Letters on Astronomy Part 16

"The firmament of Saturn will unquestionably present to view a more magnificent and diversified scene of celestial phenomena than that of any other planet in our system. It is placed nearly in the middle of that s.p.a.ce which intervenes between the sun and the orbit of the remotest planet. Including its rings and satellites, it may be considered as the largest body or system of bodies within the limits of the solar system; and it excels them all in the sublime and diversified apparatus with which it is accompanied. In these respects, Saturn may justly be considered as the sovereign among the planetary hosts. The prominent parts of its celestial scenery may be considered as belonging to its own system of rings and satellites, and the views which will occasionally be opened of the firmament of the fixed stars; for few of the other planets will make their appearance in its sky. Jupiter will appear alternately as a morning and an evening star, with about the same degree of brilliancy it exhibits to us; but it will seldom be conspicuous, except near the period of its greatest elongation; and it will never appear to remove from the sun further than thirty-seven degrees, and consequently will not appear so conspicuous, nor for such a length of time, as Venus does to us. Ura.n.u.s is the only other planet which will be seen from Saturn, and it will there be distinctly perceptible, like a star of the third magnitude, when near the time of its opposition to the sun. But near the time of its conjunction it will be completely invisible, being then eighteen hundred millions of miles more distant than at the opposition, and eight hundred millions of miles more distant from Saturn than it ever is from the earth at any period."[15]

URa.n.u.s.--Ura.n.u.s is the remotest planet belonging to our system, and is rarely visible, except to the telescope. Although his diameter is more than four times that of the earth, being thirty-five thousand one hundred and twelve miles, yet his distance from the sun is likewise nineteen times as great as the earth's distance, or about eighteen hundred millions of miles. His revolution around the sun occupies nearly eighty-four years, so that his position in the heavens, for several years in succession, is nearly stationary. His path lies very nearly in the ecliptic, being inclined to it less than one degree. The sun himself, when seen from Ura.n.u.s dwindles almost to a star, subtending, as it does, an angle of only one minute and forty seconds; so that the surface of the sun would appear there four hundred times less than it does to us. This planet was discovered by Sir William Herschel on the thirteenth of March, 1781. His attention was attracted to it by the largeness of its disk in the telescope; and finding that it shifted its place among the stars, he at first took it for a comet, but soon perceived that its...o...b..t was not eccentric, like the orbits of comets, but nearly circular, like those of the planets. It was then recognised as a new member of the planetary system, a conclusion which has been justified by all succeeding observations. It was named by the discoverer the _George Star_, (Georgium Sidus,) after his munificent patron, George the Third; in the United States, and in some other countries, it was called _Herschel_; but the name _Ura.n.u.s_, from a Greek word, (= Ouranos=, _Ouranos_,) signifying the oldest of the G.o.ds, has finally prevailed. So distant is Ura.n.u.s from the sun, that light itself, which moves nearly twelve millions of miles every minute, would require more than two hours and a half to pa.s.s to it from the sun.

And now, having contemplated all the planets separately, just cast your eyes on the diagram facing page 236, Fig. 53, and you will see a comparative view of the various magnitudes of the sun, as seen from each of the planets.

Ura.n.u.s is attended by _six satellites_. So minute objects are they, that they can be seen only by powerful telescopes. Indeed, the existence of more than two is still considered as somewhat doubtful. These two, however, offer remarkable and indeed quite unexpected and unexampled peculiarities. Contrary to the unbroken a.n.a.logy of the whole planetary system, _the planes of their orbits are nearly perpendicular to the ecliptic_, and in these orbits their motions are retrograde; that is, instead of advancing from west to east around their primary, as is the case with all the other planets and satellites, they move in the opposite direction. With this exception, all the motions of the planets, whether around their own axes, or around the sun, are from west to east.

The sun himself turns on his axis from west to east; all the primary planets revolve around the sun from west to east; their revolutions on their own axes are also in the same direction; all the secondaries, with the single exception above mentioned, move about their primaries from west to east; and, finally, such of the secondaries as have been discovered to have a diurnal revolution, follow the same course. Such uniformity among so many motions could have resulted only from forces impressed upon them by the same Omnipotent hand; and few things in the creation more distinctly proclaim that G.o.d made the world.

