>rnia al r THE MECHANISM OF THE HEAVENS. DENISON OLMSTED, LL.D. PROFESSOR OP NATURAL PHILOSOPHY AND ASTEONOMT IX TALE COLLEGB. The stars ! the stars ! go forth by night. Lift up thine eyes on high. Anil Tiew the countless orbs of light Which gem the vaulted sky : Go forth hi silence and .lone. This glorious sight to scan ; And bid thy humbled spirit own The littleness of man." BABTO.X. LONDON: T. NELSON AND SONS, PATERNOSTER ROW; EDINBURGH; AND NEW YORK. PREFACE. THE importance of divesting physical science, as far as possible, of all that is technical, and of bringing its most useful results within the reach of all classes of society, is well expressed in the following extract from the Edinburgh Review : " If the present age is distinguished by more clear and just views of social and political science, it is not less marked by the disposition, so unequivocally and universally manifested, to reject the inordinate esti- mate heretofore set upon merely ornamental literature; and while it does not refuse their just rank and influ- ence to such studies, it admits to that high considera- tion to which they are entitled, the sciences which explain the beautiful phenomena of the physical world. " The public now demand of those professionally devoted to the sciences, that they shall not confine the knowledge they have such favoured opportunities of acquiring, to the lecture-room, but shall render it, as far as practicable, available to the well-informed of all professions, and to the more intelligent, at least, of the other sex." The present work, it is hoped, will evince that it is j)ossible to present the most profound truths of the 2? PREFACE. THE importance of divesting physical science, as far as possible, of all that is technical, and of bringing its most useful results within the reach of all classes of society, is well expressed in the following extract from the Edinburgh Review: " If the present age is distinguished by more clear and just views of social and political science, it is not less marked by the disposition, so unequivocally and universally manifested, to reject the inordinate esti- mate heretofore set upon merely ornamental literature; and while it does not refuse their just rank and influ- ence to such studies, it admits to that high considera- tion to which they are entitled, the sciences which explain the beautiful phenomena of the physical world. "The public now demand of those professionally devoted to the sciences, that they shall not confine the knowledge they have such favoured opportunities of acquiring, to the lecture-room, but shall render it, as far as practicable, available to the well-informed of all professions, and to the more intelligent, at least, of the other sex." The present work, it is hoped, will evince that it is j>ossible to present the most profound truths of the 2? -:G science of Astronomy in such a form, that they may bo fully comprehended by every intelligent reader. To discover its great truths, has indeed required the highest efforts of the human mind, continued for many ages, yet the truths themselves, when once discovered, are easy to be understood, being, in general, charac- terized by a high degree of simplicity. The leading truths of our science seem to the author to resemble those of Divine Revelation so simple as to be intelligible to the ordinary capacity, but so com- prehensive as to fill the largest intellect. YALE COLLEGE. %* To the present work by PROFESSOR OLMSTED, several additions have been made by another pen, so as to include the most recent discoveries in the science the remarkable demonstrations of ADAMS and LEVERRIER the astonishing disclosures of LORD ROSSE and other fruits of recent astro- nomical observation. In its present form, it is believed that the work will be found well suited for educational purposes, and at the same time an attractive reading book for the family circle, EDINBURGH, June 18cO. CONTENTS. CLap I'aj- L Introductory Observations, 13 IL Doctrine of the Sphere, 19 III. Astronomical Instruments. Telescope, 30 IV. Telescope con tin tied, 37 V. Observatories, 47 VL Time and the Calendar 60 VII. Figure of the Earth, 70 V11I. Diurnal Revolutions, 81 IX. Parallax and Refraction, 88 X The Sun, 99 XL Annual Revolution. Seasons, 108 XIL Laws of Motion, 123 XIIL Terrestrial Gravity, 130 XIV. Sir Isaac Newton. Universal Gravitation. Figure of the Earth's Orbit. Precession of the Equinoxes, ... 138 XV. The MOOP, 151 XVL The Moon. Phases. Harvest Moon. Librations, ... 165 XVII. Moon's Orbit Her Irregularities, 174 XVI1L Eclipses, ^ 185 XIX. Longitnde.-Tides, 198 XX. Planets, Mercury and Venus, 213 XXL Superior Planets: Mars, Jupiter, Saturn, Uranus, and Neptune, 230 XXIL Copernicus. Galileo, 241 XXI IL Saturn. Uranus. Neptune and the Asteroids, 209 XXIV. The Planetary Motions. Kepler's Laws. Kepler, ... 276 XXV Comets. .. 296 Xii CONTEXTS. Chap. Page XXVL Comets, continued 314 XXVIL Meteoric Showers, 325 XXVIII. Fixed Stars, 342 XXIX. Fixed Stars.-eonft/nMd, 358 XXX System of the World, 366 XXXI. Conclusion. - ,. -. . . 380 Description of Views of Milky Way and Nebulae 387 MECHANISM OF THE HEAVENS. CHAPTER I. INTRODUCTORY OBSERVATIONS. Give me the ways of wandering stars to know, The depths of heaven above, and earth below ; Teach me the various labours of the moon. And whence proceed the eclipses of the sun; AVhy 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 VI ASTRONOMY is either a very difficult or a comparatively CHAP. I easy study, according to the view we take of it. The in- llie ^ y o vestigation of the great laws which govern the motions of astronomy, 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, " God said, let there be light, and there was light;" and the doctrine of universal gravitation, the key 14 INTRODUCTORY OBSERVATIONS. CTIAP. L which unlocks the mysteries of the universe, is simply this, Sim licit of ^at everv portion of matter in the universe tends towards the laws of every other. The three great laws of motion, in like man- the universe. ^^ ^ wlien s ^ e ^ so pl a i T , ; 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 mo- tion, will continue so, until some force stops them, appears so much a matter of course, that we may be apt to question its claim to 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. Results of It is, therefore, a pleasing consideration to those who st s udy! omicul have not either the leisure or the abilit y 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 the labour of ages to unfold. The descriptive part 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 aston- ishment. Practicaluse. The great practical use of astronomy is its 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, it is asked, what advantages the study of astronomy promises, as a branch of education, I answer, that few subjects promise to the mind so much Advantages profit and entertainment. It is agreed by writers on the of the study. numan 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 ele- vate, the latter depress, the mind, to their own level. Now, every thing in astronomy is great. The magnitudes, dis- tances, and motions of the heavenly bodies ; the amplitude of the firmament itself ; and the magnificence of the orbs INTRODUCTORY OBSERVATIONS. 15 with which it is lighted, supply exhaustless materials for CHAP. L contemplation, and stimulate the mind to its noblest efforts, influence of The emotion felt by the astronomer is not that sudden ex- tlie study, citement or ecstacy, which wears out life, but it is a con- tinued glow of exalted feeling, which gives the sensation of breathing 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. It is the privilege of the student of this department of Facilities of nature, that his cabinet is already collected, and is ever the 8tudent before him. 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 Aidofima- a personification, like that which the ancients gave to the e inatlon - 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 be- comes 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 com- power of the mand the aid of telescopes of higher and higher powers, new acquaintances are made every night. The sight of each new member of the starry train, that his instruments successively reveal 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, 16 INTRODUCTORY OBSERVATIONS. CHAP. I. unperceived and unknown to his fellow-mortals. The same personification is given to these objects as to the constella- tions, and he seems to himself, at times, when he has pene- trated into the remotest depths of ether, to enjoy the high prerogative of holding converse with the celestials. Simplicity of It is no small encouragement, to one who wishes to the subject. ac q u j re 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 conve- nience, the sphere is divided, and receiving the great laws Reqnisitesfoi O f astronomy on the authority of the eminent persons who St " dy ' have investigated them, the reader will meet with few hard terms, or technical distinctions, to repel or perplex him ; and will, I hope, find that nothing but an intelligent mind and fixed attention are requisite for perusing the following pages. I shall indeed be greatly disappointed, if the peru- sal does not inspire him with some portion of that pleasure, which I have described as enjoyed by the astronomer him- self. S-wtsT 0ntS T ^ e Dignity of the study of the heavenly bodies, and its suitableness to the most refined and cultivated mind, has been recognized in all ages. Virgil celebrates it in the beautiful strains with which I have headed this chapter, and similar sentiments have ever been cherished by the greatest minds. Scope of the As, in the course of these chapters, I propose to trace an outline of the history of astronomy, from the earliest ages to the present time, this may be thought 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 sub- Early cuiti- ject; but it may be stated here, that astronomy was culti- vated the earliest of all the sciences ; that great attention was paid to it by several very ancient nations, as the Egyp- tians and Chaldeans, and the people of India and China, before it was studied in Greece. More than six hundred years before the Christian era, however, it began to receive attention in this latter country. Thales and Pythagoras were particularly distinguished for their devotion to this INTRODUCTORY OBSERVATIONS. 17 science j and the celebrated school of Alexandria, in Egypt, CHAP. I. which originated about three hundred years before the AncienT Christian era, and flourished for several hundred years, astronomers numbered among its disciples a succession of eminent astro- nomers, 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 princi- pal text-book in astronomy for many centuries afterwards, and comparatively few improvements were made on it until the age of Copernicus. This celebrated astronomer was Copernicui 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 Theory of now known to be the true theory of the celestial motions, 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 unconscious of the motion of the ship that carries us from it. Although many of the appearances presented by the Fallacies of motions of the heavenly bodies may be explained on the uypotl 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 practi- cable 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, in- stead of threading their way through the mazes of error. Near the close of the sixteenth century, Tycho Brahe, a Tycho Braiie. native of Sweden, but resident in Denmark, carried astro- 18 INTRODUCTORY OBSERVATIONS. CHAP. I. nomical observations (which constitute the basis of all that is valuable in the science) to a far greater degree of per- fection than had ever been done before. Kepler, a native Kepler 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 labours. Galileo, the Galileo. great Italian astronomer, 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 commence- ment of the seventeenth century, (1620,) Lord Bacon, the celebrated English philosopher, pointed out the true Bacon. method of conducting all inquiries into the phenomena of Nature, and introduced the inductive method of reasoning. According to this method, we are to begin inquiries into the causes of events by first examining and classifying all the facts that relate to them, and, from the comparison of these, to deduce our conclusions. Newton But the greatest single discovery ever made in astrono- my, was the law of universal gravitation, established by Sir Isaac Newton in the latter part of the seventeenth century. The discovery of this law made us familiar with the hidden forces that move the great machinery of the universe. It furnished the key which unlocks the inner temple of Na- ture ; and from this time astronomy may be regarded as fixed on a sure and immoveable basis. I shall hereafter endeavour to explain the leading principles of universal gravitation, when we come to the proper place for inquir- ing into the causes of the celestial motions, as exemplified in the motion of the earth around the sun. DOCTBINE OF THE SI'HKliE- 19 CHAPTER IT. DOCTBINE OF THE SPHERE. All are but parts of one stupendous whole, Whose body Nature is, and God the soul. POFJS. LET us now consider what astronomy is, and into what CHAP II, great divisions it is distributed, preparatory to taking a cur- whatlT sory view of the doctrine of the sphere. This subject will astronomy \ probably be less interesting to the reader than many that are to follow ; but still I must urge upon him the necessity of studying it with attention, and reflecting upon each defi- nition, until he fully understand it ; for, unless he 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 the young student of astronomy, therefore, to pause upon eveiy para- graph of this chapter ; and if there is any point in the whole which he cannot clearly understand, I would advise him to mark it, and to recur to it repeatedly ; and, if he finally cannot obtain a clear idea of it himself, I would recommend him to apply for aid to some of his friends who may be able to assist him. Astronomy is that science which treats of the heavenly Definition. 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 astro- Subdivisions nomy 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 Deicriptire the phenomena of the heavenly bodies, whether pertaining Mtl to those bodies individually, or resulting from their motions 20 DOCTRINE OP THE SPHERE. astronomy. Doctrine of the sphere. Measuring angles. Degrees. Fig. 1. CHAP. ii. and mutual relations. It is the part of Physical Astronomy Physical' to explain the causes of these phenomena, by investigating the general lavra on which they depend ; especially, by trac- ing out all the consequences of the law of universal gravi- tation. 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 the reader's recollection a few particulars respecting the method of measuring angles. A line drawn from the centre to the circumference of a circle is called a ra- dius, as CD, CB, or CK. Any part of the circum- ference of a circle is called an arc, as AB, or BD. An angle is measured by an arc included between the two radii. Thus, in Fig. 1, the angle contained between the two radii, CA and CB, that is, the angle ACB, is measured by the arc AB. Every circle, it will be recollected, is divided into tliree hundred and sixty equal parts, called degrees ; and any arc, as AB, contains a certain number of degrees, according to its length. Thus, if the arc AB contains forty degrees, then the opposite angle ACB is said to be an angle of forty degrees, and to be measured by AB. But this arc is the same part of the smaller circle that EF is of the greater. The arc AB, therefore, contains the same number of degrees as the arc EF, and either may be taken as the measure of the angle ACB. As the whole circle contains three hundred and sixty degrees, it is evident that the quarter of a circle, or qvadrant, contains ninety degrees, and that the semicircle ABDG contains one hundred and eighty degrees. The complement of an arc, or angle, is what it wants of ninety degrees. Thus, since AD is an arc of ninety degrees, Complement of an arc. DOCTRINE OP THE SPHERE. 21 BD Is the complement of AB, and AB is the complement CHAP, n of BD. If AB denotes a certain number of degrees of lati- tude, BD 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 Supplement one hundred and eighty degrees. Thus, BA is the supple- ofan arc- ment of GDB, and GDB is the supplement of BA. If BA were twenty degrees of longitude, GDB, 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 ACK, the angle at C is subtended by the side AK, the angle at A by CK, and the angle at K by CA. In like manner, a side is said to be subtended by an angle, as AK 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 man- circles ner, is a circle. Great circles are those which pass through the centre of the sphere, and divide it into two equal hemi- spheres. 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 poiea. the point on the sphere where its axis cuts through the sphere. Every great circle has two poles, each of which is everywhere ninety degrees from the great circle. All great circles of the sphere cut each other in two points diametri- cally 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 be- tween those two circles. In order to fix the position of any place, either on the The spheres, surface of the earth, or in the heavens, both the earth and the heavens are conceived to be divided into separate por- tions, by circles, which are imagined to cut through them, in various ways. The earth thus intersected is called the 22 DOCTBINE OP THE SrHERE. CHAP. II. terrestrial, and the heavens the celestial, sphere. We must ThelTnse. bear in mind > ^ at ^ese circles have no existence in nature, but are mere landmarks, artificially contrived for convenience of reference. On account of the immense dis- tances 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, be- come circles of the celestial sphere. The horizon. The horizon is the great circle which divides the earth into upper and lower hemispheres, and separates the visi- ble heavens from the invisible. This is the rational hori- zon. 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. Zenith and 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 weight by a string) is in the axis of the horizon, and consequently directed toward its poles. Every place on the surface of the earth has its own hori- zon ; and the traveller has a new horizon at every step, always extending ninety degrees from him, in all directions. Definition of Vertical circles are those which pass through the poles of rclefL 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 though 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. DOCTRINE OP THE SPHERE. 23 The amplitude of a body is its distance, on the horizon, CHAP. IL from the prime vertical to a vertical circle passing through the body. Azimuth is reckoned ninety degrees from either the The azimuth 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 Zenith circle passing through that body. It is the complement of dlstance - the altitude. The axis of the earth is the diameter on which the earth Axis of tho is conceived to turn in its diurnal revolution. The same earth< 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 Poles, axis : the poles of the heavens, the extremities of the celes- tial axis. The equator is a great circle cutting the axis of the earth Equator. 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 Meridians passing through the poles of the equator, are called meri- dians, 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, pass- ing, as it does, through the poles of both. These seconda- ries are also called hour circles, because the arcs of the equator intercepted between them are used as measures of time. 24 DOCTRINE OF TUB SPHERE. CHAP. IL The latitude of a place on the earth is its distance from the equator north or south. The polar distance, or angular Latitude. Distance from the nearest pole, is the complement of the latitude. Longitude. The longitude of a place is its distance from some stand- ard 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 Green- wich. Ecliptic. 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 perpendi- cular 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 im- portant that we should form correct ideas of the ecliptic, and of its relations to the equator, since to these two cir- cles a great number of astronomical measurements and phe- nomena are referred. Equinoxes. 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 ver- nal equinox occurs about the twenty-first of March, and the autumnal, about the twenty-second of September. Solstices. 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 DOCTRINE OF THE SPHERE. 25 solstice about the twenty-second of December. The eclip- CHAP. IL tic is divided into twelve equal parts, of thirty degrees each, signs of the called signs, which, beginning at the vernal equinox, sue- zodiac, ceed each other in the following order : 1. Aries, 7. Libra, -d, 2. Taurus, & 8. Scorpio, n^ 3. Gemini, II 9. Sagittarius, / 4. Cancer, OB 10. Capricornus,vy 6. Leo, $[, 11. Aquarius, yz 6. Virgo, TTJ 12. Pisces, X The mode of reckoning on the ecliptic is by signs, de- Modeot grees, minutes, and seconds. The sign is denoted either by the ecliptic its name or its number. Thus, one hundred degrees may be expressed .either as the tenth degree of Cancer, or as three seconds ten degrees. 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 recognize each sign by its appropriate character. Of the various meridians, two are distinguished by the Coinres. name of colures. The equinoctial colure is the meridian which passes through the equinoctial points. From this meridian, right ascension and celestial longitude are reck- oned, as longitude on the earth is reckoned from the meri- dian of Greenwich. The solstitial colure is the meridian which passes through the solstitial points. The position of a celestial body is referred to the equa- Right aacen- tor by its right ascension and declination. Right ascension 8ion- 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 Declination body from the equator measured on a secondary to the lat- ter. 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. 26 DOCTBINE OF THE SPHERE. CHAP II. On the other hand, celestial longitude and latitude are Celestial referred, not to the equator, but to the ecliptic. Celestial longitude 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 : lati- tude, distance from the ecliptic. The north polar distance of a star is the complement of its declination. Parallels of Parallels of latitude are small circles parallel to the equa- utitude. tor> rpj iey cons ta n tiy diminish in size, as we go from the equator to the pole. The tropics are the parallels of la- titude which pass through the solstices. The northern tropic is called the tropic of Cancer ; the southern, the tro- pic 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. Elevation of The elevation of the pole of the heavens above the horizon the pole. o anv pj a(je . g a i wavs e q ua i t t h e 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 com- plement of the latitude. Thus, at the latitude of forty degrees north, the equator is elevated fifty degrees above the southern horizon. Zones. 