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diff --git a/40240-0.txt b/40240-0.txt new file mode 100644 index 0000000..12f5026 --- /dev/null +++ b/40240-0.txt @@ -0,0 +1,14060 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 40240 *** + +[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, =têle=, (_tele_,) _far_, and =schopeô=, +(_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 Cæsar, 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, (= planêtês=, +_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 cohærente, 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 Cæsar. +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 horrendæ 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 Andromedæ_ 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 +_Præsepe_, 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 Andromedæ_ 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 +Lyræ_. + +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 Hydræ_;) 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 Præsepe, 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 NEBULÆ. + +[Illustration Figures 70, 71, 72, 73. CLUSTERS OF STARS AND NEBULÆ.] + +Nebulæ 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 nebulæ, 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 nebulæ 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 nebulæ 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 nebulæ 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 NEBULÆ.] + +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 nebulæ 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 nebulæ 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 nebulæ 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 Coronæ_) 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 Cassiopeiæ_) 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 +Lyræ, amounting to one second and thirteen hundreths, and in Alpha +Aquilæ, 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 Ægean 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 nebulæ. + +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 _nebulæ_ 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 nebulæ 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 nebulæ, 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 nebulæ, 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 nebulæ, 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 nebulæ, 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 nebulæ, 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 nebulæ. + +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 _Nebulæ_. A number of +these objects before placed among the irresolvable nebulæ, 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 +nebulæ 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 nebulæ 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 nebulæ. + +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. Astræa. 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. + + Cæsar, 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 Hydræ, 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 + + Nebulæ, 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 + + Præsepe, 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. In particular many mismatched quotation marks, have not been changed. + + Page 26, "knittingneedle" changed to "knitting needle". + Page 241, "trignometry" changed to "trigonometry". + Page 303, "dedecaedron" changed to "dodecaedron". + Page 392, "generrally" changed to "generally". + + + + + +End of the Project Gutenberg EBook of Letters on Astronomy, by Denison Olmsted + +*** END OF THE PROJECT GUTENBERG EBOOK 40240 *** |