BENJAMIN PEIRCE. 445 



hdok. In it Professor Peirce set forth the general principles and 

 mctlKxls of the science as a branch of mathematical theory, and em- 

 bodied in a systematic treatise the latest and best methods and forms 

 of conceptions of the great geometers. He aimed to reduce them to 

 their utmost simplicity by freeing them from every superfluous ele- 

 ment. He made free use of the idea of the potential, developing 

 nearly the whole subject from it. Determinants are used regularly as 

 a standing instrument of analysis, and especially in the integration of 

 the differential equations of motion. Both of these features, as well as 

 Jacobi's method of integration by his principle of the last multiplier, 

 were at the time new in English treatises. 



The whole volume is marked by a directness of thought and a 

 brevity of expression which make it difficult reading for those who 

 have been accustomed only to the usual forms of notation and reason- 

 ing, and who do not read the book in course from the beginning. 

 Several of the chapters are made peculiarly interesting by the develop- 

 ment of a large number of special problems as particular cases of 

 general theorems. In his later years the author often said he wanted 

 to rewrite the "Analytic Mechanics" and introduce quaternions 

 into it. 



In 1842 Professor Peirce published, in connection with Professor 

 Lovering, four numbers of the " Cambridge Miscellany," a quarterly 

 journal devoted to mathematics, physics, and astronomy. 



In the same year he assumed the care of the mathematical part of 

 the " American Almanac," ten volumes of which were prepared by 

 him. In one of these (1847) he published a list of the known orbits 

 of comets, arranged in convenient form, to which he added to the 

 usual cometic catalogue several approximate orbits computed by him 

 for historic comets that had been imperfectly observed. 



In 1849 Congress established a Bureau for the publication of the 

 " American Ephemeris and Nautical Almanac," under the superinten- 

 dence of Lieutenant (afterwards Admiral) Davis. Professor Peirce 

 was at once appointed Consulting Astronomer. In this capacity he 

 prepared and published, in 1853, his "Tables of the Moon," which 

 have been used in making the " Ephemeris " up to the volume for the 

 year 1883. In co-operation with Lieutenant Davis, he designed the 

 form and general plan of the Ephemeris, and he decided upon all 

 the coefficients to be used. He commenced a revision of the theory 

 of the planets, especially the four outer ones ; but this seems not to 

 have been carried to serviceable results, if we except certain separate 

 communications to this Academy. He retained the position of Con- 



