PROGRESS OF PURE MATHEMATICS IN 1900. 163 
ises a series of memoirs containing the complete analysis, 
together with applications to mechanics, notably to the 
problem of Madam Kowalevski. The first of these mem¬ 
oirs is soon to appear in the Acta Mathematica. 
It is now obvious that Painleve’s work is a long step in 
advance of previous results. He affirms that equations (F) 
constitute the first known examples of equations whose in¬ 
tegrals have been found by the aid of the principles of the 
theory of functions, which equations are not reducible to 
any combination of linear equations, quadratures, or even 
equations of the first order. 
Encyklopadia dev Mathematischen Wissenschaften. —Fore¬ 
most among the new mathematical publications of the year 
worthy of special notice is the great Encyklopadia der Mathe¬ 
matischen Wissenschaften. This work is planned to exhibit 
a synopsis of the whole field of pure and applied mathe¬ 
matics, is to be comprised in six volumes, and is to conclude 
with a seventh containing philosophical and historical essays 
on mathematical and related theories. Two volumes have 
been issued, the subjects and authors for three more have 
been announced, and of the remaining two volumes only 
the general plan has been published. The two volumes 
which have been issued, cover the field of pure analysis, 
and appear to be all that German scholarship and genius 
can make them. What more need be said? True, there 
are many contributors outside of Germany; yet the whole 
work was conceived, planned, edited, and published by Ger¬ 
mans or by those who drew their inspiration directly from 
German sources. A French translation of this great work 
is already announced, and two volumes are promised within 
a year. An English translation by the British mathemati¬ 
cians is understood to be in contemplation. 
Forsyth’s Differential Equations. —Since the publication of 
Dr. Salmon’s unrivaled treatises on contemporaneous mathe¬ 
matics, Professor Forsyth, of Cambridge, England, has sur¬ 
passed all others in making the latest developments accessi¬ 
ble to English-speaking mathematicians. The appearance 
23—Bull. Phil. Soc., Wash., Vol. 14. 
