LAW OF GRAVITATION. 227 



lation from the law of gravitation seems at first 

 sight to give. According to the theory, it ap- 

 peared that this line ought to move round once 

 in eighteen years ; according to observation, it 

 moves round once in nine years. This difference, 

 the only obvious failure of the theory of gravita- 

 tion, embarrassed mathematicians exceedingly. 

 It is true, it was subsequently discovered that the 

 apparent discrepancy arose from a mistake ; the 

 calculation, which is long and laborious, was sup- 

 posed to have been carried far enough to get close 

 to the truth ; but it appeared afterwards that the 

 residue which had been left out as insignificant, 

 produced, by an unexpected turn in the reckon- 

 ing, an effect as large as that which had been 

 taken for the whole. But this discovery was not 

 made till a later period ; and in the mean time 

 the law of the inverse square appeared to be at 

 fault. Clairault tried to remedy the defect by 

 supposing that the force of the earth's gravity 

 consisted of a large force varying inversely as the 

 square of the distance, and a very small force 

 varying inversely as the fourth power (the square 

 of the square). By such a supposition, observa- 

 tion and theory could be reconciled ; but on the 

 suggestion of it, Buffon came forward with the 

 assertion that the force could not vary according 

 to any other law than the inverse square. His 

 arguments are rather metaphysical than physical 

 or mathematical. Gravity, he urges, is a quality, 



