LETTER XXIV. THE PLANETARY MOTIONS.----KEPLER'S LAWS.----KEPLER. "God of the rolling orbs above! Thy name is written clearly bright In the warm day's unvarying blaze, Or evening's golden shower of light; For every fire that fronts the sun, And every spark that walks alone Around the utmost verge of heaven, Was kindled at thy burning throne."-- Peabody.

If we could stand upon the sun and view the planetary motions, they would appear to us as simple as the motions of equestrians riding with different degrees of speed around a large ring, of which we occupied the centre. We should see all the planets coursing each other from west to east, through the same great highway, (the Zodiac,) no one of them, with the exception of the asteroids, deviating more than seven degrees from the path pursued by the earth. Most of them, indeed, would always be seen moving much nearer than that to the ecliptic. We should see the planets moving on their way with various degrees of speed. Mercury would make the entire circuit in about three months, hurrying on his course with a speed about one third as great as that by which the moon revolves around the earth. The most distant planets, on the other hand, move at so slow a pace, that we should see Mercury, Venus, the Earth, and Mars, severally overtaking them a great many times, before they had completed their revolutions. But though the movements of some were comparatively rapid, and of others extremely slow, yet they would not seem to differ materially, in other respects: each would be making a steady and nearly uniform march along the celestial vault.

Such would be the simple and harmonious motions of the planets, as they would be seen from the sun, the centre of their motions; and such they are, in fact. But two circumstances conspire to make them appear exceedingly different from these, and vastly more complicated; one is, that we view them out of the centre of their motions; the other, that we are ourselves in motion. I have already explained to you the effect which these two causes produce on the apparent motions of the inferior planets, Mercury and Venus. Let us now see how they effect those of the superior planets, Mars, Jupiter, Saturn, and Uranus.

Orreries, or machines intended to exhibit a model of the solar system, are sometimes employed to give a popular view of the planetary motions; but they oftener mislead than give correct ideas. They may assist reflection, but they can never supply its place. The impossibility of representing things in their just proportions will be evident, when we reflect that, to do this, if in an orrery we make Mercury as large as a cherry, we should have to represent the sun six feet in diameter. If we preserve the same proportions, in regard to distance, we must place Mercury two hundred and fifty feet, and Uranus twelve thousand five hundred feet, or more than two miles from the sun. The mind of the student of astronomy must, therefore, raise itself from such imperfect representations of celestial phenomena, as are afforded by artificial mechanism, and, transferring his contemplations to the celestial regions themselves, he must conceive of the sun and planets as bodies that bear an insignificant ratio to the immense spaces in which they circulate, resembling more a few little birds flying in the open sky, than they do the crowded machinery of an orrery.

The real motions of the planets, indeed, or such as orreries usually exhibit, are very easily conceived of, as before explained; but the apparent motions are, for the most part, entirely different from these. The apparent motions of the inferior planets have been already explained. You will recollect that Mercury and Venus move backwards and forwards across the sun, the former never being seen further than twenty-nine degrees, and the latter never more than about forty-seven degrees, from that luminary; that, while passing from the greatest elongation on one side, to the greatest elongation on the other side, through the superior conjunction, the apparent motions of these planets are accelerated by the motion of the earth; but that, while moving through the inferior conjunction, at which time their motions are retrograde, they are apparently retarded by the earth's motion. Let us now see what are the apparent motions of the superior planets.

