trious men are requisite to produce good instruments, but energy and assiduity depend on the man himself."

Hipparchus was the author of other great discoveries and improvements in astronomy, besides the establishment of the doctrine of eccentrics and epicycles; but this, being the greatest advance in the theory of the celestial motions which was made by the ancients, must be the leading subject of our attention in the present work; our object being to discover in what the progress of real theoretical knowledge consists, and under what circumstances it has gone on.

IT

Sect. 2.-Estimate of the Value of the Theory of Eccentrics and Epicycles.

may be useful here to explain the value of the theoretical step which Hipparchus thus made; and the more so, as there are, perhaps, opinions in popular circulation, which might lead men to think lightly of the merit of introducing or establishing the doctrine of epicycles. For, in the first place, this doctrine is now acknowledged to be false; and some of the greatest men in the more modern history of astronomy owe the brightest part of their fame to their having been instrumental in overturning this hypothesis. And, moreover, in the next place, the theory is not only false, but extremely perplexed and entangled, so that it is usually

conceived as a mass of arbitrary and absurd complication. Most persons are familiar with passages in which it is thus spoken of1o.

He his fabric of the heavens
Hath left to their disputes, perhaps to move
His laughter at their quaint opinions wide;
Hereafter when they come to model heaven
And calculate the stars, how will they wield
The mighty frame! how build, unbuild, contrive,
To save appearances! how gird the sphere
With centric and eccentric scribbled o'er,
Cycle in epicycle, orb in orb!

And every one will recollect the celebrated saying of Alphonso X., king of Castile", when this complex system was explained to him; that "if God had consulted him at the creation, the universe should have been on a better and simpler plan." In addition to this, the system is represented as involving an extravagant conception of the nature of the orbs which it introduces;-that they are crystalline spheres, and that the vast spaces which intervene between the celestial luminaries are a solid mass, formed by the fitting together of many masses perpetually in motion; an imagination which is presumed to be incredible and monstrous.

We must endeavour to correct or remove these prejudices, not only in order that we may do justice to the Hipparchian, or, as it is usually called, Ptolemaic system of astronomy, and to its founder; but

pur

may see how

though they real state of

for another reason, much more important to the pose of this work; namely, that we theories may be highly estimable, contain false representations of the things, and may be extremely useful, though they involve unnecessary complexity. In the advance of knowledge, the value of the true part of a theory may much outweigh the accompanying error, and the use of a rule may be little impaired by its want of simplicity. The first steps of our progress do not lose their importance because they are not the last; and the outset of the journey may require no less vigour and activity than its close.

That which is true in the Hipparchian theory, and which no succeeding discoveries have deprived of its value, is the resolution of the apparent motions of the heavenly bodies into an assemblage of circular motions. The test of the truth and reality of this resolution is, that it leads to the construction of theoretical tables of the motions of the luminaries, by which their places are given at any time, agreeing nearly with their places as actually observed. The assumption that these circular motions, thus introduced, are all exactly uniform, is the fundamental principle of the whole process. This assumption is, it may be said, false; and we have seen how fantastic some of the arguments were, which were originally urged in its favour. But some assumption is necessary, in order that the motions, at different points of a revolution may be somewhat connected, that is,

in order that we may have any theory of the motions; and no assumption more simple than the one now mentioned can be selected. The merit of the theory is this; that obtaining the amount of the eccentricity, the place of the apogee, and, it may be, other elements, from a few observations, it deduces from these, results agreeing with all observations, however numerous and distant. To express an inequality by means of an epicycle, implies not only that there is an inequality, but further;-that the inequality is at its greatest value at a certain known place;-diminishes in proceeding from that place by a known law;continues its diminution for a known portion of the revolution of the luminary;-then increases again; and so on: that is, the introduction of the epicycle represents the inequality of motion, as completely as it can be represented with respect to its quantity.

We may further illustrate this, by remarking that such a resolution of the unequal motions of the heavenly bodies into equable circular motions, is, in fact, equivalent to the most recent and improved processes by which modern astronomers deal with such motions. Their universal method is to resolve all unequal motions into a series of terms, or expressions of partial motions; and these terms involve sines and cosines, that is, certain technical modes of measuring circular motion, the circular motion having some constant relation to the time. And thus the problem of the resolution of the celestial motions into

equable circular ones, which was propounded above two thousand years ago in the school of Plato, is still the great object of the study of modern astronomers, whether observers or calculators.

That Hipparchus should have succeeded in the first great steps of this resolution for the sun and moon, and should have seen its applicability in other cases, is a circumstance which gives him one of the most distinguished places in the roll of great astronomers. As to the charges or the sneers against the complexity of his system, to which we have referred, it is easy to see that they are of no force. As a system of calculation, his is not only good, but, as we have just said, in many cases no better has yet been discovered. If, when the actual motions of the heavens are calculated in the best possible way, the process is complex and difficult, and if we are discontented at this, nature, and not the astronomer, must be the object of our displeasure. This plea of the astronomers must be allowed to be reasonable. "We must not be repelled," says Ptolemy12, "by the complexity of the hypotheses, but explain the phenomena as well as we can. If the hypotheses satisfy each apparent inequality separately, the combination of them will represent the truth; and why should it appear wonderful to any that such a complexity should exist in the heavens, when we know nothing of their nature