J0LY 23, 1915] 



SCIENCE 



107 



ment in natural science, and tlie increase in 

 funds available to support publication of 

 new results. For the second fact, tbe con- 

 densation of reviews, it is certain tbat much 

 space is saved by the possibility of refer- 

 ence to earlier volumes where similar 

 articles were reported; and it may be sus- 

 pected that the haste to print has given us 

 many articles of little importance; and 

 further, it is increasingly necessary to save 

 the time of the reader — Fechner's law may 

 perhaps hold here, as in the ratio between 

 nerve-stimuli and sensations: the referees 

 are competent, busy workers in various de- 

 partments of research, and fatigue effects 

 must be looked for in their treatment of 

 minor matters at least. 



For convenience I separate the list of 

 contents into five principal groups, each 

 group embracing several chapters or sec- 

 tions; these will suffice at least for a first 

 study. They are philosophy and biography, 

 algebra, analysis, geometry and applied 

 mathematics. To any specialist this seems 

 too coarse a division for any definite result, 

 but we are seeking general information. 

 Our division algebra includes not only the 

 theory of equations and their systems, but 

 also such diverse subjects as Galois groups, 

 theory of integers and other numbers, deter- 

 minants, invariants of linear substitutions, 

 probability and series. So too analysis 

 covers a long range, from the elements of 

 differential and integral calculus to the 

 theory of real and complex functions of one 

 or of several variables, general and par- 

 ticular. Geometry covers both the Euclid- 

 ean and non-Euclidean, synthetic and an- 

 alytic, the elementary and much that is so 

 advanced as to be hardly distinguishable 

 from algebra or from abstract logic. So 

 Mechanics, all branches of mathematical 

 physics, astronomy, geodesy and even 

 meteorology are combined under the single 

 rubric, Applied Mathematics. 



There is a possibility of testing roughly 

 those data, by comparison through the years 

 1891-1909 with the Bevue Semestrille, a 

 briefer report issued half-yearly and with 

 less delay by the mathematical societies of 

 the Netherlands, chiefly of Amsterdam. 

 The comparison can not be quite satis- 

 factory because the Bevue classifies one 

 article often under several rubrics, some- 

 times giving six or more references by 

 different members for an article listed only 

 once among the Titles in the Jahrbuch. Of 

 course the tedious process of counting titles 

 page by page through every volume is not 

 to be thought of. Making this allowance, 

 I have prepared with the help of Dr. 

 Cowley, a collaborator on the staff of the 

 Bevue, graphs showing the numbers of 



1830 



Fi(3. A, AlgeSbra, TStlsa Jahrbuch, SoUdj 

 Bevue Semestrielle, Dotted Curve. 



'3i 



Fig. B. Analysis, Titles. Jahrbuch, Solid; 

 Bevue Semestrielle, Dotted Curve. 



titles listed by both reports in the four 

 topics, excluding philosophy and biog- 

 raphy. 



These may be considered satisfactory 

 confirmation of the others, if we make two 

 or three assumptions or observations. First, 

 the scale adopted for comparison is prob- 

 ably too great on the Jahrbuch side. Titles 

 here were measured in inches, and have 