Let A, B, C, Fig. 62, page 294, represent the earth in different positions in its orbit, M, a superior planet, as Mars, and N R, an arc of the concave sphere of the heavens. First, suppose the planet to remain at rest in M, and let us see what apparent motions it will receive from the real motions of the earth. When the earth is at B, it will see the planet in the heavens at N; and as the earth moves successively through C, D, E, F, the planet will appear to move through O, P, Q, R. B and F are the two points of greatest elongation of the earth from the sun, as seen from the planet; hence, between these two points, while passing through its orbit most remote from the planet, (when the planet is seen in superior conjunction,) the earth, by its own motion, gives an apparent motion to the planet in the order of the signs; that is, the apparent motion given by the real motion of the earth is direct. But in passing from F to B through A, when the planet is seen in opposition, the apparent motion given to the planet by the earth's motion is from R to N, and is therefore retrograde. As the arc described by the earth, when the motion is direct, is much greater than when the motion is retrograde, while the apparent arc of the heavens described by the planet from N to R, in the one case, and from R to N, in the other, is the same in both cases, the retrograde motion is much swifter than the direct, being performed in much less time.

But the superior planets are not in fact at rest, as we have supposed, but are all the while moving eastward, though with a slower motion than the earth. Indeed, with respect to the remotest planets, as Saturn and Uranus, the forward motion is so exceedingly slow, that the above representation is nearly true for a single year. Still, the effect of the real motions of all the superior planets, eastward, is to increase the direct apparent motion communicated by the earth, and to diminish the retrograde motion. This will be evident from inspecting the figure; for if the planet actually moves eastward while it is apparently carried eastward by the earth's motion, the whole motion eastward will be equal to the sum of the two; and if, while it is really moving eastward, it is apparently carried westward still more by the earth's motion, the retrograde movement will equal the difference of the two.

If Mars stood still while the earth went round the sun, then a second opposition, as at A, would occur at the end of one year from the first; but, while the earth is performing this circuit, Mars is also moving the same way, more than half as fast; so that, when the earth returns to A, the planet has already performed more than half the same circuit, and will have completed its whole revolution before the earth comes up with it. Indeed Mars, after having been seen once in opposition, does not come into opposition again until after two years and fifty days. And since the planet is then comparatively near to us, as at M, while the earth is at A, and appears very large and bright, rising unexpectedly about the time the sun sets, he surprises the world as though it were some new celestial body. But on account of the slow progress of Saturn and Uranus, we find, after having performed one circuit around the sun, that they are but little advanced beyond where we left them at the last opposition. The time between one opposition of Saturn and another is only a year and thirteen days.

It appears, therefore, that the superior planets steadily pursue their course around the sun, but that their apparent retrograde motion, when in opposition, is occasioned by our passing by them with a swifter motion, of which we are unconscious, like the apparent backward motion of a vessel, when we overtake it and pass by it rapidly in a steam-boat.

Such are the real and the apparent motions of the planets. Let us now turn our attention to the laws of the planetary orbits.

There are three great principles, according to which the motions of the earth and all the planets around the sun are regulated, called Kepler's Laws, having been first discovered by the astronomer whose name they bear. They may appear to you, at first, dry and obscure; yet they will be easily understood from the explanations which follow; and so important have they proved in astronomical inquiries, that they have acquired for their renowned discoverer the appellation of the 'Legislator of the Skies.' We will consider each of these laws separately; and, for the sake of rendering the explanation clear and intelligible, I shall perhaps repeat some things that have been briefly mentioned before.

First Law.—The orbits of the earth and all the planets are ellipses, having the sun in the common focus. In a circle, all the diameters are equal to one another; but if we take a metallic wire or hoop, and draw it out on opposite sides, we elongate it into an ellipse, of which the different diameters are very unequal. That which connects the points most distant from each other is called the transverse, and that which is at right angles to this is called the conjugate, axis. Thus, A B, Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A B C. By such a process of elongating the circle into an ellipse, the centre of the circle may be conceived of as drawn opposite ways to E and F, each of which becomes a focus, and both together are called the foci of the ellipse. The distance G E, or G F, of the focus from the centre is called the eccentricity of the ellipse; and the ellipse is said to be more or less eccentric, as the distance of the focus from the centre is greater or less. Figure 64 represents such a collection of ellipses around the common focus F, the innermost, A G D, having a small eccentricity, or varying little from a circle, while the outermost, A C B, is an eccentric ellipse. The orbits of all the bodies that revolve about the sun, both planets and comets, have, in like manner, a common focus, in which the sun is situated, but they differ in eccentricity. Most of the planets have orbits of very little eccentricity, differing little from circles, but comets move in very eccentric ellipses. The earth's path around the sun varies so little from a circle, that a diagram representing it truly would scarcely be distinguished from a perfect circle; yet, when the comparative distances of the sun from the earth are taken at different seasons of the year, we find that the difference between their greatest and least distances is no less than three millions of miles.

