692 THE POPULAR SCIENCE MONTHLY. 



of infinitesimals or of limits into elementary books ; the recognition of 

 direction as a fundamental idea ; the use of Hassler's definition of a 

 sine as an arithmetical quotient, free from entangling alliance with the 

 size of the triangle ; the similar deliverance of the expression of deriv- 

 ative functions and differential coefficients from the superfluous intro- 

 duction of infinitesimals ; the fearless and avowed introduction of new 

 axioms, when confinement to Euclid's made a demonstration long and 

 tedious in one or two of these points European writers moved simul- 

 taneously with Peirce, but in all he was an independent inventor, and 

 nearly all are now generally adopted. 



" All his writings are characterized by singular directness and con- 

 ciseness, and particularly by a happy choice of notation a point of 

 great importance to the mathematician, lessening not only his mechani- 

 cal labor in writing, but also his intellectual labor in grasping and 

 handling the difficult conceptions of his science. 



" His text-books were also complained of for their condensation, as 

 being therefore obscure ; but, under competent teachers, their brevity 

 was the cause of their superior lucidity. In the Waltham High School 

 his books were used for many years, and the graduates attained there- 

 by 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 stu- 

 dents 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 coordinates of his own devising, several problems concern- 

 ing the involutes and evolutes of ciirves, which would probably have 

 proved impregnable by any other mode of approach. 



" During the year 1842, Professors Peirce and Lovering published 

 a ' Cambridge 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 the 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 communi- 

 cated to the American Academy. 



" The comet of 1843 gave Professor Peirce the opportunity, by a 

 few strikinor 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 acquaintance, and prepared for the still more 

 important services to astronomy which they rendered after the discov- 

 ery of Neptune. This planet was discovered in September, 1846, in 



