46 



SCIENCE. 



[N. S. Vol. XXIV. No. 602. 



there were offered five and a half courses 

 primarily for undergraduates, of which two 

 are of as advanced a nature as the electives 

 offered in 1854; six courses intended for 

 graduates and undergraduates; seven and 

 a half courses of lectures primarily for 

 graduates, and six courses of reading and 

 research; in addition many other courses 

 are named and described in the catalogue 

 which are to be given in following years. 

 As chairman of his department James 

 Peirce was a most liberal-minded and con- 

 scientious administrator. He favored al- 

 ways the introduction of new courses, he 

 was always desirous that the younger 

 teachers should have an opportunity to 

 give advanced instruction, he was scru- 

 pulously careful and painstaking in the 

 details of administrative work. He seldom 

 tried to impress his own opinion on the 

 department, but preferred to be guided by 

 the wish of the majority. 



He gave himself a great variety of 

 courses. Although his chief interest lay 

 along the lines followed by his father, qua- 

 ternions and other linear associative alge- 

 bras, he was also much interested in geom- 

 etry and in mechanics. In 1904-5 he re- 

 turned to the teaching of mechanics after 

 having laid the subject aside for many 

 years. The course in which he is best 

 known to the present generation of stu- 

 dents are the two courses on ' Quaternions, ' 

 mathematics 6 and 9, and courses on 'Al- 

 gebraic Curves and Surfaces,' mathematics 

 la, 75 and 7c. These courses were well 

 attended, especially those on ' Quaternions, ' 

 the number of students in mathematics 6 

 ranging from ten to twenty-five. He gave 

 usually a course or two half courses each 

 year, to a small number of students, on 

 'Linear Associative Algebras' or on the 

 ' Algebra of Logic. ' He never fell into the 

 narrowing habit of giving year after year 

 the same courses, but was eager always to 



undertake the teaching of some new 

 branch of mathematics. In the last year 

 of his life he gave a new half-course, an 

 'Introduction to Higher Plane Curves,' to 

 serve as a preparation for his other courses 

 on that topic. Indeed, so anxious was he 

 to avoid falling into a rut that he made 

 very slight notes for his lectures, prefer- 

 ring, in repeating a course, to work it out 

 anew. This method resulted in a continual 

 freshness and variety of presentation in 

 his teaching. His courses were conducted 

 by lectures, but his students had always 

 opportunity for questions and discussion. 

 His lectures were extremely clear and ex- 

 cellent in form. He loved to develop a 

 subject with great generality without, how- 

 ever, sacrificing detail. In his courses he 

 covered the ground slowly, and a younger 

 generation of students have occasionally 

 felt some impatience with his very careful 

 and methodical discussions. He was not a 

 great believer in the 'problem method' of 

 teaching and he gave almost no home-work 

 to his students. He was a mathematician 

 of wide and varied learning. His life was 

 given to his teaching, and to administrative 

 work, rather than to research. He pub- 

 lished little. In 1857, at the age of twenty- 

 three, he published an ' Analytic Geometry, ' 

 based on a part of his father's famous 

 work called 'Curves and Functions.' This 

 'Analytic Geometry' was used for many 

 years as a text-book at Harvard, and was 

 considered an admirable treatise. Of it 

 Joseph Henry Allen, writing in the Har- 

 vard Register in 1881, ^says: 'I call (it) 

 the very best text-book I ever used, and I 

 never cease to bewail (that it) has gone 

 out of print if not out of use. ' This book, 

 of 228 pages, contains a development of 

 the elements of the subject with the usual 

 applications to the study of conic sections. 

 Written- in a very attractive style, it is 

 much more interesting reading, though it 



