawn away from the intermediate parts of the -earth, where it must at the same time be low water. Thus, in Fig. 46, -the moon, M, raises the waters beneath itself at Z and N, at which -places it is high water, but at the same time depresses the waters at H -and R, at which places it is low water. Hence, the interval between the -high and low tide, on successive days, is about fifty minutes, -corresponding to the progress of the moon in her orbit from west to -east, which causes her to come to the meridian about fifty minutes later -every day. There occurs, however, an intermediate tide, when the moon is -on the lower meridian, so that the interval between two high tides is -about twelve hours, and twenty-five minutes. - -Were it not for the impediments which prevent the force from producing -its full effects, we might expect to see the great tide-wave, as the -elevated crest is called, always directly beneath the moon, attending it -regularly around the globe. But the inertia of the waters prevents their -instantly obeying the moon's attraction, and the friction of the waters -on the bottom of the ocean still further retards its progress. It is -not, therefore, until several hours (differing at different places) -after the moon has passed the meridian of a place, that it is high tide -at that place. - -The _sun_ has an action similar to that of the moon, but only _one -third_ as great. On account of the great mass of the sun, compared with -that of the moon, we might suppose that his action in raising the tides -would be greater than the moon's; but the nearness of the moon to the -earth more than compensates for the sun's greater quantity of matter. -As, however, wrong views are frequently entertained on this subject, let -us endeavor to form a correct idea of the advantage which the moon -derives from her proximity. It is not that her actual amount of -attraction is thus rendered greater than that of the sun; but it is that -her attraction for the _different parts_ of the earth is very unequal, -while that of the sun is nearly uniform. It is the _inequality_ of this -action, and not the absolute force, that produces the tides. The sun -being ninety-five millions of miles from the earth, while the diameter -of the earth is only one twelve thousandth part of this distance, the -effects of the sun's attraction will be nearly the same on all parts of -the earth, and therefore will not, as was explained of the moon, tend to -separate the waters from the earth on the nearest side, or the earth -from the waters on the remotest side, but in a degree proportionally -smaller. But the diameter of the earth is one thirtieth the distance of -the moon, and therefore the moon acts with considerably greater power on -one part of the earth than on another. - -As the sun and moon both contribute to produce the tides, and as they -sometimes act together and sometimes in opposition to each other, so -corresponding variations occur in the height of the tide. The _spring -tides_, or those which rise to an unusual height twice a month, are -produced by the sun and moon's acting together; and the _neap tides_, or -those which are unusually low twice a month, are produced by the sun and -moon's acting in opposition to each other. The spring tides occur at the -syzygies: the neap tides at the quadratures. At the time of new moon, -the sun and moon both being on the same side of the earth, and acting -upon it in the same line, their actions conspire, and the sun may be -considered as adding so much to the force of the moon. We have already -seen how the moon contributes to raise a tide on the opposite side of -the earth. But the sun, as well as the moon, raises its own tide-wave, -which at new moon coincides with the lunar tide-wave. This will be plain -on inspecting the diagram, Fig. 47, on page 220, where S represents the -sun, C, the moon in conjunction, O, the moon in opposition, and Z, N, -the tide-wave. Since the sun and moon severally raise a tide-wave, and -the two here coincide, it is evident that a peculiarly high tide must -occur when the two bodies are in conjunction, or at new moon. At full -moon, also, the two luminaries conspire in the same way to raise the -tide; for we must recollect that each body contributes to raise a tide -on the opposite side. Thus, when the sun is at S and the moon at O, the -sun draws the waters on the side next to it away from the earth, and -the moon draws the earth away from the waters on that side; their united -actions, therefore, conspire, and an unusually high tide is the result. -On the side next to O, the two forces likewise conspire: for while the -moon draws the waters away from the earth, the sun draws the earth away -from the waters. In both cases an unusually low tide is produced; for -the more the water is elevated at Z and N, the more it will be depressed -at H and R, the places of low tide. - -[Illustration Fig. 47.] - -Twice a month, also, namely, at the quadratures of the moon, the tides -neither rise so high nor fall so low as at other times, because then the -sun and moon act against each other. Thus, in Fig. 48, while F tends to -raise the water at Z, S tends to depress it, and consequently the high -tide is less than usual. Again, while F tends to depress the water at R, -S tends to elevate it, and therefore the low tide is less than usual. -Hence the difference between high and low water is only half as great at -neap as at spring tide. In the diagrams, the elevation and depression of -the waters is represented, for the sake of illustration, as far greater -than it really is; for you must recollect that the average height of the -tides for the whole globe is only about two and a half feet, a quantity -so small, in comparison with the diameter of the earth, that were the -due proportions preserved in the figures, the effect would be wholly -insensible. - -[Illustration Fig. 48.] - -The variations of distance in the sun are not great enough to influence -the tides very materially, but the variations in the moon's distances -have a striking effect. The tides which happen, when the moon is in -perigee, are considerably greater than when she is in apogee; and if she -happens to be in perigee at the time of the syzygies, the spring tides -are unusually high. - -The motion of the tide-wave is not a _progressive_ motion, but a mere -undulation, and is to be carefully distinguished from the currents to -which it gives rise. If the ocean completely covered the earth, the sun -and moon being in the equator, the tide-wave would travel at the same -rate as the earth revolves on its axis. Indeed, the correct way of -conceiving of the tide-wave, is to consider the moon at rest, and the -earth, in its rotation from west to east, as bringing successive -portions of water under the moon, which portions being elevated -successively, at the same rate as the earth revolves on its axis, have a -relative motion westward, at the same rate. - -The tides of rivers, narrow bays, and shores far from the main body of -the ocean, are not produced in those places by the direct action of the -sun and moon, but are subordinate waves propagated from the great -tide-wave, and are called _derivative_ tides, while those raised -directly by the sun and moon are called _primitive_ tides. - -[Illustration Fig. 49.] - -The velocity with which the tide moves will depend on various -circumstances, but principally on the depth, and probably on the -regularity, of the channel. If the depth is nearly uniform the tides -will be regular; but if some parts of the channel are deep while others -are shallow, the waters will be detained by the greater friction of the -shallow places, and the tides will be irregular. The direction, also, of -the derivative tide may be totally different from that of the primitive. -Thus, in Fig. 49, if the great tide-wave, moving from east to west, is -represented by the lines 1, 2, 3, 4, the derivative tide, which is -propagated up a river or bay, will be represented by the lines 3, 4, 5, -6, 7. Advancing faster in the channel than next the bank, the tides will -lag behind towards the shores, and the tide-wave will take the form of -curves, as represented in the diagram. - -On account of the retarding influence of shoals, and an uneven, indented -coast, the tide-wave travels more slowly along the shores of an island -than in the neighboring sea, assuming convex figures at a little -distance from the island, and on opposite sides of it. These convex -lines sometimes meet, and become blended in such a way, as to create -singular anomalies in a sea much broken by islands, as well as on coasts -indented with numerous bays and rivers. Peculiar phenomena are also -produced, when the tide flows in at opposite extremities of a reef or -island, as into the two opposite ends of Long-Island Sound. In certain -cases, a tide-wave is forced into a narrow arm of the sea, and produces -very remarkable tides. The tides of the Bay of Fundy (the highest in the -world) are ascribed to this cause. The tides on the coast of North -America are derived from the great tide-wave of the South Atlantic, -which runs steadily northward along the coast to the mouth of the Bay of -Fundy, where it meets the northern tide-wave flowing in the opposite -direction. This accumulated wave being forced into the narrow space -occupied by the Bay, produces the remarkable tide of that place. - -The largest lakes and inland seas have no perceptible tides. This is -asserted by all writers respecting the Caspian and Euxine; and the same -is found to be true of the largest of the North-American lakes, Lake -Superior. Although these several tracts of water appear large, when -taken by themselves, yet they occupy but small portions of the surface -of the globe, as will appear evident from the delineation of them on the -artificial globe. Now, we must recollect that the primitive tides are -produced by the _unequal_ action of the sun and moon upon the different -parts of the earth; and that it is only at points whose distance from -each other bears a considerable ratio to the whole distance of the sun -or moon, that the inequality of action becomes manifest. The space -required to make the effect sensible is larger than either of these -tracts of water. It is obvious, also, that they have no opportunity to -be subject to a derivative tide. - -Although all must admit that the tides have _some connexion_ with the -sun and the moon, yet there are so many seeming anomalies, which at -first appear irreconcilable with the theory of gravitation, that some -are unwilling to admit the explanation given by this theory. Thus, the -height of the tide is so various, that at some places on the earth there -is scarcely any tide at all, while at other places it rises to seventy -feet. The time of occurrence is also at many places wholly unconformable -to the motions of the moon, as is required by the theory, being low -water where it should be high water; or, instead of appearing just -beneath the moon, as the theory would lead us to expect, following it at -the distance of six, ten, or even fifteen, hours; and finally, the moon -sometimes appears to have no part at all in producing the tide, but it -happens uniformly at noon and midnight, (as is said to be the case at -the Society Islands,) and therefore seems wholly dependent on the sun. - -Notwithstanding these seeming inconsistencies with the law of universal -gravitation, to which the explanation of the tides is referred, the -correspondence of the tides to the motions of the sun and moon, in -obedience to the law of attraction, is in general such as to warrant the -application of that law to them, while in a great majority of the cases -which appear to be exceptions to the operation of that law, local causes -and impediments have been discovered, which modified or overruled the -uniform operation of the law of gravitation. Thus it does not disprove -the reality of the existence of a force which carries bodies near the -surface of the earth towards its centre, that we see them sometimes -compelled, by the operation of local causes, to move in the opposite -direction. A ball shot from a cannon is still subject to the law of -gravitation, although, for a certain time, in obedience to the impulse -given it, it may proceed in a line contrary to that in which gravity -alone would carry it. The fact that water may be made to run up hill -does not disprove the fact that it usually runs down hill by the force -of gravity, or that it is still subject to this force, although, from -the action of modifying or superior forces, it may be proceeding in a -direction contrary to that given by gravity. Indeed, those who have -studied the doctrine of the tides most profoundly consider them as -affording a striking and palpable exhibition of the truth of the -doctrine of universal gravitation. - -FOOTNOTE: - -[11] The exact longitude of the City Hall, in the city of New York, is -4h. 56m. 33.5s. - - - - -LETTER XX. - -PLANETS.--MERCURY AND VENUS. - - "First, Mercury, amidst full tides of light, - Rolls next the sun, through his small circle bright; - Our earth would blaze beneath so fierce a ray, - And all its marble mountains melt away. - Fair Venus next fulfils her larger round, - With softer beams, and milder glory crowned; - Friend to mankind, she glitters from afar, - Now the bright evening, now the morning, star."--_Baker._ - - -THERE is no study in which more is to be hoped for from a lucid -arrangement, than in the study of astronomy. Some subjects involved in -this study appear very difficult and perplexing to the learner, before -he has fully learned the doctrine of the sphere, and gained a certain -familiarity with astronomical doctrines, which would seem very easy to -him after he had made such attainments. Such an order ought to be -observed, as shall bring out the facts and doctrines of the science just -in the place where the mind of the learner is prepared to receive them. -Some writers on astronomy introduce their readers at once to the most -perplexing part of the whole subject,--the planetary motions. I have -thought a different course advisable, and have therefore commenced these -Letters with an account of those bodies which are most familiarly known -to us, the earth, the sun, and the moon. In connexion with the earth, we -are able to acquire a good knowledge of the artificial divisions and -points of reference that are established on the earth and in the -heavens, constituting the doctrine of the sphere. You thus became -familiar with many terms and definitions which are used in astronomy. -These ought to be always very clearly borne in mind; and if you now meet -with any term, the definition of which you have either partially or -wholly forgotten, let me strongly recommend to you, to turn back and -review it, until it becomes as familiar to you as household words. -Indeed, you will find it much to your advantage to go back frequently, -and reiterate the earlier parts of the subject, before you advance to -subjects of a more intricate nature. If this process should appear to -you a little tedious, still you will find yourself fully compensated by -the clear light in which all the succeeding subjects will appear. This -clear and distinct perception of the ground we have been over shows us -just where we are on our journey, and helps us to find the remainder of -the way with far greater ease than we could otherwise do. I do not, -however, propose by any devices to relieve you from the trouble of -thinking. Those who are not willing to incur this trouble can never -learn much of astronomy. - -In introducing you to the planets, (which next claim our attention,) I -will, in the first place, endeavor to convey to you some clear views of -these bodies individually, and afterwards help you to form as correct a -notion as possible of their motions and mutual relations. - -The name _planet_ is derived from a Greek word, (= planźtźs=, -_planetes_,) which signifies a _wanderer_, and is applied to this class -of bodies, because they shift their positions in the heavens, whereas -the fixed stars constantly maintain the same places with respect to each -other. The planets known from a high antiquity are, Mercury, Venus, -Earth, Mars, Jupiter, and Saturn. To these, in 1781, was added Uranus, -(or _Herschel_, as it is sometimes called, from the name of its -discoverer;) and, as late as the commencement of the present century, -four more were added, namely, Ceres, Pallas, Juno, and Vesta. These -bodies are designated by the following characters: - - 1. Mercury, [Planet: Mercury] - 2. Venus, [Planet: Venus] - 3. Earth, [Planet: Earth] - 4. Mars, [Planet: Mars] - 5. Vesta, [Planet: Vesta] - 6. Juno, [Planet: Juno] - 7. Ceres, [Planet: Ceres] - 8. Pallas, [Planet: Pallas] - 9. Jupiter, [Planet: Jupiter] - 10. Saturn, [Planet: Saturn] - 11. Uranus, [Planet: Uranus] - -The foregoing are called the _primary_ planets. Several of these have -one or more attendants, or satellites, which revolve around them as they -revolve around the sun. The Earth has one satellite, namely, the Moon; -Jupiter has four; Saturn, seven; and Uranus, six. These bodies are also -planets, but, in distinction from the others, they are called -_secondary_ planets. Hence, the whole number of planets are twenty-nine, -namely, eleven primary, and eighteen secondary, planets. - -You need never look for a planet either very far in the north or very -far in the south, since they are always near the ecliptic. Mercury, -which deviates furthest from that great circle, never is seen more than -seven degrees from it; and you will hardly ever see one of the planets -so far from it as this, but they all pursue nearly the same great route -through the skies, in their revolutions around the sun. The new planets, -however, make wider excursions from the plane of the ecliptic, -amounting, in the case of Pallas, to thirty-four and a half degrees. - -Mercury and Venus are called _inferior_ planets, because they have their -orbits nearer to the sun than that of the earth; while all the others, -being more distant from the sun than the earth, are called _superior_ -planets. The planets present great diversities among themselves, in -respect to distance from the sun, magnitude, time of revolution, and -density. They differ, also, in regard to satellites, of which, as we -have seen, three have respectively four, six, and seven, while more than -half have none at all. It will aid the memory, and render our view of -the planetary system more clear and comprehensive, if we classify, as -far as possible, the various particulars comprehended under the -foregoing heads. As you have had an opportunity, in preceding Letters, -of learning something respecting the means which astronomers have of -ascertaining the distances and magnitudes of these bodies, you will not -doubt that they are really as great as they are represented; but when -you attempt to conceive of spaces so vast, you will find the mind wholly -inadequate to the task. It is indeed but a comparatively small space -that we can fully comprehend at one grasp. Still, by continual and -repeated efforts, we may, from time to time, somewhat enlarge the -boundaries of our mental vision. Let us begin with some known and -familiar space, as the distance between two places we are accustomed to -traverse. Suppose this to be one hundred miles. Taking this as our -measure, let us apply it to some greater distance, as that across the -Atlantic Ocean,--say three thousand miles. From this step we may advance -to some faint conception of the diameter of the earth; and taking that -as a new measure, we may apply it to such greater spaces as the distance -of the planets from the sun. I hope you will make trial of this method -on the following comparative statements respecting the planets. - - _Distances from the Sun, in miles._ - - 1. Mercury, 37,000,000 - 2. Venus, 68,000,000 - 3. Earth, 95,000,000 - 4. Mars, 142,000,000 - 5. Vesta, 225,000,000 - 6. Juno, } - 7. Ceres, } 261,000,000 - 8. Pallas, } - 9. Jupiter, 485,000,000 - 10. Saturn, 890,000,000 - 11. Uranus, or Herschel, 1800,000,000 - -The _dimensions_ of the planetary system are seen from this table to be -vast, comprehending a circular space thirty-six hundred millions of -miles in diameter. A rail-way car, travelling constantly at the rate of -twenty miles an hour, would require more than twenty thousand years to -cross the orbit of Uranus. - - _Magnitudes._ - - Diam. in miles. - 1. Mercury, 3140 - 2. Venus, 7700 - 3. Earth, 7912 - 4. Mars, 4200 - 5. Ceres, 160 - 6. Jupiter, 89,000 - 7. Saturn, 79,000 - 8. Uranus, 35,000 - -We remark here a great diversity in regard to magnitude,--a diversity -which does not appear to be subject to any definite law. While Venus, an -inferior planet, is nine tenths as large as the earth, Mars, a superior -planet, is only one seventh, while Jupiter is twelve hundred and -eighty-one times as large. Although several of the planets, when nearest -to us, appear brilliant and large, when compared with most of the fixed -stars, yet the angle which they subtend is very small,--that of Venus, -the greatest of all, never exceeding about one minute, which is less -than one thirtieth the apparent diameter of the sun or moon. Jupiter, -also, by his superior brightness, sometimes makes a striking figure -among the stars; yet his greatest apparent diameter is less than one -fortieth that of the sun. - - _Periodic Times_. - - Mercury revolves around the sun in nearly 3 months. - Venus, " " " " 7-1/2 " - Earth, " " " " 1 year. - Mars, " " " " 2 years. - Ceres, " " " " 4-2/3 " - Jupiter, " " " " 12 " - Saturn, " " " " 29 " - Uranus, " " " " 84 " - -From this view, it appears that the planets nearest the sun move most -rapidly. Thus, Mercury performs nearly three hundred and fifty -revolutions while Uranus performs one. The apparent progress of the most -distant planets around the sun is exceedingly slow. Uranus advances only -a little more than four degrees in a whole year; so that we find this -planet occupying the same sign, and of course remaining nearly in the -same part of the heavens, for several years in succession. - -After this comparative view of the planets in general, let us now look -at them individually; and first, of the inferior planets, Mercury and -Venus. - -MERCURY and VENUS, having their orbits so far within that of the earth, -appear to us as attendants upon the sun. Mercury never appears further -from the sun than twenty-nine degrees, and seldom so far; and Venus, -never more than about forty-seven degrees. Both planets, therefore, -appear either in the west soon after sunset, or in the east a little -before sunrise. In high latitudes, where the twilight is long, Mercury -can seldom be seen with the naked eye, and then only when its angular -distance from the sun is greatest. Copernicus, the great Prussian -astronomer, (who first distinctly established the order of the solar -system, as at present received,) lamented, on his death-bed, that he had -never been able to obtain a sight of Mercury; and Delambre, a -distinguished astronomer of France, saw it but twice. In our latitude, -however, we may see this planet for several evenings and mornings, if we -will watch the time (as usually given in the almanac) when it is at its -greatest elongations from the sun. It will not, however, remain long for -our gaze, but will soon run back to the sun. The reason of this will be -readily understood from the following diagram, Fig. 50. Let S represent -the sun, E, the earth, and M, N, Mercury at its greatest elongations -from the sun, and O Z P, a portion of the sky. Then, since we refer all -distant bodies to the same concave sphere of the heavens, it is evident -that we should see the sun at Z, and Mercury at O, when at its greatest -eastern elongation, and at P, when at its greatest western elongation; -and while passing from M to N through Q, it would appear to describe the -arc O P; and while passing from N to M through R, it would appear to run -back across the sun on the same arc. It is further evident that it would -be visible only when at or near one of its greatest elongations; being -at all other times so near the sun as to be lost in his light. - -[Illustration Fig. 50.] - -A planet is said to be in _conjunction_ with the sun when it is seen in -the same part of the heavens with the sun. Mercury and Venus have each -two conjunctions, the inferior and the superior conjunction. The -_inferior conjunction_ is its position when in conjunction on the same -side of the sun with the earth, as at Q, in the figure; the _superior -conjunction_ is its position when on the side of the sun most distant -from the earth, as at R. - -The time which a planet occupies in making one entire circuit of the -heavens, from any star, until it comes round to the same star again, is -called its _sidereal revolution_. The period occupied by a planet -between two successive conjunctions with the earth is called its -_synodical revolution_. Both the planet and the earth being in motion, -the time of the synodical revolution of Mercury or Venus exceeds that of -the sidereal; for when the planet comes round to the place where it -before overtook the earth, it does not find the earth at that point, but -far in advance of it. Thus, let Mercury come into inferior conjunction -with the earth at C, Fig. 51. In about eighty-eight days, the planet -will come round to the same point again; but, mean-while, the earth has -moved forward through the arc E E“, and will continue to move while the -planet is moving more rapidly to overtake her; the case being analogous -to that of the hour and minute hand of a clock. - -[Illustration Fig. 51.] - -The synodical period of Mercury is one hundred and sixteen days, and -that of Venus five hundred and eighty-four days. The former is increased -twenty-eight days, and the latter, three hundred and sixty days, by the -motion of the earth; so that Venus, after being in conjunction with the -earth, goes more than twice round the sun before she comes into -conjunction again. For, since the earth is likewise in motion, and moves -more than half as fast as Venus, by the time the latter has gone round -and returned to the place where the two bodies were together, the earth -is more than half way round, and continues moving, so that it will be a -long time before Venus comes up with it. - -The motion of an inferior planet is _direct_ in passing through its -superior conjunction, and _retrograde_ in passing through its inferior -conjunction. You will recollect that the motion of a heavenly body is -said to be direct when it is in the order of the signs from west to -east, and retrograde when it is contrary to the order of the signs, or -from east to west. Now Venus, while going from B through D to A, (Fig. -51,) moves from west to east, and would appear to traverse the celestial -vault B“ S“ A“, from right to left; but in passing from A through C to -B, her course would be retrograde, returning on the same arc from left -to right. If the earth were at rest, therefore, (and the sun, of course, -at rest,) the inferior planets would appear to oscillate backwards and -forwards across the sun. But it must be recollected that the earth is -moving in the same direction with the planet, as respects the signs, but -with a slower motion. This modifies the motions of the planet, -accelerating it in the superior, and retarding it in the inferior, -conjunction. Thus, in Fig. 51, Venus, while moving through B D A, would -seem to move in the heavens from B“ to A“, were the earth at rest; but, -mean-while, the earth changes its position from E to E“, on which -account the planet is not seen at A“, but at A““, being accelerated by -the arc A“ A““, in consequence of the earth's motion. On the other hand, -when the planet is passing through its inferior conjunction A C B, it -appears to move backwards in the heavens from A“ to B“, if the earth is -at rest, but from A“ to B““, if the earth has in the mean time moved -from E to E“, being retarded by the arc B“ B““. Although the motions of -the earth have the effect to accelerate the planet in the superior -conjunction, and to retard it in the inferior, yet, on account of the -greater distance, the apparent motion of the planet is much slower in -the superior than in the inferior conjunction, Venus being the whole -breadth of her orbit, or one hundred and thirty-six millions of miles -further from us when at her greatest, than when at her least, distance, -as is evident from Fig. 51. When passing from the superior to the -inferior conjunction, or from the inferior to the superior, through the -greatest elongations, the inferior planets are _stationary_. Thus, (Fig. -51,) when the planet is at A, the earth being at E, as the planet's -motion is directly towards the spectator, he would constantly project it -at the same point in the heavens, namely, A“; consequently, it would -appear to stand still. Or, when at its greatest elongation on the other -side, at B, as its motion would be directly from the spectator, it would -be seen constantly at B“. If the earth were at rest, the stationary -points would be at the greatest elongations, as at A and B; but the -earth itself is moving nearly at right angles to the planet's motion, -which makes the planet appear to move in the opposite direction. Its -direct motion will therefore continue longer on the one side, and its -retrograde motion longer on the other side, than would be the case, were -it not for the motion of the earth. Mercury, whose greatest angular -distance from the sun is nearly twenty-nine degrees, is stationary at an -elongation of from fifteen to twenty degrees; and Venus, at about -twenty-nine degrees, although her greatest elongation is about -forty-seven degrees. - -Mercury and Venus exhibit to the telescope _phases_ similar to those of -the moon. When on the side of their inferior conjunction, as from B to C -through D, Fig. 52, less than half their enlightened disk is turned -towards us, and they appear horned, like the moon in her first and last -quarters; and when on the side of the superior conjunction, as from C to -B through A, more than half the enlightened disk is turned towards us, -and they appear gibbous. At the moment of superior conjunction, the -whole enlightened orb of the planet is turned towards the earth, and the -appearance would be that of the full moon; but the planet is too near -the sun to be commonly visible. - -[Illustration Fig. 52.] - -We should at first thought expect, that each of these planets would be -largest and brightest near their inferior conjunction, being then so -much nearer to us than at other times; but we must recollect that, when -in this situation, only a small part of the enlightened disk is turned -toward us. Still, the period of greatest brilliancy cannot be when most -of the illuminated side is turned towards us, for then, being at the -superior conjunction, its light will be diminished, both by its great -distance, and by its being so near the sun as to be partially lost in -the twilight. Hence, when Venus is a little within her place of greatest -elongation, about forty degrees from the sun, although less than half -her disk is enlightened, yet, being comparatively near to us, and -shining at a considerable altitude after the evening or before the -morning twilight, she then appears in greatest splendor, and presents an -object admired for its beauty in all ages. Thus Milton, - - "Fairest of stars, last in the train of night, - If better thou belong not to the dawn, - Sure pledge of day that crown'st the smiling morn - With thy bright circlet." - -Mercury and Venus both _revolve on their axes_ in nearly the same time -with the earth. The diurnal period of Mercury is a little greater, and -that of Venus a little less, than twenty-four hours. These revolutions -have been determined by means of some spot or mark seen by the -telescope, as the revolution of the sun on his axis is ascertained by -means of his spots. Mercury owes most of its peculiarities to its -proximity to the sun. Its light and heat, derived from the sun, are -estimated to be neatly seven times as great as on the earth, and the -apparent magnitude of the sun to a spectator on Mercury would be seven -times greater than to us. Hence the sun would present to an inhabitant -of that planet, with eyes like ours, an object of insufferable -brightness; and all objects on the surface would be arrayed in a light -more glorious than we can well imagine. (See Fig. 53.) The average heat -on the greater portion of this planet would exceed that of boiling -water, and therefore be incompatible with the existence both of an -animal and a vegetable kingdom constituted like ours. - -The motion of Mercury, in his revolution round the sun, is swifter than -that of any other planet, being more than one hundred thousand miles -every hour; whereas that of the earth is less than seventy thousand. -Eighteen hundred miles every minute,--crossing the Atlantic ocean in -less than two minutes,--this is a velocity of which we can form but a -very inadequate conception, although, as we shall see hereafter, it is -far less than comets sometimes exhibit. - -Venus is regarded as the most beautiful of the planets, and is well -known as the _morning and evening star_. The most ancient nations, -indeed, did not recognise the morning and evening star as one and the -same body, but supposed they were different planets, and accordingly -gave them different names, calling the morning star Lucifer, and the -evening star Hesperus. At her period of greatest splendor, Venus casts a -shadow, and is sometimes visible in broad daylight. Her light is then -estimated as equal to that of twenty stars of the first magnitude. In -the equatorial regions of the earth, where the twilight is short, and -Venus, at her greatest elongation, appears very high above the -horizon, her splendors are said to be far more conspicuous than in -our latitude. - -[Illustration Fig. 53. APPARENT MAGNITUDES OF THE SUN, AS SEEN FROM THE -DIFFERENT PLANETS.] - -[Illustration Figures 54, 55, 56. VENUS AND MARS.] - -Every eight years, Venus forms her conjunction with the sun in the same -part of the heavens. Whatever appearances, therefore, arise from her -position with respect to the earth and the sun, they are repeated every -eight years, in nearly the same form. - -Thus, every eight years, Venus is remarkably conspicuous, so as to be -visible in the day-time, being then most favorably situated, on several -accounts; namely, being nearest the earth, and at the point in her orbit -where she gives her greatest brilliancy, that is, a little within the -place of greatest elongation. This is the period for obtaining fine -telescopic views of Venus, when she is seen with spots on her disk. Thus -two figures of the annexed diagram (Fig. 54) represent Venus as seen -near her inferior conjunction, and at the period of maximum brilliancy. -The former situation is favorable for viewing her inequalities of -surface, as indicated by the roughness of the line which separates the -enlightened from the unenlightened part, (the _terminator_.) According -to Schroeter, a German astronomer, Venus has mountains twenty-two miles -high. Her mountains, however, are much more difficult to be seen than -those of the moon. - -The sun would appear, as seen from Venus, twice as large as on the -earth, and its light and heat would be augmented in the same proportion. -(See Fig. 53.) In many respects, however, the phenomena of this planet -are similar to those of our own; and the general likeness between Venus -and the earth, in regard to dimensions, revolutions, and seasons, is -greater than exists between any other two bodies of the system. - -I will only add to the present Letter a few words on the _transits_ of -the inferior planets. - -The transit of Mercury or Venus is its passage across the sun's disk, as -the moon passes over it in a solar eclipse. The planet is seen projected -on the sun's disk in a small, black, round spot, moving slowly over the -face of the sun. As the transit takes place only when the planet is in -inferior conjunction, at which time her motion is retrograde, it is -always from left to right; and, on account of its motion being retarded -by the motion of the earth, (as was explained by Fig. 51, page 232,) it -remains sometimes a long time on the solar disk. Mercury, when it makes -its transit across the sun's centre, may remain on the sun from five to -seven hours. - -You may ask, why we do not observe this appearance every time one of the -inferior planets comes into inferior conjunction, for then, of course, -it passes between us and the sun. It must, indeed, at this time, cross -the meridian at the same time with the sun; but, because its orbit is -inclined to that of the sun, it may cross it (and generally does) a -little above or a little below the sun. It is only when the conjunction -takes place at or very near the point where the two orbits cross one -another, that is, near the _node_, that a transit can occur. Thus, if -the orbit of Mercury, N M R, Fig. 50, (page 231,) were in the same plane -with the earth's orbit, (and of course with the sun's apparent orbit,) -then, when the planet was at Q, in its inferior conjunction, the earth -being at E, it would always be projected on the sun's disk at Z, on the -concave sphere of the heavens, and a transit would happen at every -inferior conjunction. But now let us take hold of the point R, and lift -the circle which represents the orbit of Mercury upwards seven degrees, -letting it turn upon the diameter _d b_; then, we may easily see that a -spectator at E would project the planet higher in the heavens than the -sun; and such would always be the case, except when the conjunction -takes place at the node. Then the point of intersection of the two -orbits being in one and the same plane, both bodies would be referred to -the same point on the celestial sphere. As the sun, in his apparent -revolution around the earth every year, passes through every point in -the ecliptic, of course he must every year be at each of the points -where the orbit of Mercury or Venus crosses the ecliptic, that is, at -each of the nodes of one of these planets;[12] and as these nodes are on -opposite sides of the ecliptic, consequently, the sun will pass through -them at opposite seasons of the year, as in January and July, February -and August. Now, should Mercury or Venus happen to come between us and -the sun, just as the sun is passing one of the planet's nodes, a transit -would happen. Hence the transits of Mercury take place in May and -November, and those of Venus, in June and December. - -Transits of Mercury occur more frequently than those of Venus. The -periodic times of Mercury and the earth are so adjusted to each other, -that Mercury performs nearly twenty-nine revolutions while the earth -performs seven. If, therefore, the two bodies meet at the node in any -given year, seven years afterwards they will meet nearly at the same -node, and a transit may take place, accordingly, at intervals of seven -years. But fifty-four revolutions of Mercury correspond still nearer to -thirteen revolutions of the earth; and therefore a transit is still more -probable after intervals of thirteen years. At intervals of thirty-three -years, transits of Mercury are exceedingly probable, because in that -time Mercury makes almost exactly one hundred and thirty-seven -revolutions. Intermediate transits, however, may occur at the other -node. Thus, transits of Mercury happened at the ascending node in 1815, -and 1822, at intervals of seven years; and at the descending node in -1832, which will return in 1845, after thirteen years. - -Transits of Venus are events of very unfrequent occurrence. Eight -revolutions of the earth are completed in nearly the same time as -thirteen revolutions of Venus; and hence two transits of Venus may occur -after an interval of eight years, as was the case at the last return of -the phenomenon, one transit having occurred in 1761, and another in -1769. But if a transit does not happen after eight years, it will not -happen at the same node, until an interval of two hundred and -thirty-five years: but intermediate transits may occur at the other -node. The next transit of Venus will take place in 1874, being two -hundred and thirty-five years after the first that was ever _observed_, -which occurred in 1639. This was seen, for the first time by mortal -eyes, by two youthful English astronomers, Horrox and Crabtree. Horrox -was a young man of extraordinary promise, and indicated early talents -for practical astronomy, which augured the highest eminence; but he died -in the twenty-third year of his age. He was only twenty when the transit -appeared, and he had made the calculations and observations, by which he -was enabled to anticipate its arrival several years before. At the -approach of the desired time for observing the transit, he received the -sun's image through a telescope in a dark room upon a white piece of -paper, and after waiting many hours with great impatience, (as his -calculation did not lead him to a knowledge of the precise time of the -occurrence,) at last, on the twenty-fourth of November, 1639, old style, -at three and a quarter hours past twelve, just as he returned from -church, he had the pleasure to find a large round spot near the limb of -the sun's image. It moved slowly across the sun's disk, but had not -entirely left it when the sun set. - -The great interest attached by astronomers to a transit of Venus arises -from its furnishing the most accurate means in our power of determining -the _sun's horizontal parallax_,--an element of great importance, since -it leads us to a knowledge of the distance of the earth from the sun, -which again affords the means of estimating the distances of all the -other planets, and possibly, of the fixed stars. Hence, in 1769, great -efforts were made throughout the civilized world, under the patronage of -different governments, to observe this phenomenon under circumstances -the most favorable for determining the parallax of the sun. - -The common methods of finding the parallax of a heavenly body cannot be -relied on to a greater degree of accuracy than four seconds. In the case -of the moon, whose greatest parallax amounts to about one degree, this -deviation from absolute accuracy is not very material; but it amounts to -nearly half the entire parallax of the sun. - -If the sun and Venus were equally distant from us, they would be equally -affected by parallax, as viewed by spectators in different parts of the -earth, and hence their _relative_ situation would not be altered by it; -but since Venus, at the inferior conjunction, is only about one third as -far off as the sun, her parallax is proportionally greater, and -therefore spectators at distant points will see Venus projected on -different parts of the solar disk, as the planet traverses the disk. -Astronomers avail themselves of this circumstance to ascertain the sun's -horizontal parallax, which they are enabled to do by comparing it with -that of Venus, in a manner which, without a knowledge of trigonometry, -you will not fully understand. In order to make the difference in the -apparent places of Venus on the sun's disk as great as possible, very -distant places are selected for observation. Thus, in the transits of -1761 and 1769, several of the European governments fitted out expensive -expeditions to parts of the earth remote from each other. For this -purpose, the celebrated Captain Cook, in 1769, went to the South Pacific -Ocean, and observed the transit at the island of Otaheite, while others -went to Lapland, for the same purpose, and others still, to many other -parts of the globe. Thus, suppose two observers took their stations on -opposite sides of the earth, as at A, and B, Fig. 57, page 242; at A, -the planet V would be seen on the sun's disk at _a_, while at B, it -would be seen at _b_. - -The appearance of Venus on the sun's disk being that of a well-defined -black spot, and the exactness with which the moment of external or -internal contact may be determined, are circumstances favorable to the -exactness of the result; and astronomers repose so much confidence in -the estimation of the sun's horizontal parallax, as derived from -observations on the transit of 1769, that this important element is -thought to be ascertained within one tenth of a second. The general -result of all these observations gives the sun's horizontal parallax -eight seconds and six tenths,--a result which shows at once that the sun -must be a great way off, since the semidiameter of the earth, a line -nearly four thousand miles in length, would appear at the sun under an -angle less than one four hundredth of a degree. During the transits of -Venus over the sun's disk, in 1761 and 1769, a sort of penumbral light -was observed around the planet, by several astronomers, which was -thought to indicate an _atmosphere_. This appearance was particularly -observable while the planet was coming on or going off the solar disk. -The total immersion and emersion were not instantaneous; but as two -drops of water, when about to separate, form a ligament between them, so -there was a dark shade stretched out between Venus and the sun; and when -the ligament broke, the planet seemed to have got about an eighth part -of her diameter from the limb of the sun. The various accounts of the -two transits abound with remarks like these, which indicate the -existence of an atmosphere about Venus of nearly the density and extent -of the earth's atmosphere. Similar proofs of the existence of an -atmosphere around this planet are derived from appearances of twilight. - -[Illustration Fig. 57.] - -The elder astronomers imagined that they had discovered a _satellite_ -accompanying Venus in her transit. If Venus had in reality any -satellite, the fact would be obvious at her transits, as, in some of -them at least, it is probable that the satellite would be projected near -the primary on the sun's disk; but later astronomers have searched in -vain for any appearances of the kind, and the inference is, that former -astronomers were deceived by some optical illusion. - -FOOTNOTE: - -[12] You will recollect that the sun is said to be at the node, when the -places of the node and the sun are both projected, by a spectator on the -earth, upon the same part of the heavens. - - - - -LETTER XXI. - -SUPERIOR PLANETS: MARS, JUPITER, SATURN, AND URANUS. - - "With what an awful, world-revolving power, - Were first the unwieldy planets launched along - The illimitable void! There to remain - Amidst the flux of many thousand years, - That oft has swept the toiling race of men, - And all their labored monuments, away."