168 : Benjamin Peirce. 
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 Harvard College, and in 1833 was made Professor of Mathe- 
matics and Natural Philosophy. 
The earlier years of his professorship were fruitful as to pub- 
lication, principally in a series of text-books for use in college. 
The first that appeared were treatises on ‘‘ Plane and Spherical 
Trigonometry ” in 1835 and 1836, which were published in a 
more complete form, with a “Spherical Astronomy,” in 1840. 
ext came a “Treatise on Sound,” in 1836, which was based 
upon Herschel’s work in the ‘Encyclopedia Metropolitana,” 
but with very important changes. The bibliography of the 
subject in the Introduction is of permanent value. ‘This was 
followed, in 1887, by his ‘‘ Plane and Solid Geometry,” and by 
a “ Treatise on Algebra.” 
work on “Curves, Functions and Forces” was begun in 
1841 by the publication of a volume on “ Analytical Geometry 
and Differential Calculus.” A second volume, on the “ Calcu- 
lus of Imaginaries, 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. . : 
ead 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. 
n 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 intro- 
duced, along with the axiom, “Infinitely small quantities may 
be neglected.” ‘T'he demonstrations are given only in outline, 
ing in respect of fulness the entire opposite o Euclid. 
like brevity is characteristic of the other books, and in fact of 
especially in the treatment of differential equations. It 1s ap 
excellent example of Professor Peirce’s concise and logical sty le. 
The “ Analytic Mechanics ” was rather a treatise than a text 
book. In it Professor Peirce set forth the general principles 
and methods of the science as a branch of mathematical theory; 
