44 



SCIENCE. 



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



of mathematics will be given to those de- 

 siroiis of receiving it by competent in- 

 structors residing at the university. ' These 

 instructors were Professor Benjamin and 

 James Peirce. 



In the autumn of 1869 Charles W. Eliot 

 became president of the university, and at 

 once occupied himself with the develop- 

 ment of the advanced instruction. Various 

 short courses in related subjects were com- 

 bined; many new and longer courses were 

 offered. To quote again the words of 

 James Peirce, 'a settled purpose was mani- 

 fested to establish the instruction of ad- 

 vanced special students on a permanent 

 and efficient footing.' In addition to cer- 

 tain university lectures there were offered 

 that year two 'university courses of in- 

 struction,' one in philosophy and one in 

 modern literature, each consisting of three 

 lectures a week throughout the year, and 

 each given by several instructors. The 

 university lectures in mathematics were 

 'Linear Algebra/ thirty-five lectures by 

 Benjamin Peirce; 'Algebraic, Periodic and 

 Double Periodic Functions,' thirty- five lec- 

 tures, and 'Higher Geometry,' eighteen lec- 

 tures by James Peirce. This was the first 

 year in which James Peirce gave university 

 lectures. It was, too, the first time that 

 any branch of the theory of functions was 

 taught at Harvard. In this year the 

 regular elective courses in mathematics 

 were greatly increased in number, and 

 James Peirce was then and thereafter en- 

 tirely freed from giving freshman instruc- 

 tion. He taught that year four elective 

 courses, each of two hours a week, on an- 

 alytic geometry, differential calculus, in- 

 tegral calculus and elementary mechanics. 

 Four electives were offered also by his 

 father, consisting each of from one to three 

 lectures a week, on mechanics, astronomy, 

 quaternions and linear algebra. 



During the next ten years there were no 



important changes made in the regular 

 courses offered in mathematics. Benjamin 

 Peirce, who was in 1869 sixty years of age, 

 withdrew somewhat from active academic 

 work, giving after 1870 not more than two 

 courses a year, those generally on 'Quater- 

 nions, Mechanics and Linear Algebras.' 

 The teaching of the elective courses was 

 taken over almost wholly by James Peirce. 

 He gave a great variety of courses, usu- 

 ally giving about twelve lectures a week. 

 In 1870-1 he gave for the first time a regu- 

 lar course on 'The Theory of Functions,' 

 in 1874—5 a course on 'Elliptic Functions,' 

 in 1876-7 a course on the 'Functions of a 

 Complex Variable,' following Briot and 

 Bouquet. In 1878-9 he gave for the first 

 time an elementary course on quaternions, 

 his father giving the second course. In 

 the following year James Peirce gave the 

 advanced course, his father giving the first 

 course. This plan of giving courses of two 

 years on one subject, with two instructors 

 alternating, has since that time been often 

 followed at Harvard. 



In 1870-1 the mathematical university 

 lectures consisted of two courses, one on 

 'Celestial Mechanics,' two lectures a week 

 for half the year by Benjamin Peirce, and 

 a course of the same length on 'Modern 

 Methods in Geometry' by James Peirce. 

 The latter course has now become a fixture 

 in the elective courses given every year, 

 and, under the name of mathematics 3, is 

 known to almost all students of mathemat- 

 ics who have been at Harvard during the 

 last thirty years. In this year the number 

 of courses of university lectures offered 

 was thirty-three. The number of persons 

 recorded in the catalogue as attending 

 them is twenty-six. 



Whether or not on account of the small 

 attendance, it was found that the univer- 

 sity lecture system was not satisfactory, 

 and in 1872 these lectures were abandoned. 



