152 THE GREEK ASTRONOMY. 



namely, that we may see how theories may be highly estimable, though 

 they contain false representations of the real state of 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 prog- 

 ress do not lose their importance because they are not the last ; and 

 the outset of the journey may require no less vigor and activity than 

 its close. 



That which is true in the Hipparchian theory, and which no suc- 

 ceeding 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 fun- 

 damental 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 favor. But some assumption 

 is necessary, in order that the motions, at different points of a revolu- 

 tion, may be somehow 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 afeiv observations, it de- 

 duces from these, results agreeing with all observations, however 

 numerous and distant. To express an inequality by means of an epi- 

 cycle, implies, not only that there is an inequality, but further, — that 

 the inequality is at its greatest value at a certain known place, — dimin- 

 ishes 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 epi- 

 cycle 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 pro- 

 cesses by which modern astronomers deal with such motions. Their 

 universal method is to l'esolve all unequal motions into a series of 