Second Law.—The radius vector of the earth, or of any planet, describes equal areas in equal times. You will recollect that the radius vector is a line drawn from the centre of the sun to a planet revolving about the sun. This definition I have somewhere given you before, and perhaps it may appear to you like needless repetition to state it again. In a book designed for systematic instruction, where all the articles are distinctly numbered, it is commonly sufficient to make a reference back to the article where the point in question is explained; but I think, in Letters like these, you will bear with a little repetition, rather than be at the trouble of turning to the Index and hunting up a definition long since given.

In Figure 65, E a, E b, E c, &c., are successive representations of the radius vector. Now, if a planet sets out from a, and travels round the sun in the direction of a b c, it will move faster when nearer the sun, as at a, than when more remote from it, as at m; yet, if a b and m n be arcs described in equal times, then, according to the foregoing law, the space E a b will be equal to the space E m n; and the same is true of all the other spaces described in equal times. Although the figure E a b is much shorter than E m n, yet its greater breadth exactly counterbalances the greater length of those figures which are described by the radius vector where it is longer.

Third Law.—The squares of the periodical times are as the cubes of the mean distances from the sun. The periodical time of a body is the time it takes to complete its orbit, in its revolution about the sun. Thus the earth's periodic time is one year, and that of the planet Jupiter about twelve years. As Jupiter takes so much longer time to travel round the sun than the earth does, we might suspect that his orbit is larger than that of the earth, and of course, that he is at a greater distance from the sun; and our first thought might be, that he is probably twelve times as far off; but Kepler discovered that the distance does not increase as fast as the times increase, but that the planets which are more distant from the sun actually move slower than those which are nearer. After trying a great many proportions, he at length found that, if we take the squares of the periodic times of two planets, the greater square contains the less, just as often as the cube of the distance of the greater contains that of the less. This fact is expressed by saying, that the squares of the periodic times are to one another as the cubes of the distances.

This law is of great use in determining the distance of the planets from the sun. Suppose, for example, that we wish to find the distance of Jupiter. We can easily determine, from observation, what is Jupiter's periodical time, for we can actually see how long it takes for Jupiter, after leaving a certain part of the heavens to come round to the same part again. Let this period be twelve years. The earth's period is of course one year; and the distance of the earth, as determined from the sun's horizontal parallax, as already explained, is about ninety-five millions of miles. Now, we have here three terms of a proportion to find the fourth, and therefore the solution is merely a simple case of the rule of three. Thus:—the square of 1 year : square of 12 years : cube of 95,000,000 : cube of Jupiter's distance. The three first terms being known, we have only to multiply together the second and third and divide by the first, to obtain the fourth term, which will give us the cube of Jupiter's distance from the sun; and by extracting the cube root of this sum, we obtain the distance itself. In the same manner we may obtain the respective distances of all the other planets.

So truly is this a law of the solar system, that it holds good in respect to the new planets, which have been discovered since Kepler's time, as well as in the case of the old planets. It also holds good in respect to comets, and to all bodies belonging to the solar system, which revolve around the sun as their centre of motion. Hence, it is justly regarded as one of the most interesting and important principles yet developed in astronomy.

But who was this Kepler, that gained such an extraordinary insight into the laws of the planetary system, as to be called the 'Legislator of the Skies?' John Kepler was one of the most remarkable of the human race, and I think I cannot gratify or instruct you more, than by occupying the remainder of this Letter with some particulars of his history.

