108 



SCIENCE 



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



130O 



'C5 



Tig. C. Geometry, Titles. Jahriuch, Solid; 

 Hevue Semestrielle, Dotted Curve. 



Fig. D. Applied Mathematics. Jahriuch, 

 Solid; Revue Semestrielle, Dotted Curve. 



been plotted as containing 10 to the inch. 

 By random samples it appears that 7 or 8 

 would have been nearly correct. Second: 

 If by this correction the JaJiJ'iuch curve 

 were lowered relatively, still the diver- 

 gence would be disproportionate for differ- 

 ent years; less in earlier and later years, 

 greater near the middle of the period. As 

 to this, it is possible to surmise that the 

 frequent change in the personnel of the 

 staff, together with the fact that each one 

 turns in reports on all the contents of his 

 assigned periodicals rather than upon a list 

 pertaining to his own few specialties, will 

 explain much of the observed effect. In the 

 firat few years habits of work were not yet 

 settled, and after several years it may easily 

 have happened that cross-references of 

 minor importance were found too numer- 

 ous for utility and gradually reduced. 

 Probably, thirdly, irregularities due to post- 

 ponement or to lack of prompt arrival of 

 publications would affect the Revue more 

 markedly than the more leisurely Jahriuch. 



1870 '80 '80 1000 1910 



Fig. 4. Proportions of Titles in Large Divi- 

 sions. (1) Philosophy, (2) Algebra, (3) Analysis, 

 (4) Greometry, (5) Applied Mathematics. 



Figs. 5-6. Proportional Numbers of Titles in 

 Four General Divisions of Mathematics. {x, 

 Maxima. ) 



I show graphs of the proportionate 

 amounts {i. e., percentages) of the success- 

 ive volumes, that fall into the several divi- 

 sions ; the first with boundaries straight and 

 parallel, like covers of a book, the second 

 with a straight line separating the abstract 

 algebra and analysis on one side from the 

 more concrete geometry and applied mathe- 

 matics on the other. In this latter the outer 

 boundaries are parallel curves, and their 

 fluctuations enable us to trace the occasional 

 shift of interest toward concrete or abstract. 



On this diagram it is noticeable that the 

 proportions of writings in the different 

 divisions are by no means constant. 

 Eoughly estimated, the averages are: Ap- 

 plied mathematics 30 per cent., geometry 

 25 per cent., analysis 20 per cent., algebra 

 18 per cent, and philosophy, history, etc., 

 together 7 per cent. But there are certain 

 times of wide variation from the average. 

 In physics, for example, there is a period 

 of increase from 1883 to 1890, a time when 

 Maxwell's "Electricity and Magnetism," 

 Rowland's researches in the spectrum. 