--_Thomson._ - - -MERCURY AND VENUS, as we have seen, are always observed near the sun, -and from this circumstance, as well as from the changes of magnitude and -form which they undergo, we know that they have their orbits within that -of the earth, and hence we call them _inferior_ planets. On the other -hand, Mars, Jupiter, Saturn, and Uranus, exhibit such appearances, at -different times, as show that they revolve around the sun at a greater -distance than the earth, and hence we denominate them _superior_ -planets. We know that they never come between us and the sun, because -they never undergo those changes which Mercury and Venus, as well as the -moon, sustain, in consequence of their coming into such a position. -They, however, wander to the greatest angular distance from the sun, -being sometimes seen one hundred and eighty degrees from him, so as to -rise when the sun sets. All these different appearances must naturally -result from their orbits' being exterior to that of the earth, as will -be evident from the following representation. Let E, Fig. 58, page 244, -be the earth, and M, one of the superior planets, Mars, for example, -each body being seen in its path around the sun. At M, the planet would -be in opposition to the sun, like the moon at the full; at Q and Q“, it -would be seen ninety degrees off, or in quadrature; and at M“, in -conjunction. We know, however, that this must be a superior and not an -inferior conjunction, for the illuminated disk is still turned towards -us; whereas, if it came between us and the sun, like Mercury, or Venus, -in its inferior conjunction, its dark side would be presented to us. - -[Illustration Fig. 58.] - -The superior planets do not exhibit to the telescope different phases, -but, with a single exception, they always present the side that is -turned towards the earth fully enlightened. This is owing to their great -distance from the earth; for were the spectator to stand upon the sun, -he would of course always have the illuminated side of each of the -planets turned towards him; but so distant are all the superior planets, -except Mars, that they are viewed by us very nearly, in the same manner -as they would be if we actually stood on the sun. Mars, however, is -sufficiently near to appear somewhat gibbous when at or near one of its -quadratures. Thus, when the planet is at Q, it is plain that, of the -hemisphere that is turned towards the earth, a small part is -unilluminated. - -Mars is a small planet, his diameter being only about half that of the -earth, or four thousand two hundred miles. He also, at times, comes -nearer to the earth than any other planet, except Venus. His _mean_ -distance from the sun is one hundred and forty-two millions of miles; -but his orbit is so elliptical, that his distance varies much in -different parts of his revolution. Mars is always very near the -ecliptic, never varying from it more than two degrees. He is -distinguished from all the planets by his deep red color, and fiery -aspect; but his brightness and apparent magnitude vary much, at -different times, being sometimes nearer to us than at others by the -whole diameter of the earth's orbit; that is, by about one hundred and -ninety millions of miles. When Mars is on the same side of the sun with -the earth, or at his opposition, he comes within forty-seven millions of -miles of the earth, and, rising about the time the sun sets, surprises -us by his magnitude and splendor; but when he passes to the other side -of the sun, to his superior conjunction, he dwindles to the appearance -of a small star, being then two hundred and thirty-seven millions of -miles from us. Thus, let M, Fig, 58, represent Mars in opposition, and -M“, in the superior conjunction, while E represents the earth. It is -obvious that, in the former situation, the planet must be nearer to the -earth than in the latter, by the whole diameter of the earth's orbit. -When viewed with a powerful telescope, the surface of Mars appears -diversified with numerous varieties of light and shade. The region -around the poles is marked by white spots, (see Fig. 56, page 237,) -which vary their appearances with the changes of seasons in the planet. -Hence Dr. Herschel conjectured that they were owing to ice and snow, -which alternately accumulate and melt away, according as it is Winter or -Summer, in that region. They are greatest and most conspicuous when that -part of the planet has just emerged from a long Winter, and they -gradually waste away, as they are exposed to the solar heat. Fig. 56, -represents the planet, as exhibited, under the most favorable -circumstances, to a powerful telescope, at the time when its gibbous -form is strikingly obvious. It has been common to ascribe the ruddy -light of Mars to an extensive and dense atmosphere, which was said to be -distinctly indicated by the gradual diminution of light observed in a -star, as it approaches very near to the planet, in undergoing an -occultation; but more recent observations afford no such evidence of an -atmosphere. - -By observations on the spots, we learn that Mars revolves on his axis in -very nearly the same time with the earth, (twenty-four hours thirty-nine -minutes twenty-one seconds and three tenths,) and that the inclination -of his axis to that of his orbit is also nearly the same, being thirty -degrees eighteen minutes ten seconds and eight tenths. Hence the changes -of day and night must be nearly the same there as here, and the seasons -also very similar to ours. Since, however, the distance of Mars from the -sun is one hundred and forty-two while that of the earth is only -ninety-five millions of miles, the sun will appear more than twice as -small on that planet as on ours, (see Fig. 53, page 236,) and its light -and heat will be diminished in the same proportion. Only the equatorial -regions, therefore, will be suitable for the existence of animals and -vegetables. - -The earth will be seen from Mars as an inferior planet, always near the -sun, presenting appearances similar, in many respects, to those which -Venus presents to us. It will be to that planet the evening and morning -star, sung by their poets (if poets they have) with a like enthusiasm. -The moon will attend the earth as a little star, being never seen -further from her side than about the diameter under which we view the -moon. To the telescope, the earth will exhibit phases similar to those -of Venus; and, finally, she will, at long intervals, make her transits -over the solar disk. Mean-while, Venus will stand to Mars in a relation -similar to that of Mercury [Illustration Figures 59, 60. JUPITER AND -SATURN.] to us, revealing herself only when at the periods of her -greatest elongation, and at all other times hiding herself within the -solar blaze. Mercury will never be visible to an inhabitant of Mars. - -Jupiter is distinguished from all the other planets by his great -_magnitude_. His diameter is eighty-nine thousand miles, and his volume -one thousand two hundred and eighty times that of the earth. His figure -is strikingly spheroidal, the equatorial being more than six thousand -miles longer than the polar diameter. Such a figure might naturally be -expected from the rapidity of his diurnal rotation, which is -accomplished in about ten hours. A place on the equator of Jupiter must -turn twenty-seven times as fast as on the terrestrial equator. The -distance of Jupiter from the sun is nearly four hundred and ninety -millions of miles, and his revolution around the sun occupies nearly -twelve years. Every thing appertaining to Jupiter is on a grand scale. A -world in itself, equal in dimensions to twelve hundred and eighty of -ours; the whole firmament rolling round it in the short space of ten -hours, a movement so rapid that the eye could probably perceive the -heavenly bodies to change their places every moment; its year dragging -out a length of more than four thousand days, and more than ten thousand -of its own days, while its nocturnal skies are lighted up with four -brilliant moons;--these are some of the peculiarities which characterize -this magnificent planet. - -The view of Jupiter through a good telescope is one of the most splendid -and interesting spectacles in astronomy. The disk expands into a large -and bright orb, like the full moon; the spheroidal figure which theory -assigns to revolving spheres, especially to those which turn with great -velocity, is here palpably exhibited to the eye; across the disk, -arranged in parallel stripes, are discerned several dusky bands, called -_belts_; and four bright satellites, always in attendance, and ever -varying their positions, compose a splendid retinue. Indeed, astronomers -gaze with peculiar interest on Jupiter and his moons, as affording a -miniature representation of the whole solar system, repeating, on a -smaller scale, the same revolutions, and exemplifying more within the -compass of our observation, the same laws as regulate the entire -assemblage of sun and planets. Figure 59, facing page 247, gives a -correct view of Jupiter, as exhibited to a powerful telescope in a clear -evening. You will remark his flattened or spheroidal figure, the belts -which appear in parallel stripes across his disk, and the four -satellites, that are seen like little stars in a straight line with the -equator of the planet. - -The _belts of Jupiter_ are variable in their number and dimensions. With -the smaller telescopes only one or two are seen, and those across the -equatorial regions; but with more powerful instruments, the number is -increased, covering a large part of the entire disk. Different opinions -have been entertained by astronomers respecting the cause of these -belts; but they have generally been regarded as clouds formed in the -atmosphere of the planet, agitated by winds, as is indicated by their -frequent changes, and made to assume the form of belts parallel to the -equator, like currents that circulate around our globe. Sir John -Herschel supposes that the belts are not ranges of clouds, but portions -of the planet itself, brought into view by the removal of clouds and -mists, that exist in the atmosphere of the planet, through which are -openings made by currents circulating around Jupiter. - -The _satellites of Jupiter_ may be seen with a telescope of very -moderate powers. Even a common spyglass will enable us to discern them. -Indeed, one or two of them have been occasionally seen with the naked -eye. In the largest telescopes they severally appear as bright as -Sirius. With such an instrument, the view of Jupiter, with his moons and -belts, is truly a magnificent spectacle. As the orbits of the satellites -do not deviate far from the plane of the ecliptic, and but little from -the equator of the planet, they are usually seen in nearly a straight -line with each other, extending across the central part of the disk. -(See Fig. 59, facing page 247.) - -Jupiter and his satellites exhibit in miniature all the phenomena of the -solar system. The satellites perform, around their primary, revolutions -very analogous to those which the planets perform around the sun, -having, in like manner, motions alternately direct, stationary, and -retrograde. They are all, with one exception, a little larger than the -moon; and the second satellite, which is the smallest, is nearly as -large as the moon, being two thousand and sixty-eight miles in diameter. -They are all very small compared with the primary, the largest being -only one twenty-sixth part of the primary. The outermost satellite -extends to the distance from the planet of fourteen times his diameter. -The whole system, therefore, occupies a region of space more than one -million miles in breadth. Rapidity of motion, as well as greatness of -dimensions, is characteristic of the system of Jupiter. I have already -mentioned that the planet itself has a motion on its own axis much -swifter than that of the earth, and the motions of the satellites are -also much more rapid than that of the moon. The innermost, which is a -little further off than the moon is from the earth, goes round its -primary in about a day and three quarters; and the outermost occupies -less than seventeen days. - -The orbits of the satellites are nearly or quite circular, and deviate -but little from the plane of the planet's equator, and of course are but -slightly inclined to the plane of his orbit. They are therefore in a -similar situation with respect to Jupiter, as the moon would be with -respect to the earth, if her orbit nearly coincided with the ecliptic, -in which case, she would undergo an eclipse at every opposition. The -eclipses of Jupiter's satellites, in their general circumstances, are -perfectly analogous to those of the moon, but in their details they -differ in several particulars. Owing to the much greater distance of -Jupiter from the sun, and its greater magnitude, the cone of its shadow -is much longer and larger than that of the earth. On this account, as -well as on account of the little inclination of their orbit to that of -the primary, the three inner satellites of Jupiter pass through his -shadow, and are totally eclipsed, at every revolution. The fourth -satellite, owing to the greater inclination of its orbit, sometimes, -though rarely, escapes eclipse, and sometimes merely grazes the limits -of the shadow, or suffers a partial eclipse. These eclipses, moreover, -are not seen, as is the case with those of the moon, from the centre of -their motion, but from a remote station, and one whose situation with -respect to the line of the shadow is variable. This makes no difference -in the _times_ of the eclipses, but it makes a very great one in their -visibility, and in their apparent situations with respect to the planet -at the moment of their entering or quitting the shadow. - -[Illustration Fig. 61.] - -The eclipses of Jupiter's satellites present some curious phenomena, -which you will easily understand by studying the following diagram. Let -A, B, C, D, Fig. 61, represent the earth in different parts of its -orbit; J, Jupiter, in his orbit, surrounded by his four satellites, the -orbits of which are marked 1, 2, 3, 4. At _a_, the first satellite -enters the shadow of the planet, emerges from it at _b_, and advances to -its greatest elongation at _c_. The other satellites traverse the shadow -in a similar manner. The apparent place, with respect to the planet, at -which these eclipses will be seen to occur, will be altered by the -position the earth happens at that moment to have in its orbit; but -their appearances for any given night, as exhibited at Greenwich, are -calculated and accurately laid down in the Nautical Almanac. - -When one of the satellites is passing between Jupiter and the sun, it -casts its shadow on the primary, as the moon casts its shadow on the -earth in a solar eclipse. We see with the telescope the shadow -traversing the disk. Sometimes, the satellite itself is seen projected -on the disk; but, being illuminated as well as the primary, it is not so -easily distinguished as Venus or Mercury, when seen on the sun's disk in -one of their transits, since these bodies have their dark sides turned -towards us; but the satellite is illuminated by the sun, as well as the -primary, and therefore is not easily distinguishable from it. - -The eclipses of Jupiter's satellites have been studied with great -attention by astronomers, on account of their affording one of the -easiest methods of determining the _longitude_. On this subject, Sir -John Herschel remarks: "The discovery of Jupiter's satellites by -Galileo, which was one of the first fruits of the invention of the -telescope, forms one of the most memorable epochs in the history of -astronomy. The first astronomical solution of the problem of 'the -longitude,'--the most important problem for the interests of mankind -that has ever been brought under the dominion of strict scientific -principles,--dates immediately from this discovery. The final and -conclusive establishment of the Copernican system of astronomy may also -be considered as referable to the discovery and study of this exquisite -miniature system, in which the laws of the planetary motions, as -ascertained by Kepler, and especially that which connects their periods -and distances, were speedily traced, and found to be satisfactorily -maintained." - -The entrance of one of Jupiter's satellites into the shadow of the -primary, being seen like the entrance of the moon into the earth's -shadow at the same moment of absolute time, at all places where the -planet is visible, and being wholly independent of parallax, that is, -presenting the same phenomenon to places remote from each other; being, -moreover, predicted beforehand, with great accuracy, for the instant of -its occurrence at Greenwich, and given in the Nautical Almanac; this -would seem to be one of those events which are peculiarly adapted for -finding the longitude. For you will recollect, that "any instantaneous -appearance in the heavens, visible at the same moment of absolute time -at any two places, may be employed for determining the difference of -longitude between those places; for the difference in their local times, -as indicated by clocks or chronometers, allowing fifteen degrees for -every hour, will show their difference of longitude." - -With respect to the method by the eclipses of Jupiter's satellites, it -must be remarked, that the extinction of light in the satellite, at its -immersion, and the recovery of its light at its emersion, are not -instantaneous, but gradual; for the satellite, like the moon, occupies -some time in entering into the shadow, or in emerging from it, which -occasions a progressive diminution or increase of light. Two observers -in the same room, observing with different telescopes the same eclipse, -will frequently disagree, in noting its time, to the amount of fifteen -or twenty seconds. Better methods, therefore, of finding the longitude, -are now employed, although the facility with which the necessary -observations can be made, and the little calculation required, still -render this method eligible in many cases where extreme accuracy is not -important. As a telescope is essential for observing an eclipse of one -of the satellites, it is obvious that this method cannot be practised at -sea, since the telescope cannot be used on board of ship, for want of -the requisite steadiness. - -The grand discovery of the _progressive motion of light_ was first made -by observations on the eclipses of Jupiter's satellites. In the year -1675, it was remarked by Roemer, a Danish astronomer, on comparing -together observations of these eclipses during many successive years, -that they take place sooner by about sixteen minutes, when the earth is -on the same side of the sun with the planet, than when she is on the -opposite side. The difference he ascribes to the progressive motion of -light, which takes that time to pass through the diameter of the earth's -orbit, making the velocity of light about one hundred and ninety-two -thousand miles per second. So great a velocity startled astronomers at -first, and produced some degree of distrust of this explanation of the -phenomenon; but the subsequent discovery of what is called the -aberration of light, led to an independent estimation of the velocity of -light, with almost precisely the same result. - -Few greater feats have ever been performed by the human mind, than to -measure the speed of light,--a speed so great, as would carry it across -the Atlantic Ocean in the sixty-fourth part of a second, and around the -globe in less than the seventh part of a second! Thus has man applied -his scale to the motions of an element, that literally leaps from world -to world in the twinkling of an eye. This is one example of the great -power which the invention of the telescope conferred on man. - -Could we plant ourselves on the surface of this vast planet, we should -see the same starry firmament expanding over our heads as we see now; -and the same would be true if we could fly from one planetary world to -another, until we made the circuit of them all; but the sun and the -planetary system would present themselves to us under new and strange -aspects. The sun himself would dwindle to one twenty-seventh of his -present surface, (Fig. 53, facing page 236,) and afford a degree of -light and heat proportionally diminished; Mercury, Venus, and even the -Earth, would all disappear, being too near the sun to be visible; Mars -would be as seldom seen as Mercury is by us, and constitute the only -inferior planet. On the other hand, Saturn would shine with greatly -augmented size and splendor. When in opposition to the sun, (at which -time it comes nearest to Jupiter,) it would be a grand object, appearing -larger than either Venus or Jupiter does to us. When, however, passing -to the other side of the sun, through its superior conjunction, it would -gradually diminish in size and brightness, and at length become much -less than it ever appears to us, since it would then be four hundred -millions of miles further from Jupiter than it ever is from us. - -Although Jupiter comes four hundred millions of miles nearer to Uranus -than the earth does, yet it is still thirteen hundred millions of miles -distant from that planet. Hence the augmentation of the magnitude and -light of Uranus would be barely sufficient to render it distinguishable -by the naked eye. It appears, therefore, that Saturn is the peculiar -ornament of the firmament of Jupiter, and would present to the telescope -most interesting and sublime phenomena. As we owe the revelation of the -system of Jupiter and his attendant worlds wholly to the telescope, and -as the discovery and observation of them constituted a large portion of -the glory of Galileo, I am now forcibly reminded of his labors, and will -recur to his history, and finish the sketch which I commenced in a -previous Letter. - - - - -LETTER XXII. - -COPERNICUS.--GALILEO. - - "They leave at length the nether gloom, and stand - Before the portals of a better land; - To happier plains they come, and fairer groves, - The seats of those whom Heaven, benignant, loves; - A brighter day, a bluer ether, spreads - Its lucid depths above their favored heads; - And, purged from mists that veil our earthly skies, - Shine suns and stars unseen by mortal eyes."--_Virgil._ - - -IN order to appreciate the value of the contributions which Galileo made -to astronomy, soon after the invention of the telescope, it is necessary -to glance at the state of the science when he commenced his discoveries -For many centuries, during the middle ages, a dark night had hung over -astronomy, through which hardly a ray of light penetrated, when, in the -eastern part of civilized Europe, a luminary appeared, that proved the -harbinger of a bright and glorious day. This was Copernicus, a native of -Thorn, in Prussia. He was born in 1473. Though destined for the -profession of medicine, from his earliest years he displayed a great -fondness and genius for mathematical studies, and pursued them with -distinguished success in the University of Cracow. At the age of -twenty-five years, he resorted to Italy, for the purpose of studying -astronomy, where he resided a number of years. Thus prepared, he -returned to his native country, and, having acquired an ecclesiastical -living that was adequate to his support in his frugal mode of life, he -established himself at Frauenberg, a small town near the mouth of the -Vistula, where he spent nearly forty years in observing the heavens, and -meditating on the celestial motions. He occupied the upper part of a -humble farm-house, through the roof of which he could find access to an -unobstructed sky, and there he carried on his observations. His -instruments, however, were few and imperfect, and it does not appear -that he added any thing to the art of practical astronomy. This was -reserved for Tycho Brahe, who came a half a century after him. Nor did -Copernicus enrich the science with any important discoveries. It was not -so much his genius or taste to search for new bodies, or new phenomena -among the stars, as it was to explain the reasons of the most obvious -and well-known appearances and motions of the heavenly bodies. With this -view, he gave his mind to long-continued and profound meditation. - -Copernicus tells us that he was first led to think that the apparent -motions of the heavenly bodies, in their diurnal revolution, were owing -to the real motion of the earth in the opposite direction, from -observing instances of the same kind among terrestrial objects; as when -the shore seems to the mariner to recede, as he rapidly sails from it; -and as trees and other objects seem to glide by us, when, on riding -swiftly past them, we lose the consciousness of our own motion. He was -also smitten with the _simplicity_ prevalent in all the works and -operations of Nature, which is more and more conspicuous the more they -are understood; and he hence concluded that the planets do not move in -the complicated paths which most preceding astronomers assigned to them. -I shall explain to you, hereafter, the details of his system. I need -only at present remind you that the hypothesis which he espoused and -defended, (being substantially the same as that proposed by Pythagoras, -five hundred years before the Christian era,) supposes, first, that the -apparent movements of the sun by day, and of the moon and stars by -night, from east to west, result from the actual revolution of the earth -on its own axis from west to east; and, secondly, that the earth and all -the planets revolve about the sun in circular orbits. This hypothesis, -when he first assumed it, was with him, as it had been with Pythagoras, -little more than mere conjecture. The arguments by which its truth was -to be finally established were not yet developed, and could not be, -without the aid of the telescope, which was not yet invented. Upon this -hypothesis, however, he set out to explain all the phenomena of the -visible heavens,--as the diurnal revolutions of the sun, moon, and -stars, the slow progress of the planets through the signs of the zodiac, -and the numerous irregularities to which the planetary motions are -subject. These last are apparently so capricious,--being for some time -forward, then stationary, then backward, then stationary again, and -finally direct, a second time, in the order of the signs, and constantly -varying in the velocity of their movements,--that nothing but -long-continued and severe meditation could have solved all these -appearances, in conformity with the idea that each planet is pursuing -its simple way all the while in a circle around the sun. Although, -therefore, Pythagoras fathomed the profound doctrine that the sun is the -centre around which the earth and all the planets revolve, yet we have -no evidence that he ever solved the irregular motions of the planets in -conformity with his hypothesis, although the explanation of the diurnal -revolution of the heavens, by that hypothesis, involved no difficulty. -Ignorant as Copernicus was of the principle of gravitation, and of most -of the laws of motion, he could go but little way in following out the -consequences of his own hypothesis; and all that can be claimed for him -is, that he solved, by means of it, most of the common phenomena of the -celestial motions. He indeed got upon the road to truth, and advanced -some way in its sure path; but he was able to adduce but few independent -proofs, to show that it was the truth. It was only quite at the close of -his life that he published his system to the world, and that only at the -urgent request of his friends; anticipating, perhaps, the opposition of -a bigoted priesthood, whose fury was afterwards poured upon the head of -Galileo, for maintaining the same doctrines. - -Although, therefore, the system of Copernicus afforded an explanation of -the celestial motions, far more simple and rational than the previous -systems which made the earth the centre of those motions, yet this fact -alone was not sufficient to compel the assent of astronomers; for the -greater part, to say the least, of the same phenomena, could be -explained on either hypothesis. With the old doctrine astronomers were -already familiar, a circumstance which made it seem easier; while the -new doctrines would seem more difficult, from their being imperfectly -understood. Accordingly, for nearly a century after the publication of -the system of Copernicus, he gained few disciples. Tycho Brahe rejected -it, and proposed one of his own, of which I shall hereafter give you -some account; and it would probably have fallen quite into oblivion, had -not the observations of Galileo, with his newly-invented telescope, -brought to light innumerable proofs of its truth, far more cogent than -any which Copernicus himself had been able to devise. - -Galileo no sooner had completed his telescope, and directed it to the -heavens, than a world of wonders suddenly burst upon his enraptured -sight. Pointing it to the moon, he was presented with a sight of her -mottled disk, and of her mountains and valleys. The sun exhibited his -spots; Venus, her phases; and Jupiter, his expanded orb, and his retinue -of moons. These last he named, in honor of his patron, Cosmo d'Medici, -_Medicean stars_. So great was this honor deemed of associating one's -name with the stars, that express application was made to Galileo, by -the court of France, to award this distinction to the reigning Monarch, -Henry the Fourth, with plain intimations, that by so doing he would -render himself and his family rich and powerful for ever. - -Galileo published the result of his discoveries in a paper, denominated -'_Nuncius Sidereus_,' the 'Messenger of the Stars.' In that ignorant and -marvellous age, this publication produced a wonderful excitement. "Many -doubted, many positively refused to believe, so novel an announcement; -all were struck with the greatest astonishment, according to their -respective opinions, either at the new view of the universe thus offered -to them, or at the high audacity of Galileo, in inventing such fables." -Even Kepler, the great German astronomer, of whom I shall tell you more -by and by, wrote to Galileo, and desired him to supply him with -arguments, by which he might answer the objections to these pretended -discoveries with which he was continually assailed. Galileo answered him -as follows: "In the first place, I return you my thanks that you first, -and almost alone, before the question had been sifted, (such is your -candor, and the loftiness of your mind,) put faith in my assertions. You -tell me you have some telescopes, but not sufficiently good to magnify -distant objects with clearness, and that you anxiously expect a sight of -mine, which magnifies images more than a thousand times. It is mine no -longer, for the Grand Duke of Tuscany has asked it of me, and intends to -lay it up in his museum, among his most rare and precious curiosities, -in eternal remembrance of the invention. - -"You ask, my dear Kepler, for other testimonies. I produce, for one, the -Grand Duke, who, after observing the Medicean planets several times with -me at Pisa, during the last months, made me a present, at parting, of -more than a thousand florins, and has now invited me to attach myself to -him, with the annual salary of one thousand florins, and with the title -of 'Philosopher and Principal Mathematician to His Highness;' without -the duties of any office to perform, but with the most complete leisure. -I produce, for another witness, myself, who, although already endowed in -this College with the noble salary of one thousand florins, such as no -professor of mathematics ever before received, and which I might -securely enjoy during my life, even if these planets should deceive me -and should disappear, yet quit this situation, and take me where want -and disgrace will be my punishment, should I prove to have been -mistaken." - -The learned professors in the universities, who, in those days, were -unaccustomed to employ their senses in inquiring into the phenomena of -Nature, but satisfied themselves with the authority of Aristotle, on all -subjects, were among the most incredulous with respect to the -discoveries of Galileo. "Oh, my dear Kepler," says Galileo, "how I wish -that we could have one hearty laugh together. Here, at Padua, is the -principal Professor of Philosophy, whom I have repeatedly and urgently -requested to look at the moon and planets through my glass, which he -pertinaciously refuses to do. Why are you not here? What shouts of -laughter we should have at this glorious folly, and to hear the -Professor of Philosophy at Pisa laboring before the Grand Duke, with -logical arguments, as if with magical incantations, to charm the new -planets out of the sky." - -The following argument by Sizzi, a contemporary astronomer of some note, -to prove that there can be only seven planets, is a specimen of the -logic with which Galileo was assailed. "There are seven windows given -to animals in the domicile of the head, through which the air is -admitted to the tabernacle of the body, to enlighten, to warm, and to -nourish it; which windows are the principal parts of the microcosm, or -little world,--two nostrils, two eyes, two ears, and one mouth. So in -the heavens, as in a macrocosm, or great world, there are two favorable -stars, Jupiter and Venus; two unpropitious, Mars and Saturn; two -luminaries, the Sun and Moon; and Mercury alone, undecided and -indifferent. From which, and from many other phenomena of Nature, such -as the seven metals, &c., which it were tedious to enumerate, we gather -that the number of planets is necessarily seven. Moreover, the -satellites are invisible to the naked eye, and therefore can exercise no -influence over the earth, and therefore would be useless, and therefore -do not exist. Besides, as well the Jews and other ancient nations, as -modern Europeans, have adopted the division of the week into seven days, -and have named them from the seven planets. Now, if we increase the -number of planets, this whole system falls to the ground." - -When, at length, the astronomers of the schools found it useless to deny -the fact that Jupiter is attended by smaller bodies, which revolve -around him, they shifted their ground of warfare, and asserted that -Galileo had not told the whole truth; that there were not merely _four_ -satellites, but a still greater number; one said five; another, nine; -and another, twelve; but, in a little time, Jupiter moved forward in his -orbit, and left all behind him, save the four Medicean stars. - -It had been objected to the Copernican system, that were Venus a body -which revolved around the sun in an orbit interior to that of the earth, -she would undergo changes similar to those of the moon. As no such -changes could be detected by the naked eye, no satisfactory answer could -be given to this objection; but the telescope set all right, by showing, -in fact, the phases of Venus. The same instrument, disclosed, also, in -the system of Jupiter and his moons, a miniature exhibition of the solar -system itself. It showed the actual existence of the motion of a number -of bodies around one central orb, exactly similar to that which was -predicated of the sun and planets. Every one, therefore, of these new -and interesting discoveries, helped to confirm the truth of the system -of Copernicus. - -But a fearful cloud was now rising over Galileo, which spread itself, -and grew darker every hour. The Church of Rome had taken alarm at the -new doctrines respecting the earth's motion, as contrary to the -declarations of the Bible, and a formidable difficulty presented itself, -namely, how to publish and defend these doctrines, without invoking the -terrible punishments inflicted by the Inquisition on heretics. No work -could be printed without license from the court of Rome; and any -opinions supposed to be held and much more known to be taught by any -one, which, by an ignorant and superstitious priesthood, could be -interpreted as contrary to Scripture, would expose the offender to the -severest punishments, even to imprisonment, scourging, and death. We, -who live in an age so distinguished for freedom of thought and opinion, -can form but a very inadequate conception of the bondage in which the -minds of men were held by the chains of the Inquisition. It was -necessary, therefore, for Galileo to proceed with the greatest caution -in promulgating truths which his own discoveries had confirmed. He did -not, like the Christian martyrs, proclaim the truth in the face of -persecutions and tortures; but while he sought to give currency to the -Copernican doctrines, he labored, at the same time, by cunning -artifices, to blind the ecclesiastics to his real designs, and thus to -escape the effects of their hostility. - -Before Galileo published his doctrines in form, he had expressed himself -so freely, as to have excited much alarm among the ecclesiastics. One of -them preached publicly against him, taking for his text, the passage, -"Ye men of Galilee, why stand ye here gazing up into heaven?" He -therefore thought it prudent to resort to Rome, and confront his enemies -face to face. A contemporary describes his appearance there in the -following terms, in a letter addressed to a Romish Cardinal: "Your -Eminence would be delighted with Galileo, if you heard him holding -forth, as he often does, in the midst of fifteen or twenty, all -violently attacking him, sometimes in one house, sometimes in another. -But he is armed after such fashion, that he laughs all of them to scorn; -and even if the novelty of his opinions prevents entire persuasion, at -least he convicts of emptiness most of the arguments with which his -adversaries endeavor to overwhelm him." - -In 1616, Galileo, as he himself states, had a most gracious audience of -the Pope, Paul the Fifth, which lasted for nearly an hour, at the end of -which his Holiness assured him, that the Congregation were no longer in -a humor to listen lightly to calumnies against him, and that so long as -he occupied the Papal chair, Galileo might think himself out of all -danger. Nevertheless, he was not allowed to return home, without -receiving formal notice not to teach the opinions of Copernicus, "that -the sun is in the centre of the system, and that the earth moves about -it," from that time forward, in any manner. - -Galileo had a most sarcastic vein, and often rallied his persecutors -with the keenest irony. This he exhibited, some time after quitting -Rome, in an epistle which he sent to the Arch Duke Leopold, accompanying -his 'Theory of the Tides.' "This theory," says he, "occurred to me when -in Rome, whilst the theologians were debating on the prohibition of -Copernicus's book, and of the opinion maintained in it of the motion of -the earth, which I at that time believed; until it pleased those -gentlemen to suspend the book, and to declare the opinion false and -repugnant to the Holy Scriptures. Now, as I know how well it becomes me -to obey and believe the decisions of my superiors, which proceed out of -more profound knowledge than the weakness of my intellect can attain -to, this theory, which I send you, which is founded on the motion of the -earth, I now look upon as a fiction and a dream, and beg your Highness -to receive it as such. But, as poets often learn to prize the creations -of their fancy, so, in like manner, do I set some value on this -absurdity of mine. It is true, that when I sketched this little work, I -did hope that Copernicus would not, after eighty years, be convicted of -error; and I had intended to develope and amplify it further; but a -voice from heaven suddenly awakened me, and at once annihilated all my -confused and entangled fancies." - -It is difficult, however, sometimes to decide whether the language of -Galileo is ironical, or whether he uses it with subtlety, with the hope -of evading the anathemas of the Inquisition. Thus he ends one of his -writings with the following passage: "In conclusion, since the motion -attributed to the earth, which I, as a pious and Catholic person, -consider most false, and not to exist, accommodates itself so well to -explain so many and such different phenomena, I shall not feel sure -that, false as it is, it may not just as deludingly correspond with the -phenomena of comets." - -In the year 1624, soon after the accession of Urban the Eighth to the -Pontifical chair, Galileo went to Rome again, to offer his -congratulations to the new Pope, as well as to propitiate his favor. He -seems to have been received with unexpected cordiality; and, on his -departure, the Pope commended him to the good graces of Ferdinand, Grand -Duke of Tuscany, in the following terms: "We find in him not only -literary distinction, but also the love of piety, and he is strong in -those qualities by which Pontifical good-will is easily obtained. And -now, when he has been brought to this city, to congratulate Us on Our -elevation, We have lovingly embraced him; nor can We suffer him to -return to the country whither your liberality recalls him, without an -ample provision of Pontifical love. And that you may know how dear he is -to Us, we have willed to give him this honorable testimonial of virtue -and piety. And We further signify, that every benefit which you shall -confer upon him will conduce to Our gratification." - -In the year 1630, Galileo finished a great work, on which he had been -long engaged, entitled, 'The Dialogue on the Ptolemaic and Copernican -Systems.' From the notion which prevailed, that he still countenanced -the Copernican doctrine of the earth's motion, which had been condemned -as heretical, it was some time before he could obtain permission from -the Inquisitors (whose license was necessary to every book) to publish -it. This he was able to do, only by employing again that duplicity or -artifice which would throw dust in the eyes of the vain and -superstitious priesthood. In 1632, the work appeared under the following -title: 'A Dialogue, by Galileo Galilei, Extraordinary Mathematician of -the University of Pisa, and Principal Philosopher and Mathematician of -the Most Serene Grand Duke of Tuscany; in which, in a Conversation of -four days, are discussed the two principal Systems of the World, the -Ptolemaic and Copernican, indeterminately proposing the Philosophical -Arguments as well on one side as on the other.' The subtle disguise -which he wore, may be seen from the following extract from his -'Introduction,' addressed 'To the discreet Reader.' - -"Some years ago, a salutary edict was promulgated at Rome, which, in -order to obviate the perilous scandals of the present age, enjoined an -opportune silence on the Pythagorean opinion of the earth's motion. Some -were not wanting, who rashly asserted that this decree originated, not -in a judicious examination, but in ill-informed passion; and complaints -were heard, that counsellors totally inexperienced in astronomical -observations ought not, by hasty prohibitions, to clip the wings of -speculative minds. My zeal could not keep silence when I heard these -rash lamentations, and I thought it proper, as being fully informed with -regard to that most prudent determination, to appear publicly on the -theatre of the world, as a witness of the actual truth. I happened at -that time to be in Rome: I was admitted to the audiences, and enjoyed -the approbation, of the most eminent prelates of that court; nor did the -publication of that decree occur without my receiving some prior -intimation of it. Wherefore, it is my intention, in this present work, -to show to foreign nations, that as much is known of this matter in -Italy, and particularly in Rome, as ultramontane diligence can ever have -formed any notion of, and collecting together all my own speculations on -the Copernican system, to give them to understand that the knowledge of -all these preceded the Roman censures; and that from this country -proceed not only dogmas for the salvation of the soul, but also -ingenious discoveries for the gratification of the understanding. With -this object, I have taken up in the 'Dialogue' the Copernican side of -the question, treating it as a pure mathematical hypothesis; and -endeavoring, in every artificial manner, to represent it as having the -advantage, not over the opinion of the stability of the earth -absolutely, but according to the manner in which that opinion is -defended by some, who indeed profess to be Aristotelians, but retain -only the name, and are contented, without improvement, to worship -shadows, not philosophizing with their own reason, but only from the -recollection of the four principles imperfectly understood." - -Although the Pope himself, as well as the Inquisitors, had examined -Galileo's manuscript, and, not having the sagacity to detect the real -motives of the author, had consented to its publication, yet, when the -book was out, the enemies of Galileo found means to alarm the court of -Rome, and Galileo was summoned to appear before the Inquisition. The -philosopher was then seventy years old, and very infirm, and it was with -great difficulty that he performed the journey. His unequalled dignity -and celebrity, however, commanded the involuntary respect of the -tribunal before which he was summoned, which they manifested by -permitting him to reside at the palace of his friend, the Tuscan -Ambassador; and when it became necessary, in the course of the inquiry, -to examine him in person, although his removal to the Holy Office was -then insisted upon, yet he was not, like other heretics, committed to -close and solitary confinement. On the contrary, he was lodged in the -apartments of the Head of the Inquisition, where he was allowed the -attendance of his own servant, who was also permitted to sleep in an -adjoining room, and to come and go at pleasure. These were deemed -extraordinary indulgences in an age when the punishment of heretics -usually began before their trial. - -About four months after Galileo's arrival in Rome, he was summoned to -the Holy Office. He was detained there during the whole of that day; and -on the next day was conducted, in a penitential dress, to the Convent of -Minerva, where the Cardinals and Prelates, his judges, were assembled -for the purpose of passing judgement upon him, by which this venerable -old man was solemnly called upon to renounce and abjure, as impious and -heretical, the opinions which his whole existence had been consecrated -to form and strengthen. Probably there is not a more curious document in -the history of science, than that which contains the sentence of the -Inquisition on Galileo, and his consequent abjuration. It teaches us so -much, both of the darkness and bigotry of the terrible Inquisition, and -of the sufferings encountered by those early martyrs of science, that I -will transcribe for your perusal, from the excellent 'Life of Galileo' -in the 'Library of Useful Knowledge,' (from which I have borrowed much -already,) the entire record of this transaction. The sentence of the -Inquisition is as follows: - -"We, the undersigned, by the grace of God, Cardinals of the Holy Roman -Church, Inquisitors General throughout the whole Christian Republic, -Special Deputies of the Holy Apostolical Chair against heretical -depravity: - -"Whereas, you, Galileo, son of the late Vincenzo Galilei of Florence, -aged seventy years, were denounced in 1615, to this Holy Office, for -holding as true a false doctrine taught by many, namely, that the sun is -immovable in the centre of the world, and that the earth moves, and also -with a diurnal motion; also, for having pupils which you instructed in -the same opinions; also, for maintaining a correspondence on the same -with some German mathematicians; also, for publishing certain letters on -the solar spots, in which you developed the same doctrine as true; also, -for answering the objections which were continually produced from the -Holy Scriptures, by glozing the said Scriptures, according to your own -meaning; and whereas, thereupon was produced the copy of a writing, in -form of a letter, professedly written by you to a person formerly your -pupil, in which, following the hypothesis of Copernicus, you include -several propositions contrary to the true sense and authority of the -Holy Scriptures: therefore, this Holy Tribunal, being desirous of -providing against the disorder and mischief which was thence proceeding -and increasing, to the detriment of the holy faith, by the desire of His -Holiness, and of the Most Eminent Lords Cardinals of this supreme and -universal Inquisition, the two propositions of the stability of the sun, -and motion of the earth, were _qualified_ by the _Theological -Qualifiers_, as follows: - -"1. The proposition that the sun is in the centre of the world, and -immovable from its place, is absurd, philosophically false, and formally -heretical; because it is expressly contrary to the Holy Scriptures. - -"2. The proposition that the earth is not the centre of the world, nor -immovable, but that it moves, and also with a diurnal motion, is also -absurd, philosophically false, and, theologically considered, equally -erroneous in faith. - -"But whereas, being pleased at that time to deal mildly with you, it was -decreed in the Holy Congregation, held before His Holiness on the -twenty-fifth day of February, 1616, that His Eminence the Lord Cardinal -Bellarmine should enjoin you to give up altogether the said false -doctrine; if you should refuse, that you should be ordered by the -Commissary of the Holy Office to relinquish it, not to teach it to -others, nor to defend it, and in default of the acquiescence, that you -should be imprisoned; and in execution of this decree, on the following -day, at the palace, in presence of His Eminence the said Lord Cardinal -Bellarmine, after you had been mildly admonished by the said Lord -Cardinal, you were commanded by the acting Commissary of the Holy -Office, before a notary and witnesses, to relinquish altogether the said -false opinion, and in future neither to defend nor teach it in any -manner, neither verbally nor in writing, and upon your promising -obedience, you were dismissed. - -"And, in order that so pernicious a doctrine might be altogether rooted -out, nor insinuate itself further to the heavy detriment of the Catholic -truth, a decree emanated from the Holy Congregation of the Index, -prohibiting the books which treat of this doctrine; and it was declared -false, and altogether contrary to the Holy and Divine Scripture. - -"And whereas, a book has since appeared, published at Florence last -year, the title of which showed that you were the author, which title -is, '_The Dialogue of Galileo Galilei, on the two principal Systems of -the World, the Ptolemaic and Copernican_;' and whereas, the Holy -Congregation has heard that, in consequence of printing the said book, -the false opinion of the earth's motion and stability of the sun is -daily gaining ground; the said book has been taken into careful -consideration, and in it has been detected a glaring violation of the -said order, which had been intimated to you; inasmuch as in this book -you have defended the said opinion, already, and in your presence, -condemned; although in the said book you labor, with many -circumlocutions, to induce the belief that it is left by you undecided, -and in express terms probable; which is equally a very grave error, -since an opinion can in no way be probable which has been already -declared and finally determined contrary to the Divine Scripture. -Therefore, by Our order, you have been cited to this Holy Office, where, -on your examination upon oath, you have acknowledged the said book as -written and printed by you. You also confessed that you began to write -the said book ten or twelve years ago, after the order aforesaid had -been given. Also, that you demanded license to publish it, but without -signifying to those who granted you this permission, that you had been -commanded not to hold, defend, or teach, the said doctrine in any -manner. You also confessed, that the style of said book was, in many -places, so composed, that the reader might think the arguments adduced -on the false side to be so worded, as more effectually to entangle the -understanding than to be easily solved, alleging, in excuse, that you -have thus run into an error, foreign (as you say) to your intention, -from writing in the form of a dialogue, and in consequence of the -natural complacency which every one feels with regard to his own -subtilties, and in showing himself more skilful than the generality of -mankind in contriving, even in favor of false propositions, ingenious -and apparently probable arguments. - -"And, upon a convenient time being given you for making your defence, -you produced a certificate in the handwriting of His Eminence, the Lord -Cardinal Bellarmine, procured, as you said, by yourself, that you might -defend yourself against the calumnies of your enemies, who reported that -you had abjured your opinions, and had been punished by the Holy Office; -in which certificate it is declared, that you had not abjured, nor had -been punished, but merely that the declaration made by his Holiness, and -promulgated by the Holy Congregation of the Index, had been announced to -you, which declares that the opinion of the motion of the earth, and -stability of the sun, is contrary to the Holy Scriptures, and therefore -cannot be held or defended. Wherefore, since no mention is there made of -two articles of the order, to wit, the order 'not to teach,' and 'in any -manner,' you argued that we ought to believe that, in the lapse of -fourteen or sixteen years, they had escaped your memory, and that this -was also the reason why you were silent as to the order, when you sought -permission to publish your book, and that this is said by you, not to -excuse your error, but that it may be attributed to vain-glorious -ambition rather than to malice. But this very certificate, produced on -your behalf, has greatly aggravated your offence, since it is therein -declared, that the said opinion is contrary to the Holy Scriptures, and -yet you have dared to treat of it, and to argue that it is probable; nor -is there any extenuation in the license artfully and cunningly extorted -by you, since you did not intimate the command imposed upon you. But -whereas, it appeared to Us that you had not disclosed the whole truth -with regard to your intentions, We thought it necessary to proceed to -the rigorous examination of you, in which (without any prejudice to what -you had confessed, and which is above detailed against you, with regard -to your said intention) you answered like a good Catholic. - -"Therefore, having seen and maturely considered the merits of your -cause, with your said confessions and excuses, and every thing else -which ought to be seen and considered, We have come to the underwritten -final sentence against you: - -"Invoking, therefore, the most holy name of our Lord Jesus Christ, and -of his Most Glorious Virgin Mother, Mary, by this Our final sentence, -which, sitting in council and judgement for the tribunal of the Reverend -Masters of Sacred Theology, and Doctors of both Laws, Our Assessors, We -put forth in this writing touching the matters and controversies before -Us, between the Magnificent Charles Sincerus, Doctor of both Laws, -Fiscal Proctor of this Holy Office, of the one part, and you, Galileo -Galilei, an examined and confessed criminal from this present writing -now in progress, as above, of the other part, We pronounce, judge, and -declare, that you, the said Galileo, by reason of these things which -have been detailed in the course of this writing, and which, as above, -you have confessed, have rendered yourself vehemently suspected, by this -Holy Office, of heresy; that is to say, that you believe and hold the -false doctrine, and contrary to the Holy and Divine Scriptures, namely, -that the sun is the centre of the world, and that it does not move from -east to west, and that the earth does move, and is not the centre of the -world; also, that an opinion can be held and supported, as probable, -after it has been declared and finally decreed contrary to the Holy -Scripture, and consequently, that you have incurred all the censures and -penalties enjoined and promulgated in the sacred canons, and other -general and particular constitutions against delinquents of this -description. From which it is Our pleasure that you be absolved, -provided that, with a sincere heart and unfeigned faith, in Our -presence, you abjure, curse, and detest, the said errors and heresies, -and every other error and heresy, contrary to the Catholic and Apostolic -Church of Rome, in the form now shown to you. - -"But that your grievous and pernicious error and transgression may not -go altogether unpunished, and that you may be made more cautious in -future, and may be a warning to others to abstain from delinquencies of -this sort, We decree, that the book of the Dialogues of Galileo Galilei -be prohibited by a public edict, and We condemn you to the formal prison -of this Holy Office for a period determinable at Our pleasure; and, by -way of salutary penance, We order you, during the next three years, to -recite, once a week, the seven penitential psalms, reserving to -Ourselves the power of moderating, commuting, or taking off the whole or -part of the said punishment, or penance. - -"And so We say, pronounce, and by Our sentence declare, decree, and -reserve, in this and in every other better form and manner, which -lawfully We may and can use. So We, the subscribing Cardinals, -pronounce." [Subscribed by seven Cardinals.] - -In conformity with the foregoing sentence, Galileo was made to kneel -before the Inquisition, and make the following _Abjuration_: - -"I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged -seventy years, being brought personally to judgement, and kneeling -before you, Most Eminent and Most Reverend Lords Cardinals, General -Inquisitors of the Universal Christian Republic against heretical -depravity, having before my eyes the Holy Gospels, which I touch with my -own hands, swear, that I have always believed, and with the help of God -will in future believe, every article which the Holy Catholic and -Apostolic Church of Rome holds, teaches, and preaches. But because I had -been enjoined, by this Holy Office, altogether to abandon the false -opinion which maintains that the sun is the centre and immovable, and -forbidden to hold, defend, or teach, the said false doctrine, in any -manner: and after it had been signified to me that the said doctrine is -repugnant to the Holy Scripture, I have written and printed a book, in -which I treat of the same doctrine now condemned, and adduce reasons -with great force in support of the same, without giving any solution, -and therefore have been judged grievously suspected of heresy; that is -to say, that I held and believed that the sun is the centre of the world -and immovable, and that the earth is not the centre and movable; -willing, therefore, to remove from the minds of Your Eminences, and of -every Catholic Christian, this vehement suspicion rightfully entertained -towards me, with a sincere heart and unfeigned faith, I abjure, curse, -and defeat, the said errors and heresies, and generally every other -error and sect contrary to the said Holy Church; and I swear, that I -will never more in future say or assert any thing, verbally or in -writing, which may give rise to a similar suspicion of me: but if I -shall know any heretic, or any one suspected of heresy, that I will -denounce him to this Holy Office, or to the Inquisitor and Ordinary of -the place in which I may be. I swear, moreover, and promise, that I will -fulfil and observe fully, all the penances which have been or shall be -laid on me by this Holy Office. But if it shall happen that I violate -any of my said promises, oaths, and protestations, (which God avert!) I -subject myself to all the pains and punishments which have been decreed -and promulgated by the sacred canons, and other general and particular -constitutions, against delinquents of this description. So may God help -me, and his Holy Gospels, which I touch with my own hands. I, the -above-named Galileo Galilei, have abjured, sworn, promised, and bound -myself, as above; and in witness thereof, with my own hand have -subscribed this present writing of my abjuration, which I have recited, -word for word. - -"At Rome, in the Convent of Minerva, twenty-second June, 1633, I, -Galileo Galilei, have abjured as above, with my own hand." - -From the court Galileo was conducted to prison, to be immured for life -in one of the dungeons of the Inquisition. His sentence was afterwards -mitigated, and he was permitted to return to Florence; but the -humiliation to which he had been subjected pressed heavily on his -spirits, beset as he was with infirmities, and totally blind, and he -never more talked or wrote on the subject of astronomy. - -There was enough in the character of Galileo to command a high -admiration. There was much, also, in his sufferings in the cause of -science, to excite the deepest sympathy, and even compassion. He is -moreover universally represented to have been a man of great equanimity, -and of a noble and generous disposition. No scientific character of the -age, or perhaps of any age, forms a structure of finer proportions, or -wears in a higher degree the grace of symmetry. Still, we cannot approve -of his employing artifice in the promulgation of truth; and we are -compelled to lament that his lofty spirit bowed in the final conflict. -How far, therefore, he sinks below the dignity of the Christian martyr! -"At the age of seventy," says Dr. Brewster, in his life of Sir Isaac -Newton, "on his bended knees, and with his right hand resting on the -Holy Evangelists, did this patriarch of science avow his present and -past belief in the dogmas of the Romish Church, abandon as false and -heretical the doctrine of the earth's motion and of the sun's -immobility, and pledge himself to denounce to the Inquisition any other -person who was even suspected of heresy. He abjured, cursed, and -detested, those eternal and immutable truths which the Almighty had -permitted him to be the first to establish. Had Galileo but added the -courage of the martyr to the wisdom of the sage; had he carried the -glance of his indignant eye round the circle of his judges; had he -lifted his hands to heaven, and called the living God to witness the -truth and immutability of his opinions; the bigotry of his enemies would -have been disarmed, and science would have enjoyed a memorable triumph." - - - - -LETTER XXIII. - -SATURN.