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. Zodiac. The zodiac is the part of the celestial sphere which lies about eight degrees on each side of the ecliptic. This por- tion of the heavens is thus marked off by itself, because all the planets move within it. After endeavouring to form, from the definitions, as clear DOCTRINE OP THE SPHERE, 27 an idea as we can of the various circles of the sphere, we CHAP. n. may next resort to an artificial globe, and see how they are Mod will be the equator; and several other circles cut between the equator and the poles, parallel to the equator, will re- present parallels of latitude; of which, two, drawn twenty- three and a half degrees from the equator, will be the tro- pics, 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 meri- 28 DOCTRINE OP THE SPHERE. CHAP. II. dian, 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 Meridians circles. A great circle cut through the centre of the earth, and plane. f rom 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 terres- trial 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. Horizon. The horizon is best represented -by a circular piece of pasteboard, cut so as to fit closely to the apple, being move- able 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 de- grees every way from it. Suppose we are in latitude forty degrees ; then let us place our moveable 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. Value of the Simple as the foregoing device is, if the student will take the trouble to construct one for himself, it will lead him to more correct views of the doctrine of the sphere, than he 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 in- adequate. When he has thus made a sphere for himself, or, with an artificial globe before him, if he have access to one, he must proceed to point out on it the various arcs of azimuth and altitude, right ascension and declination, ter- restrial and celestial latitude and longitude, these last being referred to the equator on the earth, and to the ecliptic in the heavens. Projection of When the circles of the sphere are well learned, we may the sphere, advantageously employ projections of them in various illus- trations. By the projection of the sphere is meant a repre- sentation of all its parts on a plane. The plane itself is BOCTBINE OF THE SPHERE. 29 called the plane of projection. Let us take any circular CHAP. IL ring, as a wire bent into a circle, and hold it in different pj a ne of positions before the eye. If we hold it parallel to the face, Projection, 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 perpendi- cular 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. It is in this manner that the circles of the sphere are illustration of projected, as represented in the following diagram, (Fig. 2.) the sphere. z Here, various circles are represented as projected on the me- ridian, which is sup- posed to be situated directly before the eye, at some distance from it. The horizon HO, being perpendi- cular to the meridian, is seen edgewise, and consequently is pro jected into a straight line. The same is the case with the prime vertical ZN, with the equator EQ, 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, ex- except the prime vertical, being seen obliquely, as ZMN, will be projected into an ellipse, one-half only of which is 30 ASTRONOMICAL INSTRUMENTS. TELESCOPE. seen, the other half being on the other side of the plane of projection. In the same manner, PUP, an hour circle, is represented by an ellipse on the plane of projection. CHAPTER 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. BEATIIK. CHAP. in. IF, as I trust, the reader has gained a clear and familiar Advantage of knowledge of the circles and divisions of the sphere, and of previous the mode of estimating the position of a heavenly body by its azimuth and altitude, or by its right ascension and de- clination, or by its longitude and latitude, he 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. Observations The most ancient astronomers employed no instruments astronomers ^ 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. Our apparent Wherever we are situated on the earth, we appear to be position. j n ^ e cen t re O f a vas t S pi iere} 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 DBH (Fig. 3) represents the con- TELESCOPE. 31 CHAP. I1L cave surface of the sphere, AB, two points on it, as two Arc of the stars, and CA, CB, straight lines drawn from the spectator sky- to those points, then the angular distance between them is measured by the arc AB, or the angle ACB. But this angle may be measured on a much smaller circle, having the same centre as GFK, since the arc EF will have the same number of degrees as the arc AB. The simplest Modeoftak - mode of taking an angle between two stars is by means of in s ^ an s!e. an arm opening at a joint like the blade of a penknife, the end of the arm moving like CE upon the graduated circle KFG. In fact, an instrument constructed on this prin- ciple, resembling a carpenter's rule with a folding joint, with a semicircle attached, constituted the first rude appa- ratus 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. The common surveyor's compass, affords a simple example surreyor's of angular measurement. Here, the needle lies in a north c 0111 ? 888 - 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 Advantage of more minutely its limb may be divided. If the circle is one a l * rse circle ' 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 32 ASTRONOMICAL INSTRUMENTS. CHAP. III. space one thirtieth of an inch. Refined astronomical circles DiTision~of are now divided with very great skill and accuracy, the astronomical 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 in- struments, the measurements extend to a single second of space, or one thirty-six hundredth part of a degree, a Minute mea- space, on a circle twelve feet in diameter, no greater than surement one fifty. seve n hundredth part of an inch. To divide, or graduate, astronomical instruments, to such a degree of nicety, requires the highest efforts of mechanical skill. In- deed, 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. Astronomical I will endeavour to make the reader acquainted with instruments, several of the principal instruments employed in astrono- mical observations, but especially with the telescope, which is the most important and interesting of them all. I think I shall consult his wishes, as well as his improvement, by giving him 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 tele- ^ ne Telescope, as its name implies, is an instrument em- seop- ployed for viewing distant objects.* 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 prin- ciple 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 ly a microscope, ' From two Greek words, rtt A, I. (tefe,) far, and rxtviu- (skopeo,) te tee. TELESCOPE. 33 Let us first see how the image is formed. This may be CHAP. in. done either by a convex lens, or by a concave mirror. A F 0rn ^^ n { convex lens is a flat piece of glass, having its two faces con- Hie imaga. vex, or spherical, as is seen in a common sun-glass, or a spectacle-eye. 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 repre- sented in the following diagram. Let ABCD (Fig. 4) Refracting 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, Combination which receives the rays of light from the moon, and col- lects them into the focus at a, forming an image of the moon. This image is viewed by a magnifier attached to the end BC. The lens, L, is called the object-glass, and the microscope in BC, the eye-glass. We apply a microscope use of the to this- image just as we would to any object ; and, by Bllcro co P- greatly enlarging its dimensions, we may render its various pails far more distinct than they would otherwise be ; while, at the same time, the lens collects a.nd conveys to the eye a much greater quantity of light than would- pro- ceed 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. 34 ASTRONOMICAL INSTRUMENTS. CHAP. II L But the image may also be formed by means of a concave Concave" mirror, which, as well as the convex lens, has the property mirror. o f 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 micro- scope, in the same manner as when formed by the convex lens. When the lens is used to form an image, the instru- ment is called a refracting telescope; when a concave mirror is used, it is called a reflecting telescope. Object glass. 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 eye-glass. 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. inventor of 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 acciden- tally hit upon a discovery, by which distant objects might be brought apparently nearer ; and, without further infor- mation, 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 tele- scope which bears his name. Galileo's Although the telescopes made by Galileo were no larger telescopes, than a common glass 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 satel- lites of Jupiter, and multitudes of stars which are invisible to the naked eye, the discovery 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 Scottish astronomer, whose name is still employed to designate the Gregorian telescope. Newton's first The first telescope made by Newton was only six inches telescope. long, and its reflector was little more than an inch in diameter. Notwithstanding its small dimensions, it per- TELESCOPE. 35 formed so well, as to encourage further efforts ; and this CHAP. ill. 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 care- fully preserved in the library of the Society. Newton was induced to undertake the construction of Newton's reflecting telescopes, from the belief that refracting tele- ifmitsof'' 6 scopes were necessarily limited to a very small size, with ^JJ^g^ only moderate illuminating powers, whereas the dimensions and powers of the former admitted of being indefinitely in- creased. 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. The experi- ments of Newton on colours led him to believe, that it would be impossible to employ large lenses in the construc- tion of telescopes, since such glasses would give to the images they formed, the colours of the rainbow. But later Experience opticians have found means of correcting these imperfec- of I* 4 ? 1 " tions, 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 chromatic a name implying the absence of prismatic or rainbow telescope, colours 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 they distort the light, and produce confused images. The achromatic telescope (that is, the refracting tele- Dollond's . . . instrument scope, having such an object-glass as to give a colourless 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 en- abled him to carry his invention at once to a high degree of perfection. It has ever since been a matter of the greatest difficulty, with the manufacturers of telescopes, to find 30 ASTRONOMICAL INSTRUMENTS. CHAP. in. pieces of glass, of a suitable quality for object-glasses, Difficulty of niore than two or three inches in diameter. Hence, large obtaining achromatic telescopes are veiy 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 twenty-four pounds, one whose aperture is eight inches would cost one thousand five hundred and twenty pounds. Comparison Since it is so much easier to make large reflecting than and e refracf- lar g e refracting telescopes, it may be asked, why the latter ing tele- ar e 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 the next chapter, I shall give an account of some of the most celebrated telescopes that have ever been con- structed, and point out the method of using this excellent instrument, so as to obtain with it the finest views of the heavenly bodies. 37 CHAPTER IV. TELESCOPE CONTINUED. the broad circnmference Hung on his shoulders like the moon, whose orb Through optic glass the Tuscan artist views At evening, from the top of Kesole Or in Valdarno, to descry new lands. Rivers or mountains, !n her spotted globe. MTLTOM. THE three most celebrated telescopes, hitherto made, are CHAP. IV Herschel's forty-feet reflector, the great Dorpat refractor, c r~r . and the still more remarkable telescope recently completed telescopes. by Lord Rosse. 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 III., he Herschel's completed, in 1789, his great telescope, having a tube of telescope- iron, forty feet long, and a speculum, forty-nine and a half inches, or more than four feet in diameter. Let us endea- vour 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. The reflector alone weighed nearly Requisite a ton. So large and ponderous an instrument must require macluner y. a vast deal of machinery to work it, and to keep it steady ; and, accordingly, the frame-work surrounding it was formed of heavy timbers, and resembled the frame of a large build- ing. When one of the largest of the fixed stars, as Sirius, Sirius, is entering the field of this telescope, its approach is an- nounced 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 in- 38 ASTRONOMICAL INSTRUMENTS. CHAP. IV. numerable multitudes of stars are scattered like glittering dust over the celestial vault. Dorpat The great Dorpat telescope is of more recent construc- telescope. ^.j on ^ jj. wftg ma( j e fry F ra unhofer, a German optician, of the greatest eminence, at Munich, in Bavaria, and takes its name from 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. its cost Although the price of this instrument was nearly one thousand two hundred pounds sterling, yet it is said that this sum barely covered the actual expenses. It weighs five thousand pounds, and yet is turned with the Superiority finger. In facility of management, it has greatly the advantage of Herschel's telescope. Moreover, the sky of England is so frequently unfavourable 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, as well as from 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 to ^ of"" eat part of tlie neavens - This remark shows that such great telescopes, telescopes are unsuited to the common purposes of astrono- mical 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 sufficient. The highest power of the Dorpat telescope is only seven hundred, and yet the Director of this instrument, Professor Struve, is of opinion that it is nearly or quite equal in quality, all things considered, to Herschel's forty- feet reflector. Lord Rosse's j} u t ^he largest astronomical instrument yet constructed for the purpose of surveying the heavens, is what has been popularly styled Lord Rosse's Monster Telescope. The Earl of Rosse, an Irish nobleman, who greatly distinguished himself even while a student at one of the English univer- sities, has devoted his wealth and skill to the construction of reflecting telescopes of the most gigantic proportions. By TELESCOPE. 39 means of the most ingenious mechanical contrivances, he CHAP, iv has succeeded in overcoming the difficulties which have Manufacture hitherto impeded the manufacture, grinding, and polish- of specula, ing of specula. The student who is only accustomed to the small hand instruments usually furnished by the opti- cian, will find it almost as difficult to conceive of the proportions of this gigantic telescope, as to form any ade- quate conceptions of some of the vast computations which enter into the calculations of the astronomer. The weight of the instrument is above fifteen tons. Nevertheless such is the admirable nature of the machinery attached to it, that two men can move it with ease, while the observer, by means of shifting galleries completely under his own con- trol, is rendered almost as independent as in the use of a small refracting telescope. The great tube is constructed Construction of deal, and the lower part, in which the speculum is placed, is a cube of eight feet. The circular part of the tube, at the upper end, measures at its centre seven and a half feet in diameter, and at its extremities six and a half feet. The diameter of the large speculum, on which nearly the whole value of the instrument depends, is six feet, its thickness five and a half inches, and its focal length fifty-four feet. It is composed of one hundred and twenty-six parts of copper to fifty-seven and a half parts of tin, and weighs three and three-fourth tons. This great telescope is sus- Mode of pended between two stone walls about fifty feet high, placed, suspena as nearly as possible, parallel with the meridian. In the interior face of the eastern wall, a very strong iron arc, of about forty-three feet radius, is firmly fixed, and provided with adjustments, whereby its surface facing the telescope may be accurately set in the plane of the meridian. The first time this wonderful instrument was turned to the heavens, many of the most remarkable nebulae were found to be resolved into groups, or clusters of stars, seen then for the first time as such, by human eye, since their creation. " Never," says Sir James South, in describing his first view First view o( of the heavens through Lord Rosse's telescope " never, in tlie heaTens> my life, did I see such glorious sidereal pictures as this in- strument afforded us." Still further improvements, however, have since greatly increased the power of this remarkable astronomical instru- 40 ASTRONOMICAL INSTRUMENTS. Improve- ments sug- gested. Disposition of the specula. Plan pro- posed by Newton. Improve- ments of Le Maire. ment, and chiefly by the combination of the Le Mairean, with the Newtonian principle. Sir James South illustrates the value which such an improvement would give, in the following remarks on Lord Rosse's Telescope : " Thus the difficulty of constructing a Newtonian telescope of dimensions never before contemplated, is completely over- come ; but to render the part on which I am about to enter more generally intelligible, let me say, that the Newtonian telescope is composed of a large concave speculum, of a small flat speculum, and of an eye-glass. The large concave specxilum lies in the closed end of the tube, at right angles to the tube's axis. The small flat speculum is placed near the open end of the tube in its centre, but at half right angles with the tube ; whilst the eye-glass (a hole for the purpose being pierced in the tube's side) is fixed opposite the centre of the flat speculum. The rays from the object to which the telescope is directed fall on the large concave speculum, are reflected from it into a point called the focus, in which the image of the object is formed ; this image falls on the flat speculum, and is reflected from it to the eye- glass, by which it becomes magnified, and enters the ob- server's eye. But only a part of the light which falls on the large concave speculum is reflected on the small specu- lum ; and again, only a part of that which falls from the large speculum on the small one, is reflected from the latter to the eye-glass. Newton to avoid the loss of light by the second reflection, proposed the substitution of a glass prism for the small flat speculum ; but from some difficulties which have attended its use, it has (perhaps too hastily) been laid aside. " In 1728, Le Maire presented to the Academic des Sciences the plan of a reflecting telescope, in which the use of the small flat speculum was suppressed ; for by giving the large concave speculum a little inclination, he threw the image formed in its focus near to one side of the tube, where an eye-glass magnifying it, the observer viewed it, his back at the time being turned towards the object in the heavens ; thus the light lost in the Newtonian telescope by the second reflection was saved. " No one, however, seems to have availed himself of this form of construction till 1776, when Herschel, with a ten- TELESCOPE. 41 feet reflector, tried it, and rejected it. In 1784 he again CHAP. IV. tried it with a twenty-feet reflector, but again abandoned Herachei'i it. In 1786 he adopted it, eulogized it very much, among experiment* other advantages, for 'giving almost double the light of the Newtonian construction,' and called it ' the front view.' Sub- sequently to this period, all his twenty-feet telescopes, as well as his forty-feet telescope, were constructed as Le Maireans. " The excess of light, however, is very much overrated by Sir W. Herschel ; for experiments since made indicate that the diameter of the Newtonian telescope must be in- creased about one -fifth only to obtain equal light with one of the Le Mairean construction. " That we might have a practical proof of the advantages Lord Rosse's of the light of the Le Mairean construction, the three feet tnaL Newtonian of twenty-seven feet focus, which stands in the demesne by the side of the Leviathan, was temporarily fitted up as a Le Mairean. Stars of the first magnitude were seen, not well defined as in the Newtonian form of the instrument, but the superiority of the Le Mairean, where a large quantity of light was required, was most decided. The small pole-star was as bright as a star of the fourth superiority magnitude, when seen in an eight-feet achromatic of three and three quarters inches aperture. The dumb-bell nebulae, or twenty-seven of Messier, was resolved into clusters of stars in a manner never before seen with it. The annular nebulae of Lyra, brilliant beyond what it had ever yet ap- peared, was surrounded by stars too bright to escape imme- diate notice, although neither the dumb-bell nebulae nor the annular nebulas had more than fifteen degrees of altitude when I placed the telescope on them. " On the 15th of March, when the moon was seven days and a-half old, I never saw her unillumined disc so beau- ot the mooiL tifully, nor her mountains so temptingly measurable. On my first looking into the telescope, a star of about the seventh magnitude was some minutes of a degree distant from the moon's dark limb. Seeing that its occultation by the moon was inevitable, as it was the first occultation which had been observed by that telescope, I was anxious that it should be observed by its noble maker ; and very much do I regret that, through kindness towards me, he would not accede to my wish ; for the star, instead of dis- 42 ASTRONOMICAL INSTRUMENTS. CHAP. iv. appearing the moment the moon's edge came in contact Decollation with **> apparently glided on the moon's dark face, as if it of a star. had been seen through a transparent moon, or as if the star were between me and the moon. It remained on the moon's disc nearly two seconds of time, and then instantly disap- peared, at lOh. 9m. 5972s. sidereal time. I have seen this apparent projection of a star on the moon's face several times, but, from the great brilliancy of the star, this was the most beautiful I ever saw." Sir James South thus proceeds to compare the great telescopes : Comparison f]^ e on jy telescopes, in point of size, comparable with Lord Rosse's three feet and six feet, are Sir William Her- schel's twenty feet and forty feet Le Mairean's. The twenty feet had a speculum of 18'8 inches diameter, and the forty feet one of four feet. "The Le Mairean of 18'8 inches diameter, in point of light is equal to a Newtonian of twenty-two and a half inches diameter. " The Le Mairean of four feet diameter is equal to a New- tonian of fifty-seven inches and four-tenths. " The Le Mairean of three feet is equal to a Newtonian of forty-three inches. " And the Le Mairean of six feet is equal to a Newtonian of eighty-six inches. Effect of " By substituting, then, the Le Mairean form for the Le^airean 6 Newtonian, the present three feet Newtonian will be made principle. as effective as if it were forty-three inches diameter, and the six feet as if it were eighty-six inches in diameter ; or the quantity of light in each telescope, after the alteration, will be, to its present light, as seven to five nearly, or almost half as much again as it now has. " Seeing, then, that the change from the Newtonian to the Le Mairean construction will be attended with such an accession of light, Lord Rosse, having determined geome- trically the form of the curve requisite to produce with it a definition of objects equal to that which each of the tele- scopes at present gives, is devising mechanical means for producing it." Influence on The influence of this great instrument on modern science Science! has already been shown, by its discoveries completely over- throwing the nebular theory, by means of which philoso- TELESCOPE. 43 phers had fancied themselves able to expound a natural CHAP. IV doctrine of creation, and thereby establishing new views of the vastness of the universe, such as surpass even the most gigantic conceptions, which the calculations of the astro- nomer were so well fitted to suggest. It is not generally understood in what way greatness increase of of size in a telescope increases its powers ; and it conveys tefescopes. ' but an imperfect idea of the excellence of a telescope to tell how much it magnifies. In the same instrument, an in- crease of magnifying power is always attended with a dimi- nution 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 bpace. The several circumstances which influence the qua- Different lities of a telescope are illuminating power, magnifying power, distinctness, and field of view. 