Retiring now to this furthest verge of the solar system, let us for a moment glance at the aspect of the firmament by night. Notwithstanding we have taken a flight of eighteen hundred millions of miles, the same starry canopy bends over our heads; Sirius still shines with exactly the same splendor as here; Orion, the Scorpion, the Great and the Little Bear, all occupy the same stations; and the Galaxy spans the sky with the same soft and mysterious light. The planets, however, with the exception of Saturn, are all lost to the view, being too near the sun ever to be seen; and Saturn himself is visible only at distant intervals, at periods of fifteen years, when at its greatest elongations from the sun, and is then too near the sun to permit a clear view of his rings, much less of the satellites that unite with the rings to compose his gorgeous retinue. Comets, moving slowly as they do when so distant from the sun, will linger much longer in the firmament of Ura.n.u.s than in ours.

Although the sun sheds by day a dim and cheerless light, yet the six satellites that enlighten and diversify the nocturnal sky present interesting aspects. "Let us suppose one satellite presenting a surface in the sky eight or ten times larger than our moon; a second, five or six times larger; a third, three times larger; a fourth, twice as large; a fifth, about the same size as the moon; a sixth, somewhat smaller; and, perhaps, three or four others of different apparent dimensions: let us suppose two or three of those, of different phases, moving along the concave of the sky, at one period four or five of them dispersed through the heavens, one rising above the horizon, one setting, one on the meridian, one towards the north, and another towards the south; at another period, five or six of them displaying their l.u.s.tre in the form of a half moon, or a crescent, in one quarter of the heavens; and, at another time, the whole of these moons shining, with full enlightened hemispheres, in one glorious a.s.semblage, and we shall have a faint idea of the beauty, variety, and sublimity of the firmament of Ura.n.u.s."[16]

_The New Planets,--Ceres, Pallas, Juno, and Vesta._--The commencement of the present century was rendered memorable in the annals of astronomy, by the discovery of four new planets, occupying the long vacant tract between Mars and Jupiter. Kepler, from some a.n.a.logy which he found to subsist among the distances of the planets from the sun, had long before suspected the existence of one at this distance; and his conjecture was rendered more probable by the discovery of Ura.n.u.s, which follows the a.n.a.logy of the other planets. So strongly, indeed, were astronomers impressed with the idea that a planet would be found between Mars and Jupiter, that, in the hope of discovering it, an a.s.sociation was formed on the continent of Europe, of twenty-four observers, who divided the sky into as many zones, one of which was allotted to each member of the a.s.sociation. The discovery of the first of these bodies was, however, made accidentally by Piazzi, an astronomer of Palermo, on the first of January, 1801. It was shortly afterwards lost sight of on account of its proximity to the sun, and was not seen again until the close of the year, when it was re-discovered in Germany. Piazzi called it _Ceres_, in honor of the tutelary G.o.ddess of Sicily, and her emblem, the sickle, ([Planet: Ceres]) has been adopted as its appropriate symbol.

The difficulty of finding Ceres induced Dr. Olbers, of Bremen, to examine with particular care all the small stars that lie near her path, as seen from the earth; and, while prosecuting these observations, in March, 1802, he discovered another similar body, very nearly at the same distance from the sun, and resembling the former in many other particulars. The discoverer gave to this second planet the name of _Pallas_, choosing for its symbol the lance, ([Planet: Pallas]) the characteristic of Minerva.

The most surprising circ.u.mstance connected with the discovery of _Pallas_ was the existence of two planets at nearly the same distance from the sun, and apparently crossing the ecliptic in the same part of the heavens, or having the same node. On account of this singularity, Dr. Olbers was led to conjecture that Ceres and Pallas are only fragments of a larger planet, which had formerly circulated at the same distance, and been shattered by some internal convulsion. The hypothesis suggested the probability that there might be other fragments, whose orbits might be expected to cross the ecliptic at a common point, or to have the same node. Dr. Olbers, therefore, proposed to examine carefully, every month, the two opposite parts of the heavens in which the orbits of Ceres and Pallas intersect one another, with a view to the discovery of other planets, which might be sought for in those parts with a greater chance of success, than in a wider zone, embracing the entire limits of these orbits. Accordingly, in 1804, near one of the nodes of Ceres and Pallas, a third planet was discovered. This was called _Juno_, and the character ([Planet: Juno]) was adopted for its symbol, representing the starry sceptre of the Queen of Olympus.

Pursuing the same researches, in 1807 a fourth planet was discovered, to which was given the name of _Vesta_, and for its symbol the character ([Planet: Vesta]) was chosen,--an altar surmounted with a censer holding the sacred fire.

The _average distance_ of these bodies from the sun is two hundred and sixty-one millions of miles; and it is remarkable that their orbits are very near together. Taking the distance of the earth from the sun for unity, their respective distances are 2.77, 2.77, 2.67, 2.37. Their _times_ of revolution around the sun are nearly equal, averaging about four and a half years.