--URANUS.--ASTEROIDS. - - "Into the Heaven of Heavens I have presumed, - An earthly guest, and drawn empyreal air."--_Milton._ - - -THE consideration of the system of Jupiter and his satellites led us to -review the interesting history of Galileo, who first, by means of the -telescope, disclosed the knowledge of that system to the world. I will -now proceed with the other superior planets. - -Saturn, as well as Jupiter, has within itself a system on a scale of -great magnificence. In size it is next to Jupiter the largest of the -planets, being seventy-nine thousand miles in diameter, or about one -thousand times as large as the earth. It has likewise belts on its -surface, and is attended by seven satellites. But a still more wonderful -appendage is its _Ring_, a broad wheel, encompassing the planet at a -great distance from it. As Saturn is nine hundred millions of miles from -us, we require a more powerful telescope to see his glories, in all -their magnificence, than we do to enjoy a full view of the system of -Jupiter. When we are privileged with a view of Saturn, in his most -favorable positions, through a telescope of the larger class, the -mechanism appears more wonderful than even that of Jupiter. - -Saturn's ring, when viewed with telescopes of a high power, is found to -consist of two concentred rings, separated from each other by a dark -space. Although this division of the rings appears to us, on account of -our immense distance, as only a fine line, yet it is, in reality, an -interval of not less than eighteen hundred miles. The dimensions of the -whole system are, in round numbers, as follows: - - Miles. - Diameter of the planet, 79,000 - From the surface of the planet to the inner ring, 20,000 - Breadth of the inner ring, 17,000 - Interval between the rings, 1,800 - Breadth of the outer ring, 10,500 - Extreme dimensions from outside to outside, 176,000 - -Figure 60, facing page 247, represents Saturn, as it appears to a -powerful telescope, surrounded by its rings, and having its body striped -with dark belts, somewhat similar, but broader and less strongly marked -than those of Jupiter. In telescopes of inferior power, but still -sufficient to see the ring distinctly, we should scarcely discern the -belts at all. We might, however, observe the shadow cast upon the ring -by the planet, (as seen in the figure on the right, on the upper side;) -and, in favorable situations of the planet, we might discern glimpses of -the shadow of the ring on the body of the planet, on the lower side -beneath the ring. To see the division of the ring and the satellites -requires a better telescope than is in possession of most observers. -With smaller telescopes, we may discover an oval figure of peculiar -appearance, which it would be difficult to interpret. Galileo, who first -saw it in the year 1610, recognised this peculiarity, but did not know -what it meant. Seeing something in the centre with two projecting arms, -one on each side, he concluded that the planet was triple-shaped. This -was, at the time, all he could learn respecting it, as the telescopes he -possessed were very humble, compared with those now used by astronomers. -The first constructed by him magnified but three times; his second, -eight times; and his best, only thirty times, which is no better than a -common ship-glass. - -It was the practice of the astronomers of those days to give the first -intimation of a new discovery in a Latin verse, the letters of which -were transposed. This would enable them to claim priority, in case any -other person should contest the honor of the discovery, and at the same -time would afford opportunity to complete their observations, before -they published a full account of them. Accordingly, Galileo announced -the discovery of the singular appearance of Saturn under this disguise, -in a line which, when the transposed letters were restored to their -proper places, signified that he had observed, "that the most distant -planet is triple-formed."[13] He shortly afterwards, at the request of -his patron, the Emperor Rodolph, gave the solution, and added, "I have, -with great admiration, observed that Saturn is not a single star, but -three together, which, as it were, touch each other; they have no -relative motion, and are constituted of this form, oOo, the middle one -being somewhat larger than the two lateral ones. If we examine them with -an eyeglass which magnifies the surface less than one thousand times, -the three stars do not appear very distinctly, but Saturn has an oblong -appearance, like that of an olive, thus, {oblong symbol}. Now, I have -discovered a court for Jupiter, (alluding to his satellites,) and two -servants for this old man, (Saturn,) who aid his steps, and never quit -his side." - -It was by this mystic light that Galileo groped his way through an -organization which, under the more powerful glasses of his successors, -was to expand into a mighty orb, encompassed by splendid rings of vast -dimensions, the whole attended by seven bright satellites. This system -was first fully developed by Huyghens, a Dutch astronomer, about forty -years afterwards.[14] It requires a superior telescope to see it to -advantage; but, when seen through such a telescope, it is one of the -most charming spectacles afforded to that instrument. To give some idea -of the properties of a telescope suited to such observations, I annex an -extract from an account, that was published a few years since, of a -telescope constructed by Mr. Tully, a distinguished English artist. "The -length of the instrument was twelve feet, but was easily adjusted, and -was perfectly steady. The magnifying powers ranged from two hundred to -seven hundred and eighty times; but the great excellence of the -telescope consisted more in the superior distinctness and brilliancy -with which objects were seen through it, than in its magnifying powers. -With a power of two hundred and forty, the light of Jupiter was almost -more than the eye could bear, and his satellites appeared as bright as -Sirius, but with a clear and steady light; and the belts and spots on -the face of the planet were most distinctly defined. With a power of -nearly four hundred, Saturn appeared large and well defined, and was one -of the most beautiful objects that can well be conceived." - -That the ring is a solid opaque substance, is shown by its throwing its -shadow on the body of the planet on the side nearest the sun, and on the -other side receiving that of the body. The ring encompasses the -equatorial regions of the planet, and the planet revolves on an axis -which is perpendicular to the plane of the ring in about ten and a half -hours. This is known by observing the rotation of certain dusky spots, -which sometimes appear on its surface. This motion is nearly the same -with the diurnal motion of Jupiter, subjecting places on the equator of -the planet to a very swift revolution, and occasioning a high degree of -compression at the poles, the equatorial being to the polar diameter in -the high ratio of eleven to ten. - -Saturn's ring, in its revolution around the sun, _always remains -parallel to itself_. If we hold opposite to the eye a circular ring or -disk, like a piece of coin, it will appear as a complete circle only -when it is at right angles to the axis of vision. When it is oblique to -that axis, it will be projected into an ellipse more and more flattened, -as its obliquity is increased, until, when its plane coincides with the -axis of vision, it is projected into a straight line. Please to take -some circle, as a flat plate, (whose rim may well represent the ring of -Saturn,) and hold it in these different positions before the eye. Now, -place on the table a lamp to represent the sun, and holding the ring at -a certain distance, inclined a little towards the lamp, carry it round -the lamp, always keeping it parallel to itself. During its revolution, -it will twice present its edge to the lamp at opposite points; and -twice, at places ninety degrees distant from those points, it will -present its broadest face towards the lamp. At intermediate points, it -will exhibit an ellipse more or less open, according as it is nearer one -or the other of the preceding positions. It will be seen, also, that in -one half of the revolution, the lamp shines on one side of the ring, and -in the other half of the revolution, on the other side. - -Such would be the successive appearances of Saturn's ring to a spectator -on the sun; and since the earth is, in respect to so distant a body as -Saturn, very near the sun, these appearances are presented to us nearly -in the same manner as though we viewed them from the sun. Accordingly, -we sometimes see Saturn's ring under the form of a broad ellipse, which -grows continually more and more acute, until it passes into a line, and -we either lose sight of it, altogether, or, by the aid of the most -powerful telescopes, we see it as a fine thread of light drawn across -the disk, and projecting out from it on each side. As the whole -revolution occupies thirty years, and the edge is presented to the sun -twice in the revolution, this last phenomenon, namely, the disappearance -of the ring, takes place every fifteen years. - -[Illustration Fig. 61.] - -You may perhaps gain a still clearer idea of the foregoing appearances -from the following diagram, Fig. 61. Let A, B, C, &c., represent -successive positions of Saturn and his ring, in different parts of his -orbit, while _a b_ represents the orbit of the earth. Please to remark, -that these orbits are drawn so elliptical, not to represent the -eccentricity of either the earth's or Saturn's orbit, but merely as the -projection of circles seen very obliquely. Also, imagine one half of the -body of the planet and of the ring to be above the plane of the paper, -and the other half below it. Were the ring, when at C and G, -perpendicular to C G, it would be seen by a spectator situated at _a_ or -_b_ as a perfect circle; but being inclined to the line of vision -twenty-eight degrees four minutes, it is projected into an ellipse. This -ellipse contracts in breadth as the ring passes towards its nodes at A -and E, where it dwindles into a straight line. From E to G the ring -opens again, becomes broadest at G, and again contracts, till it -becomes a straight line at A, and from this point expands, till it -recovers its original breadth at C. These successive appearances are all -exhibited to a telescope of moderate powers. - -The ring is extremely _thin_, since the smallest satellite, when -projected on it, more than covers it. The thickness is estimated at only -one hundred miles. Saturn's ring shines wholly by _reflected light_ -derived from the sun. This is evident from the fact that that side only -which is turned towards the sun is enlightened; and it is remarkable, -that the illumination of the ring is greater than that of the planet -itself, but the outer ring is less bright than the inner. Although we -view Saturn's ring nearly as though we saw it from the sun, yet the -plane of the ring produced may pass between the earth and the sun, in -which case, also, the ring becomes invisible, the illuminated side being -wholly turned from us. Thus, when the ring is approaching its node at E, -a spectator at _a_ would have the dark side of the ring presented to -him. The ring was invisible in 1833, and will be invisible again in -1847. The northern side of the ring will be in sight until 1855, when -the southern side will come into view. It appears, therefore, that there -are three causes for the disappearance of Saturn's ring: first, when the -edge of the ring is presented to the sun; secondly, when the edge is -presented to the earth; and thirdly, when the unilluminated side is -towards the earth. - -Saturn's ring _revolves_ in its own plane in about ten and a half hours. -La Place inferred this from the doctrine of universal gravitation. He -proved that such a rotation was necessary; otherwise, the matter of -which the ring is composed would be precipitated upon its primary. He -showed that, in order to sustain itself, its period of rotation must be -equal to the time of revolution of a satellite, circulating around -Saturn at a distance from it equal to that of the middle of the ring, -which period would be about ten and a half hours. By means of spots in -the ring, Dr. Herschel followed the ring in its rotation, and actually -found its period to be the same as assigned by La Place,--a coincidence -which beautifully exemplifies the harmony of truth. - -Although the rings have very nearly the same centre with the planet -itself, yet, recent measurements of extreme delicacy have demonstrated, -that the coincidence is not mathematically exact, but that the centre of -gravity of the rings describes around that of the body a very minute -orbit. "This fact," says Sir J. Herschel, "unimportant as it may seem, -is of the utmost consequence to the stability of the system of rings. -Supposing them mathematically perfect in their circular form, and -exactly concentric with the planet, it is demonstrable that they would -form (in spite of their centrifugal force) a system in a state of -unstable equilibrium, which the slightest external power would subvert, -not by causing a rupture in the substance of the rings, but by -precipitating them unbroken upon the surface of the planet." The ring -may be supposed of an unequal breadth in its different parts, and as -consisting of irregular solids, whose common centre of gravity does not -coincide with the centre of the figure. Were it not for this -distribution of matter, its equilibrium would be destroyed by the -slightest force, such as the attraction of a satellite, and the ring -would finally precipitate itself upon the planet. Sir J. Herschel -further observes, that, "as the smallest difference of velocity between -the planet and its rings must infallibly precipitate the rings upon the -planet, never more to separate, it follows, either that their motions in -their common orbit round the sun must have been adjusted to each other -by an external power, with the minutest precision, or that the rings -must have been formed about the planet while subject to their common -orbitual motion, and under the full and free influence of all the acting -forces. - -"The rings of Saturn must present a magnificent spectacle from those -regions of the planet which lie on their enlightened sides, appearing -as vast arches spanning the sky from horizon to horizon, and holding an -invariable situation among the stars. On the other hand, in the region -beneath the dark side, a solar eclipse of fifteen years in duration, -under their shadow, must afford (to our ideas) an inhospitable abode to -animated beings, but ill compensated by the full light of its -satellites. But we shall do wrong to judge of the fitness or unfitness -of their condition, from what we see around us, when, perhaps, the very -combinations which convey to our minds only images of horror, may be in -reality theatres of the most striking and glorious displays of -beneficent contrivance." - -Saturn is attended by _seven satellites_. Although they are bodies of -considerable size, their great distance prevents their being visible to -any telescope but such as afford a strong light and high magnifying -powers. The outermost satellite is distant from the planet more than -thirty times the planet's diameter, and is by far the largest of the -whole. It exhibits, like the satellites of Jupiter, periodic variations -of light, which prove its revolution on its axis in the time of a -sidereal revolution about Saturn, as is the case with our moon, while -performing its circuit about the earth. The next satellite in order, -proceeding inwards, is tolerably conspicuous; the three next are very -minute, and require powerful telescopes to see them; while the two -interior satellites, which just skirt the edge of the ring, and move -exactly in its plane, have never been discovered but with the most -powerful telescopes which human art has yet constructed, and then only -under peculiar circumstances. At the time of the disappearance of the -rings, (to ordinary telescopes,) they were seen by Sir William Herschel, -with his great telescope, projected along the edge of the ring, and -threading, like beads, the thin fibre of light to which the ring is then -reduced. Owing to the obliquity of the ring, and of the orbits of the -satellites, to that of their primary, there are no eclipses of the -satellites, the two interior ones excepted, until near the time when -the ring is seen edgewise. - -"The firmament of Saturn will unquestionably present to view a more -magnificent and diversified scene of celestial phenomena than that of -any other planet in our system. It is placed nearly in the middle of -that space which intervenes between the sun and the orbit of the -remotest planet. Including its rings and satellites, it may be -considered as the largest body or system of bodies within the limits of -the solar system; and it excels them all in the sublime and diversified -apparatus with which it is accompanied. In these respects, Saturn may -justly be considered as the sovereign among the planetary hosts. The -prominent parts of its celestial scenery may be considered as belonging -to its own system of rings and satellites, and the views which will -occasionally be opened of the firmament of the fixed stars; for few of -the other planets will make their appearance in its sky. Jupiter will -appear alternately as a morning and an evening star, with about the same -degree of brilliancy it exhibits to us; but it will seldom be -conspicuous, except near the period of its greatest elongation; and it -will never appear to remove from the sun further than thirty-seven -degrees, and consequently will not appear so conspicuous, nor for such a -length of time, as Venus does to us. Uranus is the only other planet -which will be seen from Saturn, and it will there be distinctly -perceptible, like a star of the third magnitude, when near the time of -its opposition to the sun. But near the time of its conjunction it will -be completely invisible, being then eighteen hundred millions of miles -more distant than at the opposition, and eight hundred millions of miles -more distant from Saturn than it ever is from the earth at any -period."[15] - -URANUS.--Uranus is the remotest planet belonging to our system, and is -rarely visible, except to the telescope. Although his diameter is more -than four times that of the earth, being thirty-five thousand one -hundred and twelve miles, yet his distance from the sun is likewise -nineteen times as great as the earth's distance, or about eighteen -hundred millions of miles. His revolution around the sun occupies nearly -eighty-four years, so that his position in the heavens, for several -years in succession, is nearly stationary. His path lies very nearly in -the ecliptic, being inclined to it less than one degree. The sun -himself, when seen from Uranus dwindles almost to a star, subtending, as -it does, an angle of only one minute and forty seconds; so that the -surface of the sun would appear there four hundred times less than it -does to us. This planet was discovered by Sir William Herschel on the -thirteenth of March, 1781. His attention was attracted to it by the -largeness of its disk in the telescope; and finding that it shifted its -place among the stars, he at first took it for a comet, but soon -perceived that its orbit was not eccentric, like the orbits of comets, -but nearly circular, like those of the planets. It was then recognised -as a new member of the planetary system, a conclusion which has been -justified by all succeeding observations. It was named by the discoverer -the _George Star_, (Georgium Sidus,) after his munificent patron, George -the Third; in the United States, and in some other countries, it was -called _Herschel_; but the name _Uranus_, from a Greek word, (= Ouranos=, -_Ouranos_,) signifying the oldest of the gods, has finally prevailed. So -distant is Uranus from the sun, that light itself, which moves nearly -twelve millions of miles every minute, would require more than two hours -and a half to pass to it from the sun. - -And now, having contemplated all the planets separately, just cast your -eyes on the diagram facing page 236, Fig. 53, and you will see a -comparative view of the various magnitudes of the sun, as seen from each -of the planets. - -Uranus is attended by _six satellites_. So minute objects are they, that -they can be seen only by powerful telescopes. Indeed, the existence of -more than two is still considered as somewhat doubtful. These two, -however, offer remarkable and indeed quite unexpected and unexampled -peculiarities. Contrary to the unbroken analogy of the whole planetary -system, _the planes of their orbits are nearly perpendicular to the -ecliptic_, and in these orbits their motions are retrograde; that is, -instead of advancing from west to east around their primary, as is the -case with all the other planets and satellites, they move in the -opposite direction. With this exception, all the motions of the planets, -whether around their own axes, or around the sun, are from west to east. -The sun himself turns on his axis from west to east; all the primary -planets revolve around the sun from west to east; their revolutions on -their own axes are also in the same direction; all the secondaries, with -the single exception above mentioned, move about their primaries from -west to east; and, finally, such of the secondaries as have been -discovered to have a diurnal revolution, follow the same course. Such -uniformity among so many motions could have resulted only from forces -impressed upon them by the same Omnipotent hand; and few things in the -creation more distinctly proclaim that God made the world. - -Retiring now to this furthest verge of the solar system, let us for a -moment glance at the aspect of the firmament by night. Notwithstanding -we have taken a flight of eighteen hundred millions of miles, the same -starry canopy bends over our heads; Sirius still shines with exactly the -same splendor as here; Orion, the Scorpion, the Great and the Little -Bear, all occupy the same stations; and the Galaxy spans the sky with -the same soft and mysterious light. The planets, however, with the -exception of Saturn, are all lost to the view, being too near the sun -ever to be seen; and Saturn himself is visible only at distant -intervals, at periods of fifteen years, when at its greatest elongations -from the sun, and is then too near the sun to permit a clear view of his -rings, much less of the satellites that unite with the rings to compose -his gorgeous retinue. Comets, moving slowly as they do when so distant -from the sun, will linger much longer in the firmament of Uranus than in -ours. - -Although the sun sheds by day a dim and cheerless light, yet the six -satellites that enlighten and diversify the nocturnal sky present -interesting aspects. "Let us suppose one satellite presenting a surface -in the sky eight or ten times larger than our moon; a second, five or -six times larger; a third, three times larger; a fourth, twice as large; -a fifth, about the same size as the moon; a sixth, somewhat smaller; -and, perhaps, three or four others of different apparent dimensions: let -us suppose two or three of those, of different phases, moving along the -concave of the sky, at one period four or five of them dispersed through -the heavens, one rising above the horizon, one setting, one on the -meridian, one towards the north, and another towards the south; at -another period, five or six of them displaying their lustre in the form -of a half moon, or a crescent, in one quarter of the heavens; and, at -another time, the whole of these moons shining, with full enlightened -hemispheres, in one glorious assemblage, and we shall have a faint idea -of the beauty, variety, and sublimity of the firmament of Uranus."[16] - -_The New Planets,--Ceres, Pallas, Juno, and Vesta._--The commencement of -the present century was rendered memorable in the annals of astronomy, -by the discovery of four new planets, occupying the long vacant tract -between Mars and Jupiter. Kepler, from some analogy which he found to -subsist among the distances of the planets from the sun, had long before -suspected the existence of one at this distance; and his conjecture was -rendered more probable by the discovery of Uranus, which follows the -analogy of the other planets. So strongly, indeed, were astronomers -impressed with the idea that a planet would be found between Mars and -Jupiter, that, in the hope of discovering it, an association was formed -on the continent of Europe, of twenty-four observers, who divided the -sky into as many zones, one of which was allotted to each member of the -association. The discovery of the first of these bodies was, however, -made accidentally by Piazzi, an astronomer of Palermo, on the first of -January, 1801. It was shortly afterwards lost sight of on account of its -proximity to the sun, and was not seen again until the close of the -year, when it was re-discovered in Germany. Piazzi called it _Ceres_, in -honor of the tutelary goddess of Sicily, and her emblem, the sickle, -([Planet: Ceres]) has been adopted as its appropriate symbol. - -The difficulty of finding Ceres induced Dr. Olbers, of Bremen, to -examine with particular care all the small stars that lie near her path, -as seen from the earth; and, while prosecuting these observations, in -March, 1802, he discovered another similar body, very nearly at the same -distance from the sun, and resembling the former in many other -particulars. The discoverer gave to this second planet the name of -_Pallas_, choosing for its symbol the lance, ([Planet: Pallas]) the -characteristic of Minerva. - -The most surprising circumstance connected with the discovery of -_Pallas_ was the existence of two planets at nearly the same distance -from the sun, and apparently crossing the ecliptic in the same part of -the heavens, or having the same node. On account of this singularity, -Dr. Olbers was led to conjecture that Ceres and Pallas are only -fragments of a larger planet, which had formerly circulated at the same -distance, and been shattered by some internal convulsion. The hypothesis -suggested the probability that there might be other fragments, whose -orbits might be expected to cross the ecliptic at a common point, or to -have the same node. Dr. Olbers, therefore, proposed to examine -carefully, every month, the two opposite parts of the heavens in which -the orbits of Ceres and Pallas intersect one another, with a view to the -discovery of other planets, which might be sought for in those parts -with a greater chance of success, than in a wider zone, embracing the -entire limits of these orbits. Accordingly, in 1804, near one of the -nodes of Ceres and Pallas, a third planet was discovered. This was -called _Juno_, and the character ([Planet: Juno]) was adopted for its -symbol, representing the starry sceptre of the Queen of Olympus. -Pursuing the same researches, in 1807 a fourth planet was discovered, to -which was given the name of _Vesta_, and for its symbol the character -([Planet: Vesta]) was chosen,--an altar surmounted with a censer holding -the sacred fire. - -The _average distance_ of these bodies from the sun is two hundred and -sixty-one millions of miles; and it is remarkable that their orbits are -very near together. Taking the distance of the earth from the sun for -unity, their respective distances are 2.77, 2.77, 2.67, 2.37. Their -_times_ of revolution around the sun are nearly equal, averaging about -four and a half years. - -In respect to the _inclination of their orbits_ to the ecliptic, there -is also considerable diversity. The orbit of Vesta is inclined only -about seven degrees, while that of Pallas is more than thirty-four -degrees. They all, therefore, have a higher inclination than the orbits -of the old planets, and of course make excursions from the ecliptic -beyond the limits of the zodiac. Hence they have been called the -_ultra-zodiacal planets_. When first discovered, before their place in -the system was fully ascertained it was also proposed to call them -_asteroids_, a name implying that they were planets under the form of -stars. Their title, however, to take their rank among the primary -planets, is now generally conceded. - -The _eccentricity of their orbits_ is also, in general, greater than -that of the old planets. You will recollect that this language denotes -that their orbits are more elliptical, or depart further from the -circular form. The eccentricities of the orbits of Pallas and Juno -exceed that of the orbit of Mercury. The asteroids differ so much, -however, in eccentricity, that their orbits may cross each other. The -orbits of the old planets are so nearly circular, and at such a great -distance apart, that there is no danger of their interfering with each -other. The earth, for example, when at its nearest distance from the -sun, will never come so near it as Venus is when at its greatest -distance, and therefore can never cross the orbit of Venus. But since -the average distance of Ceres and Pallas from the sun is about the same, -while the eccentricity of the orbit of Pallas is much greater than that -of Ceres, consequently, Pallas may come so near to the sun at its -perihelion, as to cross the orbit of Ceres. - -The _small size_ of the asteroids constitutes one of their most -remarkable peculiarities. The difficulty of estimating the apparent -diameter of bodies at once so very small and so far off, would lead us -to expect different results in the actual estimates. Accordingly, while -Dr. Herschel estimates the diameter of Pallas at only eighty miles, -Schroeter places it as high as two thousand miles, or about the diameter -of the moon. The volume of Vesta is estimated at only one fifteen -thousandth part of the earth's, and her surface is only about equal to -that of the kingdom of Spain. - -These little bodies are surrounded by _atmospheres_ of great extent, -some of which are uncommonly luminous, and others appear to consist of -nebulous matter, like that of comets. These planets shine with a more -vivid light than might be expected, from their great distance and -diminutive size; but a good telescope is essential for obtaining a -distinct view of their phenomena. - -Although the great chasm which occurs between Mars and Jupiter,--a chasm -of more than three hundred millions of miles,--suggested long ago the -idea of other planetary bodies occupying that part of the solar system, -yet the discovery of the asteroids does not entirely satisfy expectation -since they are bodies so dissimilar to the other members of the series -in size, in appearance, and in the form and inclinations of their -orbits. Hence, Dr. Olbers, the discoverer of three of these bodies, held -that they were fragments of a single large planet, which once occupied -that place in the system, and which exploded in different directions by -some internal violence. Of the fragments thus projected into space, some -would be propelled in such directions and with such velocities, as, -under the force of projection and that of the solar attraction would -make them revolve in regular orbits around the sun. Others would be so -projected among the other bodies in the system, as to be thrown in very -irregular orbits, apparently wandering lawless through the skies. The -larger fragments would receive the least impetus from the explosive -force, and would therefore circulate in an orbit deviating less than any -other of the fragments from the original path of the large planet; while -the lesser fragments, being thrown off with greater velocity, would -revolve in orbits more eccentric, and more inclined to the ecliptic. - -Dr. Brewster, editor of the 'Edinburgh Encyclopedia,' and the well-known -author of various philosophical works, espoused this hypothesis with -much zeal; and, after summing up the evidence in favor of it, he remarks -as follows: "These singular resemblances in the motions of the greater -fragments, and in those of the lesser fragments, and the striking -coincidences between theory and observation in the eccentricity of their -orbits, in their inclination to the ecliptic, in the position of their -nodes, and in the places of their perihelia, are phenomena which could -not possibly result from chance, and which concur to prove, with an -evidence amounting almost to demonstration, that the four new planets -have diverged from one common node, and have therefore composed a single -planet." - -The same distinguished writer supposes that some of the smallest -fragments might even have come within reach of the earth's attraction, -and by the combined effects of their projectile forces and the -attraction of the earth, be made to revolve around this body as the -larger fragments are carried around the sun; and that these are in fact -the bodies which afford those _meteoric stones_ which are -occasionally precipitated to the earth. It is now a well-ascertained -fact, a fact which has been many times verified in our own country, that -large meteors, in the shape of fire-balls, traversing the atmosphere, -sometimes project to the earth masses of stony or ferruginous matter. -Such were the meteoric stones which fell at Weston, in Connecticut, in -1807, of which a full and interesting account was published, after a -minute examination of the facts, by Professors Silliman and Kingsley, of -Yale College. Various accounts of similar occurrences may be found in -different volumes of the American Journal of Science. It is for the -production of these wonderful phenomena that Dr. Brewster supposes the -explosion of the planet, which, according to Dr. Olbers, produced the -asteroids, accounts. Others, however, as Sir John Herschel, have been -disposed to ascribe very little weight to the doctrine of Olbers. - -FOOTNOTES: - -[13] Altissimum planetam tergeminum observavi. Or, as transposed, -Smaismrmilme poeta leumi bvne nugttaviras. - -[14] In imitation of Galileo, Huyghens announced his discovery in this -form: a a a a a a a c c c c c d e e e e e g h i i i i i i i l l l l m m -n n n n n n n n n o o o o p p q r r s t t t t t u u u u u; which he -afterwards recomposed into this sentence: _Annulo cingitur, tenui, -plano, nusquam cohęrente, ad eclipticam inclinato._ - -[15] Dick's 'Celestial Scenery.' - -[16] Dick's 'Celestial Scenery.' - - - - -LETTER XXIV. - -THE PLANETARY MOTIONS.----KEPLER'S LAWS.----KEPLER. - - "God of the rolling orbs above! - Thy name is written clearly bright - In the warm day's unvarying blaze, - Or evening's golden shower of light; - For every fire that fronts the sun, - And every spark that walks alone - Around the utmost verge of heaven, - Was kindled at thy burning throne."--_Peabody._ - - -IF we could stand upon the sun and view the planetary motions, they -would appear to us as simple as the motions of equestrians riding with -different degrees of speed around a large ring, of which we occupied the -centre. We should see all the planets coursing each other from west to -east, through the same great highway, (the Zodiac,) no one of them, with -the exception of the asteroids, deviating more than seven degrees from -the path pursued by the earth. Most of them, indeed, would always be -seen moving much nearer than that to the ecliptic. We should see the -planets moving on their way with various degrees of speed. Mercury would -make the entire circuit in about three months, hurrying on his course -with a speed about one third as great as that by which the moon revolves -around the earth. The most distant planets, on the other hand, move at -so slow a pace, that we should see Mercury, Venus, the Earth, and Mars, -severally overtaking them a great many times, before they had completed -their revolutions. But though the movements of some were comparatively -rapid, and of others extremely slow, yet they would not seem to differ -materially, in other respects: each would be making a steady and nearly -uniform march along the celestial vault. - -Such would be the simple and harmonious motions of the planets, as they -would be seen from the sun, the centre of their motions; and such they -are, in fact. But two circumstances conspire to make them appear -exceedingly different from these, and vastly more complicated; one is, -that we view them out of the centre of their motions; the other, that we -are ourselves in motion. I have already explained to you the effect -which these two causes produce on the apparent motions of the inferior -planets, Mercury and Venus. Let us now see how they effect those of the -superior planets, Mars, Jupiter, Saturn, and Uranus. - -Orreries, or machines intended to exhibit a model of the solar system, -are sometimes employed to give a popular view of the planetary motions; -but they oftener mislead than give correct ideas. They may assist -reflection, but they can never supply its place. The impossibility of -representing things in their just proportions will be evident, when we -reflect that, to do this, if in an orrery we make Mercury as large as a -cherry, we should have to represent the sun six feet in diameter. If we -preserve the same proportions, in regard to distance, we must place -Mercury two hundred and fifty feet, and Uranus twelve thousand five -hundred feet, or more than two miles from the sun. The mind of the -student of astronomy must, therefore, raise itself from such imperfect -representations of celestial phenomena, as are afforded by artificial -mechanism, and, transferring his contemplations to the celestial regions -themselves, he must conceive of the sun and planets as bodies that bear -an insignificant ratio to the immense spaces in which they circulate, -resembling more a few little birds flying in the open sky, than they do -the crowded machinery of an orrery. - -The _real_ motions of the planets, indeed, or such as orreries usually -exhibit, are very easily conceived of, as before explained; but the -_apparent_ motions are, for the most part, entirely different from -these. The apparent motions of the inferior planets have been already -explained. You will recollect that Mercury and Venus move backwards and -forwards across the sun, the former never being seen further than -twenty-nine degrees, and the latter never more than about forty-seven -degrees, from that luminary; that, while passing from the greatest -elongation on one side, to the greatest elongation on the other side, -through the superior conjunction, the apparent motions of these planets -are accelerated by the motion of the earth; but that, while moving -through the inferior conjunction, at which time their motions are -retrograde, they are apparently retarded by the earth's motion. Let us -now see what are the apparent motions of the superior planets. - -Let A, B, C, Fig. 62, page 294, represent the earth in different -positions in its orbit, M, a superior planet, as Mars, and N R, an arc -of the concave sphere of the heavens. First, suppose the planet to -remain at rest in M, and let us see what apparent motions it will -receive from the real motions of the earth. When the earth is at B, it -will see the planet in the heavens at N; and as the earth moves -successively through C, D, E, F, the planet will appear to move through -O, P, Q, R. B and F are the two points of greatest elongation of the -earth from the sun, as seen from the planet; hence, between these two -points, while passing through its orbit most remote from the planet, -(when the planet is seen in superior conjunction,) the earth, by its own -motion, gives an apparent motion to the planet in the order of the -signs; that is, the _apparent_ motion given by the _real_ motion of the -earth is _direct_. But in passing from F to B through A, when the planet -is seen in opposition, the apparent motion given to the planet by the -earth's motion is from R to N, and is therefore _retrograde_. As the arc -described by the earth, when the motion is direct, is much greater than -when the motion is retrograde, while the apparent arc of the heavens -described by the planet from N to R, in the one case, and from R to N, -in the other, is the same in both cases, the retrograde motion is much -swifter than the direct, being performed in much less time. - -[Illustration Fig. 62.] - -But the superior planets are not in fact at rest, as we have supposed, -but are all the while moving eastward, though with a slower motion than -the earth. Indeed, with respect to the remotest planets, as Saturn and -Uranus, the forward motion is so exceedingly slow, that the above -representation is nearly true for a single year. Still, the effect of -the real motions of all the superior planets, eastward, is to increase -the direct apparent motion communicated by the earth, and to diminish -the retrograde motion. This will be evident from inspecting the figure; -for if the planet _actually_ moves eastward while it is _apparently_ -carried eastward by the earth's motion, the whole motion eastward will -be equal to the sum of the two; and if, while it is really moving -eastward, it is apparently carried westward still more by the earth's -motion, the retrograde movement will equal the difference of the two. - -If Mars stood still while the earth went round the sun, then a second -opposition, as at A, would occur at the end of one year from the first; -but, while the earth is performing this circuit, Mars is also moving the -same way, more than half as fast; so that, when the earth returns to A, -the planet has already performed more than half the same circuit, and -will have completed its whole revolution before the earth comes up with -it. Indeed Mars, after having been seen once in opposition, does not -come into opposition again until after two years and fifty days. And -since the planet is then comparatively near to us, as at M, while the -earth is at A, and appears very large and bright, rising unexpectedly -about the time the sun sets, he surprises the world as though it were -some new celestial body. But on account of the slow progress of Saturn -and Uranus, we find, after having performed one circuit around the sun, -that they are but little advanced beyond where we left them at the last -opposition. The time between one opposition of Saturn and another is -only a year and thirteen days. - -It appears, therefore, that the superior planets steadily pursue their -course around the sun, but that their apparent retrograde motion, when -in opposition, is occasioned by our passing by them with a swifter -motion, of which we are unconscious, like the apparent backward motion -of a vessel, when we overtake it and pass by it rapidly in a steam-boat. - -Such are the real and the apparent motions of the planets. Let us now -turn our attention to the _laws of the planetary orbits_. - -There are three great principles, according to which the motions of the -earth and all the planets around the sun are regulated, called KEPLER'S -LAWS, having been first discovered by the astronomer whose name they -bear. They may appear to you, at first, dry and obscure; yet they will -be easily understood from the explanations which follow; and so -important have they proved in astronomical inquiries, that they have -acquired for their renowned discoverer the appellation of the -'_Legislator of the Skies_.' We will consider each of these laws -separately; and, for the sake of rendering the explanation clear and -intelligible, I shall perhaps repeat some things that have been briefly -mentioned before. - -[Illustration Fig. 63.] - -FIRST LAW.--_The orbits of the earth and all the planets are ellipses, -having the sun in the common focus._ In a circle, all the diameters are -equal to one another; but if we take a metallic wire or hoop, and draw -it out on opposite sides, we elongate it into an ellipse, of which the -different diameters are very unequal. That which connects the points -most distant from each other is called the _transverse_, and that which -is at right angles to this is called the _conjugate_, axis. Thus, A B, -Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A -B C. By such a process of elongating the circle into an ellipse, the -centre of the circle may be conceived of as drawn opposite ways to E and -F, each of which becomes a _focus_, and both together are called the -_foci_ of the ellipse. The distance G E, or G F, of the focus from the -centre is called the _eccentricity_ of the ellipse; and the ellipse is -said to be more or less eccentric, as the distance of the focus from the -centre is greater or less. Figure 64 represents such a collection of -ellipses around the common focus F, the innermost, A G D, having a small -eccentricity, or varying little from a circle, while the outermost, A C -B, is an eccentric ellipse. The orbits of all the bodies that revolve -about the sun, both planets and comets, have, in like manner, a common -focus, in which the sun is situated, but they differ in eccentricity. -Most of the planets have orbits of very little eccentricity, differing -little from circles, but comets move in very eccentric ellipses. The -earth's path around the sun varies so little from a circle, that a -diagram representing it truly would scarcely be distinguished from a -perfect circle; yet, when the comparative distances of the sun from the -earth are taken at different seasons of the year, we find that the -difference between their greatest and least distances is no less than -three millions of miles. - -[Illustration Fig. 64.] - -SECOND LAW.