Kepler was a native of Germany. He was born in the Duchy of Wurtemberg, in 1571. As Copernicus, Tycho Brahe, Galileo, Kepler, and Newton, are names that are much associated in the history of astronomy, let us see how they stood related to each other in point of time. Copernicus was born in 1473; Tycho, in 1546; Galileo, in 1564; Kepler, in 1571; and Newton, in 1642. Hence, Copernicus was seventy-three years before Tycho, and Tycho ninety-six years before Newton. They all lived to an advanced age, so that Tycho, Galileo, and Kepler, were contemporary for many years; and Newton, as I mentioned in the sketch I gave you of his life, was born the year that Galileo died.

Kepler was born of parents who were then in humble circumstances, although of noble descent. Their misfortunes, which had reduced them to poverty, seem to have been aggravated by their own unhappy dispositions; for his biographer informs us, that "his mother was treated with a degree of barbarity by her husband and brother-in-law, that was hardly exceeded by her own perverseness." It is fortunate, therefore, that Kepler, in his childhood, was removed from the immediate society and example of his parents, and educated at a public school at the expense of the Duke of Wurtemberg. He early imbibed a taste for natural philosophy, but had conceived a strong prejudice against astronomy, and even a contempt for it, inspired, probably, by the arrogant and ridiculous pretensions of the astrologers, who constituted the principal astronomers of his country. A vacant post, however, of teacher of astronomy, occurred when he was of a suitable age to fill it, and he was compelled to take it by the authority of his tutors, though with many protestations, on his part, wishing to be provided for in some other more brilliant profession.

Happy is genius, when it lights on a profession entirely consonant to its powers, where the objects successively presented to it are so exactly suited to its nature, that it clings to them as the loadstone to its kindred metal among piles of foreign ores. Nothing could have been more congenial to the very mental constitution of Kepler, than the study of astronomy,—a science where the most capacious understanding may find scope in unison with the most fervid imagination.

Much as has been said against hypotheses in philosophy, it is nevertheless a fact, that some of the greatest truths have been discovered in the pursuit of hypotheses, in themselves entirely false; truths, moreover, far more important than those assumed by the hypotheses; as Columbus, in searching for a northwest passage to India, discovered a new world. Thus Kepler groped his way through many false and absurd suppositions, to some of the most sublime discoveries ever made by man. The fundamental principle which guided him was not, however, either false or absurd. It was, that God, who made the world, had established, throughout all his works, fixed laws,—laws that are often so definite as to be capable of expression in exact numerical terms. In accordance with these views, he sought for numerical relations in the disposition and arrangement of the planets, in respect to their number, the times of their revolution, and their distances from one another. Many, indeed, of the subordinate suppositions which he made, were extremely fanciful; but he tried his own hypotheses by a rigorous mathematical test, wherever he could apply it; and as soon as he discovered that a supposition would not abide this test, he abandoned it without the least hesitation, and adopted others, which he submitted to the same severe trial, to share, perhaps, the same fate. "After many failures," he says, "I was comforted by observing that the motions, in every case, seemed to be connected with the distances; and that, when there was a great gap between the orbits, there was the same between the motions. And I reasoned that, if God had adapted motions to the orbits in some relation to the distances, he had also arranged the distances themselves in relation to something else."

