NATURE AND LAW. 375 



celestial bodies imcst be " perfect," they must revolve in circles ; — 

 whether round the sun, as Pythagoras maintained, or round the 

 earth, as Aristotle and the later Schoolmen taught. Every tyro 

 knows how the Ptolemaic system of astronomy, based on the latter 

 conception, developed itself into a mechanism of most ingeniously 

 devised complexity, by the necessity of continually adding new 

 cycles and epicycles to "account for" the new discordances which 

 improved methods of observation were continually bringing to light 

 between the actual and the predicted places of the heavenly bodies. 

 This method of " accounting for '' them was a pure assumption ; 

 and yet it answered its purpose so well, as to form the basis of the 

 methods of astronomical computation in use at the present time.* 

 But when Copernicus revived the scheme of Pythagoras, and the 

 comparative simplicity of his system (doing away with a large part 

 of the cumbrous machinery of the Ptolemaic) recommended it to 

 the acceptance of minds not trammelled by their own scholastic 

 prejudices, or dominated by ecclesiastical tyranny, the whole 

 question had to be studied afresh ; and it was by the marvellous 

 perseverance and ingenuity of Kepler, the contemporary and friend 

 of Galileo, that the solution of it was found. Starting with the 

 conviction that there must be an " order " (if he could only find it 

 out), he passed his life in a series of guesses as to what that order 

 might be ; and his ingenuity in guessing was only surpassed by his 

 eagerness in subjecting every guess to the test of its strict con- 

 formity with observed facts, and by his candid readiness to abandon 

 it so soon as its discordance became clear to him. Limiting his 

 studies to the orbit of Mars, he brought to the explanation of the 

 observed places of that planet all the resources of eccentric but 

 uniform circular motion, which he could devise both for Mars and 



* It is not a little singular that, notwithstanding the great advance which 

 mathemalical science has made since Newton's time, no formula has yet Ijeen 

 devised for (//rtr/Zi' computing the place of a planet or comet in an elliptic orliit ; 

 all such computations being still made on the assumption of uniform circnlar 

 motion, with cycles and epicycles " interpolated " (after the method of Ptolemy) 

 so as to attain any required appn^ximation to absolute correctness. And thus, 

 both as generalizing the facts of observation, and as furnishing the only basis 

 for accurate prediction, this complex conception (as now perfected) would have 

 liad even a higher claim to be received as true to Nature than Kepler's " laws " 

 o{ elliptic motion, until these were shown to be deducible from Newton's grand 

 and simple assumptions. 