--_The radius vector of the earth, or of any planet, -describes equal areas in equal times._ You will recollect that the -radius vector is a line drawn from the centre of the sun to a planet -revolving about the sun. This definition I have somewhere given you -before, and perhaps it may appear to you like needless repetition to -state it again. In a book designed for systematic instruction, where all -the articles are distinctly numbered, it is commonly sufficient to make -a reference back to the article where the point in question is -explained; but I think, in Letters like these, you will bear with a -little repetition, rather than be at the trouble of turning to the Index -and hunting up a definition long since given. - -[Illustration Fig. 65. ] - -In Figure 65, _E a_, _E b_, _E c_, &c., are successive representations -of the radius vector. Now, if a planet sets out from _a_, and travels -round the sun in the direction of _a b c_, it will move faster when -nearer the sun, as at _a_, than when more remote from it, as at _m_; -yet, if _a b_ and _m n_ be arcs described in equal times, then, -according to the foregoing law, the space _E a b_ will be equal to the -space _E m n_; and the same is true of all the other spaces described in -equal times. Although the figure _E a b_ is much shorter than _E m n_, -yet its greater breadth exactly counterbalances the greater length of -those figures which are described by the radius vector where it is -longer. - -THIRD LAW.--_The squares of the periodical times are as the cubes of the -mean distances from the sun._ The periodical time of a body is the time -it takes to complete its orbit, in its revolution about the sun. Thus -the earth's periodic time is one year, and that of the planet Jupiter -about twelve years. As Jupiter takes so much longer time to travel round -the sun than the earth does, we might suspect that his orbit is larger -than that of the earth, and of course, that he is at a greater distance -from the sun; and our first thought might be, that he is probably twelve -times as far off; but Kepler discovered that the distance does not -increase as fast as the times increase, but that the planets which are -more distant from the sun actually move slower than those which are -nearer. After trying a great many proportions, he at length found that, -if we take the squares of the periodic times of two planets, the greater -square contains the less, just as often as the cube of the distance of -the greater contains that of the less. This fact is expressed by saying, -that the squares of the periodic times are to one another as the cubes -of the distances. - -This law is of great use in determining the distance of the planets from -the sun. Suppose, for example, that we wish to find the distance of -Jupiter. We can easily determine, from observation, what is Jupiter's -periodical time, for we can actually see how long it takes for Jupiter, -after leaving a certain part of the heavens to come round to the same -part again. Let this period be twelve years. The earth's period is of -course one year; and the distance of the earth, as determined from the -sun's horizontal parallax, as already explained, is about ninety-five -millions of miles. Now, we have here three terms of a proportion to find -the fourth, and therefore the solution is merely a simple case of the -rule of three. Thus:--the square of 1 year : square of 12 years :: cube -of 95,000,000 : cube of Jupiter's distance. The three first terms being -known, we have only to multiply together the second and third and divide -by the first, to obtain the fourth term, which will give us the cube of -Jupiter's distance from the sun; and by extracting the cube root of this -sum, we obtain the distance itself. In the same manner we may obtain the -respective distances of all the other planets. - -So truly is this a law of the solar system, that it holds good in -respect to the new planets, which have been discovered since Kepler's -time, as well as in the case of the old planets. It also holds good in -respect to comets, and to all bodies belonging to the solar system, -which revolve around the sun as their centre of motion. Hence, it is -justly regarded as one of the most interesting and important principles -yet developed in astronomy. - -But who was this Kepler, that gained such an extraordinary insight into -the laws of the planetary system, as to be called the 'Legislator of the -Skies?' John Kepler was one of the most remarkable of the human race, -and I think I cannot gratify or instruct you more, than by occupying the -remainder of this Letter with some particulars of his history. - -Kepler was a native of Germany. He was born in the Duchy of Wurtemberg, -in 1571. As Copernicus, Tycho Brahe, Galileo, Kepler, and Newton, are -names that are much associated in the history of astronomy, let us see -how they stood related to each other in point of time. Copernicus was -born in 1473; Tycho, in 1546; Galileo, in 1564; Kepler, in 1571; and -Newton, in 1642. Hence, Copernicus was seventy-three years before -Tycho, and Tycho ninety-six years before Newton. They all lived to an -advanced age, so that Tycho, Galileo, and Kepler, were contemporary for -many years; and Newton, as I mentioned in the sketch I gave you of his -life, was born the year that Galileo died. - -Kepler was born of parents who were then in humble circumstances, -although of noble descent. Their misfortunes, which had reduced them to -poverty, seem to have been aggravated by their own unhappy dispositions; -for his biographer informs us, that "his mother was treated with a -degree of barbarity by her husband and brother-in-law, that was hardly -exceeded by her own perverseness." It is fortunate, therefore, that -Kepler, in his childhood, was removed from the immediate society and -example of his parents, and educated at a public school at the expense -of the Duke of Wurtemberg. He early imbibed a taste for natural -philosophy, but had conceived a strong prejudice against astronomy, and -even a contempt for it, inspired, probably, by the arrogant and -ridiculous pretensions of the astrologers, who constituted the principal -astronomers of his country. A vacant post, however, of teacher of -astronomy, occurred when he was of a suitable age to fill it, and he was -compelled to take it by the authority of his tutors, though with many -protestations, on his part, wishing to be provided for in some other -more brilliant profession. - -Happy is genius, when it lights on a profession entirely consonant to -its powers, where the objects successively presented to it are so -exactly suited to its nature, that it clings to them as the loadstone to -its kindred metal among piles of foreign ores. Nothing could have been -more congenial to the very mental constitution of Kepler, than the study -of astronomy,--a science where the most capacious understanding may find -scope in unison with the most fervid imagination. - -Much as has been said against hypotheses in philosophy, it is -nevertheless a fact, that some of the greatest truths have been -discovered in the pursuit of hypotheses, in themselves entirely false; -truths, moreover, far more important than those assumed by the -hypotheses; as Columbus, in searching for a northwest passage to India, -discovered a new world. Thus Kepler groped his way through many false -and absurd suppositions, to some of the most sublime discoveries ever -made by man. The fundamental principle which guided him was not, -however, either false or absurd. It was, that God, who made the world, -had established, throughout all his works, fixed laws,--laws that are -often so definite as to be capable of expression in exact numerical -terms. In accordance with these views, he sought for numerical relations -in the disposition and arrangement of the planets, in respect to their -number, the times of their revolution, and their distances from one -another. Many, indeed, of the subordinate suppositions which he made, -were extremely fanciful; but he tried his own hypotheses by a rigorous -mathematical test, wherever he could apply it; and as soon as he -discovered that a supposition would not abide this test, he abandoned it -without the least hesitation, and adopted others, which he submitted to -the same severe trial, to share, perhaps, the same fate. "After many -failures," he says, "I was comforted by observing that the motions, in -every case, seemed to be connected with the distances; and that, when -there was a great gap between the orbits, there was the same between the -motions. And I reasoned that, if God had adapted motions to the orbits -in some relation to the distances, he had also arranged the distances -themselves in relation to something else." - -In two years after he commenced the study of astronomy, he published a -book, called the '_Mysterium Cosmographicum_,' a name which implies an -explanation of the mysteries involved in the construction of the -universe. This work was full of the wildest speculations and most -extravagant hypotheses, the most remarkable of which was, that the -distances of the planets from the sun are regulated by the relations -which subsist between the five regular solids. It is well known to -geometers, that there are and can be only five _regular solids_. These -are, first, the _tetraedron_, a four-sided figure, all whose sides are -equal and similar triangles; secondly, the _cube_, contained by six -equal squares; thirdly, an _octaedron_, an eight-sided figure, -consisting of two four-sided pyramids joined at their bases; fourthly, a -_dodecaedron_, having twelve five-sided or pentagonal faces; and, -fifthly, an _icosaedron_, contained by twenty equal and similar -triangles. You will be much at a loss, I think, to imagine what relation -Kepler could trace between these strange figures and the distances of -the several planets from the sun. He thought he discovered a connexion -between those distances and the spaces which figures of this kind would -occupy, if interposed in certain ways between them. Thus, he says the -Earth is a circle, the measure of all; round it describe a dodecaedron, -and the circle including this will be the orbit of Mars. Round this -circle describe a tetraedron, and the circle including this will be the -orbit of Jupiter. Describe a cube round this, and the circle including -it will be the orbit of Saturn. Now, inscribe in the earth an -icosaedron, and the circle included in this will give the orbit of -Venus. In this inscribe an octaedron, and the circle included in this -will be the orbit of Mercury. On this supposed discovery Kepler exults -in the most enthusiastic expressions. "The intense pleasure I have -received from this discovery never can be told in words. I regretted no -more time wasted; I tired of no labor; I shunned no toil of reckoning; -days and nights I spent in calculations, until I could see whether this -opinion would agree with the orbits of Copernicus, or whether my joy was -to vanish into air. I willingly subjoin that sentiment of Archytas, as -given by Cicero; 'If I could mount up into heaven, and thoroughly -perceive the nature of the world and the beauty of the stars, that -admiration would be without a charm for me, unless I had some one like -you, reader, candid, attentive, and eager for knowledge, to whom to -describe it.' If you acknowledge this feeling, and are candid, you will -refrain from blame, such as, not without cause, I anticipate; but if, -leaving that to itself, you fear, lest these things be not ascertained, -and that I have shouted triumph before victory, at least approach these -pages, and learn the matter in consideration: you will not find, as just -now, new and unknown planets interposed; that boldness of mine is not -approved; but those old ones very little loosened, and so furnished by -the interposition (however absurd you may think it) of rectilinear -figures, that in future you may give a reason to the rustics, when they -ask for the hooks which keep the skies from falling." - -When Tycho Brahe, who had then retired from his famous Uraniburg, and -was settled in Prague, met with this work of Kepler's, he immediately -recognised under this fantastic garb the lineaments of a great -astronomer. He needed such an unwearied and patient calculator as he -perceived Kepler to be, to aid him in his labors, in order that he might -devote himself more unreservedly to the taking of observations,--an -employment in which he delighted, and in which, as I mentioned, in -giving you a sketch of his history, he excelled all men of that and -preceding ages. Kepler, therefore, at the express invitation of Tycho, -went to Prague, and joined him in the capacity of assistant. Had Tycho -been of a nature less truly noble, he might have looked with contempt on -one who had made so few observations, and indulged so much in wild -speculation; or he might have been jealous of a rising genius, in which -he descried so many signs of future eminence as an astronomer; but, -superior to all the baser motives, he extends to the young aspirant the -hand of encouragement, in the following kind invitation: "Come not as a -stranger, but as a very welcome friend; come, and share in my -observations, with such instruments as I have with me." - -Several years previous to this, Kepler, after one or two unsuccessful -trials, had found him a wife, from whom he expected a considerable -fortune; but in this he was disappointed; and so poor was he, that, when -on his journey to Prague, in company with his wife, being taken sick, he -was unable to defray the expenses of the journey, and was forced to cast -himself on the bounty of Tycho. - -In the course of the following year, while absent from Prague, he -fancied that Tycho had injured him, and accordingly addressed to the -noble Dane a letter full of insults and reproaches. A mild reply from -Tycho opened the eyes of Kepler to his own ingratitude. His better -feelings soon returned, and he sent to his great patron this humble -apology: "Most noble Tycho! How shall I enumerate, or rightly estimate, -your benefits conferred on me! For two months you have liberally and -gratuitously maintained me, and my whole family; you have provided for -all my wishes; you have done me every possible kindness; you have -communicated to me every thing you hold most dear; no one, by word or -deed, has intentionally injured me in any thing; in short, not to your -own children, your wife, or yourself, have you shown more indulgence -than to me. This being so, as I am anxious to put upon record, I cannot -reflect, without consternation, that I should have been so given up by -God to my own intemperance, as to shut my eyes on all these benefits; -that, instead of modest and respectful gratitude, I should indulge for -three weeks in continual moroseness towards all your family, and in -headlong passion and the utmost insolence towards yourself, who possess -so many claims on my veneration, from your noble family, your -extraordinary learning, and distinguished reputation. Whatever I have -said or written against the person, the fame, the honor, and the -learning, of your Excellency; or whatever, in any other way, I have -injuriously spoken or written, (if they admit no other more favorable -interpretation,) as to my grief I have spoken and written many things, -and more than I can remember; all and every thing I recant, and freely -and honestly declare and profess to be groundless, false, and incapable -of proof." This was ample satisfaction to the generous Tycho. - - "To err is human: to forgive, divine." - -On Kepler's return to Prague, he was presented to the Emperor by Tycho, -and honored with the title of Imperial Mathematician. This was in 1601, -when he was thirty years of age. Tycho died shortly after, and Kepler -succeeded him as principal mathematician to the Emperor; but his salary -was badly paid, and he suffered much from pecuniary embarrassments. -Although he held the astrologers, or those who told fortunes by the -stars, in great contempt, yet he entertained notions of his own, on the -same subject, quite as extravagant, and practised the art of casting -nativities, to eke out a support for his family. - -When Galileo began to observe with his telescope, and announced, in -rapid succession, his wonderful discoveries, Kepler entered into them -with his characteristic enthusiasm, although they subverted many of his -favorite hypotheses. But such was his love of truth, that he was among -the first to congratulate Galileo, and a most engaging correspondence -was carried on between these master-spirits. - -The first planet, which occupied the particular attention of Kepler, was -Mars, the long and assiduous study of whose motions conducted him at -length to the discovery of those great principles called 'Kepler's -Laws.' Rarely do we meet with so remarkable a union of a vivid fancy -with a profound intellect. The hasty and extravagant suggestions of the -former were submitted to the most laborious calculations, some of which, -that were of great length, he repeated seventy times. This exuberance of -fancy frequently appears in his style of writing, which occasionally -assumes a tone ludicrously figurative. He seems constantly to -contemplate Mars as a valiant hero, who had hitherto proved invincible, -and who would often elude his own efforts to conquer him, "While thus -triumphing over Mars, and preparing for him, as for one altogether -vanquished, tabular prisons, and equated, eccentric fetters, it is -buzzed here and there, that the victory is vain, and that the war is -raging anew as violently as before. For the enemy, left at home a -despised captive, has burst all the chains of the equation, and broken -forth of the prisons of the tables. Skirmishes routed my forces of -physical causes, and, shaking off the yoke, regained their liberty. And -now, there was little to prevent the fugitive enemy from effecting a -junction with his own rebellious supporters, and reducing me to despair, -had I not suddenly sent into the field a reserve of new physical -reasonings, on the rout and dispersion of the veterans, and diligently -followed, without allowing the slightest respite, in the direction in -which he had broken out." - -But he pursued this warfare with the planet until he gained a full -conquest, by the discovery of the first two of his laws, namely, that -_he revolves in an elliptical orbit_, and that _his radius vector passes -over equal spaces in equal times_. - -Domestic troubles, however, involved him in the deepest affliction. -Poverty, the loss of a promising and favorite son, the death of his -wife, after a long illness;--these were some of the misfortunes that -clustered around him. Although his first marriage had been an unhappy -one, it was not consonant to his genius to surrender any thing with only -a single trial. Accordingly, it was not long before he endeavored to -repair his loss by a second alliance. He commissioned a number of his -friends to look out for him, and he soon obtained a tabular list of -eleven ladies, among whom his affections wavered. The progress of his -courtship is thus narrated in the interesting 'Life' contained in the -'Library of Useful Knowledge.' It furnishes so fine a specimen of his -eccentricities, that I cannot deny myself the pleasure of transcribing -the passage for your perusal. It is taken from an account which Kepler -himself gave in a letter to a friend. - -"The first on the list was a widow, an intimate friend of his first wife -and who, on many accounts, appeared a most eligible match. At first, she -seemed favorably inclined to the proposal: it is certain that she took -time to consider it, but at last she very quietly excused herself. -Finding her afterwards less agreeable in person than he had anticipated, -he considered it a fortunate escape, mentioning, among other objections, -that she had two marriageable daughters, whom, by the way, he had got on -his list for examination. He was much troubled to reconcile his -astrology with the fact of his having taken so much pains about a -negotiation not destined to succeed. He examined the case -professionally. 'Have the stars,' says he, 'exercised any influence -here? For, just about this time, the direction of the mid-heaven is in -hot opposition to Mars, and the passage of Saturn through the ascending -point of the zodiac, in the scheme of my nativity, will happen again -next November and December. But, if these are the causes, how do they -act? Is that explanation the true one, which I have elsewhere given? For -I can never think of handing over to the stars the office of deities, to -produce effects. Let us, therefore, suppose it accounted for by the -stars, that at this season I am violent in my temper and affections, in -rashness of belief, in a show of pitiful tender-heartedness, in catching -at reputation by new and paradoxical notions, and the singularity of my -actions; in busily inquiring into, and weighing, and discussing, various -reasons; in the uneasiness of my mind, with respect to my choice. I -thank God, that that did not happen which might have happened; that this -marriage did not take place. Now for the others.' Of these, one was too -old; another, in bad health; another, too proud of her birth and -quarterings; a fourth had learned nothing but showy accomplishments, not -at all suitable to the kind of life she would have to lead with him. -Another grew impatient, and married a more decided admirer while he was -hesitating. 'The mischief,' says he, 'in all these attachments was, -that, whilst I was delaying, comparing, and balancing, conflicting -reasons, every day saw me inflamed with a new passion.' By the time he -reached No. 8, of his list, he found his match in this respect. 'Fortune -has avenged herself at length on my doubtful inclinations. At first, she -was quite complying, and her friends also. Presently, whether she did or -did not consent, not only I, but she herself, did not know. After the -lapse of a few days, came a renewed promise, which, however, had to be -confirmed a third time: and, four days after that, she again repented -her conformation, and begged to be excused from it. Upon this, I gave -her up, and this time all my counsellors were of one opinion.' This was -the longest courtship in the list, having lasted three whole months; -and, quite disheartened by its bad success, Kepler's next attempt was of -a more timid complexion. His advances to No. 9 were made by confiding to -her the whole story of his recent disappointment, prudently determining -to be guided in his behavior, by observing whether the treatment he -experienced met with a proper degree of sympathy. Apparently, the -experiment did not succeed; and, when almost reduced to despair, Kepler -betook himself to the advice of a friend, who had for some time past -complained that she was not consulted in this difficult negotiation. -When she produced No. 10, and the first visit was paid, the report upon -her was as follows: 'She has, undoubtedly, a good fortune, is of good -family, and of economical habits: but her physiognomy is most horribly -ugly; she would be stared at in the streets, not to mention the striking -disproportion in our figures. I am lank, lean, and spare; she is short -and thick. In a family notorious for fatness, she is considered -superfluously fat.' The only objection to No. 11 seems to have been, her -excessive youth; and when this treaty was broken off, on that account, -Kepler turned his back upon all his advisers, and chose for himself one -who had figured as No. 5, in his list, to whom he professes to have felt -attached throughout, but from whom the representations of his friends -had hitherto detained him, probably on account of her humble station." - -Having thus settled his domestic affairs, Kepler now betook himself, -with his usual industry, to his astronomical studies, and brought before -the world the most celebrated of his publications, entitled 'Harmonics.' -In the fifth book of this work he announced his _Third Law_,--that the -squares of the periodical times of the planets are as the cubes of the -distances. Kepler's rapture on detecting it was unbounded. "What," says -he, "I prophesied two-and-twenty years ago, as soon as I discovered the -five solids among the heavenly orbits; what I firmly believed long -before I had seen Ptolemy's Harmonics; what I had promised my friends in -the title of this book, which I named before I was sure of my discovery; -what, sixteen years ago, I urged as a thing to be sought; that for which -I joined Tycho Brahe, for which I settled in Prague, for which I have -devoted the best part of my life to astronomical contemplations;--at -length I have brought to light, and have recognised its truth beyond my -most sanguine expectations. It is now eighteen months since I got the -first glimpse of light, three months since the dawn, very few days since -the unveiled sun, most admirable to gaze on, burst out upon me. Nothing -holds me: I will indulge in my sacred fury; I will triumph over mankind -by the honest confession, that I have stolen the golden vases of the -Egyptians to build up a tabernacle for my God, far from the confines of -Egypt. If you forgive me, I rejoice: if you are angry, I can bear it; -the die is cast, the book is written, to be read either now or by -posterity,--I care not which. I may well wait a century for a reader, as -God has waited six thousand years for an observer." In accordance with -the notion he entertained respecting the "music of the spheres," he made -Saturn and Jupiter take the bass, Mars the tenor, the Earth and Venus -the counter, and Mercury the treble. - -"The misery in which Kepler lived," says Sir David Brewster, in his -'Life of Newton,' "forms a painful contrast with the services which he -performed for science. The pension on which he subsisted was always in -arrears; and though the three emperors, whose reigns he adorned, -directed their ministers to be more punctual in its payment, the -disobedience of their commands was a source of continual vexation to -Kepler. When he retired to Silesia, to spend the remainder of his days, -his pecuniary difficulties became still more harassing. Necessity at -length compelled him to apply personally for the arrears which were due; -and he accordingly set out, in 1630, when nearly sixty years of age, for -Ratisbon; but, in consequence of the great fatigue which so long a -journey on horseback produced, he was seized with a fever, which put an -end to his life." - -Professor Whewell (in his interesting work on Astronomy and General -Physics considered with reference to Natural Theology) expresses the -opinion that Kepler, notwithstanding his constitutional oddities, was a -man of strong and lively piety. His 'Commentaries on the Motions of -Mars' he opens with the following passage: "I beseech my reader, that, -not unmindful of the Divine goodness bestowed on man, he do with me -praise and celebrate the wisdom and greatness of the Creator, which I -open to him from a more inward explication of the form of the world, -from a searching of causes, from a detection of the errors of vision; -and that thus, not only in the firmness and stability of the earth, he -perceive with gratitude the preservation of all living things in Nature -as the gift of God, but also that in its motion, so recondite, so -admirable, he acknowledge the wisdom of the Creator. But him who is too -dull to receive this science, or too weak to believe the Copernican -system without harm to his piety,--him, I say, I advise that, leaving -the school of astronomy, and condemning, if he please, any doctrines of -the philosophers, he follow his own path, and desist from this wandering -through the universe; and, lifting up his natural eyes, with which he -alone can see, pour himself out in his own heart, in praise of God the -Creator; being certain that he gives no less worship to God than the -astronomer, to whom God has given to see more clearly with his inward -eye, and who, for what he has himself discovered, both can and will -glorify God." - -In a Life of Kepler, very recently published in his native country, -founded on manuscripts of his which have lately been brought to light, -there are given numerous other examples of a similar devotional spirit. -Kepler thus concludes his Harmonics: "I give Thee thanks, Lord and -Creator, that Thou has given me joy through Thy creation; for I have -been ravished with the work of Thy hands. I have revealed unto mankind -the glory of Thy works, as far as my limited spirit could conceive their -infinitude. Should I have brought forward any thing that is unworthy of -Thee, or should I have sought my own fame, be graciously pleased to -forgive me." - -As Galileo experienced the most bitter persecutions from the Church of -Rome, so Kepler met with much violent opposition and calumny from the -Protestant clergy of his own country, particularly for adopting, in an -almanac which, as astronomer royal, he annually published, the reformed -calendar, as given by the Pope of Rome. His opinions respecting -religious liberty, also, appear to have been greatly in advance of the -times in which he lived. In answer to certain calumnies with which he -was assailed, for his boldness in reasoning from the light of Nature, he -uttered these memorable words: "The day will soon break, when pious -simplicity will be ashamed of its blind superstition; when men will -recognise truth in the book of Nature as well as in the Holy Scriptures, -and rejoice in the two revelations." - - - - -LETTER XXV. - -COMETS. - - ----"Fancy now no more - Wantons on fickle pinions through the skies, - But, fixed in aim, and conscious of her power, - Sublime from cause to cause exults to rise, - Creation's blended stores arranging as she flies."--_Beattie._ - -NOTHING in astronomy is more truly admirable, than the knowledge which -astronomers have acquired of the motions of comets, and the power they -have gained of predicting their return. Indeed, every thing appertaining -to this class of bodies is so wonderful, as to seem rather a tale of -romance than a simple recital of facts. Comets are truly the -knights-errant of astronomy. Appearing suddenly in the nocturnal sky, -and often dragging after them a train of terrific aspect, they were, in -the earlier ages of the world, and indeed until a recent period, -considered as peculiarly ominous of the wrath of Heaven, and as -harbingers of wars and famines, of the dethronement of monarchs, and the -dissolution of empires. - -Science has, it is true, disarmed them of their terrors, and -demonstrated that they are under the guidance of the same Hand, that -directs in their courses the other members of the solar system; but she -has, at the same time, arrayed them in a garb of majesty peculiarly her -own. - -Although the ancients paid little attention to the ordinary phenomena of -Nature, hardly deeming them worthy of a reason, yet, when a comet blazed -forth, fear and astonishment conspired to make it an object of the most -attentive observation. Hence the aspects of remarkable comets, that have -appeared at various times, have been handed down to us, often with -circumstantial minuteness, by the historians of different ages. The -comet which appeared in the year 130, before the Christian era, at the -birth of Mithridates, is said to have had a disk equal in magnitude to -that of the sun. Ten years before this, one was seen, which, according -to Justin, occupied a fourth part of the sky, that is, extended over -forty-five degrees, and surpassed the sun in splendor. In the year 400, -one was seen which resembled a sword in shape, and extended from the -zenith to the horizon. - -Such are some of the accounts of comets of past ages; but it is probable -we must allow much for the exaggerations naturally accompanying the -descriptions of objects in themselves so truly wonderful. - -A comet, when perfectly formed, consists of three parts, the nucleus, -the envelope, and the tail. The nucleus, or body of the comet, is -generally distinguished by its forming a bright point in the centre of -the head, conveying the idea of a solid, or at least of a very dense, -portion of matter. Though it is usually exceedingly small, when compared -with the other parts of the comet, and is sometimes wanting altogether, -yet it occasionally subtends an angle capable of being measured by the -telescope. The envelope (sometimes called the _coma_, from a Latin word -signifying hair, in allusion to its hairy appearance) is a dense -nebulous covering, which frequently renders the edge of the nucleus so -indistinct, that it is extremely difficult to ascertain its diameter -with any degree of precision. Many comets have no nucleus, but present -only a nebulous mass, exceedingly attenuated on the confines, but -gradually increasing in density towards the centre. Indeed, there is a -regular gradation of comets, from such as are composed merely of a -gaseous or vapory medium, to those which have a well-defined nucleus. In -some instances on record, astronomers have detected with their -telescopes small stars through the densest part of a comet. The tail is -regarded as an expansion or prolongation of the coma; and presenting, as -it sometimes does, a train of appalling magnitude, and of a pale, -portentous light, it confers on this class of bodies their peculiar -celebrity. These several parts are exhibited in Fig. 67, which -[Illustration Figures 67, 68. COMETS OF 1680 AND 1811.] represents the -appearance of the comet of 1680. Fig. 68 also exhibits that of the comet -of 1811. - -The _number_ of comets belonging to the solar system, is probably very -great. Many no doubt escape observation, by being above the horizon in -the day-time. Seneca mentions, that during a total eclipse of the sun, -which happened sixty years before the Christian era, a large and -splendid comet suddenly made its appearance, being very near the sun. -The leading particulars of at least one hundred and thirty have been -computed, and arranged in a table, for future comparison. Of these, -_six_ are particularly remarkable; namely, the comets of 1680, 1770, and -1811; and those which bear the names of Halley, Biela, and Encke. The -comet of 1680 was remarkable, not only for its astonishing size and -splendor, and its near approach to the sun, but is celebrated for having -submitted itself to the observations of Sir Isaac Newton, and for having -enjoyed the signal honor of being the first comet whose elements were -determined on the sure basis of mathematics. The comet of 1770 is -memorable for the changes its orbit has undergone by the action of -Jupiter, as I shall explain to you more particularly hereafter. The -comet of 1811 was the most remarkable in its appearance of all that have -been seen in the present century. It had scarcely any perceptible -nucleus, but its train was very long and broad, as is represented in -Fig. 68. Halley's comet (the same which reappeared in 1835) is -distinguished as that whose return was first successfully predicted, and -whose orbit is best determined; and Biela's and Encke's comets are well -known for their short periods of revolution, which subject them -frequently to the view of astronomers. - -In _magnitude and brightness_, comets exhibit great diversity. History -informs us of comets so bright, as to be distinctly visible in the -day-time, even at noon, and in the brightest sunshine. Such was the -comet seen at Rome a little before the assassination of Julius Cęsar. -The comet of 1680 covered an arc of the heavens of ninety-seven -degrees, and its length was estimated at one hundred and twenty-three -millions of miles. That of 1811 had a nucleus of only four hundred and -twenty-eight miles in diameter, but a tail one hundred and thirty-two -millions of miles long. Had it been coiled around the earth like a -serpent, it would have reached round more than five thousand times. -Other comets are exceedingly small, the nucleus being in one case -estimated at only twenty-five miles; and some, which are destitute of -any perceptible nucleus, appear to the largest telescopes, even when -nearest to us, only as a small speck of fog, or as a tuft of down. The -majority of comets can be seen only by the aid of the telescope. Indeed, -the same comet has very different aspects, at its different returns. -Halley's comet, in 1305, was described by the historians of that age as -the comet of terrific magnitude; (_cometa horrendę magnitudinis_;) in -1456 its tail reached from the horizon to the zenith, and inspired such -terror, that, by a decree of the Pope of Rome, public prayers were -offered up at noonday in all the Catholic churches, to deprecate the -wrath of heaven; while in 1682 its tail was only thirty degrees in -length; and in 1759 it was visible only to the telescope until after it -had passed its perihelion. At its recent return, in 1835, the greatest -length of the tail was about twelve degrees. These changes in the -appearance of the same comet are partly owing to the different positions -of the earth with respect to them, being sometimes much nearer to them -when they cross its track than at others; also, one spectator, so -situated as to see the comet at a higher angle of elevation, or in a -purer sky, than another, will see the train longer than it appears to -another less favorably situated; but the extent of the changes are such -as indicate also a real change in magnitude and brightness. - -The _periods_ of comets in their revolutions around the sun are equally -various. Encke's comet, which has the shortest known period, completes -its revolution in three and one third years; or, more accurately, in -twelve hundred and eight days; while that of 1811 is estimated to have -a period of thirty-three hundred and eighty three years. - -The _distances_ to which different comets recede from the sun are -equally various. While Encke's comet performs its entire revolution -within the orbit of Jupiter, Halley's comet recedes from the sun to -twice the distance of Uranus; or nearly thirty-six hundred millions of -miles. Some comets, indeed, are thought to go a much greater distance -from the sun than this, while some are supposed to pass into curves -which do not, like the ellipse, return into themselves; and in this case -they never come back to the sun. (See Fig. 34, page 153.) - -Comets shine _by reflecting the light of the sun_. In one or two -instances, they have been thought to exhibit distinct _phases_, like the -moon, although the nebulous matter with which the nucleus is surrounded -would commonly prevent such phases from being distinctly visible, even -when they would otherwise be apparent. Moreover, certain qualities of -_polarized_ light,--an affection by which a ray of light seems to have -different properties on different sides,--enable opticians to decide -whether the light of a given body is direct or reflected; and M. Arago, -of Paris, by experiments of this kind on the light of the comet of 1819, -ascertained it to be reflected light. - -The tail of a comet usually increases very much as it approaches the -sun; and it frequently does not reach its maximum until after the -perihelion passage. In receding from the sun, the tail again contracts, -and nearly or quite disappears before the body of the comet is entirely -out of sight. The tail is frequently divided into two portions, the -central parts, in the direction of the axis, being less bright than the -marginal parts. In 1744 a comet appeared which had six tails spread out -like a fan. - -The tails of comets extend in a direct line from the sun, although more -or less curved, like a long quill or feather, being convex on the side -next to the direction in which they are moving,--a figure which may -result from the less velocity of the portion most remote from the sun. -Expansions of the envelope have also been at times observed on the side -next the sun; but these seldom attain any considerable length. - -The _quantity of matter_ in comets is exceedingly small. Their tails -consist of matter of such tenuity, that the smallest stars are visible -through them. They can only be regarded as masses of thin vapor, -susceptible of being penetrated through their whole substance by the -sunbeams, and reflecting them alike from their interior parts and from -their surfaces. It appears perhaps incredible, that so thin a substance -should be visible by reflected light, and some astronomers have held -that the matter of comets is self-luminous; but it requires but very -little light to render an object visible in the night, and a light vapor -may be visible when illuminated throughout an immense stratum, which -could not be seen if spread over the face of the sky like a thin cloud. -"The highest clouds that float in our atmosphere," says Sir John -Herschel, "must be looked upon as dense and massive bodies, compared -with the filmy and all but spiritual texture of a comet." - -The small quantity of matter in comets is proved by the fact, that they -have at times passed very near to some of the planets, without -disturbing their motions in any appreciable degree. Thus the comet of -1770, in its way to the sun, got entangled among the satellites of -Jupiter, and remained near them four months; yet it did not perceptibly -change their motions. The same comet, also, came very near the earth; so -that, had its quantity of matter been equal to that of the earth, it -would, by its attraction, have caused the earth to revolve in an orbit -so much larger than at present, as to have increased the length of the -year two hours and forty-seven minutes. Yet it produced no sensible -effect on the length of the year, and therefore its mass, as is shown by -La Place, could not have exceeded 1/5000 of that of the earth, and -might have been less than this to any extent. It may indeed be asked, -what proof we have that comets have any matter, and are not mere -reflections of light. The answer is, that, although they are not able by -their own force of attraction to disturb the motions of the planets, yet -they are themselves exceedingly disturbed by the action of the planets, -and in exact conformity with the laws of universal gravitation. A -delicate compass may be greatly agitated by the vicinity of a mass of -iron, while the iron is not sensibly affected by the attraction of the -needle. - -By approaching very near to a large planet, a comet may have its orbit -entirely changed. This fact is strikingly exemplified in the history of -the comet of 1770. At its appearance in 1770, its orbit was found to be -an ellipse, requiring for a complete revolution only five and a half -years; and the wonder was, that it had not been seen before, since it -was a very large and bright comet. Astronomers suspected that its path -had been changed, and that it had been recently compelled to move in -this short ellipse, by the disturbing force of Jupiter and his -satellites. The French Institute, therefore, offered a high prize for -the most complete investigation of the elements of this comet, taking -into account any circumstances which could possibly have produced an -alteration in its course. By tracing back the movements of this comet, -for some years previous to 1770, it was found that, at the beginning of -1767, it had entered considerably within the sphere of Jupiter's -attraction. Calculating the amount of this attraction from the known -proximity of the two bodies, it was found what must have been its orbit -previous to the time when it became subject to the disturbing action of -Jupiter. It was therefore evident why, as long as it continued to -circulate in an orbit so far from the centre of the system, it was never -visible from the earth. In January, 1767, Jupiter and the comet happened -to be very near to one another, and as both were moving in the same -direction, and nearly in the same plane, they remained in the -neighborhood of each other for several months, the planet being between -the comet and the sun. The consequence was, that the comet's orbit was -changed into a smaller ellipse, in which its revolution was accomplished -in five and a half years. But as it approached the sun, in 1779, it -happened again to fall in with Jupiter. It was in the month of June that -the attraction of the planet began to have a sensible effect; and it was -not until the month of October following, that they were finally -separated. - -At the time of their nearest approach, in August, Jupiter was distant -from the comet only 1/491 of its distance from the sun, and exerted an -attraction upon it two hundred and twenty-five times greater than that -of the sun. By reason of this powerful attraction, Jupiter being further -from the sun than the comet, the latter was drawn out into a new orbit, -which even at its perihelion came no nearer to the sun than the planet -Ceres. In this third orbit, the comet requires about twenty years to -accomplish its revolution; and being at so great a distance from the -earth, it is invisible, and will for ever remain so unless, in the -course of ages, it may undergo new perturbations, and move again in some -smaller orbit, as before. - -With the foregoing leading facts respecting comets in view, I will now -explain to you a few things equally remarkable respecting their -_motions_. - -The paths of the planets around the sun being nearly circular, we are -able to see a planet in every part of its orbit. But the case is very -different with comets. For the greater part of their course, they are -wholly out of sight, and come into view only while just in the -neighborhood of the sun. This you will readily see must be the case, by -inspecting the frontispiece, which represents the orbit of Biela's -comet, in 1832. Sometimes, the orbit is so eccentric, that the place of -the focus occupied by the sun appears almost at the extremity of the -orbit. This was the case with the orbit of the comet of 1680. Indeed, -this comet, at its perihelion, came in fact nearer to the sun than the -sixth part of the sun's diameter, being only one hundred and forty-six -thousand miles from the surface of the sun, which, you will remark, is -only a little more than half the distance of the moon from the earth; -while, at its aphelion, it was estimated to be thirteen thousand -millions of miles from the sun,--more than eleven thousand millions of -miles beyond the planet Uranus. Its _velocity_, when nearest the sun, -exceeded a million of miles an hour. To describe such an orbit as was -assigned to it by Sir Isaac Newton, would require five hundred and -seventy-five years. During all this period, it was entirely out of view -to the inhabitants of the earth, except the few months, while it was -running down to the sun from such a distance as the orbit of Jupiter and -back. The velocity of bodies moving in such eccentric orbits differs -widely in different parts of their orbits. In the remotest parts it is -so slow, that years would be required to pass over a space equal to that -which it would run over in a single day, when near the sun. - -The appearances of the same comet at different periods of its return are -so various, that we can never pronounce a given comet to be the same -with one that has appeared before, from any peculiarities in its -physical aspect, as from its color, magnitude, or shape; since, in all -these respects, it is very different at different returns; but it is -judged to be the same if its _path_ through the heavens, as traced among -the stars, is the same. - -The comet whose history is the most interesting, and which both of us -have been privileged to see, is Halley's. Just before its latest visit, -in 1835, its return was anticipated with so much expectation, not only -by astronomers, but by all classes of the community, that a great and -laudable eagerness universally prevailed, to learn the particulars of -its history. The best summary of these, which I met with, was given in -the Edinburgh Review for April, 1835. I might content myself with barely -referring you to that well-written article; but, as you may not have the -work at hand, and would, moreover, probably not desire to read the -whole article, I will abridge it for your perusal, interspersing some -remarks of my own. I have desired to give you, in the course of these -Letters, some specimen of the labors of astronomers, and shall probably -never be able to find a better one. - -It is believed that the first recorded appearance of Halley's comet was -that which was supposed to signalize the birth of Mithridates, one -hundred and thirty years before the birth of Christ. It is said to have -appeared for twenty-four days; its light is said to have surpassed that -of the sun; its magnitude to have extended over a fourth part of the -firmament; and it is stated to have occupied, consequently, about four -hours in rising and setting. In the year 323, a comet appeared in the -sign Virgo. Another, according to the historians of the Lower Empire, -appeared in the year 399, seventy-six years after the last, at an -interval corresponding to that of Halley's comet. The interval between -the birth of Mithridates and the year 323 was four hundred and -fifty-three years, which would be equivalent to six periods of -seventy-five and a half years. Thus it would seem, that in the interim -there were five returns of this comet unobserved, or at least -unrecorded. The appearance in the year 399 was attended with -extraordinary circumstances. It was described in the old writers as a -"comet of monstrous size and appalling aspect, its tail seeming to reach -down to the ground." The next recorded appearance of a comet agreeing -with the ascertained period marks the taking of Rome, in the year -550,--an interval of one hundred and fifty-one years, or two periods of -seventy-five and a half years having elapsed. One unrecorded return -must, therefore, have taken place in the interim. The next appearance of -a comet, coinciding with the assigned period, is three hundred and -eighty years afterwards; namely, in the year 930,--five revolutions -having been completed in the interval. The next appearance is recorded -in the year 1005, after an interval of a single period of seventy-five -years. Three revolutions would now seem to have passed unrecorded, when -the comet again makes its appearance in 1230. In this, as well as in -former appearances, it is proper to state, that the sole test of -identity of these cornets with that of Halley is the coincidence of the -times, as near as historical records enable us to ascertain, with the -epochs at which the comet of Halley might be expected to appear. That -such evidence, however, is very imperfect, must be evident, if the -frequency of cometary appearances be considered, and if it be -remembered, that hitherto we find no recorded observations, which could -enable us to trace, even with the rudest degree of approximation, the -paths of those comets, the times of whose appearances raise a -presumption of their identity with that of Halley. We now, however, -descend to times in which more satisfactory evidence may be expected. - -In the year 1305, a year in which the return of Halley's comet might -have been expected, there is recorded a comet of remarkable character: -"A comet of terrific dimensions made its appearance about the time of -the feast of the Passover, which was followed by a Great Plague." Had -the terrific appearance of this body alone been recorded, this -description might have passed without the charge of great exaggeration; -but when we find the Great Plague connected with it as a consequence, it -is impossible not to conclude, that the comet was seen by its historians -through the magnifying medium of the calamity which followed it. Another -appearance is recorded in the year 1380, unaccompanied by any other -circumstance than its mere date. This, however, is in strict accordance -with the ascertained period of Halley's comet. - -We now arrive at the first appearance at which observations were taken, -possessing sufficient accuracy to enable subsequent investigators to -determine the path of the comet; and this is accordingly the first comet -the identity of which with the comet of Halley can be said to be -conclusively established. In the year 1456, a comet is stated to have -appeared "of unheard of magnitude;" it was accompanied by a tail of -extraordinary length, which extended over sixty degrees, (a third part -of the heavens,) and continued to be seen during the whole month of -June. The influence which was attributed to this appearance renders it -probable, that in the record there is more or less of exaggeration. It -was considered as the celestial indication of the rapid success of -Mohammed the Second, who had taken Constantinople, and struck terror -into the whole Christian world. Pope Calixtus the Second levelled the -thunders of the Church against the enemies of his faith, terrestrial and -celestial; and in the same Bull excommunicated the Turks and the comet; -and, in order that the memory of this manifestation of his power should -be for ever preserved, he ordained that the bells of all the churches -should be rung at mid-day,--a custom which is preserved in those -countries to our times. - -The extraordinary length and brilliancy which was ascribed to the tail, -upon this occasion, have led astronomers to investigate the -circumstances under which its brightness and magnitude would be the -greatest possible; and upon tracing back the motion of the comet to the -year 1456, it has been found that it was then actually in the position, -with respect to the earth and sun, most favorable to magnitude and -splendor. So far, therefore, the result of astronomical calculation -corroborates the records of history. - -The next return took place in 1531. Pierre Appian, who first ascertained -the fact that the tails of comets are usually turned from the sun, -examined this comet with a view to verify his statement, and to -ascertain the true direction of its tail. He made, accordingly, numerous -observations upon its position, which, although rude, compared with the -present standard of accuracy, were still sufficiently exact to enable -Halley to identify this comet with that observed by himself. - -The next return took place in 1607, when the comet was observed by -Kepler. This astronomer first saw it on the evening of the twenty-sixth -of September, when it had the appearance of a star of the first -magnitude, and, to his vision, was without a tail; but the friends who -accompanied him had better sight, and distinguished the tail. Before -three o'clock the following morning the tail had become clearly visible, -and had acquired great magnitude. Two days afterwards, the comet was -observed by Longomontanus, a distinguished philosopher of the time. He -describes its appearance, to the naked eye, to be like Jupiter, but of a -paler and more obscured light; that its tail was of considerable length, -of a paler light than that of the head, and more dense than the tails of -ordinary comets. - -The next appearance, and that which was observed by Halley himself, took -place in 1682, a little before the publication of the '_Principia_.' In -the interval between 1607 and 1682, practical astronomy had made great -advances; instruments of observation had been brought to a state of -comparative perfection; numerous observatories had been established, and -the management of them had been confided to the most eminent men in -Europe. In 1682, the scientific world was therefore prepared to examine -the visitor of our system with a degree of care and accuracy before -unknown. - -In the year 1686, about four years afterwards, Newton published his -'_Principia_,' in which he applied to the comet of 1680 the general -principles of physical investigation first promulgated in that work. He -explained the method of determining, by geometrical construction, the -visible portion of the path of a body of this kind, and invited -astronomers to apply these principles to the various recorded -comets,--to discover whether some among them might not have appeared at -different epochs, the future returns of which might consequently be -predicted. Such was the effect of the force of analogy upon the mind of -Newton, that, without awaiting the discovery of a periodic comet, he -boldly assumed these bodies to be analogous to planets in their -revolution round the sun. - -Extraordinary as these conjectures must have appeared at the time, they -were soon strictly realized. Halley, who was then a young man, but -possessed one of the best minds in England, undertook the labor of -examining the circumstances attending all the comets previously -recorded, with a view to discover whether any, and which of them, -appeared to follow the same path. Antecedently to the year 1700, four -hundred and twenty-five of these bodies had been recorded in history; -but those which had appeared before the fourteenth century had not been -submitted to any observations by which their paths could be -ascertained,--at least, not with a sufficient degree of precision, to -afford any hope of identifying them with those of other comets. -Subsequently to the year 1300, however, Halley found twenty-four comets -on which observations had been made and recorded, with a degree of -precision sufficient to enable him to calculate the actual paths which -these bodies followed while they were visible. He examined, with the -most elaborate care, the _courses_ of each of these twenty-four bodies; -he found the exact points at which each one of them crossed the -ecliptic, or their _nodes_; also the angle which the direction of their -motion made with that plane,--that is, the _inclination of their -orbits_; he also calculated the nearest distance at which each of them -approached the sun, or their _perihelion distance_; and the exact place -of the body when at that nearest point,--that is, the _longitude of the -perihelion_. These particulars are called the _elements_ of a comet, -because, when ascertained, they afford sufficient data for determining a -comet's path. On comparing these paths, Halley found that one, which had -appeared in 1661, followed nearly the same path as one which had -appeared in 1532. Supposing, then, these to be two successive -appearances of the same comet, it would follow, that its period would be -one hundred and twenty-nine years, reckoning from 1661. Had this -conjecture been well founded, the comet must have appeared about the -year 1790. No comet, however, appeared at or near that time, following a -similar path. - -In his second conjecture, Halley was more fortunate, as indeed might be -expected, since it was formed upon more conclusive grounds. He found -that the paths of comets which had appeared in 1531 and 1607 were nearly -identical, and that they were in fact the same as the path followed by -the comet observed by himself in 1682. He suspected, therefore, that the -appearances at these three epochs were produced by three successive -returns of the same comet, and that, consequently, its period in its -orbit must be about seventy-five and a half years. The probability of -this conclusion is strikingly exhibited to the eye, by presenting the -elements in a tabular form, from which it will at once be seen how -nearly they correspond at these regular intervals. - - ===================================================================== - Time.