In two years after he commenced the study of astronomy, he published a book, called the 'Mysterium Cosmographicum,' a name which implies an explanation of the mysteries involved in the construction of the universe. This work was full of the wildest speculations and most extravagant hypotheses, the most remarkable of which was, that the distances of the planets from the sun are regulated by the relations which subsist between the five regular solids. It is well known to geometers, that there are and can be only five regular solids. These are, first, the tetraedron, a four-sided figure, all whose sides are equal and similar triangles; secondly, the cube, contained by six equal squares; thirdly, an octaedron, an eight-sided figure, consisting of two four-sided pyramids joined at their bases; fourthly, a dodecaedron, having twelve five-sided or pentagonal faces; and, fifthly, an icosaedron, contained by twenty equal and similar triangles. You will be much at a loss, I think, to imagine what relation Kepler could trace between these strange figures and the distances of the several planets from the sun. He thought he discovered a connexion between those distances and the spaces which figures of this kind would occupy, if interposed in certain ways between them. Thus, he says the Earth is a circle, the measure of all; round it describe a dodecaedron, and the circle including this will be the orbit of Mars. Round this circle describe a tetraedron, and the circle including this will be the orbit of Jupiter. Describe a cube round this, and the circle including it will be the orbit of Saturn. Now, inscribe in the earth an icosaedron, and the circle included in this will give the orbit of Venus. In this inscribe an octaedron, and the circle included in this will be the orbit of Mercury. On this supposed discovery Kepler exults in the most enthusiastic expressions. "The intense pleasure I have received from this discovery never can be told in words. I regretted no more time wasted; I tired of no labor; I shunned no toil of reckoning; days and nights I spent in calculations, until I could see whether this opinion would agree with the orbits of Copernicus, or whether my joy was to vanish into air. I willingly subjoin that sentiment of Archytas, as given by Cicero; 'If I could mount up into heaven, and thoroughly perceive the nature of the world and the beauty of the stars, that admiration would be without a charm for me, unless I had some one like you, reader, candid, attentive, and eager for knowledge, to whom to describe it.' If you acknowledge this feeling, and are candid, you will refrain from blame, such as, not without cause, I anticipate; but if, leaving that to itself, you fear, lest these things be not ascertained, and that I have shouted triumph before victory, at least approach these pages, and learn the matter in consideration: you will not find, as just now, new and unknown planets interposed; that boldness of mine is not approved; but those old ones very little loosened, and so furnished by the interposition (however absurd you may think it) of rectilinear figures, that in future you may give a reason to the rustics, when they ask for the hooks which keep the skies from falling."

When Tycho Brahe, who had then retired from his famous Uraniburg, and was settled in Prague, met with this work of Kepler's, he immediately recognised under this fantastic garb the lineaments of a great astronomer. He needed such an unwearied and patient calculator as he perceived Kepler to be, to aid him in his labors, in order that he might devote himself more unreservedly to the taking of observations,—an employment in which he delighted, and in which, as I mentioned, in giving you a sketch of his history, he excelled all men of that and preceding ages. Kepler, therefore, at the express invitation of Tycho, went to Prague, and joined him in the capacity of assistant. Had Tycho been of a nature less truly noble, he might have looked with contempt on one who had made so few observations, and indulged so much in wild speculation; or he might have been jealous of a rising genius, in which he descried so many signs of future eminence as an astronomer; but, superior to all the baser motives, he extends to the young aspirant the hand of encouragement, in the following kind invitation: "Come not as a stranger, but as a very welcome friend; come, and share in my observations, with such instruments as I have with me."

Several years previous to this, Kepler, after one or two unsuccessful trials, had found him a wife, from whom he expected a considerable fortune; but in this he was disappointed; and so poor was he, that, when on his journey to Prague, in company with his wife, being taken sick, he was unable to defray the expenses of the journey, and was forced to cast himself on the bounty of Tycho.

