106 



SCIENCE 



[N. S. Vol. XLII. No. 1073 



portunity for certain inquiries which with- 

 out them would be futile; and first, for 

 questions quite impersonal and general. 



One's first impression, on inspecting this 

 series, is that the number of authors of 

 books and contributors to Acta eruddtorum, 

 Berichte der Akademie, Comptes rendus, 

 Transactions or Journals must have ia- 

 ereased surprisingly during forty years. So 

 we count sample volumes, say those for 1875 

 and 1905. In the former, the number of 

 serials reviewed and the number of writers 

 were, respectively, about 110 and 510; in 

 the latter volume these numbers are 180 

 and 1,880. To determine more definitely 

 the quantity of mathematical literature 

 represented, two methods suggest them- 

 selves. One is to assume that the number 

 of pages filled by those reviews is propor- 

 tional, on the average, to the quantity of 

 literature published each year; or, if it 

 seems more reasonable, proportional to the 

 number and importance of ideas developed. 

 The other is to count the titles listed in each 

 table of contents, and take those for a meas- 

 ure. Diagrams are here shown, giving the 

 results of both methods, the years being 

 set at equal intervals along a horizontal 

 base, and their output in pages or in titles 

 being set off upward. A broken line joins 



Fig. 1. Jahrbuoh uber die Fortschritte der 

 MathematiTc. Increase in size during forty years. 



the points so marked ; thus the area between 

 graph and baseline, widening from decade 

 to decade with one or two interruptions, 

 conveys a fair idea of the growth in this 

 kind of literature. One of the interruptions 



comes in the years 1893-4, where a double 

 volume was issued in an attempt to over- 

 take the flight of time. It shows pre- 



FiG. 2. Annual Number of Titles of Mathe- 

 matical Articles and Books, 1868-1909. 



sumably that considerable matter properly 

 belonging in those years was pushed into the 

 preceding and the following volume, swell- 

 ing them unduly. The general impression 



Fig. 3. Number of Pages; Number of Titles, 

 for Comparison, in Dotted Curve. 



from these two curves (if I may call them 

 so) is that the two methods agree approxi- 

 mately, and that either one may be used as 

 may be convenient. But we shall test this 

 further on particular divisions of the sci- 

 ence. 



We see that the annual publication has 

 doubled during the four decades, and con- 

 siderably more ; also that the space given to 

 each review has decreased. Causes for the 

 first are the increased attendance at univer- 

 sities, the general advance in zeal for re- 

 search as a part of the great onward move- 