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 Advantage 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 tar- nished ; 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 Distinctness of an instrument. The object maybe sufficiently bright, of view< yet, if the image is distorted, or ill-defined, the illumina- tion is of little consequence. This property depends mainly on the skill with which all the imperfections of figure and colour in the glass or mirror are corrected, and can exist in 44 ASTRONOMICAL INSTRUMENTS. steadiness indispen- Use of a the student, Favourable states of weather. 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. Distinct- ness is very much affected by the steadiness of the instru- ment. 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 disc 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, when my readers have perused these chapters, or rather, while they are perusing them, they will have fre- quent opportunities of looking through a good telescope. I even anticipate that they will acquire such a taste for viewing the heavenly bodies with the aid of a good glass, that they will deem a telescope a most suitable appendage to their library, and as certainly not less an ornament to it than the more expensive statues with which some people of fortune adorn theirs. I shall therefore, before concluding this chapter, offer a few directions for using the telescope. Some states of weather, even when the sky is clear, are far more favourable 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 ex- panded, and rises, while the colder air descends, and thus ascending and descending currents of air, mingling toge- ther, create a confused and wavy medium. The same cause operates when a current of hot air rises from a chim- ney; and hence the state of the atmosphere in cities and large towns is very unfavourable 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 wea- ther also the air becomes smoky, and unfit for observation. Indeed, foggy, misty, or smoky air is so prevalent in some TELESCOPK. 45 countries, that only a very few times in the whole year can CHAP. iv. be found, which are entirely suited to observation, especially Rarityof with the higher powers ; for we must recollect that these *^ n8 f inequalities and imperfections are magnified by telescopes, observation, 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 hazi- ness, no violent wind, and no sudden change of tempera- ture. As a general fact, the warmer climates enjoy a much Advantages finer sky for the astronomer than the colder, having many climate" more clear evenings, a short twilight, and less change of temperature. The watery vapour 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 requi- Preparation site for the nicest observations with the telescope. He must be free from all agitation, and the eye must not re- cently 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 favourable state for observation. Under these disad- vantages, 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 steadiness of of the highest magnifiers ; for the motions of the instru- in truUM!nt - ment are magnified as well as the object. Hence, in the structure of observatories, the greatest pains is requisite, to avoid all tremour, and to give to the instruments all pos- sible 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 Value of low bodies than very high magnifiers. It may be thought ab- powers> 46 ASTRONOMICAL INSTRUMENTS, CHAP. iv. surd to recommend the use of low powers, in respect to large instruments especially, since it is commonly supposed other advan- 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 mag- nifying 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 magni- fiers ; for here, our object is to command as much light, and as large a field as possible, while it avails little to in- crease 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 Uses of draw- seen. Whenever we exhibit celestial objects to inexpe- rienced 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 telescopes ; 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. OBSERVATORIES, 47 CHAPTER V. OBSERVATORIES. We, though from heaven remote, to heaven will move, With strength of miud, 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 astro- CHAP. v. noraical observations, and furnished with suitable instru- ments for that purpose. The two most celebrated observatories hitherto built are Celebrated those of Tycho Brahe, and of Greenwich, near London, ^^ The observatory of Tycho Brahe was constructed at the expense of the King of Denmark, in a style of royal mag- nificence, and cost no less than two hundred thousand crowns. It was situated on the island of Huenna, at the Uranibnrg: entrance of the Baltic, and was called Uraniburg, or the palace of the skies. Before giving an account of Tycho's observatory, it will be useful to relate a few particulars respecting this great astronomer himself. Tycho Brahe was of Swedish descent, and of noble Ty*" 110 Brahe family ; but having received his education at the University of Copenhagen, and spent a large part of his life in Den- mark, he is usually considered 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, Eclipse of tha especially when he saw how accurately all the circumstances 9un - 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 48 OBSERVATORIES. CHAP. V. friends had destined him for the profession of law, and, Early mani- from the superior talents of which he gave early promise, festation of added to the advantage of powerful family connexions, they had marked out for him a distinguished career in public life. They therefore endeavoured to discourage him from pursuing a path which they deemed so much less glorious, 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 Royal did homage to his genius. The King of Denmark became his munificent patron, and James I., King of England, when he went to Denmark to complete his marriage with a Danish princess, passed eight days with Tyclio in his observatory, and, at his departure, addressed to the astro- nomer a Latin ode, accompanied with a magnificent present. Favour of the He gave him also his royal license to print his works in ' England, and added to it the following complimentary let- ter: " Nor am I acquainted with these things on the re- lation 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 4 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. Description Q) ne observatory consisted of a main building, which was vatory. " 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 splendour and ornament, by giving to every part of the structure an air of the most finished elegance. Nor were the instruments witli which it was furnished less magnificent than the buildings. They were vastly larger than had before been employed in the OBSERVATORIES. 49 survey ot the heavens, and many of them were adorned CHAP. V. with costly ornaments. One of Tycho's large and splendid Tyciio'sr instruments was his astronomical quadrant, on one side of quadrant which was figured a representation of the astronomer and his assistants in the midst of their instruments, and in- tently engaged in making and recording observations. The description of this instrument, furnished by his contempo- raries, 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, His rank and and supported throughout his establishment the etiquette 8tate 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 tele- scope, which was not yet invented. Tycho carried on his observations at Uraniburg for about Observations twenty years, during which time he accumulated an im- a mense store of accurate and valuable facts, which afforded the groundwork of the discovery of the great laws of the solar system established by Kepler, to whom I shall refer hereafter. But the high marks of distinction which Tycho enjoyed, Envy oftho not only from his own sovereign, but also from foreign cm 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 mo- narch, who did not feel the same 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 Their repre- the treasury was exhausted, and that it was necessary to entationa - retrench a number of pensions, which had been granted for useless purposes, ancf 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 withdraw to the hospitable mansion of a friend in Germany. Here he became known to the Emperor, who invited him to Prague, where, with an ample J> 50 OBSEKVATOKIES. Effects Of exile. Greenwich observatory CHAP. v. stipend, he resumed his labours. But, though surrounded Reception at with affectionate friends and admiring disciples, he was still Prague. 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 scien- tific 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 perse- vere in their scientific labours ; 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.* The observatory at Greenwich was not built until a hun- dred 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 go- vernment to lend their aid in erecting and maintaining this observatory. lit site. The site of the observatory at Greenwich is on a com- manding eminence facing the river Thames, five miles east of the central parts of London. Being part of a royal park, the neighbouring grounds are in no danger of being occu- pied by buildings, so as to obstruct the prospect. It is also Daily signal. in fall vievv of the shipping on the Thames ; and, according to a standing regulation, at the instant of one o'clock, every day, a huge ball is dropped from the top of a staff on the observatory, 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 instru- ments, 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 Brewster's Life of Newton, OBSERVATORIES. 51 observations, has contributed more than all other institu- CHAP. v. tions to perfect the science of astronomy. To preside over and direct this great institution, a man Astronomer of the highest eminence in the science is appointed by the r y 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 obser- vatory. The astronomers royal of the Greenwich observa- tory, 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 chapters. Six assistants, besides inferior labourers, are constantly Assistants. 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 Greets an observatory are, a commanding and unobstructed view of the heavens ; freedom from causes that affect the trans- parency and uniform state of the atmosphere, such as fires, smoke, or marshy grounds ; mechanical facilities for the management of instruments, and, especially, every precau- tion that is necessary to secure perfect steadiness. This last steadinew. 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 moveable dome for Movcable a roof, capable of revolving on rollers, so that instruments or penetrating through the roof may be easily brought to bear upon any point at or near the zenith. It will not perhaps be desired that I should go into a minute description of all the various instruments that are used in a well-constructed observatory. Nor is this neces- aen 52 OBSERVATORIES. CHAP. v. sary, since a very large proportion of all astronomical obser- Meriatan and va ^i ns are taken on the meridian, by means of the transit transit instrument and clock. When a body, in its diurnal revo- lution, 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 favourable 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 im- portant members of an astronomical observatory, and some account of these instruments becomes indispensable. Transit The transit instrument is a telescope which is fixed per- manently in the meridian, and moves only in that plane. The accompanying diagram (Fig 7) represents a side view Fig. 7. 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 hori- zon through the zenith to the north point. It can there- OBSERVATORIES. 53 fore be so directed as to observe the passage of a star across CHAP. v. the meridian at any altitude. The accompanying graduated Graduated circle enables the observer to set the instrument at any circl e. 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 Spirit level the axis is exactly on a level with the horizon. The frame- work 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 instru- ment to a perfect level. The transit instrument is some- times fixed immoveably to a solid foundation, as a pillar of etone, whieh 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 Use of tne instant when a heavenly body is on the meridian, or to instrument measure the time it occupies in crossing the meridian. The astronomical clock is the constant companion of the transit Astronomical instrument. This clock is so regulated as to keep exact 0< 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 Sidereal time. commences when the vernal eqxiinox is on the meridian, just as solar time commences when the sun is on the meri- dian. Hence the hour by the sidereal clock has no corres- pondence with the hour of the day, but simply indicates how long it is since the equinoctial point crossed the meri- dian. For example, the clock of an observatory points to Exnmpia three hours and twenty minutes; this may be in the morn- ing, 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, 64 OBSERVATORIES. CHAP. V. which, it will be recollected, is the angular distance mea- sured 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 astronomi- cal observations ai-e taken when the bodies are on the meri- dian, by means of the transit instrument and clock. Manner of Having now described these instruments, I will next ex- usingjnstm- pj a ; n ^ Q manner of using them for different observations. Anything becomes a measure of time, which divides dura- tion equally. The equinoctial, therefore, is peculiarly adapted ' j^ r , v lo this purpose, since, in the daily revolutions of the hea- vens, equal portions of the equinoctial pass under the meri- dianjn equal times. The only difficulty is, to ascertain the amount l)f these portions for given intervals. Now, the The clock, 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- $V i plate of the clock while the equator turns once by the revo- V lution 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 anywhere between the equator and the pole will move in its diurnal circle along with the clock, in the same manner as though . Decrees of it were in the equinoctial. Hence, if we note the interval riKiu'asceu- of time between the passage of any two stars, as shown by tkm - ' ., Jhe clock, we have a measure of the number of degrees by *- y-- rWhich 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 when a body is on the meri- -^ ^-dian; the clock indicates how long it is since the vernal *\fr* x^ u b_ qu' nox passed it, which is the right ascension itself; or it V . "^ rf /*^J> l tfells the difference of right ascension between any two ^yfe vd^* bodies, simply by indicating the difference in time between Declination their periods of passing the meridian. Again, it is easy to meridian. ta ^ e the declination of a body when on the meridian. By declination, the reader 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 meri- dian, if, on the instant of crossing the meridian wire of the OBSERVATORIES. 55 telescope, \\ e take its distance from the north pole, (which CHAP. v. may readily be done, because the position of the pole is al- Distance ways known, being equal to the latitude of the place,) and from north subtract this distance from ninety degrees, the remainder ^ e ' , . ^ ? } will be the distance from the equator, which is the declina- ; tion. It will be asked, why we take this indirect method fi^ <&. 4 of finding the declination? Why we do not rather take the j rvi ^ / 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, rs there is nothing to mark the exact situation of the equi- noctial, it is not so easy to take direct measurements from it. When we have thus determined the situation of a Laying down heavenly body, with respect to two great circles kt 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 through 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 Other uses, 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 Apparent and noon. But watches and clocks usually keep mean time, mean tini& and therefore, in order to set our time-piece by the transit instrument, we must apply to the apparent time of noon the equation of time, as is explained in the next chapter. A noon-mark may easily be made by the aid of the transit Noon mark, instrument. A window sill is frequently selected as a suit- able 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 sha- dow, 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 OBSERVATORIES. Method of making one. signal, as the stroke of a bell, the inhabitants of a town may all fix a noun-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 Ts required. As a noon-mark is convenient for regulating time-pieces, 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 thesun, with ^pair of com- passes 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 tbese 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 cross- ing the wire will be more definite, than in the winter. At this time of year, also, the sun and clock agree, or are to- gether, as is more fully explained in the next chapter; 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 flat- tened, 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, OBSERVATORIES. X 57 will be a larger space on the limb of an instrument, in CHAP. v. proportion as the instrument itself is larger. The vertical vertical" circle usually connected with the transit instrument, as in circle. 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 the Latin word, murus, which signifies a wall. Fig. 8. The diagram (Fig. 8) represents a mural circle fixed Repre*enta- to its wall, and ready for observations. It will be seen, $i fmural Expedients for firmness. Micrometer and micro- scope. Difficulty of making per- fect instru- ments. Rani of in strument makers. 58 OBSERVATORIES. that every expedient is employed to give the instru- ment firmness of parts and steadiness of position. The circle is of solid metal, usually of brass, and it is strength- ened 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, is 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 subdi- vide 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 hun- dredth 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. From these statements, the reader 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 con- structing 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 dis- tinguished 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 deli- cate 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 OBSERVATORIES. 59 described. It is particularly valuable for measuring celes- CHAP. V. tial arcs at sea, because it is not, like most astronomical instruments, affected by the motion of the ship. The prin- Principle of ciple of the sextant may be briefly described, as follows : it aon. nStl gives the angular distance between any two bodies on the celestial sphere, by reflecting the image of one of the bodies BO as to coincide with the other body, as seen directly. The arc through which the reflector is turned, to bring the re- flected body to coincide with the other body, becomes a measure of the angular distance between them. By keep- ing this principle in view, the reader will be able to under- stand the use of the several parts of the instrument, as they are exhibited in the diagram, Fig. 9. l"iff -9- Diagram. The sextant is of a triangular shape, and is made strong and firm by metallic cross-bars. It has two reflec- tors, 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 60 OBSERVATORIES. CHAP. v. to the moveable arm, ID, and turns as this is moved along GiasseTand the graduated limb, EF. This arm also carries a vernier, vernier. a t I), 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 re- flector. Angular Suppose it were required to measure the angular distance 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 moveable arm, ID, is moved from P to- wards 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. CHAPTER VI. TIME AND THE CALENDAR. From old Eternity's mysterious orb Was Time cut off, and cast beneath the sides. To UNO. CHAP. VL THE reader who has hitherto been conversant only with the Measurement many fine and sentimental things which the poets have of time. sung respecting Old Time, will, perhaps, find some difficulty V* 1 f. in bringing down his mind to the calmer consideration of what time reallyJa. and according to what different stan- dards it is measured for different purposes. He will not, however, I think, find the subject even in our matter-of- fact and unpoetical way of treating it, altogether uninter- TIME AND THE CALENDAR. 61 esting. What, then, is time.? Time is a measured portion CHAP. VI. of_j,ndefinite duration. It consists of equal portions cut off e fl^jti^ n O f from eternity, as a line on the surface of the earth is sepa- tim *- rated from the contiguous portions which 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 web of un- known or indefinite extent. Any thing, or any event which takes place at equal in- Measure of tervals, may become a measure of time. Thus, the pulsa- tions of the wrist, the flowing of a given quantity of sand from one vessel to another, as in an hour-glass, 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 this subject in some degree, in giving an account of the transit instrument and clock, but I propose, in this chapter, to enter into it more at large. The time of the earth's revolution on its axis, as already Sidereal day 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 Sidereal numerous jtars^in different ages of the world, show that hoar * 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^xact measure of time, probably more exact than any thing which can be devised by art. Solar time is reckoned by the apparent Solar time revolution of the sun from the meridian round to the meri- dian 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 G2 TIME AND THE CALENDAR. CHAP. VL 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 de- gree in four minutes. It takes, therefore, four minutes for us to overtake the sun, after we have made one complete Length of the revolution. Hence the solar day is about four_minutes 4f '* > solar day. i on g er 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 ordinary purposes of society, 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 twen- Sidereai day. ty-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 con- stitutes 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, when it is the tenth of June, at nine o'clock, A.M., according to civil time, the tenth of June has not yet com- menced by astronomical time, nor will it, until noon ; con- sequently, it is then June ninth, twenty-first hour of astro- nomical time. Astronomers, since so many of their obser- vations 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 Apparent time. The astrono mical day TIME AND THE CALENDAR. 63 understood to be looking towards the north. Hence, .left CHAP. VL 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 Mean solar time ; yet, as this is an artificial period not marked off, like time> 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 Equation of so constructed as to keep exactly with the sun, going faster time ' or slower, according as the lengths of the solar days vary, and another clock is regulated to mean time, then the dif- ference of the two clocks, at any period, would be the equa- tion of time for that moment. If the apparent clock be system of faster than the mean, then the equation of time must be re e ulatin K- subtracted ; but if the apparent clock be 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 ap- parent time is sometimes greater and sometimes less than mean time, the two must obviously be sometimes equal to each other. This is the case four times a year, namely, ?. April fifteenth, June fifteenth, September first, and De- cember twenty-fourth. Astronomical clocks are made of the best workmanship, Astronomical with every advantage that can promote their regularity. docka > Although they are brought to an astonishing degree of ac- curacy, yet they are not as regular in their movements as the stars are, and their accuracy requires to be frequently tested. Tlie" transit instrument itself, when once accurately placed in the meridian, affords the means of testing the Meansoftest- correctness of the clock, since one revolution of a star, from n ' e ^ s . colTect ~ 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 astro- 64 TIME AND THE CALENDAR. CHAP. VT. noraers. Or, by taking the difference of any two stars, on Measures of successive days, it will be seen whether the going of the uniformity, clock is unifoim 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, hut also whether it goes uniformly from hour to hour. Perfection of Although astronomical clocks have been brought to a docki 0nUCal 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 ac- cordingly. 