In the course of the following year, while absent from Prague, he fancied that Tycho had injured him, and accordingly addressed to the noble Dane a letter full of insults and reproaches. A mild reply from Tycho opened the eyes of Kepler to his own ingratitude. His better feelings soon returned, and he sent to his great patron this humble apology: "Most noble Tycho! How shall I enumerate, or rightly estimate, your benefits conferred on me! For two months you have liberally and gratuitously maintained me, and my whole family; you have provided for all my wishes; you have done me every possible kindness; you have communicated to me every thing you hold most dear; no one, by word or deed, has intentionally injured me in any thing; in short, not to your own children, your wife, or yourself, have you shown more indulgence than to me. This being so, as I am anxious to put upon record, I cannot reflect, without consternation, that I should have been so given up by God to my own intemperance, as to shut my eyes on all these benefits; that, instead of modest and respectful gratitude, I should indulge for three weeks in continual moroseness towards all your family, and in headlong passion and the utmost insolence towards yourself, who possess so many claims on my veneration, from your noble family, your extraordinary learning, and distinguished reputation. Whatever I have said or written against the person, the fame, the honor, and the learning, of your Excellency; or whatever, in any other way, I have injuriously spoken or written, (if they admit no other more favorable interpretation,) as to my grief I have spoken and written many things, and more than I can remember; all and every thing I recant, and freely and honestly declare and profess to be groundless, false, and incapable of proof." This was ample satisfaction to the generous Tycho.

On Kepler's return to Prague, he was presented to the Emperor by Tycho, and honored with the title of Imperial Mathematician. This was in 1601, when he was thirty years of age. Tycho died shortly after, and Kepler succeeded him as principal mathematician to the Emperor; but his salary was badly paid, and he suffered much from pecuniary embarrassments. Although he held the astrologers, or those who told fortunes by the stars, in great contempt, yet he entertained notions of his own, on the same subject, quite as extravagant, and practised the art of casting nativities, to eke out a support for his family.

When Galileo began to observe with his telescope, and announced, in rapid succession, his wonderful discoveries, Kepler entered into them with his characteristic enthusiasm, although they subverted many of his favorite hypotheses. But such was his love of truth, that he was among the first to congratulate Galileo, and a most engaging correspondence was carried on between these master-spirits.

The first planet, which occupied the particular attention of Kepler, was Mars, the long and assiduous study of whose motions conducted him at length to the discovery of those great principles called 'Kepler's Laws.' Rarely do we meet with so remarkable a union of a vivid fancy with a profound intellect. The hasty and extravagant suggestions of the former were submitted to the most laborious calculations, some of which, that were of great length, he repeated seventy times. This exuberance of fancy frequently appears in his style of writing, which occasionally assumes a tone ludicrously figurative. He seems constantly to contemplate Mars as a valiant hero, who had hitherto proved invincible, and who would often elude his own efforts to conquer him, "While thus triumphing over Mars, and preparing for him, as for one altogether vanquished, tabular prisons, and equated, eccentric fetters, it is buzzed here and there, that the victory is vain, and that the war is raging anew as violently as before. For the enemy, left at home a despised captive, has burst all the chains of the equation, and broken forth of the prisons of the tables. Skirmishes routed my forces of physical causes, and, shaking off the yoke, regained their liberty. And now, there was little to prevent the fugitive enemy from effecting a junction with his own rebellious supporters, and reducing me to despair, had I not suddenly sent into the field a reserve of new physical reasonings, on the rout and dispersion of the veterans, and diligently followed, without allowing the slightest respite, in the direction in which he had broken out."

But he pursued this warfare with the planet until he gained a full conquest, by the discovery of the first two of his laws, namely, that he revolves in an elliptical orbit, and that his radius vector passes over equal spaces in equal times.

Domestic troubles, however, involved him in the deepest affliction. Poverty, the loss of a promising and favorite son, the death of his wife, after a long illness;—these were some of the misfortunes that clustered around him. Although his first marriage had been an unhappy one, it was not consonant to his genius to surrender any thing with only a single trial. Accordingly, it was not long before he endeavored to repair his loss by a second alliance. He commissioned a number of his friends to look out for him, and he soon obtained a tabular list of eleven ladies, among whom his affections wavered. The progress of his courtship is thus narrated in the interesting 'Life' contained in the 'Library of Useful Knowledge.' It furnishes so fine a specimen of his eccentricities, that I cannot deny myself the pleasure of transcribing the passage for your perusal. It is taken from an account which Kepler himself gave in a letter to a friend.