In respect to the _inclination of their orbits_ to the ecliptic, there is also considerable diversity. The orbit of Vesta is inclined only about seven degrees, while that of Pallas is more than thirty-four degrees. They all, therefore, have a higher inclination than the orbits of the old planets, and of course make excursions from the ecliptic beyond the limits of the zodiac. Hence they have been called the _ultra-zodiacal planets_. When first discovered, before their place in the system was fully ascertained it was also proposed to call them _asteroids_, a name implying that they were planets under the form of stars. Their t.i.tle, however, to take their rank among the primary planets, is now generally conceded.

The _eccentricity of their orbits_ is also, in general, greater than that of the old planets. You will recollect that this language denotes that their orbits are more elliptical, or depart further from the circular form. The eccentricities of the orbits of Pallas and Juno exceed that of the orbit of Mercury. The asteroids differ so much, however, in eccentricity, that their orbits may cross each other. The orbits of the old planets are so nearly circular, and at such a great distance apart, that there is no danger of their interfering with each other. The earth, for example, when at its nearest distance from the sun, will never come so near it as Venus is when at its greatest distance, and therefore can never cross the orbit of Venus. But since the average distance of Ceres and Pallas from the sun is about the same, while the eccentricity of the orbit of Pallas is much greater than that of Ceres, consequently, Pallas may come so near to the sun at its perihelion, as to cross the orbit of Ceres.

The _small size_ of the asteroids const.i.tutes one of their most remarkable peculiarities. The difficulty of estimating the apparent diameter of bodies at once so very small and so far off, would lead us to expect different results in the actual estimates. Accordingly, while Dr. Herschel estimates the diameter of Pallas at only eighty miles, Schroeter places it as high as two thousand miles, or about the diameter of the moon. The volume of Vesta is estimated at only one fifteen thousandth part of the earth's, and her surface is only about equal to that of the kingdom of Spain.

These little bodies are surrounded by _atmospheres_ of great extent, some of which are uncommonly luminous, and others appear to consist of nebulous matter, like that of comets. These planets shine with a more vivid light than might be expected, from their great distance and diminutive size; but a good telescope is essential for obtaining a distinct view of their phenomena.

Although the great chasm which occurs between Mars and Jupiter,--a chasm of more than three hundred millions of miles,--suggested long ago the idea of other planetary bodies occupying that part of the solar system, yet the discovery of the asteroids does not entirely satisfy expectation since they are bodies so dissimilar to the other members of the series in size, in appearance, and in the form and inclinations of their orbits. Hence, Dr. Olbers, the discoverer of three of these bodies, held that they were fragments of a single large planet, which once occupied that place in the system, and which exploded in different directions by some internal violence. Of the fragments thus projected into s.p.a.ce, some would be propelled in such directions and with such velocities, as, under the force of projection and that of the solar attraction would make them revolve in regular orbits around the sun. Others would be so projected among the other bodies in the system, as to be thrown in very irregular orbits, apparently wandering lawless through the skies. The larger fragments would receive the least impetus from the explosive force, and would therefore circulate in an orbit deviating less than any other of the fragments from the original path of the large planet; while the lesser fragments, being thrown off with greater velocity, would revolve in orbits more eccentric, and more inclined to the ecliptic.

Dr. Brewster, editor of the 'Edinburgh Encyclopedia,' and the well-known author of various philosophical works, espoused this hypothesis with much zeal; and, after summing up the evidence in favor of it, he remarks as follows: "These singular resemblances in the motions of the greater fragments, and in those of the lesser fragments, and the striking coincidences between theory and observation in the eccentricity of their orbits, in their inclination to the ecliptic, in the position of their nodes, and in the places of their perihelia, are phenomena which could not possibly result from chance, and which concur to prove, with an evidence amounting almost to demonstration, that the four new planets have diverged from one common node, and have therefore composed a single planet."

The same distinguished writer supposes that some of the smallest fragments might even have come within reach of the earth's attraction, and by the combined effects of their projectile forces and the attraction of the earth, be made to revolve around this body as the larger fragments are carried around the sun; and that these are in fact the bodies which afford those _meteoric stones_ which are occasionally precipitated to the earth. It is now a well-ascertained fact, a fact which has been many times verified in our own country, that large meteors, in the shape of fire-b.a.l.l.s, traversing the atmosphere, sometimes project to the earth ma.s.ses of stony or ferruginous matter.

