CHAPTER II.

FALSE SYSTEMS-MODERN ASTRONOMY-ELEMENTS OF SATURN'S ELLIPTIC ORBIT.

BEFORE turning to the consideration of the methods and discoveries of modern astronomy, a few words on the system which explained Saturn's motions (in common with those of the other planets) on the supposition that the earth is the centre of the universe, will not be out of place. This system, and the fanciful and superstitious dreams of the middle ages, may be considered as occupying a place midway between the simple systems and intelligent inquiries of the Chaldæan astronomers, on the one hand, and the analyses and discoveries of modern times on the other.

The difficulties connected with the Ptolemaic system are not due so much to the inherent error of the system itself, as to the fanciful hypotheses with which the originators of the system perplexed themselves. All the varieties of the planetary motions, except a few irregularities only to be detected by the most exact instrumental observation, may be as exactly explained on the supposition that the earth is the centre of the system as on the true theory, and with almost equal simplicity. But the Epicyclians set themselves a problem of far greater complexity. They sought to explain the apparent motions of the heavenly bodies, not merely on the supposition that the earth is the centre of the system, but with the additional hypotheses that all the members of the system move in circular orbits and with uniform velocities. Bodies terrestrial, they argued, are gross, corrupt, and imperfect-therefore they move in imperfect orbits, with varying velocities; bodies celestial are sublime, incorrupt, and perfect-therefore they move in perfect orbits with uniform velocities; the circle is the only perfect

figure therefore the heavenly bodies move in circles; but the supposition of uniform motion in simple circular orbits is insufficient to account for the apparent motions of the heavenly bodies-therefore those motions must be explained by properly combining two or more sets of circular and uniform movements. Such was the problem they set themselves; in what manner they solved it will appear by an illustration drawn from the motions of Saturn.

Let E (fig. 1, Plate VI.) be the earth, cc'c' a circle about E as centre. Then, clearly, Saturn's progressive and retrograde motions cannot possibly be explained by supposing him to move uniformly in the circle c c'c". Suppose, however, that p p P'p' is a smaller circle, whose centre c is on the circle c c'c"; and that while Saturn moves with uniform velocity round the circle Pp P'p', the centre of this circle moves uniformly round the circle c c'c'. Then it is clear that if Saturn's velocity in the smaller circle is greater than the velocity with which the centre of that circle moves round the larger circle, his apparent motion will be retrograde when he is at or near p'; and further, that by assigning suitable dimensions to the two circles, and a proper ratio between the velocities considered, Saturn's period of retrogression and the length of his retrograde arc may be readily explained.

*

We have seen that Saturn's distance from the earth, at opposition, is variable. These variations may be explained with tolerable accuracy by supposing that the earth occupies an eccentric position within the circle c c'c", as at E'.

Saturn's looped and twisted path may also be easily explained. We have only to suppose the plane of the circle Pp P' inclined at a small angle to that of the circle cc'c"; or, instead of this, we may suppose both circles to lie in one plane which oscillates through a small angle about a fixed line through the earth at E'.

Smaller irregularities may be accounted for by supposing that Pp P'p' is not Saturn's orbit, but the path of the centre of a smaller circle, s s s's', along whose circumference Saturn moves uniformly.

* For this purpose the radius of the smaller circle must bear to the radius of the larger circle the proportion that the radius of the earth's orbit bears to that of Saturn; again, Saturn must revolve once in a year round the smaller circle, whose centre must revolve once in a Saturnian year round the earth.

Again, we may suppose that the circle c c'c" is not the path of the centre of the circle Pp P'p', but of a point near the centre; in other words, that the circle Pp P'p' is eccentric as well as the circle c c'c". We may extend this eccentricity to the circle s ss's', or introduce additional variety by supposing any or all of the circles to lie in different or in oscillating planes; in fine, by a series of such suppositions, which may be carried on ad infinitum, we may account for nearly every irregularity in Saturn's motion with a very close degree of approximation.

To explain how these motions were supposed to be impressed and maintained by a system of celestial spheres, and through the complicated effects attributed to their rotations, would be out of place. The whole system, with its

centrics and eccentrics scribbled o'er, Cycle and epicycle, orb in orb,

has been long since swept away, and its records merely remain as illustrations of perverted ingenuity.