"The first on the list was a widow, an intimate friend of his first wife and who, on many accounts, appeared a most eligible match. At first, she seemed favorably inclined to the proposal: it is certain that she took time to consider it, but at last she very quietly excused herself. Finding her afterwards less agreeable in person than he had anticipated, he considered it a fortunate escape, mentioning, among other objections, that she had two marriageable daughters, whom, by the way, he had got on his list for examination. He was much troubled to reconcile his astrology with the fact of his having taken so much pains about a negotiation not destined to succeed. He examined the case professionally. 'Have the stars,' says he, 'exercised any influence here? For, just about this time, the direction of the mid-heaven is in hot opposition to Mars, and the passage of Saturn through the ascending point of the zodiac, in the scheme of my nativity, will happen again next November and December. But, if these are the causes, how do they act? Is that explanation the true one, which I have elsewhere given? For I can never think of handing over to the stars the office of deities, to produce effects. Let us, therefore, suppose it accounted for by the stars, that at this season I am violent in my temper and affections, in rashness of belief, in a show of pitiful tender-heartedness, in catching at reputation by new and paradoxical notions, and the singularity of my actions; in busily inquiring into, and weighing, and discussing, various reasons; in the uneasiness of my mind, with respect to my choice. I thank God, that that did not happen which might have happened; that this marriage did not take place. Now for the others.' Of these, one was too old; another, in bad health; another, too proud of her birth and quarterings; a fourth had learned nothing but showy accomplishments, not at all suitable to the kind of life she would have to lead with him. Another grew impatient, and married a more decided admirer while he was hesitating. 'The mischief,' says he, 'in all these attachments was, that, whilst I was delaying, comparing, and balancing, conflicting reasons, every day saw me inflamed with a new passion.' By the time he reached No. 8, of his list, he found his match in this respect. 'Fortune has avenged herself at length on my doubtful inclinations. At first, she was quite complying, and her friends also. Presently, whether she did or did not consent, not only I, but she herself, did not know. After the lapse of a few days, came a renewed promise, which, however, had to be confirmed a third time: and, four days after that, she again repented her conformation, and begged to be excused from it. Upon this, I gave her up, and this time all my counsellors were of one opinion.' This was the longest courtship in the list, having lasted three whole months; and, quite disheartened by its bad success, Kepler's next attempt was of a more timid complexion. His advances to No. 9 were made by confiding to her the whole story of his recent disappointment, prudently determining to be guided in his behavior, by observing whether the treatment he experienced met with a proper degree of sympathy. Apparently, the experiment did not succeed; and, when almost reduced to despair, Kepler betook himself to the advice of a friend, who had for some time past complained that she was not consulted in this difficult negotiation. When she produced No. 10, and the first visit was paid, the report upon her was as follows: 'She has, undoubtedly, a good fortune, is of good family, and of economical habits: but her physiognomy is most horribly ugly; she would be stared at in the streets, not to mention the striking disproportion in our figures. I am lank, lean, and spare; she is short and thick. In a family notorious for fatness, she is considered superfluously fat.' The only objection to No. 11 seems to have been, her excessive youth; and when this treaty was broken off, on that account, Kepler turned his back upon all his advisers, and chose for himself one who had figured as No. 5, in his list, to whom he professes to have felt attached throughout, but from whom the representations of his friends had hitherto detained him, probably on account of her humble station."