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. Larger divi- As a day is the period of the revolution of the earth on ttme * its axis, so & year is the period of the revolution of the earth around the sun. This time, which constitutes the astrono- ^ Astronomical mical 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 an- cient nations determined the number of days in the year Ancient by means of the stylus, a perpendicular rod which casts its measure- shadow on a smooth plane bearing a meridian line. The ment 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 ^ v length again, would show the number of days in the year. Ancient civil This was found to be three hundred and sixty -five whole - days, and accordingly this period was adopted for the civil 3"^ year. Such a difference, however, betweeen the civil and astronomical years, at length threw all dates into confu- sion. For if, at first, the summer solstice happened on the twenty-first of June, at the end of four years the sun TIME AND THE CALENDAR. 65 would not have reached the solstice until the twenty- CHAP. VL second of June ; that is, it would have been behind its confusion of time. At the end of the next four years, the solstice would fell 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 Csesar, who was distinguished alike for the va- riety and extent of his knowledge, and his skill in arms, calendar, first attempted to make the calendar conform to the mo- tions of the sun, " Amidst Hie hurry of tumultuous war, The stars, the gods, the heavens, were still his care." Aided by Sosigenes, an Egyptian astronomer, he made ^ neg ft the first correction of the calendar, by introducing an addi- astronomer. tional 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, be- cause 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 Ju i lan year nations that submitted to the Roman power, and continued in general use until the year 1582. But the true correc- tion 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 Excegsof had, in fact, amounted to more than ten days ; for it was time. 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 ecclesias- tical council, held in the year 325, that Easter should be p er iod of celebrated upon the first Sunday after the first full moon, Easter - next following the vernal equinox ; and as certain other festivals of the Romish Church were appointed at parti- cular seasons of the year, confusion would result from such a want of constancy between any fixed date and a parti- cular season of the year. Suppose, for example, a festival, accompanied by numerous religious ceremonies, was de- li TIME AND THE CALENDAB. spring; Gregorian rule. CHAP, vi. cr eed by the Church to be held at the time when the sun Festival of 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, there- fore, they should continue to observe the twenty-first as a religious festival in honour of this event, they would commit the absurdity of celebrating it ten days after Reform of the it had passed by. Pope Gregory XIII., 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-Jive ; and every year divisible by four hundred, of three hundred and sixty-six. Thus the year 1850, not being divisible by four, con- tains three hundred and sixty-five days, while 1852 and 1856 are leap years. Yet, to make every fourth year con- sist 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 there- fore we let the four hundredth remain a leap year. This Examples. Centenary deduction. TIME AND THE CALENDAR. 67 rule involves an error of less than a day in four thousand CHAP. VI two hundred and thirty-seven years. The Pope, who in that age assumed authority over all Papal decree, secular princes, issued his decree to the reigning sovereigns of Christendom, commanding the observance of the calen- dar as reformed by him. The decree met with great oppo- sition among the Protestant states, as they recognized 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 estab- introduction lished in Great Britain by act of Parliament, and the ^yiTin 6 * dates of all deeds, and other legal papers, were to be made Britain, 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 four- teenth. 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 survived to our day, and we occasionally 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 old and new would be June twelfth of old style, or June twenty-third style< 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 1, 1740, old style, would be February 1, 1741, new style. Thus General Washing- EYampl8i ton was born February 11, 1731, old style, or February 22, 1732, new style. 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, new style, corresponds to May twenty- ninth, old style ; and March 20, 1840, to March 8, 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 ad- Ruwian here to the old style. In order, therefore, to make the dilte. 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 left to be regulated by the Extreme priests, who, from motives of interest or superstition, fre- in- eguiarity. quently omitted them, the year was made long or short at pleasure. The week is another division of time, of the highest The week, 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 Names of tiio Monday, are obviously derived from Saturn, the Sun, and daySt the Moon ; while Tuesday, Wednesday, Thursday, and Friday, are the days of Tuisco, Woden, Thor, and Friga, which are Saxon names for deities corresponding to Mars, Mercury, Jupiter, and Venus.* The common year begins and ends on the same day of Leap year, 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 ex- ample, 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 six- teenth 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 * Bonnycastle's Astronomy. 70 FIGURE OF THE EARTH. CHAP. vi. ends on Monday, and the following year begins on Tues- day ; while any given day of the month is two days later in the week than the corresponding date of the preceding year. CHAPTER VII. FIGURE OF THE EAKTH. He took the golden compasses, prepared In God's eternal store, to circumscribe This universe, and all created things j 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, world !" MILTON. CHAP. vil. IN the earliest ages the earth was regarded as one continued Original idea P^ ane j but, at the comparatively remote period of five form! earth * k unare( * years be f re 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. For example, when a ship is coming in Evidences of from sea, we first observe only the very highest parts of rotundity. ^ g^jp^ w hn e 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. 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 Example. 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 ex- actly 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 FIGURE OF THE EARTH. to be spherical, which could not be the case unless the earth CHAP^V itself were round. Thirdly, navigators, by steering conti- Practical evidence. Fig. 10. nually in one direction, as east or west, have in fact come round to the point from which they started, and thus con- Circumnavi- firmed 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. FIUUBE OF THE EARTH. CHAP. VII. Endeavours to determine the earth! Motives for gation? VeStl centrifugal Familiar sample. But I propose, in this chapter, to give some account of the unwearied labours which have been performed to ascer- t am th e ex act 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 have been bestowed on this subject have 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 exac t 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 equato- rial parts of the earth move at the rate of about one thou- sand 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, F1GUKE OP TUB EARTH. 73 consequently, those parts which move with the greatest CHAP. VIL 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 in- Inferences of vestigated 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 development of this doctrine. By combining the reasoning derived from the Demonstrar- known laws of the centrifugal force with arguments derived Newton. 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 astrono- Actual mea- mers 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 Degree of indicated by the rising of the north star, which appears in tau 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, Results with 1 the meridian of the earth would be a perfect circle, and the l^^ 1 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 A spheroid, 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 dia- meter 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 74 FIGURE OP THE EAETH. CHAP. VII. than in the equatorial region ; that is, the degrees of the Scheme of meridian would lengthen towards the poles. French The French astronomers, therefore, undertook to ascer- astronomers. . . . ' tain by actual measurements ot 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, pre- suming that if degrees of the meridian, in different lati- tudes, are really of different lengths, they will differ most in points most distant from each other. Accordingly, in Expeditions 1 735, the French Academy, aided by the Government, sent Academy. nch ou ^ * wo expeditions, one to Peru and the other to Lapland. Three distinguished mathematicians, Bouguer, La Conda- mine, 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 Torneo, the northern arm of the Baltic. This commission completed its operations several years Difficulties of sooner than the other, which met with greater difficulties detachment 1 in tlie wa ^ * ^elr enter P rise - Still, the northern detach- ment had great obstacles to contend with, arising particu- larly 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. Obstacles Meanwhile, Bouguer and hia party were prosecuting a similar work in Peru, under extraordinary difficulties. These were caused, partly by the nature of 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 neighbouring signals differed more than a mile. Encamped upon lofty mountains, they had to struggle against etorms, cold, and privations of every description, FIGURE OP THE EARTH. 75 while the invincible indifference of the Indians they were CHAP. vn. forced to employ, was not to be shaken by the fear of pun- indolence of ishment or the hope of reward. Yet, by patience and in- the natives, genuity, 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.* I have recited the foregoing facts, in order to afford some Unwearied idea of the unwearied pains which astronomers have taken to ascertain the exact figure of the earth. The reader will find, indeed, that all their labours are characterized by the same love of accuracy. Years of toilsome watchings, and incredible labour 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 varying Peru, was less than that before determined in France, and 1 J J^j[ th of course less than that of Lapland ; so that the spheroidal degrees, figure of the earth appeared now to be ascertained by actual measurement. Still, these measures were too few in num- ber, and covered too small a portion of the whole quadrant from the equator to the pole, to enable astronomers to esta- blish the exact law of curvature of the meridian, and there- fore 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. These operations are carried on by what is called a system Triangrula- of triangulation. Without some knowledge of trigonometry, tlon - the reader 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 he should understand its general principles. Let us reflect, then, that it must be a matter of the greatest diffi- culty, 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 * Library of Useful Knowledge : History of Astronomy, page 95. 76 FIGURE OP THE EARTH. CHAP.VIL or less inequalities of surface will occur; rivers must be Difficulties to crossed, morasses must be traversed, thickets must be pene- orercome. trated, and innumerable other obstacles must be surmount- ed ; and finally, every time we apply an artificial measure, as a rod, for example, we obtain a result not absolutely per- fect. Each error may indeed be very small, but small errors, often repeated, may produce a formidable aggregate. Basis of trig- Q ne unacquainted with trigonometry can easily understand measure- 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 ABC, (Fig. 12,) if we know the side AB, and Fig. 12. the angles at A and B, we can find by com- putation, the other sides, AC and BC, 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 AB, 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 AC, which was accessible, and with a compass take the bearing of B from the illustration, points A and C, by which means we should learn the value of the angles at A and C. From these data we might cal- culate, by the rules of trigonometry, the exact length of the line AB. 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 situa- tion of various places is accurately determined. Were we to undertake to run an exact north and south line through any country, as Yorkshire, we should select, near one ex- tremity, a spot of ground favourable for actual measure- ment, 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 Mode of proceeding. FIGURE OF THE EARTH. 77 with the utmost care. We should thus obtain a base line. CHAP. vn. From the extremities of this line, we should take (with Base line, 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 bear- ing 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 Example, between the two points A and Fig. 13. 0, 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 inconve- nient to measure this line di- N rectly, 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 observa- tion, to a greater degree of ex- actness, than lines. We there- fore, in the first place, measure the base line, AB, with the ut- most precision. Then, taking the bearing of some signal at C from A and B, we obtain the means of calculating the side BC, as has been already explained. Taking BC as a new base, we proceed, in like manner, to determine successively the sides CD, DE, and EF, and also AC, and CE. Although AC 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, AM ; and in the same manner we can find the portions of the meridian MN and NO, corresponding respec- 78 FIGURE OF THE EAETH. CHAP.VIL tivelyto CE and EF. Adding these several parts of the meridian together, we obtain the length of the arc from A to 0, in miles ; and by observations on the north star, at each extremity of the arc, namely, at A and at 0, we could determine the difference of latitude between these two Finding the points. Suppose, for example, that the distance between length. ^ an( j Q j g exac ti v 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. ^fMi.* 8 * Peru, 00* 00' 00" 68732 Pennsylvania, 39 12 00 68'896 France, 46 12 00 69'054 England, 51 29 54^ 69146 Sweden, 66 20 10 69'292 Differences of This comparison shows, that the length of a degree gra- a degree. dually increases, as we proceed from the equator towards the pole. Combining the results of various estimates, the dimensions of the terrestrial spheroid axe found to be as follows : Equatorial diameter, 7925'648 miles. Polar diameter, 7899'170 Average diameter, 7912'409 Eiiipticity. 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 frac- tion is denominated the ettipticity of the earth, being the excess of the equatorial over the polar diameter. Great exact- The operations, undertaken for the purpose of determin- ing 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 Base of verifl- measured, it is called the base of verification. In some catlon " surveys, the base of verification, when taken at a distance I-IGUKE OP THE EARTH. 79 of four hundred miles from the starting point, has not dif- CHAP, vn fered more than one foot from the same line, as determined by calculation. Another method of arriving at the exact figure of the Observations earth is by observations with the pendulum. If a pendu- pendulum. lum, 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 Differences of north pole. Now, the vibrations of the pendulum are pro- Vlbratlon - duced 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 equa- Equator and tor, and then carry it to the north pole, and count the pole> 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 ob- tain the polar and equatorial diameters. Observations of this kind have been taken with the greatest accuracy, in condusionm many places on the surface of the earth, at various distances from each other, and they lead to the same conclusions re- specting the figure of the earth, as those derived from mea- suring 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 otlierproofc 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 farther removed from the centre of the earth. The same accumulation of matter, by the force of attraction which it exerts, causes slight inequa- CHAP. VIL Inequalities in the motion of the moon The earth's shadow. Harmony of evidence. Bearing of the results. 80 FIOTJRE OF THE EABTu. lities 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 cal- culate the exact quantity of the matter thus accumulated, and hence to determine the figure of the earth. The re- sult 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 ex- ample 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 accumu- lation 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 estimat- ing 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. DIURNAL REVOLUTIONS. 81 CHAPTER VIII. PIURNAL REVOLUTIONS. To some she taught the fabric of the sphere, The changeful moon, the circuit of the stars, The golden zones of heaven. AKEHSIDE- WITH the elementary knowledge already acquired, the CHAP. VTIL reader will now be able to enter with pleasure and profit on the various interesting phenomena dependent on the re- volution of the earth on its axis and around the sun. The apparent diurnal revolution of the heavenly bodies, from Apparent east to west, is owing to the actual revolution of the earth a onofthe on its own axis, from west to east. If wo conceive of a ra- dius of the earth's equator extended until it meets the con- cave 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 paral- lel to this, called the circles of diurnal revolution, the hea- circles of venly bodies actually appear to move, every star having its '" al - own peculiar circle. After having first become familiar with the real motion of the earth from west to east, the student 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. It must be noted that the time occupied by a star, in A sidereal passing from any point in the meridian until it comes round **'" to the same point again, is called a sidereal day, and mea- sures 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 aU equal. Whatever star we select for the observation, the same result will be obtained. The Uuniform relative position. Different horizons. Just ideas of the earth by space. Points of sight Diurnal motion as seen from the equator. OZ DIURNAL REVOLUTIONS. 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 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 encir- cled on all sides, at an immense distance, by the starry sphere. We should free our minds from the 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 BB, CO, DD, when one is at B, C, D, respectively as in the direction AA, 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 coin- cide 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 inay be thus defined : a right sphere is one in which all the DIURNAL REVOLUTIONS. 83 daily revolutions of the stars are in circles perpendicular to CHAP. vni. the horizon. A rt&T FIR. 14. sphere. A right sphere is seen only at the equator. Any star Apparent situated in the celestial equator would appear to rise directly pathof 8tais 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 Change oi towards the north pole, his horizon reaches one degree be- yond 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 conies 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 ad- DIURNAL REVOLUTIONS. CHAP. TIIL vise the reader to follow round in imagination a number of separate stars, in their diurnal revolution, one near the horizon, one a few degrees above it, and a third near the As seen from zenith. To one who stood upon the north pole, the stars pole. 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 continu- ally 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 enjoyed the view of a sphere nearly parallel. ^ s tne c i rc ^ es ^ 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 denned : 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 A perfect parallel phere. motions. Example. of fifty degrees. His horizon reaches fifty degrees beyond the pole of the earth, and gives the same appa- rent 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 HO (Fig. 15) represent the horizon DIUENAL EEVOLUTIOX3. 85 EQ the equator, and PP the axis of the earth. Also, II, CHAP. vilt, mm, nn, parallels of latitude. Then the horizon of a spec- tator at Z, in latitude fifty degrees, reaches to fifty degrees beyond the pole ; and the angle ECH, which the equator makes with the horizon, is forty degrees, the complement of the latitude. As we advance still further north, the ele- vation 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. The circle of perpetual apparition is the boundary of that Circle of space around the elevated pole, where the stars never set. Its ap^ritSL 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 mm (Fig. 15) is the circle of perpetual apparition, between which and the north pole, the stars never set, and its distance from the pole, OP, 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 Circle of adjacent to the depressed pole never rises. Hence, the circle occuftatioa. of perpetual occupation is the boundary of that space around the depressed pole, within which the stars never rise. Thus mm (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 xi, e oblique motion unequally. Towards the elevated pole, more than sphere, 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. In the hemisphere next the depressed pole an exactly opposite result is produced. 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 nig^vts_^rejequaLaU .oxer the_globe. But when the sun is north of the equator, the days beqpme 86 DIURNAL REVOLUTIONS. CHAP. vnr. 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, it will easily be seen 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 round the earth once In twenty-four hours, or that this motion of the heavens is merely apparent, explanations, ^j^g f rom t h e 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, en- Real motion, tirely 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 the stu- dent 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. Horizon. While we retain the same place on the earth, the diurnal revolution occasions no change in our horizon, but our ho- rizon goes round along with ourselves. Let us first take our station on the equator, at sunrise ; our horizon now On the passes through both the poles and through the sun, which equator. we are ^ o CO nceive of as at a great distance from the earth, and therefore as cut, not by the terrestrial, but by the celes- tial, 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 DIURNAL REVOLUTIONS. 