576 
presented with results of far deeper reasoning 
than is contained in the writings of some authors 
who have dealt with the subject. The balancing 
of the four-crank engine and a paper on the 
graphical recording of sound waves accompanied 
by diagrams wnich seem instinctively to represent 
graphically the strident tones of the gramophone, 
have at least some relation to the vast complex of 
unsolved problems which present themselves in 
everyday life. 
In view of the ever-growing importance of 
statistical science it is gratifying to find the sub- 
section dealing with this subject represented by 
eleven papers, nearly half of them by British 
contributors. The next section deals with philo- 
sophy, history, and teaching of mathematics. 
There are ten papers and discussions on “ didac- 
tics,’ but the most important feature of this 
section is the report of the International Com- 
mission on Mathematical Teaching, which was 
constituted at Rome with Prof. Fehr, Sir George 
Greenhill, and Prof. Klein as executive committee. 
The list of publications drawn up by them and 
by the subcommittees for different 
nations occupies twelve pages of the volume. The 
publication of these reports has received sub- 
stantial financial aid from the Governments of the 
respective and they deal fairly 
thoroughly with the conditions of mathematical 
teaching in all grades of schools and in the univer- 
sities. The main danger is that tew people will 
have the time to read the reports for any except 
their own nation. 
In addition to the sectional meetings of the 
congress, we have eight lectures by Profs. 
Bécher, Borel, Brown, Enriques, Prince Galitzin, 
Prof. Landau, Sir J. Larmor, and the late Sir 
W. H. White. 
Profs. Hobson and Love are to be greatly 
congratulated on their success in organising the 
congress and bringing out this splendid record 
of some of the advances of mathematical science 
in the four years preceding the meeting. 
In the opinion of the present reviewer, how- 
various 
countries, 
ver, one important element of success was missing. 
The holding of a mathematical congress in Great 
Britain afforded a unique opportunity for bringing 
the claims of British mathematicians before the 
British public. A discussion on this subject could 
easily have been organised on purely international 
lines, and representatives of different nations would 
have been able to give us their own experiences as 
to the extent that their efforts are recognised and 
backed up by public support in their countries. 
The proceedings of such a discussion would have 
been widely circulated in Press reports, and would 
NO. 2308, VOL. 92] 
NATURE 
[JANUARY 22, I914 
have appealed to, and been read with interest 
by numbers of, people to whom papers of an 
abstract character are unintelligible and uninter- 
esting. Had the congress been a classical one, 
there is little doubt that discussions on the educa- 
tional value of Latin would have been widely re-_ 
ported in all the newspapers, and often accom- 
panied by long leading articles. 
But no such discussion was held. On the con- 
trary, the address by the late Sir William White 
on “The Place of Mathematics in Engineering 
Practice "—the one address sufficiently popular 
for the ordinary newspaper reporter and reader 
—was certainly not calculated to remove existing 
prejudices against the “‘unpractical” mathe- 
matician. But if the position of English mathe- 
matics and mathematicians did not figure in the 
official programme, it was freely discussed in the 
reception room, the refreshment tent, and the 
college halls where guests were hospitably enter- 
tained. References were not infrequent to cases 
of hardship where able mathematicians had failed 
to earn adequate incomes from teaching work, and 
to fallings-off in the numbers attending mathe- 
matical classes both in Cambridge and elsewhere. 
This private interchange of experiences between 
the initiated could scarcely serve any useful pur- 
pose; while a vigorous appeal to the public in 
plain English language, supported by a sufficient 
body of English speakers, and aided by the 
opinions of foreign experts, might have exercised 
a marked influence over the progress of future 
events. 
In short, the Cambridge Mathematical Congress 
has done nothing towards improving the prospects 
of the brilliant mathematician who is too good 
to spend his life in badly paid teaching appoint- 
ments even when he can secure them. 
It has done nothing to stop the exodus from 
our university classes of the best mathematical — 
talent that is sent up from the schools, and which 
is attracted by the better prospects that are open 
to students of chemistry or enginering. 
It has done nothing towards increasing the~ 
staffs of our university colleges, and providing 
them with an adequate number of mathematical 
professors, each a specialist in his own line; while 
on the other hand the diversion of students into’ 
other channels frequently renders such increases 
financially impossible. 
It has thus done nothing towards helping our 
English university colleges to come into line with: 
those of other countries as centres of higher study 
and mathematical research. 
And such an opportunity is not likely to recur 
for many a year to come. G. H. Bryan. 
