S40 SCIENCE PROGRESS 



on " Algebra Courses for College Juniors and Seniors " (ed. 

 U. G. Mitchell, ibid. 362-8), " A List of Mathematical Books 

 for Schools and Colleges " (Library Committee, W. B. Ford, 

 Chairman, ibid. 368-76), and " Discussion relating to Re- 

 quired Mathematics for Women " (Emilie N. Martin, ibid. 394-8) 

 while Arnold Emch {ibid. 379-82) shows the importance of 

 perspective as an introduction to projective geometry. 



In an earlier number, J. A. Nyberg {ibid. 309-12) shows how 

 the notion of function can be developed in the first year of 

 college teaching, both briefly and " so thoroughly that the 

 student will think of it as something else besides axes, co- 

 ordinates, and curves, and so comprehensively that the work 

 will be useful regardless of whether the course is trigonometry, 

 algebra, or analytics." Into the foreground is brought the 

 idea of relationship between variables, and only after the 

 notion of function and correspondence is grasped would Nyberg 

 explain the language of co-ordinates. Nyberg further {ibid. 

 406-9) begins the study of the line, and closes with some 

 illustrations of how the new point of view eliminates certain 

 difficulties . 



History. — Gino Loria {Rend, del Seminario Mat. delta Facolta 

 di Sci. delta R. Univ. di Roma, 191 7, 4) gives an excellent and 

 detailed sketch of mathematics in Japan as shown by recent 

 literature, together with several notes containing mathematical 

 developments in our usual notation. 



D. E. Smith {Bull. Amer. Math. Soc. 191 7, 24, 82-96) gives 

 an account of the cryptographic work of John Wallis, partly 

 because his biographies say little about it, " partly because of 

 the interest naturally excited by the present war, but chiefly 

 because of the new light that certain letters, hitherto unpub- 

 lished, throw upon the life and character of a mathematician 

 of merit." 



J. M. Child {Monist, 191 7, 27, 41 1-54) gives the second and 

 last part of his annotated translation of the manuscripts of 

 Leibniz on his discovery of the differential calculus, as made 

 known by the publications of Gerhardt in 1846, 1848, and 

 1855. Child also {ibid. 524-59) gives an annotated translation 

 of Gerhardt's paper of 1891 on " Leibniz in London." 



S. A. Joffe {Trans. Actuarial Soc. of America, 191 7, 18, 

 72-98) gives a systematic review of the important contribu- 

 tions to the theory of formulae of interpolation, especially 