Such were the meteoric stones which fell at Weston, in Connecticut, in 1807, of which a full and interesting account was published, after a minute examination of the facts, by Professors Silliman and Kingsley, of Yale College. Various accounts of similar occurrences may be found in different volumes of the American Journal of Science. It is for the production of these wonderful phenomena that Dr. Brewster supposes the explosion of the planet, which, according to Dr. Olbers, produced the asteroids, accounts. Others, however, as Sir John Herschel, have been disposed to ascribe very little weight to the doctrine of Olbers.

FOOTNOTES:

[13] Altissimum planetam tergeminum observavi. Or, as transposed, Smaismrmilme poeta leumi bvne nugttaviras.

[14] In imitation of Galileo, Huyghens announced his discovery in this form: a a a a a a a c c c c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o p p q r r s t t t t t u u u u u; which he afterwards recomposed into this sentence: _Annulo cingitur, tenui, plano, nusquam cohaerente, ad eclipticam inclinato._

[15] d.i.c.k's 'Celestial Scenery.'

[16] d.i.c.k's 'Celestial Scenery.'

LETTER XXIV.

THE PLANETARY MOTIONS.----KEPLER'S LAWS.----KEPLER.

"G.o.d 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 circ.u.mstances 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 Ura.n.u.s.

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 a.s.sist 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 Ura.n.u.s 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 s.p.a.ces 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 pa.s.sing 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 r.e.t.a.r.ded 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...o...b..t, 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 pa.s.sing through its...o...b..t 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 pa.s.sing 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.

[Ill.u.s.tration Fig. 62.]

But the superior planets are not in fact at rest, as we have supposed, but are all the while moving eastward, though with a slower motion than the earth. Indeed, with respect to the remotest planets, as Saturn and Ura.n.u.s, 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 Ura.n.u.s, 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 pa.s.sing by them with a swifter motion, of which we are unconscious, like the apparent backward motion of a vessel, when we overtake it and pa.s.s 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.

[Ill.u.s.tration Fig. 63.]

FIRST LAW.--_The orbits of the earth and all the planets are ellipses, having the sun in the common focus._ In a circle, all the diameters are equal to one another; but if we take a metallic wire or hoop, and draw it out on opposite sides, we elongate it into an ellipse, of which the different diameters are very unequal. That which connects the points most distant from each other is called the _transverse_, and that which is at right angles to this is called the _conjugate_, axis. Thus, A B, Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A B C. By such a process of elongating the circle into an ellipse, the centre of the circle may be conceived of as drawn opposite ways to E and F, each of which becomes a _focus_, and both together are called the _foci_ of the ellipse. The distance G E, or G F, of the focus from the centre is called the _eccentricity_ of the ellipse; and the ellipse is said to be more or less eccentric, as the distance of the focus from the centre is greater or less. Figure 64 represents such a collection of ellipses around the common focus F, the innermost, A G D, having a small eccentricity, or varying little from a circle, while the outermost, A C B, is an eccentric ellipse. The orbits of all the bodies that revolve about the sun, both planets and comets, have, in like manner, a common focus, in which the sun is situated, but they differ in eccentricity.

Most of the planets have orbits of very little eccentricity, differing little from circles, but comets move in very eccentric ellipses. The earth's path around the sun varies so little from a circle, that a diagram representing it truly would scarcely be distinguished from a perfect circle; yet, when the comparative distances of the sun from the earth are taken at different seasons of the year, we find that the difference between their greatest and least distances is no less than three millions of miles.

[Ill.u.s.tration Fig. 64.]

SECOND LAW.--_The radius vector of the earth, or of any planet, describes equal areas in equal times._ You will recollect that the radius vector is a line drawn from the centre of the sun to a planet revolving about the sun. This definition I have somewhere given you before, and perhaps it may appear to you like needless repet.i.tion 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 repet.i.tion, rather than be at the trouble of turning to the Index and hunting up a definition long since given.

[Ill.u.s.tration Fig. 65. ]

In Figure 65, _E a_, _E b_, _E c_, &c., are successive representations of the radius vector. Now, if a planet sets out from _a_, and travels round the sun in the direction of _a b c_, it will move faster when nearer the sun, as at _a_, than when more remote from it, as at _m_; yet, if _a b_ and _m n_ be arcs described in equal times, then, according to the foregoing law, the s.p.a.ce _E a b_ will be equal to the s.p.a.ce _E m n_; and the same is true of all the other s.p.a.ces 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...o...b..t, 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...o...b..t 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.