366 HISTORY OF MEgHAXICS. 



real or imagined blemishes in the work. Against the validity oi 

 Newton's determination of the path described by a body projected in 

 any part of the solar system, Bernoulli urges a cavil which it is 

 difficult to conceive that a mathematician, such as he was, could seri- 

 ously believe to be well founded. On Newton's determination of the 

 path of a body in a resisting medium, his criticism is more just. He 

 pointed out a material error in this solution : this correction came to 

 Newton's knowledge in London, in October, 17 12, when the impres- 

 sion of the second edition of the Principia was just drawing to a, 

 close, under the care of Cotes at Cambridge ; and Newton immedi- 

 ately cancelled the leaf and corrected the error. 1 



This problem of the motion of a body in a resisting medium, led to 

 another collision between the English and the German mathematicians. 

 The proposition to which we have referred, gave only an indirect view 

 of the nature of the curve described by a projectile in the air ; and it is 

 probable that Newton, when he wrote the Principia, did not see his way 

 to any direct and complete solution of this problem. At a later period, 

 in 1718, when the quarrel had waxed hot between the admirers of New- 

 ton and Leibnitz, Keill, who had come forward as a champion on the 

 English side, proposed this problem to the foreigners as a challenge. 

 Keill probably imagined that what Newton had not discovered, no one 

 of his time would be able to discover. But the sedulous cultivation 

 of analysis by the Germans had given them mathematical powers 

 beyond the expectations of the English ; who, whatever might be 

 their talents, had made little advance in the effective use of general 

 methods ; and for a long period seemed to be fascinated to the spot, 

 in their admiration of Newton's excellence. Bernoulli speedily solved 

 the problem ; and reasonably enough, according to the law of honor 

 of such challenges, called upon the challenger to produce his solution. 

 Keill was unable to do this ; and after some attempts at procrastina- 

 tion, was driven to very paltry evasions. Bernoulli then published his 

 solution, with very just expressions of scorn towards his antagonist. 

 And this may, perhaps, be considered as the first material addition 

 which was made to the Principia, by subsequent writers. 



6. Constellation of Mathematicians. We pass with admiration 

 along the great series of mathematicians, by Avhom the science of 

 theoretical mechanics has been cultivated, from the time of Newton 

 to our own. There is no group of men of science whose fame is 



MS. Correspondence in Triii. Coll. Library. 