Having thus settled his domestic affairs, Kepler now betook himself, with his usual industry, to his astronomical studies, and brought before the world the most celebrated of his publications, entitled 'Harmonics.' In the fifth book of this work he announced his Third Law,—that the squares of the periodical times of the planets are as the cubes of the distances. Kepler's rapture on detecting it was unbounded. "What," says he, "I prophesied two-and-twenty years ago, as soon as I discovered the five solids among the heavenly orbits; what I firmly believed long before I had seen Ptolemy's Harmonics; what I had promised my friends in the title of this book, which I named before I was sure of my discovery; what, sixteen years ago, I urged as a thing to be sought; that for which I joined Tycho Brahe, for which I settled in Prague, for which I have devoted the best part of my life to astronomical contemplations;—at length I have brought to light, and have recognised its truth beyond my most sanguine expectations. It is now eighteen months since I got the first glimpse of light, three months since the dawn, very few days since the unveiled sun, most admirable to gaze on, burst out upon me. Nothing holds me: I will indulge in my sacred fury; I will triumph over mankind by the honest confession, that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God, far from the confines of Egypt. If you forgive me, I rejoice: if you are angry, I can bear it; the die is cast, the book is written, to be read either now or by posterity,—I care not which. I may well wait a century for a reader, as God has waited six thousand years for an observer." In accordance with the notion he entertained respecting the "music of the spheres," he made Saturn and Jupiter take the bass, Mars the tenor, the Earth and Venus the counter, and Mercury the treble.

"The misery in which Kepler lived," says Sir David Brewster, in his 'Life of Newton,' "forms a painful contrast with the services which he performed for science. The pension on which he subsisted was always in arrears; and though the three emperors, whose reigns he adorned, directed their ministers to be more punctual in its payment, the disobedience of their commands was a source of continual vexation to Kepler. When he retired to Silesia, to spend the remainder of his days, his pecuniary difficulties became still more harassing. Necessity at length compelled him to apply personally for the arrears which were due; and he accordingly set out, in 1630, when nearly sixty years of age, for Ratisbon; but, in consequence of the great fatigue which so long a journey on horseback produced, he was seized with a fever, which put an end to his life."

Professor Whewell (in his interesting work on Astronomy and General Physics considered with reference to Natural Theology) expresses the opinion that Kepler, notwithstanding his constitutional oddities, was a man of strong and lively piety. His 'Commentaries on the Motions of Mars' he opens with the following passage: "I beseech my reader, that, not unmindful of the Divine goodness bestowed on man, he do with me praise and celebrate the wisdom and greatness of the Creator, which I open to him from a more inward explication of the form of the world, from a searching of causes, from a detection of the errors of vision; and that thus, not only in the firmness and stability of the earth, he perceive with gratitude the preservation of all living things in Nature as the gift of God, but also that in its motion, so recondite, so admirable, he acknowledge the wisdom of the Creator. But him who is too dull to receive this science, or too weak to believe the Copernican system without harm to his piety,—him, I say, I advise that, leaving the school of astronomy, and condemning, if he please, any doctrines of the philosophers, he follow his own path, and desist from this wandering through the universe; and, lifting up his natural eyes, with which he alone can see, pour himself out in his own heart, in praise of God the Creator; being certain that he gives no less worship to God than the astronomer, to whom God has given to see more clearly with his inward eye, and who, for what he has himself discovered, both can and will glorify God."

In a Life of Kepler, very recently published in his native country, founded on manuscripts of his which have lately been brought to light, there are given numerous other examples of a similar devotional spirit. Kepler thus concludes his Harmonics: "I give Thee thanks, Lord and Creator, that Thou has given me joy through Thy creation; for I have been ravished with the work of Thy hands. I have revealed unto mankind the glory of Thy works, as far as my limited spirit could conceive their infinitude. Should I have brought forward any thing that is unworthy of Thee, or should I have sought my own fame, be graciously pleased to forgive me."

As Galileo experienced the most bitter persecutions from the Church of Rome, so Kepler met with much violent opposition and calumny from the Protestant clergy of his own country, particularly for adopting, in an almanac which, as astronomer royal, he annually published, the reformed calendar, as given by the Pope of Rome. His opinions respecting religious liberty, also, appear to have been greatly in advance of the times in which he lived. In answer to certain calumnies with which he was assailed, for his boldness in reasoning from the light of Nature, he uttered these memorable words: "The day will soon break, when pious simplicity will be ashamed of its blind superstition; when men will recognise truth in the book of Nature as well as in the Holy Scriptures, and rejoice in the two revelations."

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