31, 1923] 
n is increased indefinitely (Phil. Mag., Nov. 1919, 
Pp. 526). 
In Gray’s treatise the physical applications are kept 
in view throughout the book up to the end. The re- 
‘quirements are considered of the mixed mathematician. 
Not to start with general theory, but to give definite 
‘technical examples, to show how the problem may be 
reduced to the differential equation considered, he 
will consult the appropriate part of the book as the need 
arises, and will take for granted the discussion of details 
of pure analysis, on the validity of an expansion, definite 
integral expressions, asymptotic expansions, and all the 
niceties appealing to the pure mathematician of a 
logical metaphysical intellect. 
_ These can be skipped by the physical student en- 
grossed in a physical problem, and only anxious to dig 
out the facts and apply the formula to a concrete 
numerical application, for which the tables at the end of 
e€ book will give the requisite material. 
The treatise of Watson has a different scope. A 
first short historical chapter cites name and date of the 
pioneers up to 1826 encountering the function in 
dynamical, astronomical, and heat problems, namely, 
Bernoulli, Euler, Fourier, Bessel. 
After this introduction, all definite mention of the 
physical application is dismissed by Watson in the 
subsequent 800 pages, and the reader is not encouraged 
to lift his eye from the page and look up at any 
materialisation of the analysis, or to study a geometrical 
picture. 
The book proceeds in what is now the conventional 
er of a modern analytical treatise, stopping in 
a leisurely manner to emphasise and scrutinise every 
ible objection that may arise on the part of rigour. 
Those who like this work become uncommonly fond of 
, and lose interest in a realisation of the ideas. 
“ Making possible the necessary degree of abstraction 
one of the most important merits of mathematical 
gic.” 
The Bessel function has féw attractive analytical 
qualities, and does not deserve elaborate treatment 
the exclusion of more valuable interest, say of the 
iptic function. 
The students must be few to afford the time de- 
anded for this subject, not to speak of the expense— 
r Watson’s book, 7os.; and Gray’s of 327 pages, at 36s. 
We see the tax laid on knowledge by the price of 
mathematical work ; the expense of publication has 
en far beyond anything contemplated in the old 
days of debate in the Mutual Improvement Society 
on the need of a free press and cheap diffusion of 
knowledge. % 
_ It is the fashion to-day to discard a redundant 7 in 
the name Bernoulli, as-in the Bernoullianum Mathe- 
NO. 2787, VOL. 111] 
Marcu 


































NATURE 
425 
matical Museum in Basel, Basle, Bale in Switzerland. 
But Maclaurin in his “ Account of Newton’s Philo- 
sophical Discoveries,” 1750, spells the name Bernovilli, 
and here we see the etymological derivation and a 
reason for the restoration of the banished 7. 
G. GREENHILL. 
A Yearbook of the Learned World. 
Index Generalis: Annuaire général des Universités, 
Grandes Ecoles, Académies, Archives, Bibliothéques, 
Instituts scientifiques, Jardins botaniques et zoolo- 
giques, Musées, Observatoires, Sociétés savantes. 
Published under the direction of Dr. R. de Montessus 
de Ballore. Pp. 2111. (Paris: Gauthier-Villars 
et Cie, 1923.) 355. 
E welcome the appearance of the third (1922-23) 
issue of a work which, pending the issue of 
“Minerva” in its old form, is the only comprehensive 
directory of the learned world. Its scope is shown by the 
following analysis of its 2rrr pages : (x) Directories of 
universities, colleges, and professional schools grouped 
by countries, 913 pages ; (2) astronomical observatories, 
86 pages ; (3) libraries and archives, 325 pages; (4) 
museums and scientific institutes, too pages; (5) 
learned societies and academies, 194 pages ; (6) list of 
Savants who desire to exchange original dissertations 
with their fellow-workers, 7 pages ; (7) index of names 
(more than 40,000), 428 pages ; (8) other indexes and 
vocabularies, 53 pages. In part (rz), in addition to the 
names of professors, lecturers, and other teachers and 
their subjects, are mentioned the principal adminis- 
trative officers and, in many cases, the date of founda- 
tion, the total number of students, and the total annual 
expenditure ; in part (2), publications, principal instru- 
ments, and programme of work ; in part (3), days and 
hours of admission and annual holidays, date of founda- 
tion, special features, number of volumes, MSS.., ete., 
annual budget, catalogues, rules for borrowers, name of 
librarian ; in part (4), similar particulars with general 
description of exhibits or plant and mention of publica- 
tions ; in part (5), objects and aims, number of members, 
date of foundation, names of president and secretary, 
subscription, particulars of meetings, lists of fellows 
and of foreign members of some of the more import- 
ant societies, and details of publications. 
The editing of such an enormous mass of data is a 
formidable task and Prof. R, de Montessus de Ballore, 
the distinguished scholar who has had the courage to 
undertake it and the energy and perseverance to com- 
plete it, has thereby earned the gratitude of savants of 
all countries. The editor, who states that his object 
has been to achieve “the utmost clearness for refer- 
Nez 