87 sun, and soon afterwards it rises above the level of the CHAP. VIII 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 Horizon at 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 re- volves continually round in a circle, which, during a single revolution, appears parallel to the equator, and it is con- stantly 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 Appearance! the diurnal revolutions, as exhibited to a spectator at the ^Tttona 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 Different inhabitants of different countries, are such as correspond to *f ^0^* the sphere in which they live. Thus, in the fervid climates vens. 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 inha- Near the bitants, strike with a force unknown to the people of colder e l ua t r - climates ; while in places remote from the equator, as in the north of Europe, the sun, in summer, rises very far in In the tem- the north, takes a long circuit towards the south, and sets pera 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 ex- ample, to the confines of the frigid zone, the summer's sun In ttie fri(rl( ] just grazes the northern horizon, and at noon appears only zone, twenty-three and one half degrees above the southern. On the other hand, in midwinter, in the north of Europe, as at St. Petersburg, the day dwindles almost to nothing, lasting 88 PARALLAX AND REFRACTION. CHAP. viii. only while the. sun describes a very short arc in the ex- treme "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. CHAPTER 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. POPR. Surprising calculation of astrono- CHAP. ix. IT can hardly fail to occasion the young student some astonishment that astronomers are able to calculate the exact distances and magnitudes of the sun, moon, and planets. At the first thought, it would seem that such knowledge as this must be beyond the reach of the human faculties, and we might be inclined to suspect that astrono- mers practise some deception in this, for the purpose of ex- Biting the admiration of the unlearned. I will therefore, in the present chapter, endeavour to give the reader 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 distin- guishing, 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, innu- merable millions of miles from us, yet, as our eye cannot distinguish these different distances, we acquire the habit of first Ideas of the sky. PARALLAX AND REFRACTION. referring all objects beyond a moderate height to one and CHAP. rx. the same surface, namely, an imaginary spherical surface, owectsre denominated the celestial vault. Thus, the various objects ferred tothe represented in the following diagram, though differing very vault?* 1 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 (Fig. 16), the several linea AB, CD, and EP, 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 indi- cated 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. But although all objects, beyond a certain moderate Parallax, height, are projected on the imaginary surface of the sky, yet different spectators will project the same object on dif- ferent 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 de- 90 PARALLAX AND REFRACTION. CHAP. ix. fined : parallax is the apparent change of place which bodies undergo by being viewed from different points. Fig. 17. Paralytic The arc MN is called the parattactic arc, and the angle ACB, the parattactic 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 MN, and the latter by the arc ()P. We may easily imagine bodies to be so distant, that they would appear pro- jected at very nearly the same point of the heavens, when Effect of the 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 ; and it is owing to this important fact that we are prac- tically enabled to assume the existence of a fixed sphere, and by these unchanging objects on its azure vault to ob- serve and measure the parallax of the planets, comets, and satellites of our solar system. memTof dig- ** * s b y.. me * ns * parallax that astronomers find the dis- tances and tances and magnitudes of the heavenly bodies. In order magnitudes. f u Hy to understand this subject, some knowledge of trigo- nometry is required, as this science enables us to find cer- PARALLAX AND REFRACTION. 91 tain unknown parts of a triangle from certain other parts CHAP. IX which are known. Although the reader may not be acquainted Application with the principles of trigonometry, yet he will readily un- of parallax, derstand, from his knowledge of arithmetic, that from certain given things in a problem others may be found. Every tri- angle 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 ABC (Fig. 18), if we know the length of the Fig. 18. side AB, and how many degrees each of the angles ABC and EGA contains, we can find the length of the side BC, or of the side AC, and the remaining angle at A. Now, let us apply these principles to the measurements of some of the heavenly bodies. In Fig. 19, let A represent the earth, CH the horizon, Example, and HZ a quadrant of a great circle of the heavens, ex- tending 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, HA, Yp, Rr, 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 the moon would be seen at Z, whether viewed from A or C. Since, then, a heavenly body is liable to be referred to T^, e le place different points on the celestial vault, when seen from dif- celestial ferent parts of the earth, and thus some confusion be occa- 8 P Uere sioned in the determination of points on the celestial sphere, astronomers have agreed to consider the true place of a celestial object to be that wbere it would appear, if seen 92 PARALLAX AND REFRACTION. CHAP. ix. from the centre of the earth ; and the doctrine of parallax teaches how to reduce observations made at any place on Fig. 19- Horifontal parallax. celestial bodies. 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 AEG, measures the horizontal parallax of the moon. Were a spectator to view the earth from the centre of the moon, he would see the semidiame- ter of the earth under this same angle ; hence, the horizon- tal parallax of any body is the angle subtended by the semi- diameter of the earth, as seen from the body. It is of im- portance that the reader should 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 HA; F, by the arc ~Pp; Or, by the arc Rr; while 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 sen- sible parallax. Magnitude a heavenly body. PARALLAX AND REFRACTION. 93 It is now veiy easy to see how, when the parallax of a CHAP. IX. body is known, we may find its distance from the centre of To and7he the earth. Thus, in the triangle ACE (Fig. 19), the side Jf^**^ AC is known, being the semidiameter of the earth ; the the earth, angle CAE, being a right angle, is also known ; and the parallactic angle, AEC, 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 AEC, we know all the angles and one side, namely, the side AC hence, we have the means of finding the side CE, which is the distance from the centre of the earth to the centre of the moon. When the distance of a heavenly j-j g . 20 body is known, and we can measure, with instruments, its angular breadth, we can easily determine its magni- tude. Thus, if we have the distance of the moon, ES (Fig. 20), and half the breadth of its disc SC (which is measured by the angle SEC), we can find the length of the line SC, 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. The reader will perhaps be curious to know, how the moon's horizontal parallax is found ; for it must have been previously as- parallax, certained, 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 Finding the moon's horizontal 94 PARALLAX AND BEPRACTION. CHAP. IX. B represent the positions of the spectators, M the moon, Material for an d CD an arc of the sky, then it is evident, that CD calculation. Fig 2J would be the parallactic arc. 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. Besides 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 de- presses it. It affects alike the most distant as well as nearer bodies. Refraction. 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 be- fore 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 ap- pearance, the part below the water having apparently a different direction from the part above. Thus, in Fig. 22, if Sax be the oar, Sab will be the bent appearance, as affected by refraction. The transparent substance through Medium. 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 HE ATMOSPHERE * THE EFFECT OF REFRACTION ZODIACAL LIGHT. PARALLAX AND REFRACTION. 95 into a rarer medium, as out of water into air, it is turned CHAP DC from the perpendicular. In the above case, the light, pass- Fig 22. ing out of space into air, is turned towards the radius of the earth, this being perpendicular to the surface of the atmo- sphere ; 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. Let us now conceive of the atmosphere as made up of a Refraction o< great number of parallel strata, as AA, BB, CO, and DD, 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, Sa, enters the atmosphere at a, where, being much turned towards the radius of the convex surface, it would change its direction into the line ab, and again into be, and cO, reaching the eye at 0. 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 Qc, and, consequently, the star would apparently change its place, by refraction, from S to ET, being elevated out of its true position. Moreover, since, on account of the continual increase of density in descending through the at- mosphere, 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. 96 PARALLAX AND REFBACTI05. CHAP. IX. When a bt)dy is in the zenith, since a ray of light from Appearance & enters the atmosphere at right angles to the refracting of a body in 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 atmo- sphere through its densest part, the refraction is greatest. The whole amount of refraction, when a body is in the hori- Refraction on zon, is thirty-four minutes ; while, at only an elevation of the horizon. one ( j e g ree) 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 re- fraction than at lower altitudes. Effect near Since the whole amount of refraction near the horizon 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. Change on The rapid increase of refraction near the horizon is strik- thesun! re0f * ng ^ evmce< * *>y 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 disc. Were all parts of the sun equally raised by refrac- tion, there would be no change of figure ; but, since thj lower side is more refracted than the upper, the effect is to shorten the vertical diameter, and thus to give the disc an oval form. This effect is particularly remarkable when the As seen from sun, at his rising or setting, is observed from the top of a a height mountain, or at an elevation near the seashore ; for in such situations, the rays of light make a greater angle than ordi- nary, 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. Optical The apparent enlargement of the sun and moon, when on- 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 PARALLAX AND REFRACTION. 97 to us in the latter case than in the former. The distance CHAP. KS of the sun, indeed, is so great, that it makes very little dif- ference in his apparent diameter whether he is- viewed in the horizon or on the meridian ; but with the moon, the Relative case is otherwise ; its angular diameter, when measured S with instruments, is perceptibly larger when at its culmi- nation, 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 Explanation the angle they subtend at the eye, but also by our impres- ^J^ pheno " sions 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 ob- jects 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 Twilight of the earth's atmosphere. It is that illumination of the sky which takes place just before sunrise, and which con- tinues 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 its utuses. 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 perpen- dicular 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 Daybreak, 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 pro^ gress from continual day to constant night is exceedingly gradual. To an inhabitant of an oblique sphere, the twi- light is longer in proportion as the place is nearer the ele- vated pole. PARALLAX AND REFRACTION. CHAP. IX. Were it not for the power the atmosphere has of dispers- Dispersive * n g the solar light, and scattering it in various directions, a W os if r' 16 no ^J 60 * 8 w uld be visible to us out of direct sunshine ; every shadow of a passing cloud would involve us in mid- night darkness; the stars would be visible all day; and every apartment into which the sun had not direct admis- sion would be involved in the obscurity of night. This scattering action of the atmosphere on the solar h'ght is greatly increased by the irregularity of temperature caused by the sun, which throws the atmosphere into a constant Undulations, 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.* In the upper regions of the atmosphere, as on the tops of very high moun- tains, 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. Atmospheric 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 cover- ing 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 bear- ing, 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 it* density, themselves widely. The consequence is, that the atmo- sphere 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 pro- portion, 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 vapours, which seldom rise so high as eight miles, and are usually much nearer to the earth than this. * Sir J. Herschel. So rare does the air become on the top of Mount Chimbo- CHAP. IX. razo, in South America, that it is incompetent to support Rarityofthe most of the birds that fly near the level of the sea. The hi her aimo ~ condor, a bird which has remarkably long wings, and a light body, is the only bird seen towering above this lofty sum- mit. The transparency of the atmosphere, a quality so essential to fine views of the starry heavens, is much in- Transpa- creased by containing a large proportion of water, provided renc y- it is perfectly dissolved, or in a state of invisible vapour. 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 Effect of sky to be remarkably resplendent, even in our own latitude. humidit J r - 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. CHAPTER 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 chapters CHAP. X are by no means the most interesting parts of our science. ' They constitute, indeed, little more than an introduction to the main subject, but comprise such matters as are very 100 THE SUN. CHAP. x. 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. he sun. 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 at- tention ; 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- fi ve millions of miles. It may perhaps seem incredible, that astronomers should be able to determine this fact with any degree of certainty. Some, indeed, have looked upon the marvellous things that are told respecting the distances, magnitudes, and velocities, of the heavenly bodies, as at- tempts of astronomers to impose on the credulity of the world at large ; but the certainty and exactness with which Evidences of the predictions of astronomers are fulfilled, as of an eclipse, for example, ought to inspire full confidence in their state- ments. I can assure the young student, that the evidence on which these statements are founded, is perfectly satis- factory 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 hea- venly bodies, that no class of men have ever shown a stricter regard and zeal than they for exact truth, wherever it is attainable. Comprehen- Ninety-five millions of miles is indeed a vast distance. distaiicel St 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 dis- tances, 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 Liverpool, and, after twenty days' steady sail, reaches New York. 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 SUN. 101 <* 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 Effector heat. Whenever we come nearer to any fire, the heat approach rapidly increases, being four times as great at half the dis- tance, and one hundred times as great at one-tenth the distance. This fact is expressed by saying, that the heat increases as the square ofcthe 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, consti- tuted 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 Relative largejisjthe earth ; but its matter is not more than about size- one-fourth as dense as that of the earth, being only a little ' I 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 Force of greater, in proportion as its quantity of matter is greater. Consequently, we might suppose, that the weight of a body j -v*-"- (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 102 CHAP. x. the earth, would weigh three hundred and fifty thousand Principle pounds at the sun. But we must consider that the attrac- of attraction, tion 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 in- creases, 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 thou- sand 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 hun- dred 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 disc, called solar spots. These are very variable in size and number. Solar spots. Sometimes, the sun's disc, 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. Occa- sionally, a single spot is so large as to be visible to the naked eye, especially when the sun is near the horizon, and Specific gravity. Example. Rotation of the sun. RIOl)S FORMS OF SOUR SPOTS THE SUN. 103 the glare of his light is taken off. One measured by Dr. CHAP. x. Herschel was no less than fifty thousand miles in diameter. Estimated A solar spot usually consists of two parts, the nucleus and slze - 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 sudden umbra is a wide margin, of lighter shade, and is often of chan eea. 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 Fig. 23. of the solar spots. As these spots have all a common motion from day to day, across the sun's disc ; 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 ap- parent motion is impart- ed to them by an actual revolution of the sun on his own axis. We know that the spots must be in con- inferences tact, or very nearly so, at least, with the body of the sun, '^s^^- and cannot be bodies revolving around it, which are pro- jected on the solar disc 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 fol- lowing diagram. Let S (Fig. 24) represent the sun, and b a body revolving round it in the orbit abc, and let E repre- sent 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. If it is asked what is the cause of the solar spots, I can Meas of only tell what different astronomei-s have supposed respect- abtl ' onomci Ing them. They attracted the notice of Galileo soon after Galileo's hypothesis Fig. 24. 104 THE SUK. CHAP. x. 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 sur- face 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, second- ly, the sudden disappearance which the spots sometimes un- dergo, a fact which can hardly be accounted for by supposing, as Galileo did, that such a vast ac- cumulation 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 re- flux of this fiery sea, retreating occasionally from the moun- tains, 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 constitu- tion of the sun, embracing an explanation of the solar spots, La Lande's theory. THE SU. 105 have, of late years, been very generally received by the CHAP. X. astronomical world. This great astronomer, after atten- tively viewing the surface of the sun, for a long time, with his large telescopes, came to the following conclusions re- specting the nature of this luminary. He supposes the Supposed sun to be a planetary body like our earth, diversified with ^ e of thfl mountains and valleys, to which, on account of the magni- tude 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 Sources of clouds floating in the solar atmosphere, at different distances jigh t t and from the sun. The exterior stratum of clouds he considers as the depository of the sun's light and heat, while the in- ferior 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 Proofs presented to the telescope, are such as accord better with adc 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 Solar spots clouds are easily dispersed to any extent, the great dimen- ex P lained sions 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 acknow- Objections to ledged, great powers of observation, and means of observa- thesis. tion 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 as- serts that his lower stratum of clouds are analogous to ours, and reasons respecting the upper stratum according to the 106 THE SUN. CHAP. x. same analogy) cannot exist in hot air ; they are tenants Impossibility on ly of cold regions. How can they be supposed to exist of clouds in j n the immediate vicinity of a fire so intense, that they are atmosphere, even dissipated by it at the distance of ninety-five millions of miles ? Much less can they be supposed to be the depo- sitories 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 unfavourable 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 : Logical 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 mode- rate 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. ignorance of I think, therefore, we must confess our ignorance of the nnd'omatitu- na t ure and constitution of the sun ; nor can we, as astro- tionofthe nomers, obtain much more satisfactory knowledge respect- ing 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 ae will preserve those fires from extinction, and at a nearly uniform degree of intensity. Any material change in this respect would endanger 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 id 8 " 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 Length of cause of the heat of this season of the year. This cause days * 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 causes of by several other causes, as well as by the force and duration J^erature 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 ex- cessive changes which are often experienced in less favoured climes. In ascending certain high mountains situated within 122 ANNUAL REVOLUTION. CHAP. XL the torrid zone, the traveller passes, in a short time, through every variety of climate, from the most oppressive and sul- try 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 Effects on in the products of the vegetable kingdom. While winter vegetation, j-gj^g on t ne summit of the mountain, its central regions may be edfcircled with the verdure of spring, and its base with the flowers and fruits of summer. Secondly, the prox- imity of the ocean also has a great effect to equalize the temperature of a place. As the ocean changes its tempera- ture 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 humidity or dryness of the atmosphere of a place is of great ryness> 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 un- healthy, although a hot air, when dry, may be very salu- brious. In a warm atmosphere which is dry, the evapora- tion of moisture from the surface of the body is rapid, and its cooling influence affords a most striking relief to an in- tense 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. LAWS OB MOTION. 