|Inclination of|Long. of the |Long. Per.|Per. Dist. |Course. - |the orbit. |node. | | | - ===================================================================== - 1456 | 17°56“ | 48°30“ |301°00“ | 0°58“ |Retrograde. - 1531 | 17 56 | 49 25 |301 39 | 0 57 | " - 1607 | 17 02 | 50 21 |302 16 | 0 58 | " - 1682 | 17 42 | 50 48 |301 36 | 0 58 | " - ===================================================================== - -So little was the scientific world, at this time, prepared for such an -announcement, that Halley himself only ventured at first to express his -opinion in the form of conjecture; but, after some further investigation -of the circumstances of the recorded comets, he found three which, at -least in point of time, agreed with the period assigned to the comet of -1682. Collecting confidence from these circumstances, he announced his -discovery as the result of observation and calculation combined, and -entitled to as much confidence as any other consequence of an -established physical law. - -There were, nevertheless, two circumstances which might be supposed to -offer some difficulty. First, the intervals between the supposed -successive returns were not precisely equal; and, secondly, the -inclination of the comet's path to the plane of the earth's orbit was -not exactly the same in each case. Halley, however, with a degree of -sagacity which, considering the state of knowledge at the time, cannot -fail to excite unqualified admiration, observed, that it was natural to -suppose that the same causes which disturbed the planetary motions must -likewise act upon comets; and that their influence would be so much the -more sensible upon these bodies, because of their great distances from -the sun. Thus, as the attraction of Jupiter for Saturn was known to -affect the velocity of the latter planet, sometimes retarding and -sometimes accelerating it, according to their relative position, so as -to affect its period to the extent of thirteen days, it might well be -supposed, that the comet might suffer by a similar attraction an effect -sufficiently great, to account for the inequality observed in the -interval between its successive returns: and also for the variation to -which the direction of its path upon the plane of the ecliptic was found -to be subject. He observed, in fine, that, as in the interval between -1607 and 1682, the comet passed so near Jupiter that its velocity must -have been augmented, and consequently its period shortened, by the -action of that planet, this period, therefore, having been only -seventy-five years, he inferred that the following period would probably -be seventy-six years, or upwards; and consequently, that the comet ought -not to be expected to appear until the end of 1758, or the beginning of -1759. It is impossible to imagine any quality of mind more enviable than -that which, in the existing state of mathematical physics, could have -led to such a prediction. The imperfect state of mathematical science -rendered it impossible for Halley to offer to the world a demonstration -of the event which he foretold. The theory of gravitation, which was in -its infancy in the time of Halley's investigations, had grown to -comparative maturity before the period at which his prediction could be -fulfilled. The exigencies of that theory gave birth to new and more -powerful instruments of mathematical inquiry: the differential and -integral calculus, or the science of fluxions, as it is sometimes -called,--a branch of the mathematics, expressed by algebraic symbols, -but capable of a much higher reach, as an instrument of investigation, -than either algebra or geometry,--was its first and greatest offspring. -This branch of science was cultivated with an ardor and success by -which it was enabled to answer all the demands of physics, and it -contributed largely to the advancement of mechanical science itself, -building upon the laws of motion a structure which has since been -denominated 'Celestial Mechanics.' Newton's discoveries having obtained -reception throughout the scientific world, his inquiries and his -theories were followed up; and the consequences of the great principle -of universal gravitation were rapidly developed. Since, according to -this doctrine, _every body in nature attracts and is attracted by every -other body_, it follows, that the comet was liable to be acted on by -each of the planets, as well as by the sun,--a circumstance which -rendered its movements much more difficult to follow, than would be the -case were it subject merely to the projectile force and to the solar -attraction. To estimate the time it would take for a ship to cross the -Atlantic would be an easy task, were she subject to only one constant -wind; but to estimate, beforehand, the exact influence which all other -winds and the tides might have upon her passage, some accelerating and -some retarding her course, would present a problem of the greatest -difficulty. Clairaut, however, a celebrated French mathematician, -undertook to estimate the effects that would be produced on Halley's -comet by the attractions of all the planets. His aim was to investigate -_general rules_, by which the computation could be made arithmetically, -and hand them over to the practical calculator, to make the actual -computations. Lalande, a practical astronomer, no less eminent in his -own department, and who indeed first urged Clairaut to this inquiry, -undertook the management of the astronomical and arithmetical part of -the calculation. In this prodigious labor (for it was one of most -appalling magnitude) he was assisted by the wife of an eminent -watchmaker in Paris, named Lepaute, whose exertions on this occasion -have deservedly registered her name in astronomical history. - -It is difficult to convey to one who is not conversant with such -investigations, an adequate notion of the labor which such an inquiry -involved. The calculation of the influence of any one _planet_ of the -system upon any other is itself a problem of some complexity and -difficulty; but still, one general computation, depending upon the -calculation of the terms of a certain series, is sufficient for its -solution. This comparative simplicity arises entirely from two -circumstances which characterize the planetary orbits. These are, that, -though they are ellipses, they differ very slightly from circles; and -though the planets do not move in the plane of the ecliptic, yet none of -them deviate considerably from that plane. But these characters do not -belong to the orbits of comets, which, on the contrary, are highly -eccentric, and make all possible angles with the ecliptic. The -consequence of this is, that the calculation of the disturbances -produced in the cometary orbits by the action of the planets must be -conducted not like the planets, in one general calculation applicable to -the whole orbits, but in a vast number of separate calculations; in -which the orbit is considered, as it were, bit by bit, each bit -requiring a calculation similar to the whole orbit of the planet. Now, -when it is considered that the period of Halley's comet is about -seventy-five years, and that every portion of its course, for two -successive periods, was necessary to be calculated separately in this -way, some notion may be formed of the labor encountered by Lalande and -Madame Lepaute. "During six months," says Lalande, "we calculated from -morning till night, sometimes even at meals; the consequence of which -was, that I contracted an illness which changed my constitution for the -remainder of my life. The assistance rendered by Madame Lepaute was -such, that, without her, we never could have dared to undertake this -enormous labor, in which it was necessary to calculate the distance of -each of the two planets, Jupiter and Saturn, from the comet, and their -attraction upon that body, separately, for every successive degree, and -for one hundred and fifty years." - -The attraction of a body is proportioned to its quantity of matter. -Therefore, before the attraction exerted upon the comet by the several -planets within whose influence it might fall, could be correctly -estimated, it was necessary to know the mass of each planet; and though -the planets had severally been weighed by methods supplied by Newton's -'Principia,' yet the estimate had not then attained the same measure of -accuracy as it has now reached; nor was it certain that there was not -(as it has since appeared that there actually was) one or more planets -beyond Saturn, whose attractions might likewise influence the motions of -the comet. Clairaut, making the best estimate he was able, under all -these disadvantages, of the disturbing influence of the planets, fixed -the return of the comet to the place of its nearest distance from the -sun on the fourth of April, 1759. - -In the successive appearances of the comet, subsequently to 1456, it was -found to have gradually decreased in magnitude and splendor. While in -1456 it reached across one third part of the firmament, and spread -terror over Europe, in 1607, its appearance, when observed by Kepler and -Longomontanus, was that of a star of the first magnitude; and so -trifling was its tail that, Kepler himself, when he first saw it, -doubted whether it had any. In 1682, it excited little attention, except -among astronomers. Supposing this decrease of magnitude and brilliancy -to be progressive, Lalande entertained serious apprehensions that on its -expected return it might be so inconsiderable, as to escape the -observation even of astronomers; and thus, that this splendid example -of the power of science, and unanswerable proof of the principle of -gravitation, would be lost to the world. - -It is not uninteresting to observe the misgivings of this distinguished -astronomer with respect to the appearance of the body, mixed up with his -unshaken faith in the result of the astronomical inquiry. "We cannot -doubt," says he, "that it will return; and even if astronomers cannot -see it, they will not therefore be the less convinced of its presence. -They know that the faintness of its light, its great distance, and -perhaps even bad weather, may keep it from our view. But the world will -find it difficult to believe us; they will place this discovery, which -has done so much honor to modern philosophy, among the number of chance -predictions. We shall see discussions spring up again in colleges, -contempt among the ignorant, terror among the people; and seventy-six -years will roll away, before there will be another opportunity of -removing all doubt." - -Fortunately for science, the arrival of the expected visitor did not -take place under such untoward circumstances. As the commencement of the -year 1759 approached, "astronomers," says Voltaire, "hardly went to bed -at all." The honor, however, of the first glimpse of the stranger was -not reserved for the possessors of scientific rank, nor for the members -of academies or universities. On the night of Christmas-day, 1758, -George Palitzch, of Politz, near Dresden,--"a peasant," says Sir John -Herchel, "by station, an astronomer by nature," first saw the comet. - -An astronomer of Leipzic found it soon after; but, with the mean -jealousy of a miser, he concealed his treasure, while his contemporaries -throughout Europe were vainly directing their anxious search after it to -other quarters of the heavens. At this time, Delisle, a French -astronomer, and his assistant, Messier, who, from his unweared assiduity -in the pursuit of comets, was called the _Comet-Hunter_, had been -constantly engaged, for eighteen months, in watching for the return of -Halley's comet. Messier passed his life in search of comets. It is -related of him, that when he was in expectation of discovering a comet, -his wife was taken ill and died. While attending on her, being withdrawn -from his observatory, another astronomer anticipated him in the -discovery. Messier was in despair. A friend, visiting him, began to -offer some consolation for the recent affliction he had suffered. -Messier, thinking only of the comet, exclaimed, "I had discovered -twelve: alas, that I should be robbed of the thirteenth by -Montague!"--and his eyes filled with tears. Then, remembering that it -was necessary to mourn for his wife, whose remains were still in the -house, he exclaimed, "Ah! this poor woman!" (_ah! cette pauvre femme_,) -and again wept for his comet. We can easily imagine how eagerly such an -enthusiast would watch for Halley's comet; and we could almost wish that -it had been his good fortune to be the first to announce its arrival: -but, being misled by a chart which directed his attention to the wrong -part of the firmament, a whole month elapsed after its discovery by -Palitzch, before he enjoyed the delightful spectacle. - -The comet arrived at its perihelion on the thirteenth of March, only -twenty-three days from the time assigned by Clairaut. It appeared very -round, with a brilliant nucleus, well distinguished from the surrounding -nebulosity. It had, however, no appearance of a tail. It became lost in -the sun, as it approached its perihelion, and emerged again, on the -other side of the sun, on the first of April. Its exhibiting an -appearance, so inferior to what it presented on some of its previous -returns, is partly accounted for by its being seen by the European -astronomers under peculiarly disadvantageous circumstances, being almost -always within the twilight, and in the most unfavorable situations. In -the southern hemisphere, however, the circumstances for observing it -were more favorable, and there it exhibited a tail varying from ten to -forty-seven degrees in length. - -In my next Letter I will give you some particulars respecting the late -return of Halley's comet. - - - - -LETTER XXVI. - -COMETS, CONTINUED. - - "Incensed with indignation, Satan stood - Unterrified, and like a comet burned, - That fires the length of Ophiucus huge - In the Arctic sky, and from his horrid train - Shakes pestilence and war."--_Milton._ - - -AMONG other great results which have marked the history of Halley's -comet, it has itself been a criterion of the existing state of the -mathematical and astronomical sciences. We have just seen how far the -knowledge of the great laws of physical astronomy, and of the higher -mathematics, enabled the astronomers of 1682 and 1759, respectively, to -deal with this wonderful body; and let us now see what higher advantages -were possessed by the astronomers of 1835. During this last interval of -seventy-six years, the science of mathematics, in its most profound and -refined branches, has made prodigious advances, more especially in its -application to the laws of the celestial motions, as exemplified in the -'Mecanique Celeste' of La Place. The methods of investigation have -acquired greater simplicity, and have likewise become more general and -comprehensive; and mechanical science, in the largest sense of that -term, now embraces in its formularies the most complicated motions, and -the most minute effects of the mutual influences of the various members -of our system. You will probably find it difficult to comprehend, how -such hidden facts can be disclosed by formularies, consisting of _a_'s -and _b_'s, and _x_'s and _y_'s, and other algebraic symbols; nor will it -be easy to give you a clear idea of this subject, without a more -extensive acquaintance than you have formed with algebraic -investigations; but you can easily understand that even an equation -expressed in numbers may be so changed in its form, by adding, -subtracting, multiplying and dividing, as to express some new truth at -every transformation. Some idea of this may be formed by the simplest -example. Take the following: 3+4=7. This equation expresses the fact, -that three added to four is equal to seven. By multiplying all the terms -by 2, we obtain a new equation, in which 6+8=14. This expresses a new -truth; and by varying the form, by similar operations, an indefinite -number of separate truths may be elicited from the simple fundamental -expression. I will add another illustration, which involves a little -more algebra, but not, I think, more than you can understand; or, if it -does, you will please pass over it to the next paragraph. According to a -rule of arithmetical progression, _the sum of all the terms is equal to -half the sum of the extremes multiplied into the number of terms_. -Calling the sum of the terms _s_, the first term _a_, the last _h_, and -the number of terms _n_, and we have _(1/2)n(a+h)=s_; or _n(a+h)=2s_; or -_a+h=2s/n_; or _a=(2s/n)-h_; or _h=(2s/n)-a_. These are only a few of -the changes which may be made in the original expression, still -preserving the equality between the quantities on the left hand and -those on the right; yet each of these transformations expresses a new -truth, indicating distinct and (as might be the case) before unknown -relations between the several quantities of which the whole expression -is composed. The last, for example, shows us that the last term in an -arithmetical series is always equal to twice the sum of the whole series -divided by the number of terms and diminished by the first term. In -analytical formularies, as expressions of this kind are called, the -value of a single unknown quantity is sometimes given in a very -complicated expression, consisting of known quantities; but before we -can ascertain their united value, we must reduce them, by actually -performing all the additions, subtractions, multiplications, divisions, -raising to powers, and extracting roots, which are denoted by the -symbols. This makes the actual calculations derived from such -formularies immensely laborious. We have already had an instance of this -in the calculations made by Lalande and Madame Lepaute, from formularies -furnished by Clairaut. - -The analytical formularies, contained in such works as La Place's -'Mecanique Celeste,' exhibit to the eye of the mathematician a record of -all the evolutions of the bodies of the solar system in ages past, and -of all the changes they must undergo in ages to come. Such has been the -result of the combination of transcendent mathematical genius and -unexampled labor and perseverance, for the last century. The learned -societies established in various centres of civilization have more -especially directed their attention to the advancement of physical -astronomy, and have stimulated the spirit of inquiry by a succession of -prizes, offered for the solutions of problems arising out of the -difficulties which were progressively developed by the advancement of -astronomical knowledge. Among these questions, the determination of the -return of comets, and the disturbances which they experience in their -course, by the action of the planets near which they happen to pass, -hold a prominent place. In 1826, the French Institute offered a prize -for the determination of the exact time of the return of Halley's comet -to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After -calculations," says he, "of which those alone who have engaged in such -researches can estimate the extent and appreciate the fastidious -monotony, I arrived at a result which satisfied all the conditions -proposed by the Institute. I determined the perturbations of Halley's -comet, by taking into account the simultaneous actions of Jupiter, -Saturn, Uranus, and the Earth, and I then fixed its return to its -perihelion for the seventh of November." Subsequently to this, however, -M. Pontecoulant made some further researches, which led him to correct -the former result; and he afterwards altered the time to November -fourteenth. It actually came to its perihelion on the sixteenth, within -two days of the time assigned. - -Nothing can convince us more fully of the complete mastery which -astronomers have at last acquired over these erratic bodies, than to -read in the Edinburgh Review for April, 1835, the paragraph containing -the final results of all the labors and anticipations of astronomers, -matured as they were, in readiness for the approaching visitant, and -then to compare the prediction with the event, as we saw it fulfilled a -few months afterwards. The paragraph was as follows: "On the whole, it -may be considered as tolerably certain, that the comet will become -visible in every part of Europe about the latter end of August, or -beginning of September, next. It will most probably be distinguishable -by the naked eye, like a star of the first magnitude, but with a duller -light than that of a planet, and surrounded with a pale nebulosity, -which will slightly impair its splendor. On the night of the seventh of -October, the comet will approach the well-known constellation of the -Great Bear; and between that and the eleventh, it will pass directly -through the seven conspicuous stars of that constellation, (the Dipper.) -Towards the end of November, the comet will plunge among the rays of the -sun, and disappear, and will not issue from them, on the other side, -until the end of December." - -Let us now see how far the actual appearances corresponded to these -predictions. The comet was first discovered from the observatory at -Rome, on the morning of the fifth of August; by Professor Struve, at -Dorpat, on the twentieth; in England and France, on the twenty-third; -and at Yale College, by Professor Loomis and myself, on the -thirty-first. On the morning of that day, between two and three o'clock, -in obedience to the directions which the great minds that had marked out -its path among the stars had prescribed, we directed Clarke's telescope -(a noble instrument, belonging to Yale College) towards the -northeastern quarter of the heavens, and lo! there was the wanderer so -long foretold,--a dim speck of fog on the confines of creation. It came -on slowly, from night to night, increasing constantly in magnitude and -brightness, but did not become distinctly visible to the naked eye until -the twenty-second of September. For a month, therefore, astronomers -enjoyed this interesting spectacle before it exhibited itself to the -world at large. From this time it moved rapidly along the northern sky, -until, about the tenth of October, it traversed the constellation of the -Great Bear, passing a little above, instead of "through" the seven -conspicuous stars constituting the Dipper. At this time it had a -lengthened train, and became, as you doubtless remember, an object of -universal interest. Early in November, the comet ran down to the sun, -and was lost in his beams; but on the morning of December thirty-first, -I again obtained, through Clarke's telescope, a distinct view of it on -the other side of the sun, a moment before the morning dawn. - -This return of Halley's comet was an astronomical event of transcendent -importance. It was the chronicler of ages, and carried us, by a few -steps, up to the origin of time. If a gallant ship, which has sailed -round the globe, and commanded successively the admiration of many great -cities, diverse in language and customs, is invested with a peculiar -interest, what interest must attach to one that has made the circuit of -the solar system, and fixed the gaze of successive worlds! So intimate, -moreover, is the bond which binds together all truths in one -indissoluble chain, that the establishment of one great truth often -confirms a multitude of others, equally important. Thus the return of -Halley's comet, in exact conformity with the predictions of astronomers, -established the truth of all those principles by which those predictions -were made. It afforded most triumphant proof of the doctrine of -universal gravitation, and of course of the received laws of physical -astronomy; it inspired new confidence in the power and accuracy of that -instrument (the calculus) by means of which its elements had been -investigated; and it proved that the different planets, which exerted -upon it severally a disturbing force proportioned to their quantity of -matter, had been correctly weighed, as in a balance. - -I must now leave this wonderful body to pursue its sublime march far -beyond the confines of Uranus, (a distance it has long since reached,) -and take a hasty notice of two other comets, whose periodic returns have -also been ascertained; namely, those of Biela and Encke. - -Biela's comet has a period of six years and three quarters. It has its -perihelion near the orbit of the earth, and its aphelion a little beyond -that of Jupiter. Its orbit, therefore, is far less eccentric than that -of Halley's comet; (see Frontispiece;) it neither approaches so near the -sun, nor departs so far from it, as most other known comets: some, -indeed, never come nearer to the sun than the orbit of Jupiter, while -they recede to an incomprehensible distance beyond the remotest planet. -We might even imagine that they would get beyond the limits of the sun's -attraction; nor is this impossible, although, according to La Place, the -solar attraction is sensible throughout a sphere whose radius is a -hundred millions of times greater than the distance of the earth from -the sun, or nearly ten thousand billions of miles. - -Some months before the expected return of Biela's comet, in 1832, it was -announced by astronomers, who had calculated its path, that it would -cross the plane of the earth's orbit very near to the earth's path, so -that, should the earth happen at the time to be at that point of her -revolution, a collision might take place. This announcement excited so -much alarm among the ignorant classes in France, that it was deemed -expedient by the French academy, that one of their number should prepare -and publish an article on the subject, with the express view of -allaying popular apprehension. This task was executed by M. Arago. He -admitted that the earth would in fact pass so near the point where the -comet crossed the plane of its orbit, that, should they chance to meet -there, the earth would be enveloped in the nebulous atmosphere of the -comet. He, however, showed that the earth would not be near that point -at the same time with the comet, but fifty millions of miles from it. - -The comet came at the appointed time, but was so exceedingly faint and -small, that it was visible only to the largest telescopes. In one -respect, its diminutive size and feeble light enhanced the interest with -which it was contemplated; for it was a sublime spectacle to see a body, -which, as projected on the celestial vault, even when magnified a -thousand times, seemed but a dim speck of fog, still pursuing its way, -in obedience to the laws of universal gravitation, with the same -regularity as Jupiter and Saturn. We are apt to imagine that a body, -consisting of such light materials that it can be compared only to the -thinnest fog, would be dissipated and lost in the boundless regions of -space; but so far is this from the truth, that, when subjected to the -action of the same forces of projection and solar attraction, it will -move through the void regions of space, and will describe its own orbit -about the sun with the same unerring certainty, as the densest bodies of -the system. - -Encke's comet, by its frequent returns, (once in three and a third -years,) affords peculiar facilities for ascertaining the laws of its -revolution; and it has kept the appointments made for it with great -exactness. On its return in 1839, it exhibited to the telescope a -globular mass of nebulous matter, resembling fog, and moved towards its -perihelion with great rapidity. It makes its entire excursions within -the orbit of Jupiter. - -But what has made Encke's comet particularly famous, is its having first -revealed to us the existence of a _resisting medium_ in the planetary -spaces. It has long been a question, whether the earth and planets -revolve in a perfect void, or whether a fluid of extreme rarity may not -be diffused through space. A perfect vacuum was deemed most probable, -because no such effects on the motions of the planets could be detected -as indicated that they encountered a resisting medium. But a feather, or -a lock of cotton, propelled with great velocity, might render obvious -the resistance of a medium which would not be perceptible in the motions -of a cannon ball. Accordingly, Encke's comet is thought to have plainly -suffered a retardation from encountering a resisting medium in the -planetary regions. The effect of this resistance, from the first -discovery of the comet to the present time, has been to diminish the -time of its revolution about two days. Such a resistance, by destroying -a part of the projectile force, would cause the comet to approach nearer -to the sun, and thus to have its periodic time shortened. The ultimate -effect of this cause will be to bring the comet nearer to the sun, at -every revolution, until it finally falls into that luminary, although -many thousand years will be required to produce this catastrophe. It is -conceivable, indeed, that the effects of such a resistance may be -counteracted by the attraction of one or more of the planets, near which -it may pass in its successive returns to the sun. Still, it is not -probable that this cause will exactly counterbalance the other; so that, -if there is such an elastic medium diffused through the planetary -regions, it must follow that, in the lapse of ages, every comet will -fall into the sun. Newton conjectured that this would be the case, -although he did not found his opinion upon the existence of such a -resisting medium as is now detected. To such an opinion he adhered to -the end of life. At the age of eighty-three, in a conversation with his -nephew, he expressed himself thus: "I cannot say when the comet of 1680 -will fall into the sun; possibly after five or six revolutions; but -whenever that time shall arrive, the heat of the sun will be raised by -it to such a point, that our globe will be burned, and all the animals -upon it will perish." - -Of the _physical nature_ of comets little is understood. The greater -part of them are evidently mere masses of vapor, since they permit very -small stars to be seen through them. In September, 1832, Sir John -Herschel, when observing Biela's comet, saw that body pass directly -between his eye and a small cluster of minute telescopic stars of the -sixteenth or seventeenth magnitude. This little constellation occupied a -space in the heavens, the breadth of which was not the twentieth part of -that of the moon; yet the whole of the cluster was distinctly visible -through the comet. "A more striking proof," says Sir John Herschel, -"could not have been afforded, of the extreme transparency of the matter -of which this comet consists. The most trifling fog would have entirely -effaced this group of stars, yet they continued visible through a -thickness of the comet which, calculating on its distance and apparent -diameter, must have exceeded fifty thousand miles, at least towards its -central parts." From this and similar observations, it is inferred, that -the nebulous matter of comets is vastly more rare than that of the air -we breathe, and hence, that, were more or less of it to be mingled with -the earth's atmosphere, it would not be perceived, although it might -possibly render the air unwholesome for respiration. M. Arago, however, -is of the opinion, that some comets, at least, have a solid nucleus. It -is difficult, on any other supposition, to account for the strong light -which some of them have exhibited,--a light sufficiently intense to -render them visible in the day-time, during the presence of the sun. The -intense heat to which comets are subject, in approaching so near the sun -as some of them do, is alleged as a sufficient reason for the great -expansion of the thin vapory atmospheres which form their tails; and the -inconceivable cold to which they are subject, in receding to such a -distance from the sun, is supposed to account for the condensation of -the same matter until it returns to its original dimensions. Thus the -great comet of 1680, at its perihelion, approached within one hundred -and forty-six thousand miles of the surface of the sun, a distance of -only one sixth part of the sun's diameter. The heat which it must have -received was estimated to be equal to twenty-eight thousand times that -which the earth receives in the same time, and two thousand times hotter -than red-hot iron. This temperature would be sufficient to volatilize -the most obdurate substances, and to expand the vapor to vast -dimensions; and the opposite effects of the extreme cold to which it -would be subject in the regions remote from the sun would be adequate to -condense it into its former volume. This explanation, however, does not -account for the direction of the tail, extending, as it usually does, -only in a line opposite to the sun. Some writers, therefore, suppose -that the nebulous matter of the comet, after being expanded to such a -volume that the particles are no longer attracted to the nucleus, unless -by the slightest conceivable force, are carried off in a direction from -the sun, by the impulse of the solar rays themselves. But to assign such -a power to the sun's rays, while they have never been proved to have any -momentum, is unphilosophical; and we are compelled to place the -phenomena of comets' tails among the points of astronomy yet to be -explained. - -Since comets which approach very near the sun, like the comet of 1680, -cross the orbits of all the planets, the possibility that one of them -may strike the earth has frequently been suggested. Still it may quiet -our apprehensions on this subject, to reflect on the vast amplitude of -the planetary spaces, in which these bodies are not crowded together, as -we see them erroneously represented in orreries and diagrams, but are -sparsely scattered at immense distances from each other. They are like -insects flying, singly, in the expanse of heaven. If a comet's tail lay -with its axis in the plane of the ecliptic when it was near the sun, we -can imagine that the tail might sweep over the earth; but the tail may -be situated at any angle with the ecliptic, as well as in the same plane -with it, and the chances that it will not be in the same plane are -almost infinite. It is also extremely improbable that a comet will cross -the plane of the ecliptic precisely at the earth's path in that plane, -since it may as probably cross it at any other point nearer or more -remote from the sun. A French writer of some eminence (Du Sejour) has -discussed this subject with ability, and arrived at the following -conclusions: That of all the comets whose paths had been ascertained, -none _could pass_ nearer to the earth than about twice the moon's -distance; and that none ever _did pass_ nearer to the earth than nine -times the moon's distance. The comet of 1770, already mentioned, which -became entangled among the satellites of Jupiter, came within this -limit. Some have taken alarm at the idea that a comet, by approaching -very near to the earth, might raise so high a _tide_, as to endanger the -safety of maritime countries especially: but this writer shows, that the -comet could not possibly remain more than two hours so near the earth as -a fourth part of the moon's distance; and it could not remain even so -long, unless it passed the earth under very peculiar circumstances. For -example, if its orbit were nearly perpendicular to that of the earth, it -could not remain more than half an hour in such a position. Under such -circumstances, the production of a tide would be impossible. Eleven -hours, at least, would be necessary to enable a comet to produce an -effect on the waters of the earth, from which the injurious effects so -much dreaded would follow. The final conclusion at which he arrives is, -that although, in strict geometrical rigor, it is not physically -impossible that a comet should encounter the earth, yet the probability -of such an event is absolutely nothing. - -M. Arago, also, has investigated the probability of such a collision on -the mathematical doctrine of chances, and remarks as follows: "Suppose, -now, a comet, of which we know nothing but that, at its perihelion, it -will be nearer the sun than we are, and that its diameter is equal to -one fourth that of the earth; the doctrine of chances shows that, out of -two hundred and eighty-one millions of cases, there is but one against -us; but one, in which the two bodies could meet." - -La Place has assigned the consequences that would result from a direct -collision between the earth and a comet. "It is easy," says he, "to -represent the effects of the shock produced by the earth's encountering -a comet. The axis and the motion of rotation changed; the waters -abandoning their former position to precipitate themselves towards the -new equator; a great part of men and animals whelmed in a universal -deluge, or destroyed by the violent shock imparted to the terrestrial -globe; entire species annihilated; all the monuments of human industry -overthrown;--such are the disasters which the shock of a comet would -necessarily produce." La Place, nevertheless, expresses a decided -opinion that the orbits of the planets have never yet been disturbed by -the influence of comets. Comets, moreover, have been, and are still to -some degree, supposed to exercise much influence in the affairs of this -world, affecting the weather, the crops, the public health, and a great -variety of atmospheric commotions. Even Halley, finding that his comet -must have been near the earth at the time of the Deluge, suggested the -possibility that the comet caused that event,--an idea which was taken -up by Whiston, and formed into a regular theory. In Gregory's Astronomy, -an able work, published at Oxford in 1702, the author remarks, that -among all nations and in all ages, it has been observed, that the -appearance of a comet has always been followed by great calamities; and -he adds, "it does not become philosophers lightly to set down these -things as fables." Among the various things ascribed to comets by a late -English writer, are hot and cold seasons, tempests, hurricanes, violent -hail-storms, great falls of snow, heavy rains, inundations, droughts, -famines, thick fogs, flies, grasshoppers, plague, dysentery, contagious -diseases among animals, sickness among cats, volcanic eruptions, and -meteors, or shooting stars. These notions are too ridiculous to require -a distinct refutation; and I will only add, that we have no evidence -that comets have hitherto ever exercised the least influence upon the -affairs of this world; and we still remain in darkness, with respect to -their physical nature, and the purposes for which they were created. - - - - -LETTER XXVII. - -METEORIC SHOWERS. - - "Oft shalt thou see, ere brooding storms arise, - Star after star glide headlong down the skies, - And, where they shot, long trails of lingering light - Sweep far behind, and gild the shades of night."