used for many years, and the graduates attained thereby a clearer and more 

 useful applicable knowledge of mathematics than was given at any other 

 high school in this country ; nor did they find any difficulty in mastering 

 even the demonstration of Arbogast's Polynomial Theorem, as presented by 

 Peirce. The latter half of the volume on the Integral Calculus, full of 

 marks of a great analytical genius, is the only part of all his text-books 

 really too difficult for students of average ability. 



Gill's Mathematical Miscellany contained many contributions which showed 

 in a singular light the Harvard professor's power. For example, in the 

 issues for May and November, 1839, he solved, by a system of co-ordinates 

 of his own devising, several problems concerning the involutes and evolutes 

 of curves, which would probably have proved impregnable by any other 

 mode of approach. 



During the year 1842, Professors Peirce and Levering published a " Cam- 

 bridge Miscellany of Mathematics and Physics," in which Peirce gave an 

 analytical solution of the motion of a top, a criticism of Espy's theory of 

 storms, etc. About tire same time he adapted the epicycles of Hipparchus 

 to the analytical forms of modern science ; and the method was used by 

 Lovering in meteorological discussions communicated to the American 

 Academy. 



The comet of 1843 gave Professor Peirce the opportunity by a few striking 

 lectures in Boston to arouse an interest which led to the foundation of the 

 Observatory at Cambridge ; and by his discussions of the orbit with Sears 

 C. Walker, he and that remarkable computer were brought to mutual ac- 

 quaintance, and prepared for the still more important services to astronomy 

 which they rendered after the discovery of Neptune. This planet was dis- 

 covered in September, 1846, in consequence of the request of Leverrier to 

 Galle that he should search the zodiac in the neighborhood of longitude 325 

 for a theoretical cause of certain perturbations of Uranus. But Peirce 

 showed that the discovery was a happy accident ; not, that Leverrier's calcu- 

 lations had not been exact, and wonderfully laborious, and deserving of the 

 highest honor ; but because there were, in fact, two very different solutions 

 of the perturbations of Uranus possible : Leverrier had correctly calculated 

 one, but the actual planet in the sky solved the other ; and the actual planet 

 and Leverrier's ideal one lay in the same direction from the earth only in 

 1846. Peirce's labors upon this problem, while showing him to be the peer 

 of any astronomer, were in no way directed against Leverrier's fame as a 

 mathematician : on the contrary, he testified in the strongest manner that he 