123 CHAPTER 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 CHAP, xa than that the earth is constantly on the wing, flying around Cons ^ the sun with a velocity so prodigious, that, for every breath motion of we draw, we advance on our way forty or fifty miles. If, the Klobe- 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, Familiar too, as not to disturb our slumbers ; but, with a motion iUustration - vastly more quiet and uniform, we have, in the same inter- val, 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 stupen- dous forces by which this motion is achieved. To the pious Motion of the observer of Nature it might seem sufficient, without any 8 P herea - 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 124 LAWS OF MOTION. Inquiries into the laws of motion. Former opinions. Galileo and Newton's demonstra- tions. Lnwg of motion. Particulars embraced in the first law. immediately produced and controlled, it will detract no- thing 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 respect- ing 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 uni- form 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 supposi- tions, 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 through- out 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 com- pelled by some force to change its state. By force is meant any thing which produces motion. The foregoing law has been fully established by experi- ment, 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 ia 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 LAWS OP MOTION. 125 assigning to each of these motions a force adequate, both in CHAP. XIL quantity and direction, to produce these motions, respec- tively. Secondly, when a body is once in motion, it will continue Continuous to move for ever, unless something stops it. When a ball motion - 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 inertia. -~/ 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 start- ing 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 Uniformity of uniform; that is, the body moves just as far the second motion - 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 ia naturally prone. Fourthly, a body in motion will move in a straight line, Motion in a unless diverted out of that line by some external force ; and 8trftl t' ht lma> the body will resume its straight-forward motion, whenever the force tliat turns it aside is withdrawn. Every body 126 LAWS OP MOTION. CHAP.XIL that is revolving in an orbit, like the moon around the Motionof the earth, or the earth around the sun, tends to move in a moon - straight line which is a tangent* to its orhit. Thus, if ABC (Fig. 28) represents the orbit of the moon around the Fig. 28. Familiar illustration. Centrifugal force. 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 AD. 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 tan- gent, 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 ' A tangent is a straight line teaching a circle, as AD, in Fig. 28. LAWS OF MOTION. 127 from the top of the wheel in straight lines which are tan- CHAP, xit gents to the wheel. The centrifugal force is increased as the velocity is in- illustration of creased. Thus, the parts of a millstone most remote from fo" ce ut 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 pro- jected with great violence. In like manner, as the equa- torial parts of the earth, in the diurnal revolution, revolve much faster than the parts towards the poles, so the centri- fugal force is felt most at the equator, and becomes strik- *> ingly 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 pre- Value of this sented to the mind, appears to convey no new truth, but law 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 pro- Second lawo. portioned to the force impressed, and in the direction of that mohou - force. The meaning of this law is, that every force that is ap- Explanation, plied 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 cor- responding 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 illustration same instant, with the thumb and finger of each hand, one impelling it hi 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 128 LAWS OF MOTION. CHAP.XIL impelled by two forces, acting respectively in the directions Impulsion by f ^e two sides of a parallelogram, and proportioned in in- two forces, tensity 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. Converse of The converse of this proposition is also true, namely, that ti'o e n. PlOP (I ~ 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 indivi- Resointion of dual motions that produce it, is called the resolution of force8 ' 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 direc- tion and intensity, from all which the given motion may be considered as having resulted. This composition and reso- lution of motion or forces is often of great use, in inquiries its great use. into the motions of the heavenly bodies. The composition often enables us to substitute a single force for a great num- ber of others, whose individual operations would be too complicated to be followed. By this means, the investiga- tion is greatly simplified. On the other hand, it is fre- quently 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 under* stood and managed than the single force would have been. Value of slm- It is characteristic of great minds, to simplify these inqui- ' tlon " ries. They gain an insight into complicated and difficult subjects, not so much by any extraordinary faculty of see- ing 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. influence of If every force, when applied to a body, produces its full an< ^ l e ito ma te 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 LAWS OP MOTION. 129 be truly expressed by a fraction. Thus, suppose a globe, CHAP.XH weighing a million of pounds, were suspended from the Fifth prin- ceiling by a string, and we should apply to it the snap of a c finger, it is granted that the motion would be quite insen- sible. 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 ap- plied 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 Results of the 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 wheel- ing, 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 Third luwof 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 chapter. 130 TERRESTRIAL GRAVITY CHAPTER XIII. TERRESTRIAL GRAVITY. To Him no high, no low, no great, no smalt. He fills, He bounds, connects, and equals all POPB. CHAP. xiil. WE discover in nature a tendency of every portion of mat- GravttaTion. ter towar ds every other. This tendency is called gravita- tion. 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 Terrestrial gravity were first investigated by Galileo ; those of universal Kravlty> 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 act- inconclusive ing to produce this effect ; nor is it enough to say, as the propositions ancien ts did, that bodies "naturally" fall to the earth. ancients. 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 TERRESTRIAL GRAVITY. 131 motion, this attraction is mutual ; that when a stone falls CHAP. XIIL towards the earth, it exerts the same force on the earth MntnaT that the earth exerts on the stone : but the motion of the attraction, 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 exist- ignorance of ence of such a force as gravity, causing a tendency in all ^,-a^itjr. bodies towards each other, yet we know nothing of its na- ture, nor can w r e 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 First investi- of the laws of terrestrial gravity, as exemplified in falling g r of lts 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 Galileo, 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 me- chanical 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 expe- Early devei- rimental research, predominated over his zeal for the study oped taste * of medicine, and he fortunately abandoned that for the more congenial pursuits of natural philosophy and astro- nomy. In the twenty-fifth year of his age, he was ap- pointed, by the Grand Duke of Tuscany, professor of ma- thematics 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 Aristotelian Great, a philosopher who flourished in Greece about three P hUosophT hundred years before the Christian era. Aristotle, by his great genius and learning, gained a wonderful ascendancy 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 132 TERRESTRIAL GRAVITY. Galileo. Practical methods of observation. CHAP. xiii. in the writings of Aristotle ; and, on the other, that an assertion which contradicted any thing in Aristotle could Originality of 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 geometri- cal 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 fur- nish 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 PrevionsfWse that time, the inquirers into Nature did not open their eyes reasoning. to gee J IQW t j ie factg rea j ly are; ^ u ^ ^ metaphysical pro- cesses, 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 rea- soning 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 con- stitutes 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 Baconian philosophy. Bacon's ystein. TEERESTEIAL GRAVITY. 133 single facts. Previous to the time of Lord Bacon, hardly CHAP XIIL any insight had been gained into the causes of natural phe- nomena, 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 laby- rinth of error. Bacon pointed out to them the true path, Bacon's and held before them the torch-light of experiment and guMauce. 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 myste- ries of the natural world. It is a remarkable fact, that two such characters as Contempo- Bacon and Galileo should appear on the stage at the same coveries of 8 " time, who, without any communication with each other, or Bacon and perhaps without any personal knowledge of each other's e0 ' 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 rea- son, consider Galileo as a greater philosopher than Bacon. " Bacon," says Hume, " pointed out, at a great distance, compari$ja the road to philosophy ; Galileo both pointed it out to {^J^ others, and made himself considerable advances in it. The Englishman was ignorant of geometry ; the Florentine re- vived that science, excelled in it, and was the first who ap- plied 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 Exactness of self-evident truths, and that all its conclusions are the result aemonstra? of pure demonstration, and can admit of no controversy ; tion. 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 ex- Bigotry of treme bigotry, the darkness visible, that beclouded human intellect, when it not only refused to admit conclu- sions 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 134 TERRESTRIAL GRAVITY. CHAIVXIIL m en, both possessing great influence in their respective Two classes spheres, the one consisting of the learned doctors of phi- o f ^euu." l s phy> who did nothing more, from age to age, than re- iterate the doctrines of Aristotle, and were consequently alarmed at the promulgation of principles subversive of those doctrines ; the other consisting of the Romish priest- hood, 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. Arutoti f 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 Aris- totle had said so ; and accordingly this assertion had long been received as an axiom in the science of motion. Gali- Gnliteo's leo ventured to appeal from the authority of Aristotle to biases. 10 '' 6 that of his own senses, and maintained that both weigbts 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 pave- ment 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 His removal and disgusted with the malice and folly of these Aristotelian to Padua. 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 pro- fessor of mathematics. Up to this period, Galileo had de- voted himself chiefly to the studies of the laws of motiun, and the other branches of mechanical philosophy. Soon afterwards he began to publish his writings, in rapid suc- cession, and became at once one of the most conspicuous TEKKESTRIAL GKAVITT. 135 men of his age, a rank which he afterwards well sustained CHAP, xiil and greatly exalted by the invention of the telescope, and R an k^f" by his numerous astronomical discoveries. I shall reserve ^ 1 " n eo his an account of these great achievements until we come to contempo- that part of astronomy to which they were more imme- ranes> lately related, and proceed now to explain the leading principles of terrestrial gravity, as exemplified in falling bodies. First, all bodies near the earth's surface fall in straight First prin- lines towards the centre of the earth. We are not to infer terrestrial from this fact, that there resides at the centre any peculiar gravity, 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) be the illustration, centre of the earth, and A a body yi g 29. without it. Every portion of mat- ter 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 AB, as on the other side, each half ex- erts 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 dis- tances from the line AB, 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 Aa, that of b would draw it in the direction of Ab, and it would fall in the line AB, half-way between the two. The same would hold true of any other two cor- responding particles of matter on different sides of the earth, in respect to a body situated in any place without it. Secondly, all bodies fall towards the earth from the same Second height, with equal velocities. A musket-ball, and the finest {avityl e particle of down, if let fall from a certain height towards the earth, tend to descend towards it at the same rate, and 136 TERRESTRIAL GRAVITY. CHAP, xill would proceed with equal speed, were it not for the resist- ance 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. Third Thirdly, bodies, in falling towards the earth, have their P ravJty le l Tate f mo ^ on 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 be- fore they reach the earth. Thus, a man falling from a bal- loon, 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 hun- dred 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. prtncMe of Fourthly, gravity is proportioned to the quantity of matter. gravity. 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, TERRESTRIAL GRAVITY. 137 is not as intense as it is near the earth. At such a distance CHAP. XIIL 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 Measure of nothing more than the measure of its force of gravity) is | v f eof 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 Definition. increases. This fact is generalized by saying, that the force of gravity, at different distances from tlie earth, is inversely as the square of the distance. Were a body to fall from a great distance, suppose a The force of thousand times that of the radius of the earth, the force gl ' avity - of gravity being one million times less than that at the surface of the earth, the motion of the body would be ex- ceedingly slow, carrying it over only the sixth part of an inch in a day. It would be a long time, therefore, in mak- ing 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 pro- digious violence. Falling so far, and being continually ac- Rate of celerated on the way, we might suppose that it would at acceleration. length attain a velocity infinitely great ; but it can be de- monstrated, that, if a body were to fall from an infinite dis- tance, 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 beea 138 SIK ISAAC NEWTON. CHAP. XIIL observed, and their laws had been fully investigated by investigation Galileo and others, before the cause of their falling was f 'na offtoT understood, or an y such principle as gravity, inherent in ing bodies, the earth and in all bodies, was applied to them. The de- velopment of this great principle was the work of Sir Isaac Newton ; and I shall give you, in the next chapter, some particulars respecting the life and discoveries of this won- derful man. CHAPTER XIV. SIR ISAAC NEWTOH. UNIVERSAL GRAVITATION. FIGURE OF THE EARTH'S ORBIT. PRECESSION OF THE EQUIKOXES. 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 lonp; with demonstration clear, And, nnawakeued, dream beneath the blaze Of truth. At once their pleasing visions fled, With the light shadows of the morning mixej}, When Newton rose, our philosophic sun. THOMSON'S ELEPT. CHAP. xrv. SIR ISAAC NEWTON was born in Lincolnshire, England, in Newton" 1642, just one year after the death of Galileo. His father died before he was born, and he was a helpless infant, of a dimunitive 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 His birth- and her precious charge. Fig. 30 represents the modest place. mansion, honoured as the birth-place of one who is justly styled an ornament to human nature. It will probably be found that genius has oftener emanated from the cottage than from the palace. The boyhood of Newton was distinguished chiefly for his ingenious mechanical contrivances. Among other pieces SIR ISAAC NEWTON SIB ISAAC NEWTON. 139 of mechanism, he constructed a windmill, so curious and CHAP. XIV. complete in its workmanship, as to excite universal admi- Newton's ration. After carrying it a while by the force of the wind, he resolved to substitute animal power ; and for this pur- pose 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 work- manship, 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 neighbouring market-town, to dispose of products of their farm, and to buy articles of merchandise for their family use ; but the inattention young philosopher left all these negotiations to his worthy partner, occupying himself meanwhile 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 140 UNIVERSAL GRAVITATION. CHAP. xiv. a hedge, until the servant returned. They endeavoured 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 Fondness for him one day under a hedge, with a book in his hand, and mathematics. entire ] y absorbed in meditation, took it from him, and found that it was a mathematical problem which so en- grossed his attention. His friends, therefore, wisely re- solved to favour the bent of his genius, and removed him from the farm to school, to prepare for the university. In Sent to the eighteenth year of his age, Newton was admitted to bridge. Tr j nity College, Cambridge. He made rapid and extraor- dinary advances in the mathematics, and soon afforded un- equivocal presages of that greatness which afterwards placed him foremost among the master spirits of the world. ciiosen In 1669, at the age of twenty-seven, he became professor mathematics, of mathematics at Cambridge, a post which he occupied for many years afterwards. During the four or five years pre- vious to this he had, in fact, made most of those great dis- coveries which have immortalized his name. We are at present chiefly interested in one of these, namely, that of universal gravitation. Let us see by what steps he was con- ducted to this greatest of scientific discoveries. First idea of 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 Reflections, 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 con- tinually from the straight line in which every body tends to move, and is thus made to circulate around the earth ?" It will be recollected that it was mentioned, in the chapter which contained an account of the first law of motion, that UNIVERSAL GRAVITATION. 141 If a body is put in motion by any force, it will always move CHAP. XIV. forward in a straight line, unless some other force compels LawToT it to turn aside from such a direction ; and that, when we see motion. a body moving in a curve, as a circular orbit, we are autho- rized 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 Natural laws of motion as Newton, that the moon should constantly n ' bend towards the earth, from a tendency to fall towards it, as any other heavy body would do, if carried to such a dis- tance 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 Relative force the centre of the earth increases, that is, at double the dis- of gravity> tance 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 Practical 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 exter- nal force diverted her from it 1 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 conclu- Conclusions sive it was afterwards proved that a similar force compels deii 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 uni- versal power whose influence extends to all the material creation. It is in this sense that we recognize 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 Law of universal gravitation. Its confirma- tion. ThePrincipis Application of the principles established. The earth': orbit 142 UNIVERSAL GRAVITATION. 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 quan- tity ; 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 uni- versal gravitation is therefore held to be the grand principle which governs all the celestial motions. Not only is it con- sistent 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 as- sert that such irregularities must take place, even if they had never been observed. Newton first published the doctrine of universal gravita- tion in the " Principia," in 1687. The name implies that the work contains the fundamental principles of natural philosophy and astronomy. Being founded upon the im- mutable 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 prin- ciple. 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 labour has been especially achieved by La Place, a French mathematician of the highest eminence, in his profound work, the " Me- canique Celeste." Of this work, the distinguished American astronomer, Dr. Bowditch, has given a valuable translation, and accompanied it with a commentary, which both illus- trates the original, and adds a great amount of matter hardly less profound. 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 FIGURE OF THE EARTHS ORBIT. 143 earth around the sun is learned, as I before explained to CHAP. XW. you, by the apparent path of the sun around the earth once Truepothof a year. Now, when a body revolves about the earth at a ^ great distance from us, as is the case with the sun and sun. 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 Fig. 3L 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 deter- mine from other circumstances than the actual appearance, what is the true figure of the orbit. Were the earth's path a circle, having the sun in the suppositions centre, the sun would always appear to be at the same dis- tance 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 con- stantly 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 144 FIGURE OF THE EARTH S ORBIT. CHAP. xiv. a diagram, according to their respective lengths, the extre- ModeoF mities, on being connected, give us our first idea of the shape tr^fiureof f tlie rbit ' wnicl1 a PP ears of an ova l f rm > an( i at l east the orbit resembles an ellipse ; and, on further trial, we find that it has the properties of an ellipse. Thus, let E (Fig. 32) be Fig. 32. d Relative dis- tances of the sun and Extieme variations. the place of the earth, and a, b, c, &c., successive positions of the sun ; the relative lengths of the lines Ea, E5, &c., being known, on connecting the points a, b, c, &c., the re- sulting figure indicates the true figure of the earth's orbit. These relative distances are found in two different ways ; first, ly changes in the sun's apparent diameter, and, se- condly, by variations in his angular velocity. The same object appears to us smaller in proportion as it is more dis- tant; and if we see a heavenly body varying in size, at dif- ferent times, we infer that it is at different distances from us ; that when largest, it is nearest to us, and when small- est, 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 FIGURE OP THE EARTH*S ORBIT. 145 the greatest distance from us. The point where the earth, CHAP. xiv. or any planet, in its revolution, is nearest the sun, is called its perihelion ; the point where it is furthest from the sun, Perihelion ' lion. Suppose, then, that, about the first of January, and a P helioiL when the diameter of the sun is greatest, we draw a line, Ea, (Fig. 32) to represent it, and afterwards, every ten days, draw other lines, Eb, EC, &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, ~Ebc, &c., shall be all equal to each other, for a reason that will be explained hereafter. On connect- ing the extremities of these lines, we shall obtain the figure of the earth's orbit. Similar conclusions may be drawn from observations on The snn's the sun's angular velocity. A body appears to move moat velocity, rapidly when nearest to us. Indeed, the apparent velocity increases rapidly, as it approaches us, and as rapidly dimin- ishes, 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 Relative square of the distance ; for, as the distance is diminished ten ^tance, 1 " 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 learned the fact, that the eailh moves around the impelling sun, not in a circular but in an elliptical orbit, the student 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 ia gravity which turns them aside from the straight line in which, by the first law of motion, they tend 146 FIGURE OF THE EARTH 3 ORBIT. Projectile force. CHAP. xiv. 