--_Virgil._ - - -FEW subjects of astronomy have excited a more general interest, for -several years past, than those extraordinary exhibitions of shooting -stars, which have acquired the name of meteoric showers. My reason for -introducing the subject to your notice, in this place, is, that these -small bodies are, as I believe, derived from nebulous or cometary -bodies, which belong to the solar system, and which, therefore, ought to -be considered, before we take our leave of this department of creation, -and naturally come next in order to comets. - -The attention of astronomers was particularly directed to this subject -by the extraordinary shower of meteors which occurred on the morning of -the thirteenth of November, 1833. I had the good fortune to witness -these grand celestial fire-works, and felt a strong desire that a -phenomenon, which, as it afterwards appeared, was confined chiefly to -North America, should here command that diligent inquiry into its -causes, which so sublime a spectacle might justly claim. - -As I think you were not so happy as to witness this magnificent display, -I will endeavor to give you some faint idea of it, as it appeared to me -a little before daybreak. Imagine a constant succession of fire-balls, -resembling sky-rockets, radiating in all directions from a point in the -heavens a few degrees southeast of the zenith, and following the arch of -the sky towards the horizon. They commenced their progress at different -distances from the radiating point; but their directions were uniformly -such, that the lines they described, if produced upwards, would all have -met in the same part of the heavens. Around this point, or imaginary -radiant, was a circular space of several degrees, within which no -meteors were observed. The balls, as they travelled down the vault, -usually left after them a vivid streak of light; and, just before they -disappeared, exploded, or suddenly resolved themselves into smoke. No -report of any kind was observed, although we listened attentively. - -Beside the foregoing distinct concretions, or individual bodies, the -atmosphere exhibited _phosphoric lines_, following in the train of -minute points, that shot off in the greatest abundance in a -northwesterly direction. These did not so fully copy the figure of the -sky, but moved in paths more nearly rectilinear, and appeared to be much -nearer the spectator than the fire-balls. The light of their trains was -also of a paler hue, not unlike that produced by writing with a stick of -phosphorus on the walls of a dark room. The number of these luminous -trains increased and diminished alternately, now and then crossing the -field of view, like snow drifted before the wind, although, in fact, -their course was towards the wind. - -From these two varieties, we were presented with meteors of various -sizes and degrees of splendor: some were mere points, while others were -larger and brighter than Jupiter or Venus; and one, seen by a credible -witness, at an earlier hour, was judged to be nearly as large as the -moon. The flashes of light, although less intense than lightning, were -so bright, as to awaken people in their beds. One ball that shot off in -the northwest direction, and exploded a little northward of the star -Capella, left, just behind the place of explosion, a phosphorescent -train of peculiar beauty. This train was at first nearly straight, but -it shortly began to contract in length, to dilate in breadth, and to -assume the figure of a serpent drawing itself up, until it appeared like -a small luminous cloud of vapor. This cloud was borne eastward, (by the -wind, as was supposed, which was blowing gently in that direction,) -opposite to the direction in which the meteor itself had moved, -remaining in sight several minutes. The point from which the meteors -seemed to radiate kept a fixed position among the stars, being -constantly near a star in Leo, called Gamma Leonis. - -Such is a brief description of this grand and beautiful display, as I -saw it at New Haven. The newspapers shortly brought us intelligence of -similar appearances in all parts of the United States, and many minute -descriptions were published by various observers; from which it -appeared, that the exhibition had been marked by very nearly the same -characteristics wherever it had been seen. Probably no celestial -phenomenon has ever occurred in this country, since its first -settlement, which was viewed with so much admiration and delight by one -class of spectators, or with so much astonishment and fear by another -class. It strikingly evinced the progress of knowledge and civilization, -that the latter class was comparatively so small, although it afforded -some few examples of the dismay with which, in barbarous ages of the -world, such spectacles as this were wont to be regarded. One or two -instances were reported, of persons who died with terror; many others -thought the last great day had come; and the untutored black population -of the South gave expression to their fears in cries and shrieks. - -After collecting and collating the accounts given in all the periodicals -of the country, and also in numerous letters addressed either to my -scientific friends or to myself, the following appeared to be the -_leading facts_ attending the phenomenon. The shower pervaded nearly -the whole of North America, having appeared in nearly equal splendor -from the British possessions on the north to the West-India Islands and -Mexico on the south, and from sixty-one degrees of longitude east of the -American coast, quite to the Pacific Ocean on the west. Throughout this -immense region, the duration was nearly the same. The meteors began to -attract attention by their unusual frequency and brilliancy, from _nine -to twelve_ o'clock in the evening; were most striking in their -appearance from _two to five;_ arrived at their maximum, in many places, -about _four_ o'clock; and continued until rendered invisible by the -light of day. The meteors moved either in right lines, or in such -apparent curves, as, upon optical principles, can be resolved into right -lines. Their general tendency was towards the northwest, although, by -the effect of perspective, they appeared to move in various directions. - -Such were the leading phenomena of the great meteoric shower of November -13, 1833. For a fuller detail of the facts, as well as of the reasonings -that were built on them, I must beg leave to refer you to some papers of -mine in the twenty-fifth and twenty-sixth volumes of the American -Journal of Science. - -Soon after this wonderful occurrence, it was ascertained that a similar -meteoric shower had appeared in 1799, and, what was remarkable, almost -at exactly the same time of year, namely, on the morning of the twelfth -of November; and we were again surprised as well as delighted, at -receiving successive accounts from different parts of the world of the -phenomenon, as having occurred on the morning of the same thirteenth of -November, in 1830, 1831, and 1832. Hence this was evidently an event -independent of the casual changes of the atmosphere; for, having a -periodical return, it was undoubtedly to be referred to astronomical -causes, and its recurrence, at a certain definite period of the year, -plainly indicated _some_ relation to the revolution of the earth around -the sun. It remained, however, to develope the nature of this relation, -by investigating, if possible, the origin of the meteors. The views to -which I was led on this subject suggested the probability that the same -phenomenon would recur on the corresponding seasons of the year, for at -least several years afterwards; and such proved to be the fact, although -the appearances, at every succeeding return, were less and less -striking, until 1839, when, so far as I have heard, they ceased -altogether. - -Mean-while, two other distinct periods of meteoric showers have, as -already intimated, been determined; namely, about the ninth of August, -and seventh of December. The facts relative to the history of these -periods have been collected with great industry by Mr. Edward C. -Herrick; and several of the most ingenious and most useful conclusions, -respecting the laws that regulate these singular exhibitions, have been -deduced by Professor Twining. Several of the most distinguished -astronomers of the Old World, also, have engaged in these investigations -with great zeal, as Messrs. Arago and Biot, of Paris; Doctor Olbers, of -Bremen; M. Wartmann, of Geneva; and M. Quetelet, of Brussels. - -But you will be desirous to learn what are the _conclusions_ which have -been drawn respecting these new and extraordinary phenomena of the -heavens. As the inferences to which I was led, as explained in the -twenty-sixth volume of the 'American Journal of Science,' have, at least -in their most important points, been sanctioned by astronomers of the -highest respectability, I will venture to give you a brief abstract of -them, with such modifications as the progress of investigation since -that period has rendered necessary. - -The principal questions involved in the inquiry were the following:--Was -the _origin_ of the meteors within the atmosphere, or beyond it? What -was the _height_ of the place above the surface of the earth? By what -_force_ were the meteors drawn or impelled towards the earth? In what -_directions_ did they move? With what _velocity_? What was the cause of -their _light_ and _heat_? Of what _size_ were the larger varieties? At -what height above the earth did they _disappear_? What was the nature of -the _luminous trains_ which sometimes remained behind? What _sort of -bodies_ were the meteors themselves; of what _kind of matter_ -constituted; and in what manner did they exist _before they fell to the -earth_? Finally, what _relations_ did the source from which they -emanated sustain to our earth? - -In the first place, _the meteors had their origin beyond the limits of -our atmosphere_. We know whether a given appearance in the sky is within -the atmosphere or beyond it, by this circumstance: all bodies near the -earth, including the atmosphere itself, have a common motion with the -earth around its axis from west to east. When we see a celestial object -moving regularly from west to east, at the same rate as the earth moves, -leaving the stars behind, we know it is near the earth, and partakes, in -common with the atmosphere, of its diurnal rotation: but when the earth -leaves the object behind; or, in other words, when the object moves -westward along with the stars, then we know that it is so distant as not -to participate in the diurnal revolution of the earth, and of course to -be beyond the atmosphere. The source from which the meteors emanated -thus kept pace with the stars, and hence was beyond the atmosphere. - -In the second place, _the height of the place whence the meteors -proceeded was very great, but it has not yet been accurately -determined_. Regarding the body whence the meteors emanated after the -similitude of a cloud, it seemed possible to obtain its height in the -same manner as we measure the height of a cloud, or indeed the height of -the moon. Although we could not see the body itself, yet the part of the -heavens whence the meteors came would indicate its position. This point -we called the _radiant_; and the question was, whether the radiant was -projected by distant observers on different parts of the sky; that is, -whether it had any _parallax_. I took much pains to ascertain the truth -of this matter, by corresponding with various observers in different -parts of the United States, who had accurately noted the position of the -radiant among the fixed stars, and supposed I had obtained such -materials as would enable us to determine the parallax, at least -approximately; although such discordances existed in the evidence as -reasonably to create some distrust of its validity. Putting together, -however, the best materials I could obtain, I made the height of the -radiant above the surface of the earth _twenty-two hundred and -thirty-eight miles_. When, however, I afterwards obtained, as I -supposed, some insight into the celestial origin of the meteors, I at -once saw that the meteoric body must be much further off than this -distance; and my present impression is, that we have not the means of -determining what its height really is. We may safely place it at many -thousand miles. - -In the third place, with respect to the _force_ by which the meteors -were _drawn_ or impelled towards the earth, my first impression was, -that they fell merely by the force of _gravity_; but the velocity which, -on careful investigation by Professor Twining and others, has been -ascribed to them, is greater than can possibly result from gravity, -since a body can never acquire, by gravity alone, a velocity greater -than about seven miles per second. Some other cause, beside gravity, -must therefore act, in order to give the meteors so great an apparent -velocity. - -In the fourth place, _the meteors fell towards the earth in straight -lines, and in directions which, within considerable distances, were -nearly parallel with each other_. The courses are inferred to have been -in _straight lines_, because no others could have appeared to spectators -in different situations to have described arcs of great circles. In -order to be projected into the arc of a great circle, the line of -descent must be in a plane passing through the eye of the spectator; and -the intersection of such planes, passing through the eyes of different -spectators, must be straight lines. The lines of direction are inferred -to have been _parallel_, on account of their apparent radiation from one -point, that being the vanishing point of parallel lines. This may -appear to you a little paradoxical, to infer that lines are parallel, -because they _diverge_ from one and the same point; but it is a -well-known principle of perspective, that parallel lines, when continued -to a great distance from the eye, appear to converge towards the remoter -end. You may observe this in two long rows of trees, or of street lamps. - -[Illustration Fig. 69.] - -Some idea of the manner in which the meteors fell, and of the reason of -their apparent radiation from a common point, may be gathered from the -annexed diagram. Let A B C, Fig. 69, represent the vault of the sky, -the centre of which, D, being the place of the spectator. Let 1, 2, 3, -&c., represent parallel lines directed towards the earth. A luminous -body descending through 1' 1, coinciding with the line D E, coincident -with the axis of vision, (or the line drawn from the meteoric body to -the eye,) would appear stationary all the while at 1“, because distant -bodies always appear stationary when they are moving either directly -towards us or directly from us. A body descending through 2 2, would -seem to describe the short arc 2' 2', appearing to move on the concave -of the sky between the lines drawn from the eye to the two extremities -of its line of motion; and, for a similar reason, a body descending -through 3 3, would appear to describe the larger arc 3' 3'. Hence, those -meteors which fell nearer to the axis of vision, would describe shorter -arcs, and move slower, while those which were further from the axis and -nearer the horizon would appear to describe longer arcs, and to move -with greater velocity; the meteors would all seem to radiate from a -common centre, namely, the point where the axis of vision met the -celestial vault; and if any meteor chanced to move directly in the line -of vision, it would be seen as a luminous body, stationary, for a few -seconds, at the centre of radiation. To see how exactly the facts, as -observed, corresponded to these inferences, derived from the supposition -that the meteors moved in _parallel lines_, take the following -description, as given immediately after the occurrence, by Professor -Twining. "In the vicinity of the radiant point, a few star-like bodies -were observed, possessing very little motion, and leaving very little -length of trace. Further off, the motions were more rapid and the traces -longer; and most rapid of all, and longest in their traces, were those -which originated but a few degrees above the horizon, and descended down -to it." - -In the fifth place, had the meteors come from a point twenty-two hundred -and thirty-eight miles from the earth, and derived their apparent -velocity from gravity alone, then it would be found, by a very easy -calculation, that their actual velocity was about four miles per second; -but, as already intimated, the velocity observed was estimated much -greater than could be accounted for on these principles; not less, -indeed, than fourteen miles per second, and, in some instances, much -greater even than this. The motion of the earth in its orbit is about -nineteen miles per second; and the most reasonable supposition we can -make, at present, to account for the great velocity of the meteors, is, -that they derived a relative motion from the earth's passing rapidly by -them,--a supposition which is countenanced by the fact that they -generally tended _westward_ contrary to the earth's motion in its orbit. - -In the sixth place, _the meteors consisted of combustible matter, and -took fire, and were consumed, in traversing the atmosphere_. That these -bodies underwent combustion, we had the direct evidence of the senses, -inasmuch as we saw them burn. That they took fire in the _atmosphere_, -was inferred from the fact that they were not luminous in their original -situations in space, otherwise, we should have seen the body from which -they emanated; and had they been luminous before reaching the -atmosphere, we should have seen them for a much longer period than they -were in sight, as they must have occupied a considerable time in -descending towards the earth from so great a distance, even at the rapid -rate at which they travelled. The immediate consequence of the -prodigious velocity with which the meteors fell into the atmosphere must -be a powerful condensation of the air before them, retarding their -progress, and producing, by a sudden compression of the air, a great -evolution of heat. There is a little instrument called the _air-match_, -consisting of a piston and cylinder, like a syringe, in which we strike -a light by suddenly forcing down the piston upon the air below. As the -air cannot escape, it is suddenly compressed, and gives a spark -sufficient to light a piece of tinder at the bottom of the cylinder. -Indeed, it is a well-known fact, that, whenever air is suddenly and -forcibly compressed, heat is elicited; and, if by such a compression as -may be given by the hand in the air-match, heat is evolved sufficient to -fire tinder, what must be the heat evolved by the motion of a large body -in the atmosphere, with a velocity so immense. It is common to resort to -electricity as the agent which produces the heat and light of shooting -stars; but even were electricity competent to produce this effect, its -presence, in the case before us, is not proved; and its agency is -unnecessary, since so swift a motion of the meteors themselves, suddenly -condensing the air before them, is both a known and adequate cause of an -intense light and heat. A combustible body falling into the atmosphere, -under such circumstances, would become speedily ignited, but could not -burn freely, until it became enveloped in air of greater density; but, -on reaching the lower portions of the atmosphere, it would burn with -great rapidity. - -In the seventh place, _some of the larger meteors must have been bodies -of great size_. According to the testimony of various individuals, in -different parts of the United States, a few fire-balls appeared as large -as the full moon. Dr. Smith, (then of North Carolina, but since -surgeon-general of the Texian army,) who was travelling all night on -professional business, describes one which he saw in the following -terms: "In size it appeared somewhat larger than the full moon rising. I -was startled by the splendid light in which the surrounding scene was -exhibited, rendering even small objects quite visible; but I heard no -noise, although every sense seemed to be suddenly aroused, in sympathy -with the violent impression on the sight." This description implies not -only that the body was very large, but that it was at a considerable -distance from the spectator. Its actual size will depend upon the -distance; for, as it appeared under the same angle as the moon, its -diameter will bear the same ratio to the moon's, as its distance bears -to the moon's distance. We could, therefore, easily ascertain how large -it was, provided we could find how far it was from the observer. If it -was one hundred and ten miles distant, its diameter was one mile, and in -the same proportion for a greater or less distance; and, if only at the -distance of one mile, its diameter was forty-eight feet. For a moderate -estimate, we will suppose it to have been twenty-two miles off; then its -diameter was eleven hundred and fifty-six feet. Upon every view of the -case, therefore, it must be admitted, that these were bodies of great -size, compared with other objects which traverse the atmosphere. We may -further infer the great magnitude of some of the meteors, from the -dimensions of the trains, or clouds, which resulted from their -destruction. These often extended over several degrees, and at length -were borne along in the direction of the wind, exactly in the manner of -a small cloud. - -It was an interesting problem to ascertain, if possible, the height -above the earth at which these fire-balls exploded, or resolved -themselves into a cloud of smoke. This would be an easy task, provided -we could be certain that two or more distant observers could be sure -that both saw the same meteor; for as each would refer the place of -explosion, or the position of the cloud that resulted from it, to a -different point of the sky, a parallax would thus be obtained, from -which the height might be determined. The large meteor which is -mentioned in my account of the shower, (see page 348,) as having -exploded near the star Capella, was so peculiar in its appearance, and -in the form and motions of the small cloud which resulted from its -combustion, that it was noticed and distinguished by a number of -observers in distant parts of the country. All described the meteor as -exhibiting, substantially, the same peculiarities of appearance; all -agreed very nearly in the time of its occurrence; and, on drawing lines, -to represent the course and direction of the place where it exploded to -the view of each of the observers respectively, these lines met in -nearly one and the same point, and that was over the place where it was -seen in the zenith. Little doubt, therefore, could remain, that all saw -the same body; and on ascertaining, from a comparison of their -observations, the amount of parallax, and thence deducing its height,--a -task which was ably executed by Professor Twining,--the following -results were obtained: that this meteor, and probably all the meteors, -entered the atmosphere with a velocity not less, but perhaps greater, -than _fourteen miles in a second_; that they became luminous many miles -from the earth,--in this case, over _eighty miles_; and became extinct -high above the surface,--in this case, nearly _thirty miles_. - -In the eighth place, _the meteors were combustible bodies, and were -constituted of light and transparent materials_. The fact that they -burned is sufficient proof that they belonged to the class of -_combustible_ bodies; and they must have been composed of very _light -materials_, otherwise their momentum would have been sufficient to -enable them to make their way through the atmosphere to the surface of -the earth. To compare great things with small, we may liken them to a -wad discharged from a piece of artillery, its velocity being supposed to -be increased (as it may be) to such a degree, that it shall take fire as -it moves through the air. Although it would force its way to a great -distance from the gun, yet, if not consumed too soon, it would at length -be stopped by the resistance of the air. Although it is supposed that -the meteors did in fact slightly disturb the atmospheric equilibrium, -yet, had they been constituted of dense matter, like meteoric stones, -they would doubtless have disturbed it vastly more. Their own momentum -would be lost only as it was imparted to the air; and had such a number -of bodies,--some of them quite large, perhaps a mile in diameter, and -entering the atmosphere with a velocity more than forty times the -greatest velocity of a cannon ball,--had they been composed of dense, -ponderous matter, we should have had appalling evidence of this fact, -not only in the violent winds which they would have produced in the -atmosphere, but in the calamities they would have occasioned on the -surface of the earth. The meteors were _transparent_ bodies; otherwise, -we cannot conceive why the body from which they emanated was not -distinctly visible, at least by reflecting the light of the sun. If only -the meteors which were known to fall towards the earth had been -collected and restored to their original connexion in space, they would -have composed a body of great extent; and we cannot imagine a body of -such dimensions, under such circumstances, which would not be visible, -unless formed of highly transparent materials. By these unavoidable -inferences respecting the kind of matter of which the meteors were -composed, we are unexpectedly led to recognise a body bearing, in its -constitution, a strong analogy to comets, which are also composed of -exceedingly light and transparent, and, as there is much reason to -believe, of combustible matter. - -We now arrive at the final inquiry, _what relations did the body which -afforded the meteoric shower sustain to the earth_? Was it of the nature -of a satellite, or terrestrial comet, that revolves around the earth as -its centre of motion? Was it a collection of nebulous, or cometary -matter, which the earth encountered in its annual progress? or was it a -comet, which chanced at this time to be pursuing its path along with the -earth, around their common centre of motion? It could not have been of -the nature of a satellite to the earth, (or one of those bodies which -are held by some to afford the meteoric stones, which sometimes fall to -the earth from huge meteors that traverse the atmosphere,) because it -remained so long stationary with respect to the earth. A body so near -the earth as meteors of this class are known to be, could not remain -apparently stationary among the stars for a moment; whereas the body in -question occupied the same position, with hardly any perceptible -variation, for at least two hours. Nor can we suppose that the earth, in -its annual progress, came into the vicinity of a _nebula_, which was -either stationary, or wandering lawless through space. Such a collection -of matter could not remain stationary within the solar system, in an -insulated state, for, if not prevented by a motion of its own, or by the -attraction of some nearer body, it would have proceeded directly towards -the sun; and had it been in motion in any other direction than that in -which the earth was moving, it would soon have been separated from the -earth; since, during the eight hours, while the meteoric shower was -visible, the earth moved in its orbit through the space of nearly five -hundred and fifty thousand miles. - -The foregoing considerations conduct us to the following train of -reasoning. First, if all the meteors which fell on the morning of -November 13, 1833, had been collected and restored to their original -connexion in space, they would of themselves have constituted a nebulous -body of great extent; but we have reason to suppose that they, in fact, -composed but a small part of the mass from which they emanated, since, -after the loss of so much matter as proceeded from it in the great -meteoric shower of 1799, and in the several repetitions of it that -preceded the year 1833, it was still capable of affording so copious a -shower on that year; and similar showers, more limited in extent, were -repeated for at least five years afterwards. We are therefore to regard -the part that descended only as _the extreme portions of a body or -collection of meteors, of unknown extent, existing in the planetary -spaces_. - -Secondly, since the earth fell in with this body in the same part of its -orbit, for several years in succession, it must either have remained -there while the earth was performing its whole revolution around the -sun, or it must itself have had a revolution, as well as the earth. But -I have already shown that it could not have remained stationary in that -part of space; therefore, _it must have had a revolution around the -sun_. - -Thirdly, its period of revolution must have either been greater than the -earth's, equal to it, or less. It could not have been greater, for then -the two bodies could not have been together again at the end of the -year, since the meteoric body would not have completed its revolution in -a year. Its period might obviously be the same as the earth's, for then -they might easily come together again after one revolution of each; -although their orbits might differ so much in shape as to prevent their -being together at any intermediate point. But the period of the body -might also be less than that of the earth, provided it were some -_aliquot part of a year_, so as to revolve just twice, or three times, -for example, while the earth revolves once. Let us suppose that the -period is one third of a year. Then, since we have given the periodic -times of the two bodies, and the major axis of the orbit of one of them, -namely, of the earth, we can, by Kepler's law, find the major axis of -the other orbit; for the square of the earth's periodic time 1^2 is to -the square of the body's time (1/3)^2 as the cube of the major axis of -the earth's orbit is to the cube of the major axis of the orbit in -question. Now, the three first terms of this proportion are known, and -consequently, it is only to solve a case in the simple rule of three, to -find the term required. On making the calculation, it is found, that the -supposition of a periodic time of only one third of a year gives an -orbit of insufficient length; the whole major axis would not reach from -the sun to the earth; and consequently, a body revolving in it could -never come near to the earth. On making trial of six months, we obtain -an orbit which satisfies the conditions, being such as is represented by -the diagram on page 362, Fig. 69', where the outer circle denotes the -earth's orbit, the sun being in the centre, and the inner ellipse -denotes the path of the meteoric body. The two bodies are together at -the top of the figure, being the place of the meteoric body's aphelion -on the thirteenth of November, and the figures 10, 20, &c., denote the -relative positions of the earth and the body for every ten days, for a -period of six months, in which time the body would have returned to its -aphelion. - -[Illustration Fig. 69'.] - -Such would be the relation of the body that affords the meteoric shower -of November, provided its revolution is accomplished in six months; but -it is still somewhat uncertain whether the period be half a year or a -year; it must be one or the other. - -If we inquire, now, why the meteors always appear to radiate from a -point in the constellation Leo, recollecting that this is the point to -which the body is projected among the stars, the answer is, that this -is the very point towards which the earth is moving in her orbit at that -time; so that if, as we have proved, the earth passed through or near a -nebulous body on the thirteenth of November, that body must necessarily -have been projected into the constellation Leo, else it could not have -lain directly in her path. I consider it therefore as established by -satisfactory proof, that the meteors of November thirteenth emanate from -a nebulous or cometary body, revolving around the sun, and coming so -near the earth at that time that the earth passes through its _skirts_, -or extreme portions, and thus attracts to itself some portions of its -matter, giving to the meteors a greater velocity than could be imparted -by gravity alone, in consequence of passing rapidly by them. - -All these conclusions were made out by a process of reasoning strictly -inductive, without supposing that the meteoric body itself had ever been -seen. But there are some reasons for believing that we do actually see -it, and that it is no other than that mysterious appearance long known -under the name of the _zodiacal light_. This is a faint light, which at -certain seasons of the year appears in the west after evening twilight, -and at certain other seasons appears in the east before the dawn, -following or preceding the track of the sun in a triangular figure, with -its broad base next to the sun, and its vertex reaching to a greater or -less distance, sometimes more than ninety degrees from that luminary. -You may obtain a good view of it in February or March, in the west, or -in October, in the morning sky. The various changes which this light -undergoes at different seasons of the year are such as to render it -probable, to my mind, that this is the very body which affords the -meteoric showers; its extremity coming, in November, within the sphere -of the earth's attraction. But, as the arguments for the existence of a -body in the planetary regions, which affords these showers, were drawn -without the least reference to the zodiacal light, and are good, should -it finally be proved that this light has no connexion with them, I will -not occupy your attention with the discussion of this point, to the -exclusion of topics which will probably interest you more. - -It is perhaps most probable, that the meteoric showers of August and -December emanate from the same body. I know of nothing repugnant to this -conclusion, although it has not yet been distinctly made out. Had the -periods of the earth and of the meteoric body been so adjusted to each -other that the latter was contained an exact even number of times in the -former; that is, had it been _exactly_ either a year or half a year; -then we might expect a similar recurrence of the meteoric shower every -year; but only a slight variation in such a proportion between the two -periods would occasion the repetition of the shower for a few years in -succession, and then an intermission of them, for an unknown length of -time, until the two bodies were brought into the same relative situation -as before. Disturbances, also, occasioned by the action of Venus and -Mercury, might wholly subvert this numerical relation, and increase or -diminish the probability of a repetition of the phenomenon. Accordingly, -from the year 1830, when the meteoric shower of November was first -observed, until 1833, there was a regular increase of the exhibition; in -1833, it came to its maximum; and after that time it was repeated upon a -constantly diminishing scale, until 1838, since which time it has not -been observed. Perhaps ages may roll away before the world will be again -surprised and delighted with a display of celestial fire-works equal to -that of the morning of November 13, 1833. - - - - -LETTER XXVIII. - -FIXED STARS. - - ----"O, majestic Night! - Nature's great ancestor! Day's elder born, - And fated to survive the transient sun! - By mortals and immortals seen with awe! - A starry crown thy raven brow adorns, - An azure zone thy waist; clouds, in heaven's loom - Wrought, through varieties of shape and shade, - In ample folds of drapery divine, - Thy flowing mantle form; and heaven throughout - Voluminously pour thy pompous train."--_Young._ - - -SINCE the solar system is but one among a myriad of worlds which -astronomy unfolds, it may appear to you that I have dwelt too long on so -diminutive a part of creation, and reserved too little space for the -other systems of the universe. But however humble a province our sun and -planets compose, in the vast empire of Jehovah, yet it is that which -most concerns us; and it is by the study of the laws by which this part -of creation is governed, that we learn the secrets of the skies. - -Until recently, the observation and study of the phenomena of the solar -system almost exclusively occupied the labors of astronomers. But Sir -William Herschel gave his chief attention to the _sidereal heavens_, and -opened new and wonderful fields of discovery, as well as of speculation. -The same subject, has been prosecuted with similar zeal and success by -his son, Sir John Herschel, and Sir James South, in England, and by -Professor Struve, of Dorpat, until more has been actually achieved than -preceding astronomers had ventured to conjecture. A limited sketch of -these wonderful discoveries is all that I propose to offer you. - -The fixed stars are so called, because, to common observation, they -always maintain the same situations with respect to one another. The -stars are classed by their apparent _magnitudes_. The whole number of -magnitudes recorded are _sixteen_, of which the first six only are -visible to the naked eye; the rest are _telescopic stars_. These -magnitudes are not determined by any very definite scale, but are merely -ranked according to their relative degrees of brightness, and this is -left in a great measure to the decision of the eye alone. The brightest -stars, to the number of fifteen or twenty, are considered as stars of -the first magnitude; the fifty or sixty next brightest, of the second -magnitude; the next two hundred, of the third magnitude; and thus the -number of each class increases rapidly, as we descend the scale, so that -no less than fifteen or twenty thousand are included within the first -seven magnitudes. - -The stars have been grouped in _constellations_ from the most remote -antiquity; a few, as Orion, Bootes, and Ursa Major, are mentioned in the -most ancient writings, under the same names as they bear at present. The -names of the constellations are sometimes founded on a supposed -resemblance to the objects to which they belong; as the Swan and the -Scorpion were evidently so denominated from their likeness to those -animals; but in most cases, it is impossible for us to find any reason -for designating a constellation by the figure of the animal or hero -which is employed to represent it. These representations were probably -once blended with the fables of pagan mythology. The same figures, -absurd as they appear, are still retained for the convenience of -reference; since it is easy to find any particular star, by specifying -the part of the figure to which it belongs; as when we say, a star is in -the neck of Taurus, in the knee of Hercules, or in the tail of the Great -Bear. This method furnishes a general clue to its position; but the -stars belonging to any constellation are distinguished according to -their apparent magnitudes, as follows: First, by the Greek letters, -Alpha, Beta, Gamma, &c. Thus, _Alpha Orionis_ denotes the largest star -in Orion; _Beta Andromedę_ the second star in Andromeda; and _Gamma -Leonis_, the third brightest star in the Lion. When the number of the -Greek letters is insufficient to include all the stars in a -constellation, recourse is had to the letters of the Roman alphabet, a, -b, c, &c.; and in all cases where these are exhausted the final resort -is to numbers. This is evidently necessary, since the largest -constellations contain many hundreds or even thousands of stars. -_Catalogues_ of particular stars have also been published, by different -astronomers, each author numbering the individual stars embraced in his -list according to the places they respectively occupy in the catalogue. -These references to particular catalogues are sometimes entered on large -celestial globes. Thus we meet with a star marked 84 H., meaning that -this is its number in Herschel's catalogue; or 140 M., denoting the -place the star occupies in the catalogue of Mayer. - -The earliest catalogue of the stars was made by Hipparchus, of the -Alexandrian school, about one hundred and forty years before the -Christian era. A new star appearing in the firmament, he was induced to -count the stars, and to record their positions, in order that posterity -might be able to judge of the permanency of the constellations. His -catalogue contains all that were conspicuous to the naked eye in the -latitude of Alexandria, being one thousand and twenty-two. Most persons, -unacquainted with the actual number of the stars which compose the -visible firmament, would suppose it to be much greater than this; but it -is found that the catalogue of Hipparchus embraces nearly all that can -now be seen in the same latitude; and that on the equator, where the -spectator has both the northern and southern hemispheres in view, the -number of stars that can be counted does not exceed three thousand. A -careless view of the firmament in a clear night gives us the impression -of an infinite number of stars; but when we begin to count them, they -appear much more sparsely distributed than we supposed, and large -portions of the sky appear almost destitute of stars. - -By the aid of the telescope, new fields of stars present themselves, of -boundless extent; the number continually augmenting, as the powers of -the telescope are increased. Lalande, in his 'Histoire Celeste,' has -registered the positions of no less than fifty thousand; and the whole -number visible in the largest telescopes amounts to many millions. - -When you look at the firmament on a clear Autumnal or Winter evening, it -appears so thickly studded with stars, that you would perhaps imagine -that the task of learning even the brightest of them would be almost -hopeless. Let me assure you, this is all a mistake. On the contrary, it -is a very easy task to become acquainted with the names and positions of -the stars of the first magnitude, and of the leading constellations. If -you will give a few evenings to the study, you will be surprised to -find, both how rapidly you can form these new acquaintances, and how -deeply you will become interested in them. I would advise you, at first, -to obtain, for an evening or two, the assistance of some friend who is -familiar with the stars, just to point out a few of the most conspicuous -constellations. This will put you on the track, and you will afterwards -experience no difficulty in finding all the constellations and stars -that are particularly worth knowing; especially if you have before you a -map of the stars, or, what is much better, a celestial globe. It is a -pleasant evening recreation for a small company of young astronomers to -go out together, and learn one or two constellations every favorable -evening, until the whole are mastered. If you have a celestial globe, -_rectify_ it for the evening; that is, place it in such a position, that -the constellations shall be seen on it in the same position with respect -to the horizon, that they have at that moment in the sky itself. To do -this, I first elevate the north pole until the number of degrees on the -brass meridian from the pole to the horizon corresponds to my latitude, -(forty-one degrees and eighteen minutes.) I then find the sun's place in -the ecliptic, by looking for the day of the month on the broad horizon, -and against it noting the corresponding sign and degree. I now find the -same sign and degree on the ecliptic itself, and bring that point to the -brass meridian. As that will be the position of the sun at noon, I set -the hour-index at twelve, and then turn the globe westward, until the -index points to the given hour of the evening. If I now inspect the -figures of the constellations, and then look upward at the firmament, I -shall see that the latter are spread over the sky in the same manner as -the pictures of them are painted on the globe. I will point out a few -marks by which the leading constellations may be recognised; this will -aid you in finding them, and you can afterwards learn the individual -stars of a constellation, to any extent you please, by means of the -globes or maps. Let us begin with the _Constellations of the Zodiac_, -which, succeeding each other, as they do, in a known order, are most -easily found. - -_Aries_ (_the Ram_) is a small constellation, known by two bright stars -which form his head, _Alpha_ and _Beta Arietis_. These two stars are -about four degrees apart; and directly south of Beta, at the distance of -one degree, is a smaller star, _Gamma Arietis_. It has been already -intimated that the Vernal equinox probably was near the head of Aries, -when the signs of the zodiac received their present names. - -_Taurus_ (_the Bull_) will be readily found by the seven stars, or -_Pleiades_, which lie in his neck. The largest star in Taurus is -_Aldebaran_, in the Bull's eye, a star of the first magnitude, of a -reddish color, somewhat resembling the planet Mars. Aldebaran and four -other stars, close together in the face of Taurus, compose the _Hyades_. - -_Gemini_ (_the Twins_) is known by two very bright stars, _Castor and -Pollux_, five degrees asunder. Castor (the northern) is of the first, -and Pollux of the second, magnitude. - -_Cancer_ (_the Crab_.) There are no large stars in this constellation, -and it is regarded as less remarkable than any other in the zodiac. It -contains, however, an interesting group of small stars, called -_Pręsepe_, or the nebula of Cancer, which resembles a comet, and is -often mistaken for one, by persons unacquainted with the stars. With a -telescope of very moderate powers this nebula is converted into a -beautiful assemblage of exceedingly bright stars. - -_Leo_ (_the Lion_) is a very large constellation, and has many -interesting members. _Regulus_ (_Alpha Leonis_) is a star of the first -magnitude, which lies directly in the ecliptic, and is much used in -astronomical observations. North of Regulus, lies a semicircle of bright -stars, forming a _sickle_, of which Regulus is the handle. _Denebola_, a -star of the second magnitude, is in the Lion's tail, twenty-five degrees -northeast of Regulus. - -_Virgo_ (_the Virgin_) extends a considerable way from west to east, but -contains only a few bright stars. _Spica_, however, is a star of the -first magnitude, and lies a little east of the place of the Autumnal -equinox. Eighteen degrees eastward of Denebola, and twenty degrees north -of Spica, is _Vindemiatrix_, in the arm of Virgo, a star of the third -magnitude. - -_Libra_ (_the Balance_) is distinguished by three large stars, of which -the two brightest constitute the beam of the balance, and the smallest -forms the top or handle. - -_Scorpio_ (_the Scorpion_) is one of the finest of the constellations. -His head is formed of five bright stars, arranged in the arc of a -circle, which is crossed in the centre by the ecliptic nearly at right -angles, near the brightest of the five, _Beta Scorpionis_. Nine degrees -southeast of this is a remarkable star of the first magnitude, of a -reddish color, called _Cor Scorpionis_, or _Antares_. South of this, a -succession of bright stars sweep round towards the east, terminating in -several small stars, forming the tail of the Scorpion. - -_Sagittarius_ (_the Archer_.) Northeast of the tail of the Scorpion are -three stars in the arc of a circle, which constitute the _bow_ of the -Archer, the central star being the brightest, directly west of which is -a bright star which forms the _arrow_. - -_Capricornus_ (_the Goat_) lies northeast of Sagittarius, and is known -by two bright stars, three degrees apart, which form the head. - -_Aquarius_ (_the Water-Bearer_) is recognised by two stars in a line -with _Alpha Capricorni_, forming the shoulders of the figure. These two -stars are ten degrees apart; and three degrees southeast is a third -star, which, together with the other two, make an acute triangle, of -which the westernmost is the vertex. - -_Pisces_ (_the Fishes_) lie between Aquarius and Aries. They are not -distinguished by any large stars, but are connected by a series of small -stars, that form a crooked line between them. _Piscis Australia_, the -Southern Fish, lies directly below Aquarius, and is known by a single -bright star far in the south, having a declination of thirty degrees. -The name of this star is _Fomalhaut_, and it is much used in -astronomical measurements. - -The constellations of the zodiac, being first well learned, so as to be -readily recognised, will facilitate the learning of others that lie -north and south of them. Let us, therefore, next review the principal -_Northern Constellations_, beginning north of Aries, and proceeding from -west to east. - -_Andromeda_ is characterized by three stars of the second magnitude, -situated in a straight line, extending from west to east. The middle -star is about seventeen degrees north of Beta Arietis. It is in the -girdle of Andromeda, and is named _Mirach_. The other two lie at about -equal distances, fourteen degrees west and east of Mirach. The western -star, in the head of Andromeda, lies in the equinoctial colure. The -eastern star, _Alamak_, is situated in the foot. - -_Perseus_ lies directly north of the Pleiades, and contains several -bright stars. About eighteen degrees from the Pleiades is _Algol_, a -star of the second magnitude, in the head of Medusa, which forms a part -of the figure; and nine degrees northeast of Algol is _Algenib_, of the -same magnitude, in the back of Perseus. Between Algenib and the Pleiades -are three bright stars, at nearly equal intervals, which compose the -right leg of Perseus. - -_Auriga_ (_the Wagoner_) lies directly east of Perseus, and extends -nearly parallel to that constellation, from north to south. _Capella_, a -very white and beautiful star of the first magnitude, distinguishes this -constellation. The feet of Auriga are near the Bull's horns. - -The _Lynx_ comes next, but presents nothing particularly interesting, -containing no stars above the fourth magnitude. - -_Leo Minor_ consists of a collection of small stars north of the sickle -in Leo, and south of the Great Bear. Its largest star is only of the -third magnitude. - -_Coma Berenices_ is a cluster of small stars, north of Denebola, in the -tail of the Lion, and of the head of Virgo. About twelve degrees -directly north of Berenice's hair, is a single bright star, called _Cor -Caroli_, or Charles's Heart. - -_Bootes_, which comes next, is easily found by means of _Arcturus_, a -star of the first magnitude, of a reddish color, which is situated near -the knee of the figure. Arcturus is accompanied by three small stars, -forming a triangle a little to the southwest. Two bright stars, _Gamma_ -and _Delta Bootis_, form the shoulders, and _Beta_, of the third -magnitude, is in the head, of the figure. - -_Corona Borealis_, (_the Crown_,) which is situated east of Bootes, is -very easily recognised, composed as it is of a semicircle of bright -stars. In the centre of the bright crown is a star of the second -magnitude, called _Gemma_: the remaining stars are all much smaller. - -_Hercules_, lying between the Crown on the west and the Lyre on the -east, is very thickly set with stars, most of which are quite small. -This constellation covers a great extent of the sky, especially from -north to south, the head terminating within fifteen degrees of the -equator, and marked by a star of the third magnitude, called _Ras -Algethi_, which is the largest in the constellation. - -_Ophiucus_ is situated directly south of Hercules, extending some -distance on both sides of the equator, the feet resting on the Scorpion. -The head terminates near the head of Hercules, and, like that, is marked -by a bright star within five degrees of _Alpha Herculis_ Ophiucus is -represented as holding in his hands the _Serpent_, the head of which, -consisting of three bright stars, is situated a little south of the -Crown. The folds of the serpent will be easily followed by a succession -of bright stars, which extend a great way to the east. - -_Aquila_ (_the Eagle_) is conspicuous for three bright stars in its -neck, of which the central one, _Altair_, is a very brilliant white star -of the first magnitude. _Antinous_ lies directly south of the Eagle, and -north of the head of Capricornus. - -_Delphinus_ (_the Dolphin_) is a small but beautiful constellation, a -few degrees east of the Eagle, and is characterized by four bright stars -near to one another, forming a small rhombic square. Another star of the -same magnitude, five degrees south, makes the tail. - -_Pegasus_ lies between Aquarius on the southwest and Andromeda on the -northeast. It contains but few large stars. A very regular square of -bright stars is composed of _Alpha Andromedę_ and the three largest -stars in Pegasus; namely, _Scheat_, _Markab_, and _Algenib_. The sides -composing this square are each about fifteen degrees. Algenib is -situated in the equinoctial colure. - -We may now review the _Constellations which surround the north pole_, -within the circle of perpetual apparition. - -_Ursa Minor_ (_the Little Bear_) lies nearest the pole. The pole-star, -_Polaris_, is in the extremity of the tail, and is of the third -magnitude. Three stars in a straight line, four degrees or five degrees -apart, commencing with the pole-star, lead to a trapezium of four stars, -and the whole seven form together a _dipper_,--the trapezium being the -body and the three stars the handle. - -_Ursa Major_ (_the Great Bear_) is situated between the pole and the -Lesser Lion, and is usually recognised by the figure of a larger and -more perfect dipper which constitutes the hinder part of the animal. -This has also seven stars, four in the body of the Dipper and three in -the handle. All these are stars of much celebrity. The two in the -western side of the Dipper, Alpha and Beta, are called _Pointers_, on -account of their always being in a right line with the pole-star, and -therefore affording an easy mode of finding that. The first star in the -tail, next the body, is named _Alioth_, and the second, _Mizar_. The -head of the Great Bear lies far to the westward of the Pointers, and is -composed of numerous small stars; and the feet are severally composed of -two small stars very near to each other. - -_Draco_ (_the Dragon_) winds round between the Great and the Little -Bear; and, commencing with the tail, between the Pointers and the -pole-star, it is easily traced by a succession of bright stars extending -from west to east. Passing under Ursa Minor, it returns westward, and -terminates in a triangle which forms the head of Draco, near the feet of -Hercules, northwest of Lyra. _Cepheus_ lies eastward of the breast of -the Dragon, but has no stars above the third magnitude. - -_Cassiopeia_ is known by the figure of a _chair_, composed of four stars -which form the legs, and two which form the back. This constellation -lies between Perseus and Cepheus, in the Milky Way. - -_Cygnus_ (_the Swan_) is situated also in the Milky Way, some distance -southwest of Cassiopeia, towards the Eagle. Three bright stars, which -lie along the Milky Way, form the body and neck of the Swan, and two -others, in a line with the middle one of the three, one above and one -below, constitute the wings. This constellation is among the few that -exhibit some resemblance to the animals whose names they bear. - -_Lyra_ (_the Lyre_) is directly west of the Swan, and is easily -distinguished by a beautiful white star of the first magnitude, _Alpha -Lyrę_. - -The _Southern Constellations_ are comparatively few in number. I shall -notice only the Whale, Orion, the Greater and Lesser Dog, Hydra, and the -Crow. - -_Cetus_ (_the Whale_) is distinguished rather for its extent than its -brilliancy, reaching as it does through forty degrees of longitude, -while none of its stars, except one, are above the third magnitude. -_Menkar_ (_Alpha Ceti_) in the mouth, is a star of the second -magnitude; and several other bright stars, directly south of Aries, make -the head and neck of the Whale. _Mira_, (_Omicron Ceti_,) in the neck of -the Whale, is a variable star. - -_Orion_ is one of the largest and most beautiful of the constellations, -lying southeast of Taurus. A cluster of small stars forms the head; two -large stars, _Betalgeus_ of the first and _Bellatrix_ of the second -magnitude, make the shoulders; three more bright stars compose the -buckler, and three the sword; and _Rigel_, another star of the first -magnitude, makes one of the feet. In this constellation there are -seventy stars plainly visible to the naked eye, including two of the -first magnitude, four of the second, and three of the third. - -_Canis Major_ lies southeast of Orion, and is distinguished chiefly by -its containing the largest of the fixed stars, _Sirius_. - -_Canis Minor_, a little north of the equator, between Canis Major and -Gemini, is a small constellation, consisting chiefly of two stars, of -which, _Procyon_ is of the first magnitude. - -_Hydra_ has its head near Procyon, consisting of a number of stars of -ordinary brightness. About fifteen degrees southeast of the head is a -star of the second magnitude, forming the heart, (_Cor Hydrę_;) and -eastward of this is a long succession of stars of the fourth and fifth -magnitudes, composing the body and tail, and reaching a few degrees -south of Spica Virginis. - -_Corvus_ (_the Crow_) is represented as standing on the tail of Hydra. -It consists of small stars, only three of which are as large as the -third magnitude. - -In assigning the places of individual stars, I have not aimed at great -precision; but such a knowledge as you will acquire of the -constellations and larger stars, by nothing more even than you can -obtain from the foregoing sketch, will not only add greatly to the -interest with which you will ever afterwards look at the starry heavens, -but it will enable you to locate any phenomenon that may present itself -in the nocturnal sky, and to understand the position of any object that -may be described, by assigning its true place among the stars; although -I hope you will go much further than this mere outline, in cultivating -an actual acquaintance with the stars. Leaving, now, these great -divisions of the bodies of the firmament, let us ascend to the next -order of stars, composing CLUSTERS. - -In various parts of the nocturnal heavens are seen large groups which, -either by the naked eye, or by the aid of the smallest telescope, are -perceived to consist of a great number of small stars. Such are the -Pleiades, Coma Berenices, and Pręsepe, or the Bee-hive, in Cancer. The -_Pleiades_, or Seven Stars, as they are called, in the neck of Taurus, -is the most conspicuous cluster. When we look _directly_ at this group, -we cannot distinguish more than six stars; but by turning the eye -_sideways_ upon it, we discover that there are many more; for it is a -remarkable fact that indirect vision is far more delicate than direct. -Thus we can see the zodiacal light or a comet's tail much more -distinctly and better defined, if we fix one eye on a part of the -heavens at some distance and turn the other eye obliquely upon the -object, than we can by looking directly towards it. Telescopes show the -Pleiades to contain fifty or sixty stars, crowded together, and -apparently insulated from the other parts of the heavens. _Coma -Berenices_ has fewer stars, but they are of a larger class than those -which compose the Pleiades. The _Bee-hive_, or Nebula of Cancer, as it -is called, is one of the finest objects of this kind for a small -telescope, being by its aid converted into a rich congeries of shining -points. The head of Orion affords an example of another cluster, though -less remarkable than those already mentioned. These clusters are -pleasing objects to the telescope; and since a common spyglass will -serve to give a distinct view of most of them, every one may have the -power of taking the view. But we pass, now, to the third order of stars, -which present themselves much more obscurely to the gaze of the -astronomer, and require large instruments for the full developement -of their wonderful organization. These are the NEBULĘ. - -[Illustration Figures 70, 71, 72, 73. CLUSTERS OF STARS AND NEBULĘ.] - -Nebulę are faint misty appearances which are dimly seen among the stars, -resembling comets, or a speck of fog. They are usually resolved by the -telescope into myriads of small stars; though in some instances, no -powers of the telescope have been found sufficient thus to resolve them. -The _Galaxy_ or Milky Way, presents a continued succession of large -nebulas. The telescope reveals to us innumerable objects of this kind. -Sir William Herschel has given catalogues of two thousand nebulę, and -has shown that the nebulous matter is distributed through the immensity -of space in quantities inconceivably great, and in separate parcels, of -all shapes and sizes, and of all degrees of brightness between a mere -milky appearance and the condensed light of a fixed star. In fact, more -distinct nebulę have been hunted out by the aid of telescopes than the -whole number of stars visible to the naked eye in a clear Winter's -night. Their appearances are extremely diversified. In many of them we -can easily distinguish the individual stars; in those apparently more -remote, the interval between the stars diminishes, until it becomes -quite imperceptible; and in their faintest aspect they dwindle to points -so minute, as to be appropriately denominated _star-dust_. Beyond this, -no stars are distinctly visible, but only streaks or patches of milky -light. The diagram facing page 379 represents a magnificent nebula in -the Galaxy. In objects so distant as the fixed stars, any apparent -interval must denote an immense space; and just imagine yourself -situated any where within the grand assemblage of stars, and a firmament -would expand itself over your head like that of our evening sky, only a -thousand times more rich and splendid. - -Many of the nebulę exhibit a tendency towards a globular form, and -indicate a rapid condensation towards the centre. This characteristic is -exhibited in the forms represented in Figs. 70 and 71. We have here two -specimens of nebulę of the nearer class, where the stars are easily -discriminated. In Figs. 72 and 73 we have examples of two others of the -remoter kind, one of which is of the variety called _star-dust_. These -wonderful objects, however, are not confined to the spherical form, but -exhibit great varieties of figure. Sometimes they appear as ovals; -sometimes they are shaped like a fan; and the unresolvable kind often -affect the most fantastic forms. The opposite diagram, Fig. 74, as well -as the preceding, affords a specimen of these varieties, as given in -Professor Nichols's 'Architecture of the Heavens,' where they are -faithfully copied from the papers of Herschel, in the 'Philosophical -Transactions.' - -[Illustration Figure 74. VARIOUS FORMS OF NEBULĘ.] - -Sir John Herschel has recently returned from a residence of five years -at the Cape of Good Hope, with the express view of exploring the hidden -treasures of the southern hemisphere. The kinds of nebulę are in general -similar to those of the northern hemisphere, and the forms are equally -various and singular. The _Magellan Clouds_, two remarkable objects seen -among the stars of that hemisphere, and celebrated among navigators, -appeared to the great telescope of Herschel (as we are informed by -Professor Nichols) no longer as simple milky spots, or permanent light -flocculi of cloud, as they appear to the unassisted eye, but shone with -inconceivable splendor. The _Nubecula Major_, as the larger object is -called, is a congeries of clusters of stars, of irregular form, globular -clusters and nebulę of various magnitudes and degrees of condensation, -among which is interspersed a large portion of irresolvable nebulous -matter, which may be, and probably is, star-dust, but which the power of -the twenty-feet telescope shows only as a general illumination of the -field of view, forming a bright ground on which the other objects are -scattered. The _Nubecula Minor_ (the lesser cloud) exhibited appearances -similar, though inferior in degree. - -[Illustration Figure 75. A NEBULA IN THE MILKY WAY.] - -It is a grand idea, first conceived by Sir William Herschel, and -generally adopted by astronomers, that the whole Galaxy, or Milky Way, -is nothing else than a nebula, and appears so extended, merely because -it happens to be that particular nebula to which we belong. According to -this view, our sun, with his attendant planets and comets, constitutes -but a single star of the Galaxy, and our firmament of stars, or visible -heavens, is composed of the stars of _our_ nebula alone. An inhabitant -of any of the other nebulę would see spreading over him a firmament -equally spacious, and in some cases inconceivably more brilliant. - -It is an exalted spectacle to travel over the Galaxy in a clear night, -with a powerful telescope, with the heart full of the idea that every -star is a world. Sir William Herschel, by counting the stars in a single -field of his telescope, estimated that fifty thousand had passed under -his review in a zone two degrees in breadth, during a single hour's -observation. Notwithstanding the apparent contiguity of the stars which -crowd the Galaxy, it is certain that their mutual distances must be -inconceivably great. - -It is with some reluctance that I leave, for the present, this fairy -land of astronomy; but I must not omit, before bringing these Letters to -a conclusion, to tell you something respecting other curious and -interesting objects to be found among the stars. - -VARIABLE STARS are those which undergo a periodical change of -brightness. One of the most remarkable is the star _Mira_, in the Whale, -(_Omicron Ceti_.) It appears once in eleven months, remains at its -greatest brightness about a fortnight, being then, on some occasions, -equal to a star of the second magnitude. It then decreases about three -months, until it becomes completely invisible, and remains so about five -months, when it again becomes visible, and continues increasing during -the remaining three months of its period. - -Another very remarkable variable star is _Algol_, (_Beta Persei_.) It is -usually visible as a star of the second magnitude, and continues such -for two days and fourteen hours, when it suddenly begins to diminish in -splendor, and in about three and a half hours is reduced to the fourth -magnitude. It then begins again to increase, and in three and a half -hours more is restored to its usual brightness, going through all its -changes in less than three days. This remarkable law of variation -appears strongly to suggest the revolution round it of some opaque body, -which, when interposed between us and Algol, cuts off a large portion of -its light. "It is," says Sir J. Herschel, "an indication of a high -degree of activity in regions where, but for such evidences, we might -conclude all lifeless. Our sun requires almost nine times this period to -perform a revolution on its axis. On the other hand, the periodic time -of an opaque revolving body, sufficiently large, which would produce a -similar temporary obscuration of the sun, seen from a fixed star, would -be less than fourteen hours." The duration of these periods is extremely -various. While that of Beta Persei, above mentioned, is less than three -days, others are more than a year; and others, many years. - -TEMPORARY STARS are new stars, which have appeared suddenly in the -firmament, and, after a certain interval, as suddenly disappeared, and -returned no more. It was the appearance of a new star of this kind, one -hundred and twenty-five years before the Christian era, that prompted -Hipparchus to draw up a catalogue of the stars, the first on record. -Such, also, was the star which suddenly shone out, A.D. 389, in the -Eagle, as bright as Venus, and, after remaining three weeks, disappeared -entirely. At other periods, at distant intervals, similar phenomena have -presented themselves. Thus the appearance of a star in 1572 was so -sudden, that Tycho Brahe, returning home one day, was surprised to find -a collection of country people gazing at a star which he was sure did -not exist half an hour before. It was then as bright as Sirius, and -continued to increase until it surpassed Jupiter when brightest, and was -visible at mid-day. In a month it began to diminish; and, in three -months afterwards, it had entirely disappeared. It has been supposed by -some that, in a few instances, the same star has returned, constituting -one of the periodical or variable stars of a long period. Moreover, on a -careful reexamination of the heavens, and a comparison of catalogues, -many stars are now discovered to be missing. - -DOUBLE STARS are those which appear single to the naked eye, but are -resolved into two by the telescope; or, if not visible to the naked eye, -are seen in the telescope so close together as to be recognised as -objects of this class. Sometimes, three or more stars are found in this -near connexion, constituting triple, or multiple stars. Castor, for -example, when seen by the naked eye, appears as a single star, but in a -telescope even of moderate powers, it is resolved into two stars, of -between the third and fourth magnitudes, within five seconds of each -other. These two stars are nearly of equal size; but more commonly, one -is exceedingly small in comparison with the other, resembling a -satellite near its primary, although in distance, in light, and in other -characteristics, each has all the attributes of a star, and the -combination, therefore, cannot be that of a planet with a satellite. In -most instances, also, the distance between these objects is much less -than five seconds; and, in many cases, it is less than one second. The -extreme closeness, together with the exceeding minuteness, of most of -the double stars, requires the best telescopes united with the most -acute powers of observation. Indeed, certain of these objects are -regarded as the severest _tests_ both of the excellence of the -instruments and of the skill of the observer. The diagram on page 382, -Fig. 76, represents four double stars, as seen with appropriate -magnifiers. No. 1, exhibits Epsilon Bootis with a power of three hundred -and fifty; No. 2, Rigel, with a power of one hundred and thirty; No. 3, -the Pole-star, with a power of one hundred; and No. 4, Castor, with a -power of three hundred. - -Our knowledge of the double stars almost commenced with Sir William -Herschel, about the year 1780. At the time he began his search for them, -he was acquainted with only _four_. Within five years he discovered -nearly _seven hundred_ double stars, and during his life, he observed no -less than twenty-four hundred. In his Memoirs, published in the -Philosophical Transactions, he gave most accurate measurements of the -distances between the two stars, and of the angle which a line joining -the two formed with a circle parallel to the equator. These data would -enable him, or at least posterity, to judge whether these minute bodies -ever change their position with respect to each other. Since 1821, these -researches have been prosecuted, with great zeal and industry, by Sir -James South and Sir John Herschel, in England; while Professor Struve, -of Dorpat, with the celebrated telescope of Fraunhofer, has published, -from his own observations, a catalogue of three thousand double stars, -the determination of which involved the distinct and most minute -inspection of at least one hundred and twenty thousand stars. Sir John -Herschel, in his recent survey of the southern hemisphere, is said to -have added to the catalogue of double stars nearly three thousand more. - -[Illustration Fig. 76.] - -Two circumstances add a high degree of interest to the phenomena of -double stars: the first is, that a few of them, at least, are found to -have a revolution around each other; the second, that they are supposed -to afford the means of ascertaining the parallax of the fixed stars. But -I must defer these topics till my next Letter. - - - - -LETTER XXIX. - -FIXED STARS CONTINUED. - - "O how canst thou renounce the boundless store - Of charms that Nature to her votary yields? - The warbling woodland, the resounding shore, - The pomp of groves, and garniture of fields; - All that the genial ray of morning yields, - And all that echoes to the song of even, - All that the mountain's sheltering bosom shields, - And all the dread magnificence of heaven,-- - O how canst thou renounce, and hope to be forgiven!"--_Beattie._ - - -In 1803, Sir William Herschel first determined and announced to the -world, that there exist among the stars separate systems, composed of -two stars revolving about each other in regular orbits. These he -denominated _binary stars_, to distinguish them from other double stars -where no such motion is detected, and whose proximity to each other may -possibly arise from casual juxtaposition, or from one being in the range -of the other. Between fifty and sixty instances of changes, to a greater -or less amount, of the relative positions of double stars, are mentioned -by Sir William Herschel; and a few of them had changed their places so -much, within twenty-five years, and in such order, as to lead him to the -conclusion that they performed revolutions, one around the other, in -regular orbits. These conclusions have been fully confirmed by later -observers; so that it is now considered as fully established, that there -exist among the fixed stars binary systems, in which two stars perform -to each other the office of sun and planet, and that the periods of -revolution of more than one such pair have been ascertained with some -degree of exactness. Immersions and emersions of stars behind each other -have been observed, and real motions among them detected, rapid enough -to become sensible and measurable in very short intervals of time. The -periods of the double stars are very various, ranging, in the case of -those already ascertained, from forty-three years to one thousand. -Their orbits are very small ellipses, only a few seconds in the longest -direction, and more eccentric than those of the planets. A double star -in the Northern Crown (_Eta Coronę_) has made a complete revolution -since its first discovery, and is now far advanced in its second period; -while a star in the Lion (_Gamma Leonis_) requires twelve hundred years -to complete its circuit. - -You may not at once see the reason why these revolutions of one member -of a double star around the other, should be deemed facts of such -extraordinary interest; to you they may appear rather in the light of -astronomical curiosities. But remark, that the revolutions of the binary -stars have assured us of this most interesting fact, that _the law of -gravitation extends to the fixed stars_. Before these discoveries, we -could not decide, except by a feeble analogy, that this law transcended -the bounds of the solar system. Indeed, our belief of the fact rested -more upon our idea of unity of design in the works of the Creator, than -upon any certain proof; but the revolution of one star around another, -in obedience to forces which are proved to be similar to those which -govern the solar system, establishes the grand conclusion, that the law -of gravitation is truly the law of the material universe. "We have the -same evidence," says Sir John Herschel, "of the revolutions of the -binary stars about each other, that we have of those of Saturn and -Uranus about the sun; and the correspondence between their calculated -and observed places, in such elongated ellipses, must be admitted to -carry with it a proof of the prevalence of the Newtonian law of gravity -in their systems, of the very same nature and cogency as that of the -calculated and observed places of comets round the centre of our own -system. But it is not with the revolution of bodies of a cometary or -planetary nature round a solar centre, that we are now concerned; it is -with that of sun around sun, each, perhaps, accompanied with its train -of planets and their satellites, closely shrouded from our view by the -splendor of their respective suns, and crowded into a space, bearing -hardly a greater proportion to the enormous interval which separates -them, than the distances of the satellites of our planets from their -primaries bear to their distances from the sun itself." - -Many of the double stars are of different colors; and Sir John Herschel -is of the opinion that there exist in nature suns of different colors. -"It may," says he, "be easier suggested in words than conceived in -imagination, what variety of illumination two suns, a red and a green, -or a yellow and a blue one, must afford to a planet circulating about -either; and what charming contrasts and 'grateful vicissitudes' a red -and a green day, for instance, alternating with a white one and with -darkness, might arise from the presence or absence of one or other or -both above the horizon. Insulated stars of a red color, almost as deep -as that of blood, occur in many parts of the heavens; but no green or -blue star, of any decided hue, has ever been noticed unassociated with a -companion brighter than itself." - -Beside these revolutions of the binary stars, _some of the fixed stars -appear to have a real motion in space_. There are several _apparent_ -changes of place among the stars, arising from real changes in the -earth, which, as we are not conscious of them, we refer to the stars; -but there are other motions among the stars which cannot result from any -changes in the earth, but must arise from changes in the stars -themselves. Such motions are called the _proper motions_ of the stars. -Nearly two thousand years ago, Hipparchus and Ptolemy made the most -accurate determinations in their power of the relative situations of the -stars, and their observations have been transmitted to us in Ptolemy's -'Almagest;' from which it appears that the stars retain at least _very -nearly_ the same places now as they did at that period. Still, the more -accurate methods of modern astronomers have brought to light minute -changes in the places of certain stars, which force upon us the -conclusion, _either that our solar system causes an apparent -displacement of certain stars, by a motion of its own in space, or -that they have themselves a proper motion_. Possibly, indeed, both these -causes may operate. - -If the sun, and of course the earth which accompanies him, is actually -in motion, the fact may become manifest from the apparent approach of -the stars in the region which he is leaving, and the recession of those -which lie in the part of the heavens towards which he is travelling. -Were two groves of trees situated on a plain at some distance apart, and -we should go from one to the other, the trees before us would gradually -appear further and further asunder, while those we left behind would -appear to approach each other. Some years since, Sir William Herschel -supposed he had detected changes of this kind among two sets of stars in -opposite points of the heavens, and announced that the solar system was -in motion towards a point in the constellation Hercules; but other -astronomers have not found the changes in question such as would -correspond to this motion, or to any motion of the sun; and, while it is -a matter of general belief that the sun has a motion in space, the fact -is not considered as yet entirely proved. - -In most cases, where a proper motion in certain stars has been -suspected, its annual amount has been so small, that many years are -required to assure us, that the effect is not owing to some other cause -than a real progressive motion in the stars themselves; but in a few -instances the fact is too obvious to admit of any doubt. Thus, the two -stars, 61 Cygni, which are nearly equal, have remained constantly at the -same or nearly at the same distance of fifteen seconds, for at least -fifty years past. Mean-while, they have shifted their local situation in -the heavens four minutes twenty-three seconds, the annual proper motion -of each star being five seconds and three tenths, by which quantity this -system is every year carried along in some unknown path, by a motion -which for many centuries must be regarded as uniform and rectilinear. A -greater proportion of the double stars than of any other indicate proper -motions, especially the binary stars, or those which have a revolution -around each other. Among stars not double, and no way differing from the -rest in any other obvious particular, a star in the constellation -Cassiopeia, (_Mu Cassiopeię_) has the greatest proper motion of any yet -ascertained, amounting to nearly four seconds annually. - -You have doubtless heard much respecting the "immeasurable _distances_" -of the fixed stars, and will desire to learn what is known to -astronomers respecting this interesting subject. - -We cannot ascertain the actual distance of any of the fixed stars, but -we can certainly determine that the nearest star is more than twenty -millions of millions of miles from the earth, (20,000,000,000,000.) For -all measurements relating to the distances of the _sun and planets_, the -radius of the earth furnishes the base line. The length of this line -being known, and the horizontal parallax of the sun or any planet, we -have the means of calculating the distance of the body from us, by -methods explained in a previous Letter. But any star, viewed from the -opposite sides of the earth, would appear from both stations to occupy -precisely the same situation in the celestial sphere, and of course it -would exhibit no horizontal parallax. But astronomers have endeavored to -find a parallax in some of the fixed stars, by taking the _diameter of -the earth's orbit_ as a base line. Yet even a change of position -amounting to one hundred and ninety millions of miles proved, until very -recently, insufficient to alter the place of a single star, so far as to -be capable of detection by very refined observations; from which it was -concluded that the stars have not even any _annual parallax_; that is, -the angle subtended by the semidiameter of the earth's orbit, at the -nearest fixed star, is insensible. The errors to which instrumental -measurements are subject, arising from the defects of instruments -themselves, from refraction, and from various other sources of -inaccuracy, are such, that the angular determinations of arcs of the -heavens cannot be relied on to less than one second, and therefore -cannot be appreciated by direct measurement. It follows, that, when -viewed from the nearest star, the diameter of the earth's orbit would be -insensible; the spider-line of the telescope would more than cover it. -Taking, however, the annual parallax of a fixed star at one second, it -can be demonstrated, that the distance of the nearest fixed star _must -exceed_ 95000000 × 200000 = 190000000 × 100000, or one hundred thousand -times one hundred and ninety millions of miles. Of a distance so vast we -can form no adequate conceptions, and even seek to measure it only by -the time that light (which moves more than one hundred and ninety-two -thousand miles per second, and passes from the sun to the earth in eight -minutes and seven seconds) would take to traverse it, which is found to -be more than three and a half years. - -If these conclusions are drawn with respect to the largest of the fixed -stars, which we suppose to be vastly nearer to us than those of the -smallest magnitude, the idea of distance swells upon us when we attempt -to estimate the remoteness of the latter. As it is uncertain, however, -whether the difference in the apparent magnitudes of the stars is owing -to a real difference, or merely to their being at various distances from -the eye, more or less uncertainty must attend all efforts to determine -the relative distances of the stars; but astronomers generally believe, -that the lower orders of stars are vastly more distant from us than the -higher. Of some stars it is said, that thousands of years would be -required for their light to travel down to us. - -I have said that the stars have always been held, until recently, to -have no annual parallax; yet it may be observed that astronomers were -not exactly agreed on this point. Dr. Brinkley, a late eminent Irish -astronomer, supposed that he had detected an annual parallax in Alpha -Lyrę, amounting to one second and thirteen hundreths, and in Alpha -Aquilę, of one second and forty-two hundreths. These results were -controverted by Mr. Pond, of the Royal Observatory of Greenwich; and -Mr. Struve, of Dorpat, has shown that, in a number of cases, the -supposed parallax is in a direction opposite to that which would arise -from the motion of the earth. Hence it is considered doubtful whether, -in all cases of an apparent parallax, the effect is not wholly due to -errors of observation. - -But as if nothing was to be hidden from our times, the long sought for -parallax among the fixed stars has at length been found, and -consequently the distance of some of these bodies, at least, is no -longer veiled in mystery. In the year 1838, Professor Bessel, of -Köningsberg, announced the discovery of a parallax in one of the stars -of the Swan, (61 _Cygni_,) amounting to about _one third of a second_. -This seems, indeed, so small an angle, that we might have reason to -suspect the reality of the determination; but the most competent judges -who have thoroughly examined the process by which the discovery was -made, assent to its validity. What, then, do astronomers understand, -when they say that a parallax has been discovered in one of the fixed -stars, amounting to one third of a second? They mean that the star in -question apparently shifts its place in the heavens, to that amount, -when viewed at opposite extremities of the earth's orbit, namely, at -points in space distant from each other one hundred and ninety millions -of miles. On calculating the distance of the star from us from these -data, it is found to be six hundred and fifty-seven thousand seven -hundred times ninety-five millions of miles,--a distance which it would -take light more than ten years to traverse. - -Indirect methods have been proposed, for ascertaining the parallax of -the fixed stars, by means of observations on the _double stars_. If the -two stars composing a double star are at different distances from us, -parallax would affect them unequally, and change their relative -positions with respect to each other; and since the ordinary sources of -error arising from the imperfection of instruments, from precession, and -from refraction, would be avoided, (as they would affect both objects -alike, and therefore would not disturb their relative positions,) -measurements taken with the micrometer of changes much less than one -second may be relied on. Sir John Herschel proposed a method, by which -changes may be determined that amount to only one fortieth of a second. - -The immense distance of the fixed stars is inferred also from the fact, -that the largest telescopes do not increase their apparent magnitude. -They are still points, when viewed with glasses that magnify five -thousand times. - -With respect to the NATURE OF THE STARS, it would seem fruitless to -inquire into the nature of bodies so distant, and which reveal -themselves to us only as shining points in space. Still, there are a few -very satisfactory inferences that can be made out respecting them. -First, _the fixed stars are bodies greater than our earth_. If this were -not the case, they would not be visible at such an immense distance. Dr. -Wollaston, a distinguished English philosopher, attempted to estimate -the magnitudes of certain of the fixed stars from the light which they -afford. By means of an accurate photometer, (an instrument for measuring -the relative intensities of light,) he compared the light of Sirius with -that of the sun. He next inquired how far the sun must be removed from -us, in order to appear no brighter than Sirius. He found the distance to -be one hundred and forty-one thousand times its present distance. But -Sirius is more than two hundred thousand times as far off as the sun; -hence he inferred that, upon the lowest computation, it must actually -give out twice as much light as the sun; or that, in point of splendor, -Sirius must be at least equal to two suns. Indeed, he has rendered it -probable, that its light is equal to that of fourteen suns. There is -reason, however, to believe that the stars are actually of various -magnitudes, and that their apparent difference is not owing merely to -their different distances. Bessel estimates the quantity of matter in -the two members of a double star in the Swan, as less than half that of -the sun. - -Secondly, _the fixed stars are suns_. We have already seen that they are -large bodies; that they are immensely further off than the furthest -planet; that they shine by their own light; in short, that their -appearance is, in all respects, the same as the sun would exhibit if -removed to the region of the stars. Hence we infer that they are bodies -of the same kind with the sun. We are justified, therefore, by a sound -analogy, in concluding that the stars were made for the same end as the -sun, namely, as the centres of attraction to other planetary worlds, to -which they severally dispense light and heat. Although the starry -heavens present, in a clear night, a spectacle of unrivalled grandeur -and beauty, yet it must be admitted that the chief purpose of the stars -could not have been to adorn the night, since by far the greater part of -them are invisible to the naked eye; nor as landmarks to the navigator, -for only a very small proportion of them are adapted to this purpose; -nor, finally, to influence the earth by their attractions, since their -distance renders such an effect entirely insensible. If they are suns, -and if they exert no important agencies upon our world, but are bodies -evidently adapted to the same purpose as our sun, then it is as rational -to suppose that they were made to give light and heat, as that the eye -was made for seeing and the ear for hearing. It is obvious to inquire, -next, to what they dispense these gifts, if not to planetary worlds; and -why to planetary worlds, if not for the use of percipient beings? We are -thus led, almost inevitably, to the idea of a _plurality of worlds_; and -the conclusion is forced upon us, that the spot which the Creator has -assigned to us is but a humble province in his boundless empire. - - - - -LETTER XXX. - -SYSTEM OF THE WORLD - - - "O how unlike the complex works of man, - Heaven's easy, artless, unincumbered, plan."--_Cowper._ - -HAVING now explained to you, as far as I am able to do it in so short a -space, the leading phenomena of the heavenly bodies, it only remains to -inform you of the different systems of the world which have prevailed in -different ages,--a subject which will necessarily involve a sketch of -the history of astronomy. - -By a system of the world, I understand an explanation of _the -arrangement of all the bodies that compose the material universe, and of -their relations to each other_. It is otherwise called the 'Mechanism of -the Heavens;' and indeed, in the system of the world, we figure to -ourselves a machine, all parts of which have a mutual dependence, and -conspire to one great end. "The machines that were first invented," says -Adam Smith, "to perform any particular movement, are always the most -complex; and succeeding artists generally discover that, with fewer -wheels, and with fewer principles of motion, than had originally been -employed, the same effects may be more easily produced. The first -systems, in the same manner, are always the most complex; and a -particular connecting chain or principle is generally thought necessary, -to unite every two seemingly disjointed appearances; but it often -happens, that _one great connecting principle_ is afterwards found to be -sufficient to bind together all the discordant phenomena that occur in a -whole species of things!" This remark is strikingly applicable to the -origin and progress of systems of astronomy. It is a remarkable fact in -the history of the human mind, that astronomy is the oldest of the -sciences, having been cultivated, with no small success, long before any -attention was paid to the causes of the common terrestrial phenomena. -The opinion has always prevailed among those who were unenlightened by -science, that very extraordinary appearances in the sky, as comets, -fiery meteors, and eclipses, are omens of the wrath of heaven. They -have, therefore, in all ages, been watched with the greatest attention: -and their appearances have been minutely recorded by the historians of -the times. The idea, moreover, that the aspects of the stars are -connected with the destinies of individuals and of empires, has been -remarkably prevalent from the earliest records of history down to a very -late period, and, indeed, still lingers among the uneducated and -credulous. This notion gave rise to ASTROLOGY,--an art which professed -to be able, by a knowledge of the varying aspects of the planets and -stars, to penetrate the veil of futurity, and to foretel approaching -irregularities of Nature herself, and the fortunes of kingdoms and of -individuals. That department of astrology which took cognizance of -extraordinary occurrences in the natural world, as tempests, -earthquakes, eclipses, and volcanoes, both to predict their approach and -to interpret their meaning, was called _natural astrology_: that which -related to the fortunes of men and of empires, _judicial astrology_. -Among many ancient nations, astrologers were held in the highest -estimation, and were kept near the persons of monarchs; and the practice -of the art constituted a lucrative profession throughout the middle -ages. Nor were the ignorant and uneducated portions of society alone the -dupes of its pretensions. Hippocrates, the 'Father of Medicine,' ranks -astrology among the most important branches of knowledge to the -physician; and Tycho Brahe, and Lord Bacon, were firm believers in its -mysteries. Astrology, fallacious as it was, must be acknowledged to have -rendered the greatest services to astronomy, by leading to the accurate -observation and diligent study of the stars. - -At a period of very remote antiquity, astronomy was cultivated in China, -India, Chaldea, and Egypt. The Chaldeans were particularly -distinguished for the accuracy and extent of their astronomical -observations. Calisthenes, the Greek philosopher who accompanied -Alexander the Great in his Eastern conquests, transmitted to Aristotle a -series of observations made at Babylon nineteen centuries before the -capture of that city by Alexander; and the wise men of Babylon and the -Chaldean astrologers are referred to in the Sacred Writings. They -enjoyed a clear sky and a mild climate, and their pursuits as shepherds -favored long-continued observations; while the admiration and respect -accorded to the profession, rendered it an object of still higher -ambition. - -In the seventh century before the Christian era, astronomy began to be -cultivated in Greece; and there arose successively three celebrated -astronomical schools,--the school of Miletus, the school of Crotona, and -the school of Alexandria. The first was established by Thales, six -hundred and forty years before Christ; the second, by Pythagoras, one -hundred and forty years afterwards; and the third, by the Ptolemies of -Egypt, about three hundred years before the Christian era. As Egypt and -Babylon were renowned among the most ancient nations, for their -knowledge of the sciences, long before they were cultivated in Greece, -it was the practice of the Greeks, when they aspired to the character of -philosophers and sages, to resort to these countries to imbibe wisdom at -its fountains. Thales, after extensive travels in Crete and Egypt, -returned to his native place, Miletus, a town on the coast of Asia -Minor, where he established the first school of astronomy in Greece. -Although the minds of these ancient astronomers were beclouded with much -error, yet Thales taught a few truths which do honor to his sagacity. He -held that the stars are formed of fire; that the moon receives her light -from the sun, and is invisible at her conjunctions because she is hid in -the sun's rays. He taught the sphericity of the earth, but adopted the -common error of placing it in the centre of the world. He introduced -the division of the sphere into five zones, and taught the obliquity of -the ecliptic. He was acquainted with the Saros, or sacred period of the -Chaldeans, (see page 192,) and employed it in calculating eclipses. It -was Thales that predicted the famous eclipse of the sun which terminated -the war between the Lydians and the Medes, as mentioned in a former -Letter. Indeed, Thales is universally regarded as a bright but solitary -star, glimmering through mists on the distant horizon. - -To Thales succeeded, in the school of Miletus, two other astronomers of -much celebrity, Anaximander and Anaxagoras. Among many absurd things -held by Anaximander, he first taught the sublime doctrine that the -planets are inhabited, and that the stars are suns of other systems. -Anaxagoras attempted to explain all the secrets of the skies by natural -causes. His reasonings, indeed, were alloyed with many absurd notions; -but still he alone, among the astronomers, maintained the existence of -one God. His doctrines alarmed his countrymen, by their audacity and -impiety to their gods, whose prerogatives he was thought to invade; and, -to deprecate their wrath, sentence of death was pronounced on the -philosopher and all his family,--a sentence which was commuted only for -the sad alternative of perpetual banishment. The very genius of the -heathen mythology was at war with the truth. False in itself, it trained -the mind to the love of what was false in the interpretation of nature; -it arrayed itself against the simplicity of truth, and persecuted and -put to death its most ardent votaries. The religion of the Bible, on the -other hand, lends all its aid to truth in nature as well as in morals -and religion. In its very genius it inculcates and inspires the love of -truth; it suggests, by its analogies, the existence of established laws -in the system of the world; and holds out the moon and the stars, which -the Creator has ordained, as fit objects to give us exalted views of his -glory and wisdom. - -Pythagoras was the founder of the celebrated school of Crotona. He was a -native of Samos, an island in the Ęgean sea, and flourished about five -hundred years before the Christian era. After travelling more than -thirty years in Egypt and Chaldea, and spending several years more at -Sparta, to learn the laws and institutions of Lycurgus, he returned to -his native island to dispense the riches he had acquired to his -countrymen. But they, probably fearful of incurring the displeasure of -the gods by the freedom with which he inquired into the secrets of the -skies, gave him so unwelcome a reception, that he retired from them, in -disgust, and established his school at Crotona, on the southeastern -coast of Italy. Hither, as to an oracle, the fame of his wisdom -attracted hundreds of admiring pupils, whom he instructed in every -species of knowledge. From the visionary notions which are generally -understood to have been entertained on the subject of astronomy, by the -ancients, we are apt to imagine that they knew less than they actually -did of the truths of this science. But Pythagoras was acquainted with -many important facts in astronomy, and entertained many opinions -respecting the system of the world, which are now held to be true. Among -other things well known to Pythagoras, either derived from his own -investigations, or received from his predecessors, were the following; -and we may note them as a synopsis of the state of astronomical -knowledge at that age of the world. First, the principal -_constellations_. These had begun to be formed in the earliest ages of -the world. Several of them, bearing the same name as at present, are -mentioned in the writings of Hesiod and Homer; and the "sweet influences -of the Pleiades," and the "bands of Orion," are beautifully alluded to -in the book of Job. Secondly, _eclipses_. Pythagoras knew both the -causes of eclipses and how to predict them; not, indeed, in the accurate -manner now practised, but by means of the Saros. Thirdly, Pythagoras had -divined the true _system of the world_, holding that the sun, and not -the earth, (as was generally held by the ancients, even for many ages -after Pythagoras,) is the centre around which all the planets revolve; -and that the stars are so many suns, each the centre of a system like -our own. Among lesser things, he knew that the earth is round; that its -surface is naturally divided into five zones; and that the ecliptic is -inclined to the equator. He also held that the earth revolves daily on -its axis, and yearly around the sun; that the galaxy is an assemblage of -small stars; and that it is the same luminary, namely, Venus, that -constitutes both the morning and evening star; whereas all the ancients -before him had supposed that each was a separate planet, and accordingly -the morning star was called Lucifer, and the evening star, Hesperus. He -held, also, that the planets were inhabited, and even went so far as to -calculate the size of some of the animals in the moon. Pythagoras was -also so great an enthusiast in music, that he not only assigned to it a -conspicuous place in his system of education, but even supposed that the -heavenly bodies themselves were arranged at distances corresponding to -the intervals of the diatonic scale, and imagined them to pursue their -sublime march to notes created by their own harmonious movements, called -the 'music of the spheres;' but he maintained that this celestial -concert, though loud and grand, is not audible to the feeble organs of -man, but only to the gods. With few exceptions, however, the opinions of -Pythagoras on the system of the world were founded in truth. Yet they -were rejected by Aristotle, and by most succeeding astronomers, down to -the time of Copernicus; and in their place was substituted the doctrine -of _crystalline spheres_, first taught by Eudoxus, who lived about three -hundred and seventy years before Christ. According to this system, the -heavenly bodies are set like gems in hollow solid orbs, composed of -crystal so transparent, that no anterior orb obstructs in the least the -view of any of the orbs that lie behind it. The sun and the planets have -each its separate orb; but the fixed stars are all set in the same -grand orb; and beyond this is another still, the _primum mobile_, which -revolves daily, from east to west, and carries along with it all the -other orbs. Above the whole spreads the _grand empyrean_, or third -heavens, the abode of perpetual serenity. - -To account for the planetary motions, it was supposed that each of the -planetary orbs, as well as that of the sun, has a motion of its own, -eastward, while it partakes of the common diurnal motion of the starry -sphere. Aristotle taught that these motions are effected by a tutelary -genius of each planet, residing in it, and directing its motions, as the -mind of man directs his movements. - -Two hundred years after Pythagoras, arose the famous school of -Alexandria, under the Ptolemies. These were a succession of Egyptian -kings, and are not to be confounded with Ptolemy, the astronomer. By the -munificent patronage of this enlightened family, for the space of three -hundred years, beginning at the death of Alexander the Great, from whom -the eldest of the Ptolemies had received his kingdom, the school of -Alexandria concentrated in its vast library and princely halls, erected -for the accommodation of the philosophers, nearly all the science and -learning of the world. In wandering over the immense territories of -ignorance and barbarism which covered, at that time, almost the entire -face of the earth, the eye reposes upon this little spot, as upon a -verdant island in the midst of the desert. Among the choice fruits that -grew in this garden of astronomy were several of the most distinguished -ornaments of ancient science, of whom the most eminent were Hipparchus -and Ptolemy. Hipparchus is justly considered as the Newton of antiquity. -He sought his knowledge of the heavenly bodies not in the illusory -suggestions of a fervid imagination, but in the vigorous application of -an intellect of the first order. Previous to this period, celestial -observations were made chiefly with the naked eye: but Hipparchus was in -possession of instruments for measuring angles, and knew how to resolve -spherical triangles. These were great steps beyond all his predecessors. -He ascertained the length of the year within six minutes of the truth. -He discovered the eccentricity, or elliptical figure, of the solar -orbit, although he supposed the sun actually to move uniformly in a -circle, but the earth to be placed out of the centre. He also determined -the positions of the points among the stars where the earth is nearest -to the sun, and where it is most remote from it. He formed very accurate -estimates of the obliquity of the ecliptic and of the precession of the -equinoxes. He computed the exact period of the synodic revolution of the -moon, and the inclination of the lunar orbit; discovered the backward -motion of her node and of her line of apsides; and made the first -attempts to ascertain the horizontal parallaxes of the sun and moon. -Upon the appearance of a new star in the firmament, he undertook, as -already mentioned, to number the stars, and to assign to each its true -place in the heavens, in order that posterity might have the means of -judging what changes, if any, were going forward among these apparently -unalterable bodies. - -Although Hipparchus is generally considered as belonging to the -Alexandrian school, yet he lived at Rhodes, and there made his -astronomical observations, about one hundred and forty years before the -Christian era. One of his treatises has come down to us; but his -principal discoveries have been transmitted through the 'Almagest' of -Ptolemy. Ptolemy flourished at Alexandria nearly three centuries after -Hipparchus, in the second century after Christ. His great work, the -'Almagest,' which has conveyed to us most that we know respecting the -astronomical knowledge of the ancients, was the universal text-book of -astronomers for fourteen centuries. - -[Illustration Fig. 77.] - -The name of this celebrated astronomer has also descended to us, -associated with the system of the world which prevailed from Ptolemy to -Copernicus, called the _Ptolemaic System_. The doctrines of the -Ptolemaic system did not originate with Ptolemy, but, being digested by -him out of materials furnished by various hands, it has come down to us -under the sanction of his name. According to this system, the earth is -the centre of the universe, and all the heavenly bodies daily revolve -around it, from east to west. But although this hypothesis would account -for the apparent diurnal motion of the firmament, yet it would not -account for the apparent annual motion of the sun, nor for the slow -motions of the planets from west to east. In order to explain these -phenomena, recourse was had to _deferents_ and _epicycles_,--an -explanation devised by Apollonius, one of the greatest geometers of -antiquity. He conceived that, in the circumference of a circle, having -the earth for its centre, there moves the centre of a smaller circle in -the circumference of which the planet revolves. The circle surrounding -the earth was called the deferent, while the smaller circle, whose -centre was always in the circumference of the deferent, was called the -epicycle. Thus, if E, Fig. 77, represents the earth, ABC will be the -deferent, and DFG, the epicycle; and it is obvious that the motion of a -body from west to east, in this small circle, would be alternately -direct, stationary, and retrograde, as was explained, in a previous -Letter, to be actually the case with the apparent motions of the -planets. The hypothesis, however, is inconsistent with the _phases_ of -Mercury and Venus, which, being between us and the sun, on both sides of -the epicycle, would present their dark sides towards us at both -conjunctions with the sun, whereas, at one of the conjunctions, it is -known that they exhibit their disks illuminated. It is, moreover, absurd -to speak of a geometrical centre, which has no bodily existence, moving -round the earth on the circumference of another circle. In addition to -these absurdities, the whole Ptolemaic system is encumbered with the -following difficulties: First, it is a mere hypothesis, having no -evidence in its favor except that it explains the phenomena. This -evidence is insufficient of itself, since it frequently happens that -each of two hypotheses, which are directly opposite to each other, will -explain all the known phenomena. But the Ptolemaic system does not even -do this, as it is inconsistent with the phases of Mercury and Venus, as -already observed. Secondly, now that we are acquainted with the -distances of the remoter planets, and especially the fixed stars, the -swiftness of motion, implied in a daily revolution of the starry -firmament around the earth, renders such a motion wholly incredible. -Thirdly, the centrifugal force which would be generated in these bodies, -especially in the sun, renders it impossible that they can continue to -revolve around the earth as a centre. Absurd, however, as the system of -Ptolemy was, for many centuries no great philosophic genius appeared to -expose its fallacies, and it therefore guided the faith of astronomers -of all countries down to the time of