One point, however, connected with the Ptolemaic system of the universe remains to be noticed. If the earth really occupied the central place in our system, the actual, and even the relative distances of the various members of that system must have remained for ever unknown. Let us consider, for a moment, how the geometer ascertains the distance of an inaccessible object. To effect this, he observes the directions in which the object is seen from two convenient points, the distance between which he measures. Then, either by geometrical construction, in which these relations are represented on a convenient scale, or, more exactly, by trigonometrical calculation, he determines the distance of the inaccessible object from either point. That this determination may be depended upon, it is necessary, not only that the instruments with which the requisite data are obtained should be trustworthy, but that the distance between the two points should not bear too small a proportion to the distance of the inaccessible object. For instance, a base line of ten yards, with good instruments, would be sufficient for the determination of distances up to three or four hundred yards; but it would obviously be altogether useless to

apply such a base to determine the exact distance of an object two or three miles off. The slightest error in the determination of either of the base angles would make a difference of a mile or two in the result deduced by construction or calculation. Now the length of the earth's diameter being about one-thirtieth part of the moon's distance from the earth, this distance can be determined with tolerable accuracy from a base line whose extreme points lie on the earth's surface.* But the distances of the other members of our system (including the sun) from the earth are so vast that it would be altogether impossible to determine their actual distances by using any base line on the earth. To obtain any notion of their relative distances would require the utmost perfection and power of modern instruments, and the highest skill of the modern astronomer. Even with these appliances, our ideas of the relative distances of the planets would be as vague and uncertain, if the earth were the centre of our system, as are our present ideas of the relative distances of the fixed stars from the earth.† Nor is there any point in the Epicyclic theory that would enable its supporters to form any conjectures regarding the relative distances of the planets. It is plain that to an observer placed at E (fig. 2, Plate VI.) the appearance of a planet revolving uniformly round the circle P P'P'P'", while the centre of that circle moved uniformly round the circle cc'c", would be precisely the same as that of a planet revolving uniformly round the circle pp'p"p", while

* Yet from the most trustworthy modern measurement it appears that the determination of the moon's distance hitherto adopted has been about twenty miles too great.

In the case of the sun, as in that of the moon, our base line is limited by the earth's dimensions; and since the sun's distance is so vast compared with such a base line, we could expect to obtain no very close approximation to that distance. Accordingly, we find that before the discovery of the telescope the ideas of astronomers on the subject of the sun's distance were of the most vague and indefinite kind; and the discovery lately made, that the modern determination of the sun's distance is probably too great by three millions of miles or more, shows that even in the present advanced state of the science of astronomy the problem is no easy one. In the planets Mercury and Venus, however, we have two objects, which serve, so to speak, as celestial instruments; the sun's disc, at the times of their transits, serving as an index-plate. Observers at different parts of the earth's surface, marking the different indications of this celestial theodolite, calculate thence the solar distance. At favourable parts of his orbit, Mars, though a superior planet, serves the same purpose in a somewhat different manner, the celestial sphere serving as an index-plate.

the centre of that circle moved uniformly round the circle c c'c', if the periods of revolution of the two planets and of their orbitcentres were respectively equal.

It appears, then, that if the Epicyclians merely trusted to the results of observation applied on the hypotheses which formed their system, they could have had no accurate notions, even of the relative distances of the sun and planets from the earth, far less of their actual distances. For anything they could perceive to the contrary, Saturn might (after the moon) be the nearest of the heavenly bodies-Mars, Venus, or Mercury the most distant. Yet we learn that the order of the planetary distances was known to the ancients at a very remote period. In the fanciful scheme ascribed by Philolaus to Pythagoras, in which musical tones were supposed to be produced by the revolution of the spheres bearing the planets, the note assigned to the Saturnian sphere was the hypate, or deepest tone, the note assigned to the moon's sphere the neate, or highest tone of the celestial harmonies, the spheres of the other heavenly bodies being placed in their just order in the scale. It seems probable, therefore, that the Greek astronomers had derived part of their knowledge from nations to whom the true system of the universe was not unknown.

Before turning to the discoveries of modern astronomy, it may not be uninteresting to dwell for a moment on the superstitious fancies of the astrologer. The origin of the system which ascribed. an influence on the fates of men and nations to the planetary phenomena is lost in the obscurity of a far antiquity. It was probably connected with the Sabæanism of the ancient Chaldæans and Arabians, a form of religious worship derived from a purer system, in which the stars and planets were not themselves the objects of adoration, but simply regarded as types of the divine attributes. Astrology was gradually formed into a system showing few traces of the religious source from which it had been derived. Its complex and mystical character marks it as framed rather to deceive and impress the ignorant, than as possessing the confidence of its professors. Thus it became a weapon in the hands of the priesthood of Nineveh and Babylon, a weapon which might serve good or evil purposes, according to the character of him who wielded it,