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 projec- tile 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 the reader can clearly understand the nature of this motion, and the action of the two forces that produce it, I must explain a few elementary principles upon which this and all the other planetary mo- tions depend. Combined The reader has already learned, that when a body is acted fbrc^ ftW on b y 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 direc- tion in which it was thrown, and make it descend to the earth in a curve. The particular form of the curve will Familiar depend on the velocity with which it is thrown. It will ition. a i wa y 8 lggi n to move in the line of direction in which it is projected ; but it will soon be turned from that line to wards the earth. It will, however, continue nearer to the line of projection in proportion as the velocity of projection is greater. Thus, let AC (Fig. 33) be perpendicular to the Fig. 33. horizon, and AB parallel to it, and let a stone be thrown from A, in the direction of AB. It will, in every case, com- mence its motion in the line AB, which will therefore be a FIGURE OF THE EARTH S ORBIT. 147 tangent to the curve it describes ; but, if it is thrown with CHAP. xiv. a small velocity, it will soon depart from the tangent, de- scribing the line AD ; with a greater velocity, it will de- scribe a curve nearer the tangent, as AB ; and with a still greater velocity, it will describe the curve AF. As an example of a body revolving in an orbit under the Exampla influence of two forces, suppose a body placed at any point, P, (Fig. 34) above the surface of the earth, and let PA be the direction of the earth's centre ; that is, a line perpendi- cular to the horizon. If the body were allowed to move, without receiving any impulse, it would descend to the earth in the direction PA with an accelerated motion. But suppose that, at the moment of its departure from P, it re- Velocity of ceives a blow in the direction PB, which would carry it to projection. 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 PD. If a stronger blow were given to it in the direction PB, it would describe a larger curve, PE ; or, finally, if the impulse were sufficiently strong, it would circulate quite around the earth, and return again to P, describing the circle PFG. With a velocity of projection still greater, it would describe an ellipse, PIK ; and if the velocity be in- creased to a certain degree, the figure becomes a parabola, LPM, a curve which never returns into itself. In Fig. 35, suppose the planet to have passed the point C, at the aphelion, with so small a velocity, that the attrac- 148 FIGURE OF THE EARTH'S ORBIT. Counter- balancing force*. OIIAP. XIV. tion of the sun bends its path very much, and causes it immediately to begin to approach towards the sun. The Fig. 35. sun's attraction will in- crease its velocity, as it moves through D, E, and F, for the sun's attractive force on the planet, when K at D, is acting in the direc- tion DS ; and, on account of the small angle made between DE and DS, the force acting in the line DS helps the planet forward in the path DE, and thus in- creases 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 in- crease 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 HKA, the sun's Illustration, 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 prepon- derates. 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 PRECESSION OF THE EQUINOXES. 149 shifting of the equinoctial points, from east to west. Sup- CHAP. xiv. pose that we mark the exact place in the heavens where, p rec ^i on O f during the present year, the sun crosses the equator, and the e ^ 111 - that this point is close to a certain star; next year, the sun n< " will crois 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 suc- cessively 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 readies that point. The appearance is as though the equinox Apparent goes forward to meet the sun, and hence the phenomenon P ro sr e88ion - 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 corres- ponding 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 Annual 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 illustration 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 150 PRECESSION OF THE EQUINOXES. CHAP. xiv. 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 Great circle, the inclination of the two circles. To transfer our concep- tions 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, complet- ing the circuit in about twenty-six thousand years. Hence Se EDg ie star *^ e & ^ &T ^ich we now ^l *^e pole-star has not always en- ' joyed 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 de- gree 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 The star 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 mis- apprehensions 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. Tropical ffhe time occupied by the sun, in passing from the equi- noctial point round to the same point again, is called the tropical year. As the sun does not perform a complete re- volution 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 THE MOON. 151 some interesting results in chronology. In consequence of CHAP. xrv. the retrograde motion of the equinoctial points, the signs of chanjjTon the ecliptic do not correspond, at present, to the constel- ^j e 8i *j? s of lotions 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 con- stellation Aries, and the sign Gemini, in the constellation Taurus. Undoubtedly, however, when the ecliptic was thus first divided, and the divisions named, the several constel- lations lay in the respective divisions which bear their names. CHAPTER XV. THE MOON. Soon as the evening shades prevail The Moon takes up tlie 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 CHAP. XV the earth and the sun, and the mutual relations which E art jfiina exist between them, the student is prepared to enter with win. advantage upon the survey of the other bodies that com- pose 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, lias been The moon, studied by astronomers with greater attention than any other of the heavenly bodies, since her comparative near- ness 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 espe- cially for a kind of dial-plate inscribed on the face of the sky, for weeks, and months, and times, and seasons. Distance from the earth. Source of light Inequalities on the sur- face. Mountains and valleys. Appearance through a telescope. 152 THE MOON. 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, re- volving around it every month, and accompanying us in our annual revolution around the sun. Although her near- ness 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 disc, or any portion of it, is illuminated, we can plainly discern, even with the naked eye, varieties of light and shade, indi- cating 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. By the aid of the telescope, we may see undoubted indi- cations 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 moun- tain groups, or long ranges, and another bearing all the marks of deep caverns or valleys. The observer will not, indeed, at the first sight of the moon through a telescope, recognize all these different objects. If he look at the moon when half her disc is enlightened (which is the best time for see- ing her varieties of surface), he will, at the first glance, observe a motley appearance, particularly along the line called the terminator, which separates the enlightened from THE MOON. 153 the unenlightened part of the disc, (Fig. 37.) On one side CHAP. xv. of the terminator, within the dark part of the disc, he will For ~^ te see illuminated points, and short, crooked lines, like rude see page i. characters marked with chalk on a black ground. On the other side of the terminator he will see a succession of little circular groups, appearing like numerous hubbies of oil on the surface of water. The further he carries his 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 impres- first time, having heard that mountains and valleys are to siona> 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 Preparatory advise, therefore, before the student takes even his first view 8tudy ' of the moon through a telescope, to form as clear an idea as he 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 recognized. Let him seize, if possible, the most favourable period (about the time of the first quarter), and previously learn from drawings and explana- tions how to interpret every thing he sees. What, then, ought to be the respective appearances of Appearance mountains, valleys, and deep craters, or caverns, in the the moon. moon ? The sun shines on the moon in the same way as it shines on the earth. 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 Corresponct- earth on its axis, the terminator, or the line which sepa- rates the enlightened from the unenlightened part of the eart k earth, travels along from east to west, over different places, as we see the moon's terminator travel over her disc 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 illumina- tion travels down the mountain, until at length it reaches the bottom of the valleys, and these in turn enjoy the full cf moun- tains. Effect of distance on the moon '3 appearance. Objects at the termi- nator. Plate VII. Fig. 2. Shadows of mountains. Various forms. 154 THE MOON. 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 moun- tain is very lofty. We may, moreover, form some judg- ment of the shape of a mountain by observing that of its shadow. Now, the moon is so distant that we could not easily dis- tinguish places simply by their elevations, since they would be projected into the same imaginary plane which consti- tutes the apparent disc of the moon ; but the foregoing considerations would enable us to infer their existence. Thus, when the moon is viewed at any time within her first quarter, but better near the end of that period, there will be observed on the side of the terminator, within the dark part of the disc, 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 the observer will recognize by those white specks and little crooked lines, before mentioned, as is represented in Fig. 2. These bright points and lines will be seen altering their figure, every hour, as they come more and more into the sun's light ; and meanwhile 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 disc. As they fall further and fur- ther within this part, additional proofs will be afforded 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 con- founded with the other enlightened portions of the surface ; but its position and its shape may still be recognized 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 THE MOON. THE MOON. 155 peaks, or a range with lofty cliffs. All these appearances CHAP. xv. will indeed be seen in miniature ; but a little familiarity with them will enable the observer to give them, in imaei- nation, their proper dimensions, as we 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 valleys and craters in the moon might be expected to appear. We craters - could not expect to see depressions any more than eleva- tions, since both would alike be projected on the same ima- ginary disc. But we may recognize 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 Familiar candle, in the night, the candle being elevated but little mastration - 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 simi- lar appearances in the moon, which we recognize as deep depressions. They are those circular spots near the ter- minator before spoken of, which look like bubbles of oil floating on water. They are nothing else than circular Circular craters or deep valleys. When they are so situated that the ciater8 - 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 Elevation spots on the moon cast deep shadows behind them, indicat- ^\t^ gu ' ing 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 in- stances, appears as well formed as could be described by a pair of compasses, while in the centre there not unfre- 156 THE MOON. CHAP. xv. quently is seen a conical mountain casting its pointed sha- Re eated ^ow on ^ ne bottom of the crater. I hope my readers will observations enjoy repeated opportunities to view the moon through a desirable. telescope. Allow me to recommend to them not to rest sati sited with a hasty or even with a single view, but to verify the preceding remarks by repeated and careful in- spection of the lunar disc, at different ages of the moon. Name* of The various places on the moon's disc have received ap- regions?" S propriate names. The dusky regions being formerly sup- posed to be seas, were named accordingly ; and other re- markable places have each t\vo names, one derived from some well-known spot on the earth, and the other from System of some distinguished personage. Thus, the same bright spot ture en la ~ on * ne sm 'f ace f the moon is called Mount Sinai or Tycho, and another, Mount Etna or Copernicus. The names of in- dividuals, however, are more used than the others. The Plate vil. diagram (Fig. 2) represents rudely the telescopic appear- Fig - 2- ance of the full moon. The reality is far more beautiful. A few of the most remarkable points have the .following Names of the names corresponding to the numbers and letters on the mostremark- able points. ma P' 1. Tycho. 6. Eratosthenes. 2. Kepler. 7. Plato. 3. Copernicus. 8. Archimedes. 4. Aristarchus. 9. Eudoxus. 6. Helicon. 10. Aristotle. A. Mare Humorum, Sea of Humours. 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 fully five miles high, and the valleys, in some instances, are four miles deep. Hence it is 'nferred, that the surface of the moon is more THE MOOW. 157 broken and irregular than that of the earth, its mountains CHAP. xv. 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 Varieties of of large telescopes, have been well described by Dr. Dick, surface - in his " Celestial Scenery," and I cannot give a better idea of them, than by adding 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 Insulated level, shaped like a sugar loaf, which may be supposed to mo 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 specta- tor on their summits magnificent views of the surrounding regions. Secondly, mountain ranges, extending in length two or Mountain three hundred miles. These ranges bear a distant resem- ^"K 68 - blance 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 north- east to south-west, 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 circular part of the moon's surface, particularly in its southern ran 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 dimen- sions, from a mile to forty or fifty miles in diameter, and are to be seen in great number? over every region of the 158 THE MOON. CHAP. XV. moon's surface ; they are most conspicuous, however, near the upper and lower limbs, about the time of the half moon. Elevations in The mountains which form these circular ridges are of the^circuiar 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. Central Fourthly, central mountains, or those which are placed in the middle of circular plains. In many of the plains and cavities surrrounded by circular ranges of mountains there stands a single insulated mountain, which rises from the centre of the plain, and whose shadow sometimes ex- tends, 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 six- teen miles. Lnnar The lunar caverns form a very peculiar and prominent feature of the moon's surface, and are to be seen through- out almost every region, but are most numerous in the south- west 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 shal- low egg-cup. The smaller cavities appear, within, almost Varied forms, 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 de- scribed. 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 con- tain smaller cavities of the same kind and form, particularly PHASES OF THE MOON. 159 in their sides. The mountainous ridges which surround CHAP. zv. these cavities reflect the greatest quantity of light ; and TychoT~ hence that region of the moon in which they abound ap- pears 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 distin- guished even by a small telescope. The spots named Kepler Kepler and and Copernicus are each composed of a central spot with c P enucua> luminous radiations.* The broken surface and apparent geological structure of Volcanic the moon has suggested the opinion, that the moon has been appeajl 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 favourable for observation. At such times, several astronomers, at different periods, have noticed Volcanoes in bright spots, which they took to be volcanoes. It must the moon " 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 Herschei's point with great attention, and with better means of obser- Ob8ervation8 - vation than any of his predecessors enjoyed, and fully em- braced the opinion that what he saw were volcanoes. In April, 1787, he records his observations as follows : " I per- . ceive three volcanoes in different places in the dark part of the moon. Two of them are already nearly extinct, or visible otherwise in a state of going to break out ; the third shows crn P tIo s. 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 Dick's "Celestial Scenery." chap. iv. 160 THE MOON. CHAP. XV. above three miles in diameter. The appearance resembles Appearance. a small piece of burning charcoal, when it is covered with a very thin coat of white ashes ; and it has a degree of bright- ness 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 accumula- tion of matter, such as would arise from the production of a great quantity of lava, sufficient to form a mountain. Lunar It is probable that the moon has an atmosphere, although atmosphere. i( . j g 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 atmo- sphere 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 Means of to the agency of our atmosphere, so, could we discern any 1 ' 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, indi- cating 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, distin- guished for the acuteness of his vision and his powers of observation in general, was very confident of having ob- tained, from different sources, clear evidence of a lunar atmosphere. He concluded, that the inferior or more Height of the dense part of the moon's atmosphere is not more than fif- atmosphere. teen 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 exist- ence, is not more than a mile. Presence of It has been a question, much agitated among astrono- water in the merg, 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 wan-ant such a conclusion, and we must have Schroeter's t>seryations. THE MOON. 161 recourse to other evidence, before we can decide the point. CHAP. XV. In the first place, then, there is no positive evidence in favour of the existence of water in the moon. Those exten- sive level regions before spoken of, and denominated seas Level in the geography of this planet, have no other signs of be- tue'moon! ing 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 mountain- ous regions ; but still, the inequalities are too considerable inequalities to permit the conclusion, that these level spots are such observable - 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, moreovei-, seen in those dusky spots which were supposed to be seas, are unfavourable to the supposition that those regions are covered by water. In the third place, the face of the moon, when illuminated Absence of by the sun and not obscured by the state of our own atmo- clouds> sphere, is always serene, and therefore free from clouds. Clouds are objects of great extent; they- frequently inter- cept 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 disc 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 in- tervention of clouds, ever lose sight of any portion of the moon when our own atmosphere is clear. But the want Evidence of of clouds in the lunar atmosphere almost necessarily im- of wa plies 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 sur- face of water, its tendency to pass into the state of vapour 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 162 THE MOON. CflAP. XV. Probable nature of the atmosphere. Faladons arguments. Beply. Uniformity of natural laws. Supposition of inhabi- tant* 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 sur- face 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 vapour, 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 mira- cle. 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 ana- logy ? 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 dimi- nished 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 ques- tion has often been raised, whether we may hope that our THE MOON. 163 telescopes will ever be so much improved, and our other CHAP. XV. 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 struc- identifier tures in the moon may be inferred from the fact, that a artMcui space a mile in diameter is the least space that could be structures 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 impossi- discover any inhabitants in the moon. Were we to view jjiK^vering the moon with a telescope that magnifies ten thousand inhabitants, 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, when speaking of the telescope, whenever Obstacles we increase the magnifying power of this instrument we nTtnre of the diminish its field of view, so that with very high magnifiers telescope. we can see nothing but a point, such as a fixed star. We at the same time, also, magnify the vapours 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, be- longing to Yale College, in the United States, for example, it was seldom found possible to gain anything 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 164 THE MOON. CHAP. XV. trace indications of lunar inhabitants in their works, and Dr. Dick's that they may in like manner recognize the existence of reasonings, the inhabitants of our planet. An author, who has reflected much on subjects of this kind, reasons as follows : " A na- vigator 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 satis- factory evidence that such beings exist on that planet : and it is thought possible that such operations may be traced. Possibility A telescope which magnifies twelve hundred times will en- artmciai able us to perceive, as a visible point on the surface of the ures> 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 dis- trict where no such edifices had previously been erected, such objects and operations might probably be detected by XTovements a minute inspection. Were a multitude of living creatures bodiesf 6 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 colour, which such movements would produce. Necessary J n order to detect such minute objects and operations, it observation, 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, dur- ing which time certain changes would probably be perceived, arising either from physical causes, or from the operations of living agents."* Dick's " Celestial Scenery." 165 CHAPTER XVI. THB MOON. PHASES. HAEVEST MOON. ITERATIONS. First to the neighbouring 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 CHAP. XVI. the earth, and the various changes she undergoes every phaseTofthe month, called her phases, which depend on the different moon - 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. Apparent Her apparent orbit, as traced out on the face of the sky, is or 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 previously explained. (See page 143.) 