Copernicus. - -After the age of Ptolemy, the science made little progress. With the -decline of Grecian liberty, the arts and sciences declined also; and the -Romans, then masters of the world, were ever more ambitious to gain -conquests over man than over matter; and they accordingly never produced -a single great astronomer. During the middle ages, the Arabians were -almost the only astronomers, and they cultivated this noble study -chiefly as subsidiary to astrology. - -At length, in the fifteenth century, Copernicus arose, and after forty -years of intense study and meditation, divined the true system of the -world. You will recollect that the Copernican system maintains, 1. That -the _apparent_ diurnal motions of the heavenly bodies, from east to -west, is owing to the _real_ revolution of the earth on its own axis -from west to east; and, 2. That the sun is the centre around which the -earth and planets all revolve from west to east. It rests on the -following arguments: In the first place, _the earth revolves on its own -axis_. First, because this supposition is vastly more _simple_. -Secondly, it is agreeable to _analogy_, since all the other planets that -afford any means of determining the question, are seen to revolve on -their axes. Thirdly, the _spheroidal figure_ of the earth is the figure -of equilibrium, that results from a revolution on its axis. Fourthly, -the _diminished weight_ of bodies at the equator indicates a centrifugal -force arising from such a revolution. Fifthly, bodies let fall from a -high eminence, fall _eastward of their base_, indicating that when -further from the centre of the earth they were subject to a greater -velocity, which, in consequence of their inertia, they do not entirely -lose in descending to the lower level. - -In the second place, _the planets, including the earth, revolve about -the sun_. First, the _phases_ of Mercury and Venus are precisely such, -as would result from their circulating around the sun in orbits within -that of the earth; but they are never seen in opposition, as they would -be, if they circulate around the earth. Secondly, the superior planets -do indeed revolve around the earth; but they also revolve around the -sun, as is evident from their phases, and from the known dimensions of -their orbits; and that the sun, and not the earth, is the _centre_ of -their motions, is inferred from the greater symmetry of their motions, -as referred to the sun, than as referred to the earth; and especially -from the laws of gravitation, which forbid our supposing that bodies so -much larger than the earth, as some of these bodies are, can circulate -permanently around the earth, the latter remaining all the while at -rest. - -In the third place, the annual motion of _the earth_ itself is indicated -also by the most conclusive arguments. For, first, since all the -planets, with their satellites and the comets, revolve about the sun, -analogy leads us to infer the same respecting the earth and its -satellite, as those of Jupiter and Saturn, and indicates that it is a -law of the solar system that the smaller bodies revolve about the -larger. Secondly, on the supposition that the earth performs an annual -revolution around the sun, it is embraced along with the planets, in -Kepler's law, that the squares of the times are as the cubes of the -distances; otherwise, it forms an exception, and the only known -exception, to this law. - -Such are the leading arguments upon which rests the Copernican system of -astronomy. They were, however, only very partially known to Copernicus -himself, as the state both of mechanical science, and of astronomical -observation, was not then sufficiently matured to show him the strength -of his own doctrine, since he knew nothing of the telescope, and nothing -of the principle of universal gravitation. The evidence of this -beautiful system being left by Copernicus in so imperfect a state, and -indeed his own reasonings in support of it being tinctured with some -errors, we need not so much wonder that Tycho Brahe, who immediately -followed Copernicus, did not give it his assent, but, influenced by -certain passages of Scripture, he still maintained, with Ptolemy, that -the earth is in the centre of the universe; and he accounted for the -diurnal motions in the same manner as Ptolemy had done, namely, by an -actual revolution of the whole host of heaven around the earth every -twenty-four hours. But he rejected the scheme of deferents and -epicycles, and held that the moon revolves about the earth as the centre -of her motions; but that the sun and not the earth is the centre of the -planetary motions; and that the sun, accompanied by the planets, moves -around the earth once a year, somewhat in the manner in which we now -conceive of Jupiter and his satellites as revolving around the sun. This -system is liable to most of the objections that lie against the -Ptolemaic system, with the disadvantage of being more complex. - -Kepler and Galileo, however, as appeared in the sketch of their lives, -embraced the theory of Copernicus with great avidity, and all their -labors contributed to swell the evidence of its truth. When we see with -what immense labor and difficulty the disciples of Ptolemy sought to -reconcile every new phenomenon of the heavens with their system, and -then see how easily and naturally all the successive discoveries of -Galileo and Kepler fall in with the theory of Copernicus, we feel the -full force of those beautiful lines of Cowper which I have chosen for -the motto of this Letter. - -Newton received the torch of truth from Galileo, and transmitted it to -his successors, with its light enlarged and purified; and since that -period, every new discovery, whether the fruit of refined instrumental -observation or of profound mathematical analysis, has only added lustre -to the glory of Copernicus. - -With Newton commenced a new and wonderful era in astronomy, -distinguished above all others, not merely for the production of the -greatest of men, but also for the establishment of those most important -auxiliaries to our science, the Royal Society of London, the Academy of -Sciences at Paris, and the Observatory of Greenwich. I may add the -commencement of the Transactions of the Royal Society, and the Memoirs -of the Academy of Sciences, which have been continued to the present -time,--both precious storehouses of astronomical riches. The Observatory -of Greenwich, moreover, has been under the direction of an extraordinary -succession of great astronomers. Their names are Flamstead, Halley, -Bradley, Maskeleyne, Pond, and Airy,--the last being still at his post, -and worthy of continuing a line so truly illustrious. The observations -accumulated at this celebrated Observatory are so numerous, and so much -superior to those of any other institution in the world, that it has -been said that astronomy would suffer little, if all other contemporary -observations of the same kind were annihilated. Sir William Herschel, -however, labored chiefly in a different sphere. The Astronomers Royal -devoted themselves not so much to the discovery of new objects among -the heavenly bodies, as to the exact determination of the places of the -bodies already known, and to the developement of new laws or facts among -the celestial motions. But Herschel, having constructed telescopes of -far greater reach than any ever used before, employed them to sound new -and untried depths in the profundities of space. We have already seen -what interesting and amazing discoveries he made of double stars, -clusters, and nebulę. - -The English have done most for astronomy in observation and discovery; -but the French and Germans, in developing, by the most profound -mathematical investigation, the great laws of physical astronomy. - -It only remains to inquire, whether the Copernican system is now to be -regarded as a full exposition of the 'Mechanism of the Heavens,' or -whether there subsist higher orders of relations between the fixed stars -themselves. - -The revolutions of the _binary stars_ afford conclusive evidence of at -least subordinate systems of suns, governed by the same laws as those -which regulate the motions of the solar system. The _nebulę_ also -compose peculiar systems, in which the members are evidently bound -together by some common relation. - -In these marks of organization,--of stars associated together in -clusters; of sun revolving around sun; and of nebulę disposed in regular -figures,--we recognise different members of some grand system, links in -one great chain that binds together all parts of the universe; as we see -Jupiter and his satellites combined in one subordinate system, and -Saturn and his satellites in another,--each a vast kingdom, and both -uniting with a number of other individual parts, to compose an empire -still more vast. - -This fact being now established, that the stars are immense bodies, like -the sun, and that they are subject to the laws of gravitation, we cannot -conceive how they can be preserved from falling into final disorder and -ruin, unless they move in harmonious concert, like the members of the -solar system. Otherwise, those that are situated on the confines of -creation, being retained by no forces from without, while they are -subject to the attraction of all the bodies within, must leave their -stations, and move inward with accelerated velocity; and thus all the -bodies in the universe would at length fall together in the common -centre of gravity. The immense distance at which the stars are placed -from each other would indeed delay such a catastrophe; but this must be -the ultimate tendency of the material world, unless sustained in one -harmonious system by nicely-adjusted motions. To leave entirely out of -view our confidence in the wisdom and preserving goodness of the -Creator, and reasoning merely from what we know of the stability of the -solar system, we should be justified in inferring, that other worlds are -not subject to forces which operate only to hasten their decay, and to -involve them in final ruin. - -We conclude, therefore, that the material universe is one great system; -that the combination of planets with their satellites constitutes the -first or lowest order of worlds; that next to these, planets are linked -to suns; that these are bound to other suns, composing a still higher -order in the scale of being; and finally, that all the different systems -of worlds move around their common centre of gravity. - - - - -LETTER XXXI. - -NATURAL THEOLOGY. - - ----"Philosophy, baptized - In the pure fountain of Eternal Love, - Has eyes indeed; and, viewing all she sees - As meant to indicate a God to man, - Gives Him the praise, and forfeits not her own."--_Cowper._ - - -I INTENDED, my dear Friend, to comply with your request "that I would -discuss the arguments which astronomy affords to natural theology;" but -these Letters have been already extended so much further than I -anticipated, that I shall conclude with suggesting a few of those moral -and religious reflections, which ought always to follow in the train of -such a survey of the heavenly bodies as we have now taken. - -Although there is evidence enough in the structure, arrangement, and -laws, which prevail among the heavenly bodies, to prove the _existence_ -of God, yet I think there are many subordinate parts of His works far -better adapted to this purpose than these, being more fully within our -comprehension. It was intended, no doubt, that the evidence of His being -should be accessible to all His creatures, and should not depend on a -kind of knowledge possessed by comparatively few. The mechanism of the -eye is probably not more perfect than that of the universe; but we can -analyze it better, and more fully understand the design of each part. -But the existence of God being once proved, and it being admitted that -He is the Creator and Governor of the world, then the discoveries of -astronomy are admirably adapted to perform just that office in relation -to the Great First Cause, which is assigned to them in the Bible, -namely, "to declare the glory of God, and to show His handiwork." In -other words, the discoveries of astronomy are peculiarly fitted,--more -so, perhaps, than any other department of creation,--to exhibit the -unity, power, and wisdom, of the Creator. - -The most modern discoveries have multiplied the proofs of the _unity_ of -God. It has usually been offered as sufficient evidence of the truth of -this doctrine, that the laws of Nature are found to be uniform when -applied to the utmost bounds of the _solar system_; that the law of -gravitation controls alike the motions of Mercury, and those of Uranus; -and that its operation is one and the same upon the moon and upon the -satellites of Saturn. It was, however, impossible, until recently, to -predicate the same uniformity in the great laws of the universe -respecting the starry worlds, except by a feeble analogy. However -improbable, it was still possible, that in these distant worlds other -laws might prevail, and other Lords exercise dominion. But the discovery -of the revolutions of the binary stars, in exact accordance with the law -of gravitation, not merely in a single instance, but in many instances, -in all cases, indeed, wherever those revolutions have advanced so far as -to determine their law of action, gives us demonstration, instead of -analogy, of the prevalence of the same law among the other systems as -that which rules in ours. - -The marks of a still higher organization in the structure of clusters -and nebulę, all bearing that same characteristic union of resemblance -and variety which belongs to all the other works of creation that fall -under our notice, speak loudly of one, and only one, grand design. Every -new discovery of the telescope, therefore, has added new proofs to the -great truth that God is one: nor, so far as I know, has a single fact -appeared, that is not entirely consonant with it. Light, moreover, which -brings us intelligence, and, in most cases, the only intelligence we -have, of these remote orbs, testifies to the same truth, being similar -in its properties and uniform in its motions, from whatever star it -emanates. - -In displays of the _power_ of Jehovah, nothing can compare with the -starry heavens. The magnitudes, distances, and velocities, of the -heavenly bodies are so much beyond every thing of this kind which -belongs to things around us, from which we borrowed our first ideas of -these qualities, that we can scarcely avoid looking with incredulity at -the numerical results to which the unerring principles of mathematics -have conducted us. And when we attempt to apply our measures to the -fixed stars, and especially to the nebulę, the result is absolutely -overwhelming: the mind refuses its aid in our attempts to grasp the -great ideas. Nor less conspicuous, among the phenomena of the heavenly -bodies, is the _wisdom_ of the Creator. In the first place, this -attribute is every where exhibited _in the happy adaptation of means to -their ends_. No principle can be imagined more simple, and at the same -time more effectual to answer the purposes which it serves, than -gravitation. No position can be given to the sun and planets so fitted, -as far as we can judge, to fulfil their mutual relations, as that which -the Creator has given them. I say, as far as we can judge; for we find -this to be the case in respect to our own planet and its attendant -satellite, and hence have reason to infer that the same is the case in -the other planets, evidently holding, as they do, a similar relation to -the sun. Thus the position of the earth at just such a distance from the -sun as suits the nature of its animal and vegetable kingdoms, and -confining the range of solar heat, vast as it might easily become, -within such narrow bounds; the inclination of the earth's axis to the -plane of its orbit, so as to produce the agreeable vicissitudes of the -seasons, and increase the varieties of animal and vegetable life, still -confining the degree of inclination so exactly within the bounds of -safety, that, were it much to transcend its present limits, the changes -of temperature of the different seasons would be too sudden and violent -for the existence of either animals or vegetables; the revolution of the -earth on its axis, so happily dividing time into hours of business and -of repose; the adaptation of the moon to the earth, so as to afford to -us her greatest amount of light just at the times when it is needed -most, and giving to the moon just such a quantity of matter, and placing -her at just such a distance from the earth, as serves to raise a tide -productive of every conceivable advantage, without the evils which would -result from a stagnation of the waters on the one hand, or from their -overflow on the other;--these are a few examples of the wisdom displayed -in the mutual relations instituted between the sun, the earth, and the -moon. - -In the second place, similar marks of wisdom are exhibited in _the many -useful and important purposes_ _which the same thing is made to serve_. -Thus the sun is at once the great regulator of the planetary motions, -and the fountain of light and heat. The moon both gives light by night -and raises the tides. Or, if we would follow out this principle where -its operations are more within our comprehension, we may instance the -_atmosphere_. When man constructs an instrument, he deems it sufficient -if it fulfils one single purpose as the watch, to tell the hour of the -day, or the telescope, to enable him to see distant objects; and had a -being like ourselves made the atmosphere, he would have thought it -enough to have created a medium so essential to animal life, that to -live is to breathe, and to cease to breathe is to die. But beside this, -the atmosphere has manifold uses, each entirely distinct from all the -others. It conveys to plants, as well as animals, their nourishment and -life; it tempers the heat of Summer with its breezes; it binds down all -fluids, and prevents their passing into the state of vapor; it supports -the clouds, distils the dew, and waters the earth with showers; it -multiplies the light of the sun, and diffuses it over earth and sky; it -feeds our fires, turns our machines, wafts our ships, and conveys to the -ear all the sentiments of language, and all the melodies of music. - -In the third place, the wisdom of the Creator is strikingly manifested -in the provision he has made for the _stability of the universe_. The -perturbations occasioned by the motions of the planets, from their -action on each other, are very numerous, since every body in the system -exerts an attraction on every other, in conformity with the law of -universal gravitation. Venus and Mercury, approaching, as they do at -times, comparatively near to the earth, sensibly disturb its motions; -and the satellites of the remoter planets greatly disturb each other's -movements. Nor was it possible to endow this principle with the -properties it has, and make it operate as it does in regulating the -motions of the world, without involving such an incident. On this -subject, Professor Whewell, in his excellent work composing one of the -Bridgewater Treatises, remarks: "The derangement which the planets -produce in the motion of one of their number will be very small, in the -course of one revolution; but this gives us no security that the -derangement may not become very large, in the course of many -revolutions. The cause acts perpetually, and it has the whole extent of -time to work in. Is it not easily conceivable, then, that, in the lapse -of ages, the derangements of the motions of the planets may accumulate, -the orbits may change their form, and their mutual distances may be much -increased or diminished? Is it not possible that these changes may go on -without limit, and end in the complete subversion and ruin of the -system? If, for instance, the result of this mutual gravitation should -be to increase considerably the eccentricity of the earth's orbit, or to -make the moon approach continually nearer and nearer to the earth, at -every revolution, it is easy to see that, in the one case, our year -would change its character, producing a far greater irregularity in the -distribution of the solar heat; in the other, our satellite must fall to -the earth, occasioning a dreadful catastrophe. If the positions of the -planetary orbits, with respect to that of the earth, were to change -much, the planets might sometimes come very near us, and thus increase -the effect of their attraction beyond calculable limits. Under such -circumstances, 'we might have years of unequal length, and seasons of -capricious temperature; planets and moons, of portentous size and -aspect, glaring and disappearing at uncertain intervals; tides, like -deluges, sweeping over whole continents; and perhaps the collision of -two of the planets, and the consequent destruction of all organization -on both of them.' The fact really is, that changes are taking place in -the motions of the heavenly bodies, which have gone on progressively, -from the first dawn of science. The eccentricity of the earth's orbit -has been diminishing from the earliest observations to our times. The -moon has been moving quicker from the time of the first recorded -eclipses, and is now in advance, by about four times her own breadth, -of what her own place would have been, if it had not been affected by -this acceleration. The obliquity of the ecliptic, also, is in a state of -diminution, and is now about two fifths of a degree less than it was in -the time of Aristotle." - -But amid so many seeming causes of irregularity and ruin, it is worthy -of a grateful notice, that effectual provision is made for the -_stability of the solar system_. The full confirmation of this fact is -among the grand results of physical astronomy. "Newton did not undertake -to demonstrate either the stability or instability of the system. The -decision of this point required a great number of preparatory steps and -simplifications, and such progress in the invention and improvement of -mathematical methods, as occupied the best mathematicians of Europe for -the greater part of the last century. Towards the end of that time, it -was shown by La Grange and La Place, that the arrangements of the solar -system are stable; that, in the long run, the orbits and motions remain -unchanged; and that the changes in the orbits, which take place in -shorter periods, never transgress certain very moderate limits. Each -orbit undergoes deviations on this side and on that side of its average -state; but these deviations are never very great, and it finally -recovers from them, so that the average is preserved. The planets -produce perpetual perturbations in each other's motions; but these -perturbations are not indefinitely progressive, but periodical, reaching -a maximum value, and then diminishing. The periods which this -restoration requires are, for the most part, enormous,--not less than -thousands, and in some instances, millions, of years. Indeed, some of -these apparent derangements have been going on in the same direction -from the creation of the world. But the restoration is in the sequel as -complete as the derangement; and in the mean time the disturbance never -attains a sufficient amount seriously to affect the stability of the -system. 'I have succeeded in demonstrating,' says La Place, 'that, -whatever be the masses of the planets, in consequence of the fact that -they all move in the same direction, in orbits of small eccentricity, -and but slightly inclined to each other, their secular irregularities -are periodical, and included within narrow limits; so that the planetary -system will only oscillate about a mean state, and will never deviate -from it, except by a very small quantity. The ellipses of the planets -have been and always will be nearly circular. The ecliptic will never -coincide with the equator; and the entire extent of the variation, in -its inclination, cannot exceed three degrees.'" - -To these observations of La Place, Professor Whewell adds the following, -on the importance, to the stability of the solar system, of the fact -that those planets which have _great masses_ have orbits of _small -eccentricity_. "The planets Mercury and Mars, which have much the -largest eccentricity among the old planets, are those of which the -masses are much the smallest. The mass of Jupiter is more than two -thousand times that of either of these planets. If the orbit of Jupiter -were as eccentric as that of Mercury, all the security for the stability -of the system, which analysis has yet pointed out, would disappear. The -earth and the smaller planets might, by the near approach of Jupiter at -his perihelion, change their nearly circular orbits into very long -ellipses, and thus might fall into the sun, or fly off into remoter -space. It is further remarkable, that in the newly-discovered planets, -of which the orbits are still more eccentric than that of Mercury, the -masses are still smaller, so that the same provision is established in -this case, also." - -With this hasty glance at the unity, power, and wisdom, of the Creator, -as manifested in the greatest of His works, I close. I hope enough has -been said to vindicate the sentiment that called 'Devotion, daughter of -Astronomy!' I do not pretend that this, or any other science, is -adequate of itself to purify the heart, or to raise it to its Maker; but -I fully believe that, when the heart is already under the power of -religion, there is something in the frequent and habitual contemplation -of the heavenly bodies under all the lights of modern astronomy, very -favorable to devotional feelings, inspiring, as it does, humility, in -unison with an exalted sentiment of grateful adoration. - - - - -LETTER XXXII. - -RECENT DISCOVERIES. - - "All are but parts of one stupendous whole."--_Pope._ - - -WITHIN a few years, astronomy has been enriched with a number of -valuable discoveries, of which I will endeavor to give you a summary -account in this letter. The heavens have been explored with far more -powerful telescopes than before; instrumental measurements have been -carried to an astonishing degree of accuracy; numerous additions have -been made to the list of small planets or asteroids; a comet has -appeared of extraordinary splendor, remarkable, above all others, for -its near approach to the sun; the distances of several of the fixed -stars, an element long sought for in vain, have been determined; a large -planet, composing in itself a magnificent world, has been added to the -solar system, at such a distance from the central luminary as nearly to -double the supposed dimensions of that system; various nebulę, before -held to be irresolvable, have been resolved into stars; and a new -satellite has been added to Saturn. - -IMPROVEMENTS IN THE TELESCOPE.--Herschel's forty-feet telescope, of -which I gave an account in my fourth letter (see page 36), remained for -half a century unequalled in magnitude and power; but in 1842, Lord -Rosse, an Irish nobleman, commenced a telescope on a scale still more -gigantic. Like Herschel's, it was a _reflector_, the image being formed -by a concave mirror. This was six feet in diameter, and weighed three -tons; and the tube was fifty feet in length. The entire cost of the -instrument was sixty thousand dollars. Its reflecting surface is nearly -twice as great as the great Herschelian, and consequently it greatly -exceeds all instruments hitherto constructed in the _amount of light_ -which it collects and transmits to the eye; and this adapts it -peculiarly to viewing those objects, as nebulę, whose light is -exceedingly faint. Accordingly, it has revealed to us new wonders in -this curious department of astronomy. Some idea of the great dimensions -of the _Leviathan_ telescope (as this instrument has been called) may be -formed when it is said that the Dean of Ely, a full-sized man, walked -through the tube from one end to the other, with an umbrella over his -head. - -But still greater advances have been made in refracting than in -reflecting telescopes. Such was the difficulty of obtaining large pieces -of glass which are free from impurities, and such the liability of large -lenses to form obscure and colored images, that it was formerly supposed -impossible to make a refracting telescope larger in diameter than five -or six inches; but their size has been increased from one step to -another, until they are now made more than fifteen inches in diameter; -and so completely have all the difficulties arising from the -imperfections of glass, and from optical defects inherent in lenses, -been surmounted, that the great telescopes of Pulkova, at St. -Petersburgh, and of Harvard University (the two finest refractors in the -world) are considered among the most perfect productions of the arts. A -lens of only 15 inches in diameter seems, indeed, diminutive when -compared with a concave reflector of six feet; but for most purposes of -the astronomer, the Pulkova and Cambridge instruments are more useful -than such great reflectors as those of Herschel and Rosse. If there is -any particular in which these are more effective, it is in observations -on the faintest nebulę, where it is necessary to collect and convey to -the eye the greatest possible beam of light. - -INSTRUMENTAL MEASUREMENTS.--When astronomical instruments were first -employed to measure the angular distance between two points on the -celestial sphere, it was not attempted to measure spaces smaller than -ten minutes--a space equal to the third part of the breadth of the full -moon. Tycho Brahe, however, carried his measures to sixty times that -degree of minuteness, having devised means of determining angles no -larger than ten seconds, or the one hundred and eightieth part of the -breadth of the lunar disk. For many years past, astronomers have carried -these measures to single seconds, or have determined spaces no greater -than the eighteen hundredth part of the diameter of the moon. This is -considered the smallest arc which can be accurately measured directly on -the limb of an instrument; but _differences_ between spaces may be -estimated to a far greater degree of accuracy than this, even to the -hundredth part of a second--a space less than that intercepted by a -spider's web held before the eye. - -DISCOVERY OF NEW PLANETS.--In my twenty-third letter (see page 286), I -gave an account of the small planets called asteroids, which lie between -the orbits of Mars and Jupiter. When that letter was written, no longer -ago than 1840, only four of those bodies had been discovered, namely, -Ceres, Pallas, Juno, and Vesta. Within a few years past, nineteen more -have been added, making the number of the asteroids known at present -twenty-three, and every year adds one or more to the list.[17] The idea -first suggested by Olbers, one of the earliest discoverers of asteroids, -that they are fragments of a large single planet once revolving between -Mars and Jupiter, has gained credit since the discovery of so many -additional bodies of the same class, all, like the former, exceedingly -small and irregular in their motions, although there are still great -difficulties in tracing them to a common origin. - -GREAT COMET OF 1843.--This is the most wonderful body that has appeared -in the heavens in modern times; first, on account of its appearing, when -first seen, in the broad light of noonday; and, secondly, on account of -its approaching so near the sun as almost to graze his surface. It was -first discovered, in New England, on the 28th of February, a little -eastward of the sun, shining like a white cloud illuminated by the solar -rays. It arrested the attention of many individuals from half past seven -in the morning until three o'clock in the afternoon, when the sky became -obscured by clouds. In Mexico, it was observed from nine in the morning -until sunset. At a single station in South America, it was said to have -been seen on the 27th of February, almost in contact with the sun. Early -in March, it had receded so far to the eastward of that body as to be -visible in the southwest after sunset, throwing upward a long train, -which increased in length from night to night until it covered a space -of 40 degrees. Its position may be seen on a celestial globe adjusted to -the latitude of New Haven (41° 18“) for the 20th of March, by tracing a -line, or, rather, a broad band proceeding from the place of the sun -towards the bright star Sirius, in the south, between the ears of the -Hare and the feet of Orion. - -The comet passed its perihelion on the 27th of February, at which time -it almost came in contact with the sun. To prevent its falling into the -sun it was endued with a prodigious velocity; a velocity so great that, -had it continued at the same rate as at the instant of perihelion -passage, it would have whirled round the sun in two hours and a half. It -did, in fact, complete more than half its revolution around the sun in -that short period, and it made more than three quarters of its circuit -around the sun in one day. Its velocity, when nearest the sun, exceeded -a million of miles per hour, and its tail, at its greatest elongation, -was one hundred and eight millions of miles; a length more than -sufficient to have reached from the sun to the earth. Its heat was -estimated to be 47,000 times greater than that received by the earth -from a vertical sun, and consequently it was more intense than that -produced by the most powerful blowpipes, and sufficient to melt like wax -the most infusible bodies. No doubt, when in the vicinity of the sun, -the solid matter of the comet was first melted and then converted into -vapor, which itself became red hot, or, more properly speaking, _white -hot_. Much discussion has arisen among astronomers respecting the -periodic time of this comet. Its most probable period is about 175 -years. - -DISTANCES OF THE STARS.--I have already mentioned (page 389) that the -distance of at least one of the fixed stars has at length been -determined, although at so great a distance that its annual parallax is -only about one third of a second, implying a distance from the sun of -nearly sixty millions of millions of miles. Of a distance so immense the -mind can form no adequate conception. The most successful effort towards -it is made by gradual and successive approximations. Let us, therefore, -take the motion of a rail-way car as the most rapid with which we are -familiar, and apply it first to the planetary spaces, and then to the -vast interval that separates these nether worlds from the fixed stars. A -rail-way car, travelling constantly night and day at the rate of twenty -miles per hour, would make 480 miles per day. At this rate, to travel -around the earth on a great circle would require about 50 days, and 500 -days to reach the moon. If we took our departure from the sun, and -journeyed night and day, we should reach Mercury in a little more than -200 years, Venus in nearly 400, and the Earth in 547 years; but to reach -Neptune, the outermost planet, would require 16,000 years. Great as -appear the dimensions of the solar system, when we imagine ourselves -thus borne along from world to world, yet this space is small compared -with that which separates us from the fixed stars; for to reach 61 Cygni -it would take 324,000,000 years. But this is believed, for certain -satisfactory reasons, to be one of the nearest of the stars. Several -other stars whose parallax has been determined are at a much greater -distance than 61 Cygni. The pole star is five times as far off; and the -greater part of the stars are at distances inconceivably more remote. -Such, especially, are those which compose the faintest nebulę. - -DISCOVERY OF THE PLANET NEPTUNE.--From the earliest ages down to the -year 1781, the solar system was supposed to terminate with the planet -Saturn, at the distance of nine hundred millions of miles from the sun; -but the discovery of Uranus added another world, and doubled the -dimensions of the solar system. It seemed improbable that any more -planets should exist at a distance still more remote, since such a body -could hardly receive any of the vivifying influences of the central -luminary. Still, certain irregularities to which the Uranus was subject, -led to the suspicion that there exists a planet beyond it, which, by its -attractions, caused these irregularities. Impressed with this belief, -two young astronomers of great genius, Le Verrier, of France, and Adams, -of England, applied themselves to the task of finding the hidden planet. -The direction in which the disturbed body was moved afforded some clue -to the part of the heavens where the disturbing body lay concealed; the -kind of action it excited at different times indicated that it was -beyond Uranus, and not this side of that planet; and the magnitude of -the forces it exerted gave some intimation of its size and mass. The law -of distances from the sun which the superior planets observe (Saturn -being nearly twice the distance of Jupiter, and Uranus twice that of -Saturn), led both these astronomers to assume that the body sought was -nearly double the distance of Uranus from the sun. With these few and -imperfect data, as so many leading-strings proceeding from the planet -Uranus, they felt their way into the abysses of space by the aid of two -sure guides--the law of gravitation and the higher geometry. Both -astronomers arrived at nearly the same results, although they wrought -independently of each other, and each, indeed, without the knowledge of -the other. Le Verrier was the first to make public his conclusions, -which he communicated to the French Academy at their sitting, August 31, -1846. They saw that there existed, at nearly double the distance of -Uranus from the sun, a planet larger than that body; that it lay near a -certain star seen at that season in the southwest, in the evening sky; -that, on account of its immense distance, it was invisible to the naked -eye, and could be distinctly seen with a perceptible disk only by the -most powerful telescopes; being no brighter than a star of the ninth -magnitude, and subtending an angle of only three seconds. Le Verrier -communicated these results to Dr. Galle, of Berlin, with the request -that he would search for the stranger with his powerful telescope, -pointing out the exact spot in the heavens where it would be found. On -the same evening, Dr. Galle directed his instrument to that part of the -heavens, and immediately the planet presented itself to view, within one -degree of the very spot assigned to it by Le Verrier. Subsequent -investigations have shown that its apparent size is within half a second -of that which the same sagacious mind foresaw, and that its diameter is -nearly equal to that of Uranus, being 31,000, while Uranus is 35,000 -miles.[18] The distance from the sun is less than was predicted, being -only about 3000, instead of 3600 millions of miles; and its periodic -time is 164-1/2, instead of 217 years, as was supposed by Le Verrier. -One satellite only has yet been discovered, and this was first seen by -Professor Bond with the great telescope of Harvard University. - -RECENT TELESCOPIC DISCOVERIES.--The great reflecting telescope of Lord -Rosse, and the powerful refracting telescopes of Pulkova and Cambridge, -have opened new fields of discovery to the delighted astronomer. A new -satellite has been added to Saturn, first revealed to the Cambridge -instrument, making the entire number of moons that adorn the nocturnal -sky of that remarkable planet no less than eight. Still more wonderful -things have been disclosed among the remotest _Nebulę_. A number of -these objects before placed among the irresolvable nebulę, and supposed -to consist not of stars, but of mere nebulous matter, have been resolved -into stars; others, of which we before saw only a part, have revealed -themselves under new and strange forms, one resembling an animal with -huge branching arms, and hence called the _crab_ nebula; another -imitating a scroll or vortex, and called the _whirlpool_ nebula; and -other figures, which to ordinary telescopes appear only as dim specks on -the confines of creation, are presented to these wonderful instruments -as glorious firmaments of stars. - -In the year 1833, Sir John Herschel left England for the Cape of Good -Hope, furnished with powerful instruments for observing the stars and -nebulę of the southern hemisphere, which had never been examined in a -manner suited to disclose their full glories. This great astronomer and -benefactor to science devoted five years of the most assiduous toil in -observing and delineating the astronomical objects of that portion of -the heavens. He had before extended the catalogue of nebulę begun by his -illustrious father, Sir William Herschel, to the number of 2307; and -beginning at that point, he swelled the number, by his labors at the -Cape of Good Hope, to 4015. He extended also the list of double stars -from 3346 to 5449, and showed that the luminous spots near the South -Pole, known to sailors by the name of the "Magellan Clouds," consist of -an assemblage of several hundred brilliant nebulę. - -The United States have contributed their full share to the recent -progress of astronomy. Powerful telescopes have been imported, made by -the first European artists, and numerous others, of scarcely inferior -workmanship and power, have been produced by artists of our own. The -American astronomers have also been the first to bring the electric -telegraph into use in astronomical observations; electric clocks have -been so constructed as to beat simultaneously at places distant many -hundred miles from each other, and thus to furnish means of determining -the difference of longitude between places with an astonishing degree of -accuracy; and facilities for recording observations on the stars have -been devised which render the work vastly more rapid as well as more -accurate than before. Indeed, the inventive genius for which Americans -have been distinguished in all the useful arts seems now destined to be -equally conspicuous in promoting the researches of science. - - -FOOTNOTES: - -[17] The names of all the asteroids known at present are as follows: - - 1. Ceres. 9. Metis. 17. Psyche. - 2. Pallas. 10. Hygeia. 18. Melpomene. - 3. Juno. 11. Parthenope. 19. Fortuna. - 4. Vesta. 12. Victoria. 20. Massalia. - 5. Astręa. 13. Egeria. 21. Lutetia. - 6. Hebe. 14. Irene. 22. Calliope. - 7. Iris. 15. Eunomia. 23. Un-named. - 8. Flora. 16. Thetis. - -[18] Sir John Herschel, however, states its diameter at 41,500 miles - - - - -INDEX. - - - - - A. - - Alamak, 371 - - Aldebaran, 369 - - Alexandrian school, 394 - - Algenib, 371 - - Algol, 371 - - Alioth, 374 - - Almagest, 14 - - Altair, 373 - - Altitude, 20 - - Amplitude, 20 - - Anaxagoras, 395 - - Anaximander, 395 - - Andromeda, 371 - - Antares, 370 - - Antinous, 373 - - Apogee, 187 - - Apsides, 188 - - Aquarius, 371 - - Aquila, 373 - - Archimedes, 136 - - Arcturus, 372 - - Aries, 369 - - Aristotle, 136 - - Astrology, 393 - - Astronomers royal, 48, 404 - - Astronomical clock, 51 - - Astronomical tables, 190 - - Astronomy, 17 - history of, 14, 392 - - Atmosphere, 100, 410 - - Attraction, 135 - - Auriga, 371 - - Axis of the Earth, 21 - - Azimuth, 20 - - - B. - - Bacon, 16, 136 - - Base line, 76 - - Base of verification, 79 - - Bellatrix, 375 - - Betalgeus, 375 - - Bissextile, 64 - - Bootes, 372 - - Bouguer, 74 - - Bowditch, 148 - - Brahean system, 403 - - - C. - - Cęsar, Julius, 64 - - Calendar, Grecian, 67 - Gregorian, 65 - - Cancer, 369 - - Canis Major, 375 - - Canis Minor, 375 - - Capella, 372 - - Capricorn, 370 - - Cassiopeia, 374 - - Catalogues of the stars, 367 - - Central forces, 130 - - Cepheus, 374 - - Ceres, 287 - - Cetus, 374 - - Chronology, 157 - - Chronometers, 210 - - Circles, great and small, 19 - of diurnal revolution, 81 - of perpetual apparition, 85 - of perpetual occultation, 85 - vertical, 20 - - Clusters, 376 - - Colures, 23 - - Coma Berenices, 372 - - Comet, Biela's, 339 - Encke's, 340 - Halley's, 323 - - Comets, 313 - brightness of, 315 - - Comets, distances of, 317 - light of, 317 - magnitude of, 315 - mass of, 318 - motions of, 320 - number of, 315 - periods of, 316 - perturbations of, 319 - structure of, 314 - tails of, 317 - - Complement, 18 - - Conjunction, 200 - - Constellations, 366 - - Copernican system, 256, 401 - - Copernicus, 14, 255 - - Cor Caroli, 372 - - Cor Hydrę, 375 - - Corona Borealis, 372 - - Corvus, 375 - - Crotona, 394 - - Crystalline spheres, 397 - - Cygnus, 374 - - - D. - - Day, astronomical, 61 - sidereal, 60 - solar, 60 - - Days of the week, 68 - - Declination, 24 - - Deferents, 400 - - Denebola, 370 - - Distances of the heavenly bodies, how measured, 94 - - Distances of the stars, 387 - - Dolphin, 373 - - Double stars, 381 - - Draco, 374 - - - E. - - Earth, diameter of the, 78 - ellipticity of the, 78 - figure of the, 69 - motion of the, 126 - orbit of the, 149 - - Eclipses, annular, 204 - calculation of, 201 - of the moon, 195 - of the sun, 203 - - Ecliptic, 22 - - Epicycles, 400 - - Equation of time, 61 - - Equations, periodical, 193 - secular, 193 - tabular, 190 - - Equator, 21 - - Equinoxes, 22 - precession of the, 154 - - Eudoxus, 397 - - - F. - - Fomalhaut, 371 - - Fraunhofer, 37 - - - G. - - Galaxy, 379 - - Galileo, 15 - abjuration of, 272 - condemnation of, 266 - life of, 258 - persecutions of, 265 - - Gemini, 369 - - Gemma, 372 - - Globes, artificial, 25 - - Gravitation, universal, 145 - - Gravity, terrestrial, 134 - - - H. - - Hercules, 372 - - Herschel, Sir Wm., 36, 105, 383 - - Hesperus, 397 - - Hipparchus, 398 - - Horizon, rational, 20 - sensible, 20 - - Hour-circles, 21 - - Huyghens, 72 - - - I. - - Inductive system, 137 - - Inquisition, 138 - - Instruments, astronomical, 29 - - - J. - - Juno, 288 - - Jupiter, 247 - belts of, 248 - diameter of, 247 - distance of, 247 - eclipses of, 250 - magnitude of, 247 - satellites of, 250 - scenery of, 247 - telescopic view of, 247 - - - K. - - Kepler, 300 - - Kepler's laws, 296 - - - L. - - Latitude, 22 - how found, 210 - - Laws of motion, 126 - terrestrial gravity, 139 - - Leap year, 64 - - Leo, 370 - - Leo Minor, 372 - - Libra, 370 - - Librations of the moon, 179 - - Light, velocity of, how measured, 252 - - Longitude, celestial, 24 - terrestrial, 22 - its importance, 208 - how found, 210 - by chronometers, 210 - by eclipses, 212 - by Jupiter's satellites, 251 - by lunar method, 213 - - Lucifer, 397 - - Lynx, 372 - - - M. - - Magnitudes, how measured, 94 - - Magellan clouds, 378 - - Mars, 245 - changes of, 245 - distance of, 245 - revolutions of, 246 - - Mecanique Celeste, 148 - - Mercury, 230 - conjunctions of, 231 - diurnal revolution of, 235 - phases of, 234 - sidereal revolut'n of, 231 - synodical revolut'n of, 231 - transits of, 237 - - Meridian, 20 - - Meteoric showers, 346 - origin of, 350 - - Meteoric stones, 290 - - Metonic cycle, 192 - - Miletus, school of, 394 - - Milky Way, 379 - - Mira, 375 - - Mirach, 371 - - Mizar, 374 - - Month, sidereal, 173 - synodical, 173 - - Moon, 157 - atmosphere of the, 167 - cusps of the, 174 - diameter of the, 158 - distance of the, 158 - eclipses of the, 195 - harvest, 177 - irregularities of the, 186 - librations of the, 179 - light of the, 158 - mountains in the, 159 - nodes of the, 173 - phases of the, 174 - revolutions of the, 178-182 - scenery of the, 163 - telescopic appearance of the, 158 - volcanoes in the, 166 - volume of the, 158 - - Motion, laws of, 126 - - Motions of the planets, 291 - - Mural circle, 54 - - - N. - - Nadir, 20 - - Nature of the stars, 390 - - Nebulę, 377 - - New planets, 286 - distances of, 288 - origin of, 289 - periods of, 288 - size of, 289 - - New style, 66 - - Newton, 16, 143 - - - O. - - Oblique sphere, 84 - - Obliquity of the ecliptic, 115 - effect of, on the Seasons, 123 - how found, 117 - - Observatory, 42 - Greenwich, 42-48 - Tycho's, 42 - - Old style, 66 - - Ophiucus, 372 - - Opposition, 200 - - Orion, 375 - - Orreries, 112, 292 - - - P. - - Pallas, 287 - - Parallactic arc, 91 - - Parallax, 90, 389 - annual, 387 - horizontal, 93 - how found, 94 - - Parallel sphere, 84 - - Parallels of latitude, 24 - - Pegasus, 373 - - Pendulum, 79 - - Perigee, 187 - - Periodical inequalities, 193 - - Perseus, 371 - - Pisces, 371 - - Piscis Australis, 371 - - Planets, 225 - distances of, 228 - inferior, 227 - magnitudes of, 229 - periods, 229 - superior, 243 - - Pleiades, 369 - - Pointers, 374 - - Polar distance, 22 - - Polaris, 373 - - Pole, 19 - of the earth, 21 - - Pollux, 369 - - Power of the Deity, 408 - - Pręsepe, 369 - - Precession, 155 - - Prime vertical, 20 - - Primum mobile, 398 - - Principia, 147 - - Procyon, 375 - - Projection of the sphere, 27 - - Proper motions of the stars, 384 - - Ptolemaic system, 399 - - Ptolemy, 398 - - Pythagoras, 394 - - - Q. - - Quadrant, 18 - - - R. - - Radius, 17 - - Refraction, 95 - - Regulus, 370 - - Resolution of motion, 132 - - Resultant, 132 - - Revolution, annual, 111 - diurnal, 111 - - Rigel, 375 - - Right ascension, 23 - - Right sphere, 83 - - - S. - - Sagittarius, 370 - - Saros, 192 - - Saturn, 274 - diameter of, 274 - ring of, 275 - satellites of, 282 - scenery of, 283 - - Scorpio, 370 - - Seasons, 119 - - Secondary, 19 - - Secular inequalities, 193 - - Serpent, 373 - - Sextant, 57 - - Sidereal day, 81 - month, 173 - - Signs, 23 - - Sirius, 375 - - Solstices, 23 - - Sphere, celestial, 19 - doctrine of the, 16 - oblique, 84 - parallel, 84 - right, 83 - terrestrial, 19 - - Spica, 370 - - Spots on the sun, 104 - cause of, 106 - dimensions of, 105 - number of, 104 - - Stability of the universe, 410 - - Stars, fixed, 365 - - Stylus, 63 - - Sun, 101 - attraction of the, 110 - density of the, 103 - diameter of the, 102 - distance of the, 101 - mass of the, 103 - nature and constitution of the, 107 - revolutions of the, 104 - - Sun, spots on the, 104 - volume of the, 103 - - Supplement, 18 - - System of the world, 392-406 - Brahean, 403 - Copernican, 401 - Ptolemaic, 399 - - - T. - - Tangent, 129 - - Taurus, 369 - - Telescope, the, 31 - achromatic, 34 - directions for using, 39 - Dorpat, 37 Herschelian, 36 - history of, 33 - reflecting, 34 - - Temperature, changes of, 124 - - Temporary stars, 380 - - Terminator, 119, 159 - - Thales, 394 - - Tides, 216 - cause of, 216 - spring and neap, 219 - - Time, 59 - apparent, 61 - equation of, 61 - mean, 61 - sidereal, 60 - - Transits, 237 - - Triangulation, 75 - - Tropic, 117 - - Twilight, 98 - - - U. - - Unity of the Deity, 407 - - Uranus, 283 - diameter of, 283 - distance of, 284 - history of, 284 - period of, 284 - satellites of, 284 - scenery of, 285 - - Ursa Major, 373 - - Ursa Minor, 373 - - - V. - - Variable stars, 379 - - Venus, 230 - conjunctions of, 231 - mountains of, 237 - phases of, 234 - revolutions of, 232 - transits of, 239 - - Vesta, 288 - - Vindemiatrix, 370 - - Virgo, 370 - - - Y. - - Year, astronomical, 63 - tropical, 156 - - - Z. - - Zenith, 20 - - Zenith distance, 21 - - Zodiac, 25 - - Zodiacal light, 363 - - Zones, 25 - - -RECENT DISCOVERIES. - - Improvements in the Telescope, 414 - - Rosse's Leviathan Telescope, 415 - - Pulkova and Cambridge Telescopes, 415 - - Improvements in instrumental Measurements, 416 - - New Planets and Asteroids, 416 - - Great Comet of 1843, 417 - - Distances of the Stars, 418 - - Discovery of Neptune, 419 - - Recent telescopic discoveries, 420 - - Longitude by the Electric Telegraph, 422 - - - * * * * * - -Transcriber's Notes - -Obvious punctuation and spelling errors repaired. - -Greek transliterations are inclosed by equals signs. - -Inconsistent hyphenation has been repaired. - -Characters that could not be fully expressed are "unpacked" and shown -within braces, e.g. {oblong symbol}. - -In ambiguous cases, the text has been left as it appears in the original -book. 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