740 Proceedings of the Royal Society 
College in 1831, and professor in 1833. During tire few years 
following he published a series of mathematical books covering 
the course then taught at the college from Algebra to Differential 
Equations. His elementary books were remarkable for their con- 
densation. In the geometry, especially the short and terse and 
comprehensive forms of mathematical thought and expression, 
natural to the mathematician, were substituted for the minute 
demonstrations of Euclid. Free use was also made of infinitesimals. 
The volumes of geometry and the infinitesimal calculus were 
published under the title of Curves , Functions , and Forces. The 
subject of Forces, which was intended to cover mechanics, was, 
however, dropped from the series. The concluding portion of the 
second volume is devoted to the Differential Calculus, and is 
noteworthy for the brevity and conciseness of style, and the free use 
of operative symbols. 
After the death of Bowditch in 1838, Peirce stood at the head of 
mathematical science in his country, as the leading one of the very 
few who had access to foreign journals. About 1842 he commenced, 
in connection with Professor Lovering, the publication of a serial 
under the title of the Cambridge Miscellany of Mathematics and 
Physics, of which, however, only a few numbers appeared. He 
took an active part in the foundation of the Harvard Observatory, 
the occasion being afforded by the great comet of 1843. The work 
which first extended Peirce’s reputation, was his computation of the 
general perturbations of Uranus and Hep tune. The formulas to 
which he was led were published in the first volume of the Pro- 
ceedings of the American Academy , but were accompanied by no 
description of his process. Subsequent investigations, however, 
showed them to have been remarkably accurate. In his views of 
the discrepancy between the mean distance of Neptune as predicted 
by Leverrier, and as deduced from observation, he was less fortunate, 
although, when due consideration is given to Leverrier’s conclusions, 
there was much plausibility in the position taken by Peirce. As 
the subject has frequently been discussed without a due compre- 
hension of all the circumstances, a brief review of them may be 
appropriate. 
Leverrier, from his researches, found for the mean distance of the 
disturbing planet 364539, and a consequent period of 217 years. 