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 Sidereal called a sidereal tnonth, and consists of about twenty-seven month - and one fourth days. The time which intervenes between one new moon and another is called a synodical month, and Synodical consists of nearly twenty-nine and a half days. A new montlu moon occurs when the sun and moon meet in the same part of the heavens ; but the snn as well as the moon is apparently travelling eastward, and nearly at the rate of one 166 PHASES OF THE MOOK. CHAP. xvi. degree a day, and consequently, during the twenty-seven Relative days while the moon has heen going round the earth, the progression sun y, as b een going forward ahout the same number of de- of sun and f. .__.. moon. grees 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. In-ecuinr The moon does not pursue precisely the same track tnoon fthe aroun( l 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 de- grees, 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 even- ing 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. Nodes. 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 intersec- tions of the equinoctial and ecliptic, and, like the latter, are one hundred and eighty degrees apart. Phases. 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 disc next to the sun, while the other portions of the disc shine with a feeble light, reflected to the moon from the earth. Eveiy night, we observe the moon to be further and further eastward of the sun, until, when she has reached an $ longation from the sun of ninety degrees, half her visible disc is enlight- First quarter, ened, and she is said to be in her first quarter. The termi- nator, 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, coin- ciding with the diameter of the disc ; but after passing this point, the terminator becomes concave towards the sun, PHASES OF THE MOOW. 167 bounding that side of the moon by an elliptical curve, CHAP. XVI. when the moon is said to be gibbous. When the moon Gibbous! arrives at the distance of one hundred and eighty degrees from the sun, the entire circle is illuminated, and the moon iafutt. 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 Third time until new moon, she exhibits again the form of a cres- quaner - cent before the rising sun, until, approaching her conjunc- tion 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. The reader has doubtless observed, that the moon appears Variations of much further in the south at one time than at another, patiT 00 " 18 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 hori- zon, at a given time of night, at different seasons of the year. This will be seen 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 Example, western horizon, Libra being in the west, it will represent the position of the ecliptic at sunset in the month of Sep- tember, 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 south-west, and the summer solstice very far in the north-east ; and the course of the 168 PHASES OF THE MOON'. CHAP. xvi. moon from new to full will be nearly along this track. Tracker the Keeping these things in mind, we may easily see why the moon - Fig. 38. moon runs sometimes high and sometimes low. The student mus t 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 south-west, and accordingly the new moon runs very low ; but the full moon, being in the opposite tropic, which rises far in the north-east, runs very high, as is known to be the case in mid-winter. But now let us take the position of the HARVEST MOON. 169 ecliptic in mid-summer. Then, at sunset, the tropic of CHAP, xvi Cancer is in the north-west, and the tropic of Capricorn in the south-east ; consequently, the new moons run high and the full moons low. It is a natural consequence of this arrangement, to render Excess of the moon's light the most beneficial to us, by giving it in winter ght '' greatest abundance, when we have least of the sun's light, and 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 favourably for the inhabitants of the polar Favourable 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 con- tinually 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 inhabi- tants of the other hemisphere, from whom the sun is with- drawn. About the time of the autumnal equinox, the moon, Harvest when near her full, rises about sunset a number of nights in mo 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 Harvest home, an occasion often alluded to by British poets. Thus home - Henry Kirke White : " Moon of harvest, herald mild Of, .lenty, rustic labour's child, Hail, O hail ! I erect thy beam, As soft it trembles o'er the stream, And gilds the straw-thatch'd hamlet wide, Where innocence and peace reside ; Tis tliou 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 170 HARVEST MOON. CHAP, xvi 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 Cause of the under the last head,) that, since the ecliptic cuts the meri- pUenomena. ( jj an 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 equi- noxes 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 Position of the time of the harvest home, about the time of the autum- moon at-tlie na ^ e 1 umox - The sun being then in Libra, and the moon, autumnal when full, being of course opposite to the sun, or in Aries ; equinox. an( j movm g 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. Motion of the The moon turns on her axis in the same time in which axis. 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 knit- ting-needle through it, in the direction of the stem, to re- Familiar present the axis, in which case the two eyes of the apple aiustration. will apt ] y repr esent 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 knitting-needle, carry it round the candle, and it will be seen that, unless the apple is made to turn round on the axis as it is carried about the candle, it will present different sides towards the candle ; LIBKATIONS. 171 and that, in order to make it always present the same side, CHAP. XVL it will be necessary to^ make it revolve exactly once on its concurrent axis, while it is going round the circle, the revolution on results of i i -ii. J.-L. i- -L different its axis always keeping exact pace with the motion m its motions, orbit. The same thing will be observed, in walking round a tree, always keeping the face towards the tree. If we have our face towards the tree when we set out, and walk round without turning, when we have reached the opposite side of the tree, our back will be towards it, and we will find that, in order to keep our face constantly towards the tree, it is necessary to turn round on our heel at the same rate as we go forward. Since, however, the motion of the moon on its axis is Vibrations in 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, we carry it forward a little faster than the rate at which it turns on its axis, a portion of the hemi- sphere usually out of sight is brought into view on one side ; or if the apple is moved 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 libra- tions in longitude. The moon has also a libration in lati- Miration in tude; 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 mo- tion to the moon's axis. This is owing to the fact, that the cause of the moon's axis is inclined to the plane of her orbit. If, in the varia t ion - experiment with the apple, we hold the knitting-needle parallel to the candle, (in which case the axis will be per- pendicular to the plane of revolution,) the candle will shine upon both poles during the whole circuit, and an eye situ- ated where the candle is would constantly see both poles ; but now, by inclining the needle towards the plane of revo- lution, and carrying it round, always keeping it parallel to itself, it will be observed that the two poles are alternately in and out of sight. The moon exhibits another appearance of this kind, called Diurnal her diurnal libration, depending on the daily rotation of the spectator. She turns the same face towards the centre 172 ITERATIONS. CHAP. XVL of the earth only, whereas we view her from the surface. When she is on the meridian, we view her disc nearly aa of ita course, 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 por- tion of one limb while the moon is rising, which is gradu- ally lost sight of, and we see a portion of the opposite limb, as the moon declines to the west. The reader 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 Thelnnar night depends on the revolution of a planet on its own axis, duy- and it takes the moon twenty-nine and a-half days to per- form this revolution, so that the sun shall go from the me- ridian of any place and return to the same meridian again, of course the lunar day occupies this long period. So pro- Extreme tracted an exposure to the sun's rays, especially in the equa- variations of ..-..-.! temperature, tonal regions of the moon, must occasion an excessive accu- mulation 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 succes- sion 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. Appearance Soon after this, an inhabitant of the moon would see a to tile moon, 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 luna- rians, or inhabitants of the moon, would enjoy the greatest LIBRATIONS. 173 possible benefit from the light afforded by the earth, since CHAP. x\1 in the half of her revolution where she appears to them as full, she would be present while the sun was absent, and would aftbrd her least light while the sun was present. In the second place, the earth would appear thirteen times as Apparent large to a spectator on the moon as the moon appears to us, ^ r e ^ the 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,"* with how much more reason might a lunarian exult thus, in view of the splendid orb that adorns his noc- turnal sky ! In the third place, the earth, as viewed from Position in any particular place on the moon, would occupy invariably armament, 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, Reference to a spectator at E, (Fig. 38, page 168,) in the middle of the th disc 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 * As when the moon, refulgent lamp of night, O'er heaven's clear azure sheds her sacred light, When not a breatli 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 POI''S IIOMJJB. 174 MOON'S ORBIT. CHAP. XVL would occur from the librations of the moon. In the fourth Diversified place, the earth would present to a spectator on the moon L none of that uniformit y of as pect which the moon presents to us, but would exhibit an appearance exceedingly divei 1 - sified. 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. CHAPTER XYII. MOOS'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. CHAP.XVIL WE have thus far contemplated the revolution of the moon MotioiTof around the earth as though the earth were at rest. But in the moon. 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 revo- lution. This language may convey an erroneous idea ; for Complex 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 moou is attracted towards the sun two and one-fifth times more influence of than towards the earth, and would abandon the earth, were the sun. no j. ^g 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 MOOM'S ORBIT. 175 the gravity of the moon towards the sun 5s fo'und to be CHAP.XVH greater, at the conjunction, than her gravity towards the Gn^tyot earth, some have apprehended that, if the doctrine of uni- the moon versa! gravitation is true, the moon ought necessarily to sun. 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 146, if, with a certain force of pro- Explanatlor jection acting in the direction AB, and of attraction, in the of Ua 8 rani * direction AC, the attraction which caused a body to move in the line AD were diminished, it would move nearer to the tangent, as in AE or AF. Now, when the moon is in conjunction, her gravity towards the earth acts in opposi- tion to that towards the sun, (see Fig. 38, page 168.) while Opposing her velocity remains too great to carry her with what force 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 pro- jectile force being less than that required to make her re- volve 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 eveiy where Pathoftii* greater than that of the earth, the actual path of the moon 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 walk- illustration, ing 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 176 MOON 3 OfiBIT. Irregulari- ties of the Accuracy of observations. Cause of irregulari- ties. Disturbing Influence of the sun. 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 development, and its re- sults have conspired with those of long-continued observa- tion, to furnish the means of ascertaining with great exact- ness the place of the moon in the heavens, at any given instant of time, past or future, and thus to enable astrono- mers 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 ate so small aa 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. The reader will be able to understand something of the cause of these irregularities, if he 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 ope- rates 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, be- cause 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 MOON'S IRREGULARITIES. 177 a greater distance than the earth from the sun, while the CHAp.xvir. 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 Alternate projectile motions of the earth and moon were destroyed, S'a'ttrac- and that they were allowed to fall freely towards the sun. tionofthe (See Fig. 38, page 168.) 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, In conjunc- and fall with greater velocity towards the sun ; so that the tlon- distance of the moon from the earth would be increased by the fall. If the moon was in opposition, or in the part of In opposition, 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 Alternate action of the sun would increase their distance, if they were Jjiminution of allowed to fall towards the sun, then the sun's action, by gravitation. endeavouring 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 remem- bered, 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 investigated by Sir Isaac Newton, in conformity with his doctrine of byNewton - universal gravitation, and the explanation was first pub- 178 MOON S IRREGULARITIES. Newton's commenta- tors. Figure of the moon's orbit. CHAP.XVIL lished in the " Principia ;" but, as it was given in a mathe- matical dress, there were at that age very few persons capable of reading or understanding it. Several eminent individuals, therefore, undertook to give a popular explana- tion of these difficult points. Among Newton's contem- poraries, 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 expla- nation 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 her 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, we must The moon's perigee and apogee. Changes of the moon '3 nodes. MOON'S IRREGULARITIES. 179 have very distinctly in mind the meaning of the terms CHAP.XVTI themselves ; and if, at any time, the student is at a loss Necessity for about the signification of any word that is used in express- ing an astronomical proposition, I would advise him to turn back to the previous definition of that term, and revive its meaning clearly in his mind, before proceeding any further. In the present case, it will be recollected 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 ob- serve, 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 Retrograding heavens, we shall find that it crosses the ecliptic sensibly on'the" * 168 to the westward of that star, and so on, further and further ecliptic, to the westward, every time it crosses the ecliptic at either node. This fact is expressed by saying that the nodes retro- grade 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 Line of the west to east, through her w T hole course, in about nine years. a P sldaa> The reader 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 Revolutions would come to its perigee a little further eastward than ofthe P !ri s** 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 re- volves. These are only a few of the irregularities that attend the 180 MOON'S IRREGULARITIES. CilAP.xvil 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. Numerous The moon may be regarded as a body endeavouring to motion" make its way around the earth, but as subject to be conti- nually 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 re- quired the highest powers of the human mind, aided by all the wonderful resources of mathematics. Yet, so con- sistent is truth with itself, that, where some minute inequa- Accuraeyof Hty in the moon's motions is developed, at the end of a calculations. l n g an ^ intricate mathematical process, on pointing the telescope to the moon, and watching its progress through the skies, we may actually see evidence of the same irregu- larities, 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 tele- scopes. But the truth of the law of gravitation, and of the results it gives, when followed out by a chain of mathema- tical 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. Just homage Tn e mind that was first able to elicit from the operations Newton. 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 intel- lectual powers far beyond those of the majority of the human race. We need not wonder* therefore, at the homage that is now paid to the genius of Newton, an admiration which has been continually increasing, as fresh discoveries have been made by tracing out new consequences of the law of universal gravitation. MOON'S IRREGULARITIES. 181 The chief object of astronomical tables is to give the CHAP.XVIL amount of all the irregularities that attend the motions of Astronomical the heavenly bodies, by estimating the separate value of tobies. 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 irre- gularities which would affect her longitude. These are in Number of all no less than sixty, though most of them are so exceed- yariattoiis? ingly 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. The mean We next apply the various corrections for her irregular plac& 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 Accuracy of astonishing degree of accuracy, that it has been said, by the *" highest authority, that an astronomer could now predict, for a thousand years to come, the precise moment of the pas- sage 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 seinidiameter 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 mathema- United tician, and the artist, have united their powers to produce lab 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 geo- metry and the calculus ; and, finally, the instrument-maker has furnished the means, not only of verifying these con- clusions, but of discovering new truths, as the foundation of future reasonings. 182 MOOS S IRREGULARITIES. Shifting of the moon's nodes. CIIAP.XVIL 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 de- grees 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 be- tween two successive conjunctions between the sun and the Interval moon's node is about nineteen days shorter than the solar conjunctions, 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 X 19 = 658578 days = 18 y. 10 d. And 29-5305887 X 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 rela- tions, 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 hi 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. Cycle of revolutions. Eclipses. MOON'S IRKEGCLAKITIES. 183 It was probably by this means that Thales, a Grecian astro- CHAP.XVIL nomer who flourished six hundred years before the Christian Ancient 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 there- fore, at that age, considered as a distinguished feat to pre- dict even the year in which an eclipse w r as to happen. This eclipse is memorable in ancient history, from its hav- ing 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 TheMetonic the Saros, but it is not the same with it, nor was the period c>ce ' used, like the Saros, for foretelling eclipses, but for ascer- taining the age of the moon at any given period. It con- sisted 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 Periodic f. r i ,. i .. recurrence time of the vernal equinox, in one cycle, nineteen years O f results, 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 daj's these events would occur in any other cycle ; and, since the regulation of games, Regulation feasts, and fasts, has been generally made, both in ancient fcs 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. 184 MOON S IRREGULARITIES. Athenian cycle. Periodical and secular inequalities. Acceleration ot the moon's irean mo- tion. Ancient recorded eclipse. Ideas sug- gested by this pheno- mena. The Athenians adopted the metonic cycle four hundred and thirty-three years before the Christian era, for the re- gulation 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. Secu- lar inequalities are those which are completed only in very long periods, such as centuries or ages. Hence the corres- ponding 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 disco- vered that the moon actually revolves around the earth in a less period now than she did in ancient times. The differ- ence, however, is exceedingly small, being only about ten seconds in a century. In a lunar eclipse, the moon's lon- gitude 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. More- over, 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 pro- jectile force, would have the effect to bring her nearer and ECLIPSES. 185 nearer to the earth, and thus to augment her velocity. CHAP.XVII. But, in 1786, La Place demonstrated that this acceleration cause of this is one of the legitimate effects of the sun's disturbing force, acceleration. 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 eccen- tricity 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 mo- tions will oscillate for ever about a mean value. CHAPTER 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. MILTON. HAVING now learned various particulars respecting the CHAPTER earth, the sun, and the moon, the student is prepared to XV1IL understand the explanation of solar and lunar eclipses, which have in all ages excited a high degree of interest. What, indeed, is more admirable, than that astronomers Precision of should be able to tell us, years beforehand, the exact instant pfJaTcuons! 1 of the commencement and termination of an eclipse, and describe all the attendant circumstances with the greatest fidelity. The reader has doubtless 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 en- deavour, in this chapter, to explain the leading principles of the calculation of eclipses, with as much plainness as possible. CHAPTER XVIIL Causes of eclipses. The earth and moon opaque bodies. Relative size of the sun, earth, and moon. 186 ECLIPSES. 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 be- tween the earth and the sun, covers either a part or the whole of the solar disc. The earth and the moon being both opaque, globular bodies, exposed to the sun's light, they cast shadows oppo- site to the sun, like any other bodies on which the sun shines. Were the sun of the same size w r ith 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 nar- rower 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 vortex, at a certain distance behind the body. These several cases are represented in the following dia- grams, (Figs. 39, 40, 41.) Figs. 39, 40, 41. Length of the moon's 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 ECLIPSES. 187 longest when it is furthest from the sun. Now, when both CHAPTER these circumstances conspire, that is. when the moon is in XV1IL her perigee, and along with the earth in her aphelion, her The moon ID shadow extends nearly fifteen thousand miles beyond the and'the' 866 ' centre of the earth, and covers a space on the surface one ai^ 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, Eclipse of the when the sun and moon meet in the same part of the SUE 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. The nature of eclipses will be clearly understood from the Nature of following representation. The diagram (Fig. 42) exhibits ecU P 8es - F'r- 42. the relative position of the sun, the earth, and the moon, Avenge