4-44 BENJAMIN PEIRCE, 



the college course. Doctor Bowditch's first volume was completed, 

 and the second entered for copyright, in 1829, the year of Peirce's 

 graduation ; and the proof-sheets were regularly read by him. 



After graduation, two years were spent by Professor Peirce in 

 teaching at Northampton. In 1831 he was appointed Tutor in Har- 

 vard College, and in 1833 was made Professor of Mathematics and 

 Natural Philosophy. 



The earlier years of his professorship were fruitful as to publication, 

 principally in a series of text-books for use in college. The first that 

 appeared was a "Treatise on Sound" in 1836, which was based upon 

 Herschel's work in the " Encycloptedia Metropolitana," but with very 

 important changes. The bibliography of the subject in the Introduc- 

 tion is of permanent value. This was followed in 1837 by his " Plane 

 and Solid Geometry," and a "Treatise on Algebra," and in 1840 by 

 a Treatise on " Plane and Spherical Trigonometry." 



A work on " Curves, Functions, and Forces" was begun in 1841 

 by the publication of a volume on " Analytical Geometry and Differ- 

 ential Calculus." A second volume, on the " Calculus of Imagiuaries, 

 Residual Calculus, and Integral Calculus," appeared in 1846. As the 

 word " forces " in the title shows, he intended to complete this work 

 by a third volume on the " Calculus of Variations, and on Analytical 

 Mechanics, with its Applications," but in this form it was never done. 



Instead of this, however, and so to be mentioned in this place, though 

 not properly a text-book, there appeared in 1855 the ''Analytic 

 Mechanics " in a quarto form, a work that more adequately expresses 

 Professor Peirce's peculiar power than any other of his productions, 

 with perhaps one exception. 



In all of these books he departed not a little from the beaten path. 

 In geometry the idea of direction was made the basis of the theory 

 of parallels. Infinites and infinitesimals are introduced, along with 

 the axiom, " Infinitely small quantities may be neglected." The dem- 

 onstrations are given only in outlhie, being in respect of fulness the 

 entire opposite of Euclid. A like brevity is characteristic of the other 

 books, and in fact of everything mathematical that Professor Peirce 

 ever wrote. He used a notation to wiiich he gave much thought, 

 by which his formulas were more concise than they could easily be 

 made with the usual symbols. The Integral Calculus was at the 

 period of its appearance much in advance of similar works, especially 

 in the treatment of differential equations. It is an excellent example 

 of Professor Peirce's concise and logical style. 



Tlie " Analytic Mechanics " was rather a treatise than a text- 



