
Jone 9, 1923] 
NATURE 
769 

isenormous. When our methods are more refined, such 
minor variations may possibly serve to explain the 
differences between the caseins derived from the milk 
of various animals and the highly specific behaviour 
of various proteins in immunity tests. Of outstanding 
importance is the fact that the synthetic products are 
attacked by those enzymes which normally effect 
protein digestion. Material is thus afforded for the 
systematic study of the fermentative processes in the 
organism, and it may be claimed that the chemist has 
gone a long way to meet the physiologist on common 
ground. 
"The synthesis of the type protein may be said to 
have been accomplished by Fischer, but the synthesis 
of an actual protein is quite another matter, and least 
of all will it ever be possible economically to make 
synthetic protein at a price to compare with the product 
of the vegetable world. Alike with sugar, fat, and 
protein, it is the problem of man so to increase yield, 
and maybe quality as well as quantity, as to provide 
a sufficiency of cheap food for our needs. The applica- 
tion of chemical knowledge to agriculture and to 
horticulture in ever-increasing intensity is not the least 
important of our tasks. 
At the moment of putting down this monumental 
work, with more than a pang of sorrow that its author 
has passed beyond, one cannot help the involuntary 
comparison with an entirely different type of chemist 
of our own race—Sir James Dewar. Fischer, the 
patient, untiring observer and investigator in the 
organic laboratory, never allowing himself to deviate 
from his plan. Dewar, all genius and impatience, full 
of daring, an artist above all both in his science and 
his spirit. E. F. ARMSTRONG. 

Actuarial Mathematics. 
(1) Calculus and Probability for Actuarial Students. 
By A. Henry. (Published by the Authority of and 
on Behalf of the Institute of Actuaries.) Pp. vii+ 152. 
(London: C. and E. Layton, 1922.) 12s. 6d. 
(2) Life Contingencies. By E. F. Spurgeon. (Pub- 
lished by the Authority and on Behalf of the Institute 
of Actuaries.) Pp. xxvii+477. (London: C. and 
E. Layton, 1922.) 30s. 
b(t) R. HENRY’S volume contains a course of 
differential and integral calculus, coupled 
with finite differences, designed primarily to meet the 
requirements of actuarial students. Stress is laid 
throughout on the numerical methods with which 
actuaries are mainly concerned. The treatment of the 
differential and integral calculus suffers from lack of 
rigour and would not satisfy a modern pure mathema- 
tician. It contains nothing, however, likely to mis- 
NO. 2797, VOL. III] 
lead those whose main interest lies in the numerical 
applications. 
The eight chapters on finite differences give all 
the most useful rules for interpolation, both direct 
and inverse. A numerical example, to evaluate 
F (2°33333), given f (2:30103)=200, f (2°32222)=210, 
f (2°34242)=220, f (2:36173)=230, is worked out by 
four methods which lead to the same result, 215-442. 
Such illustrations as this tend to increase the faith 
of a reader sceptical about the validity of the formule. 
The section on integral calculus contains a useful 
chapter on approximate numerical integration includ- 
ing the formule of Lubbock, Woolhouse, Simpson, 
Weddle, and G. F. Hardy. A chapter on probability 
and a collection of examples conclude the volume. 
Mr. Henry’s book is one which can be strongly recom- 
mended, not only to actuarial students, but to all 
whose work lies in the numerical applications of the 
calculus and finite differences. 
(2) The second volume before us is issued as the 
“official” text-book on life contingencies. It dis- 
cusses mathematically such subjects as mortality 
tables and their statistical application, probabilities 
of life and death, and all the usual types of assurance 
and annuity. A mortality table, on which the calcula- 
tion of assurance data rests, is necessarily constructed 
from experimental evidence: it gives the number of 
people, among N aged m years, who may be expected 
to attain the age of m+ years. The usual tables are : 
(x) English life tables compiled from census returns 
and death registers, (2) tables compiled from the 
experience of British life offices, relating to the select 
class of lives with which the companies have dealt, 
and (3) such tables as Gompertz’s and Makeham’s, 
which are based on conjectured theoretical expressions 
for the functions occurring in a life-table. 
Mr. Spurgeon’s volume will now be accepted as 
the standard treatise, so far as the subjects with which 
it deals are concerned. A reader possessing a fair 
working knowledge of elementary mathematics, in- 
cluding the calculus and finite differences so far as 
they are contained in Mr. Henry’s companion volume, 
should be sufficiently prepared to read most of it. 
The arguments throughout the book are clearly pre- 
sented, and the theory is illustrated by many solved 
numerical examples—most of which involve using 
data supplied by the tables. 
We cannot help thinking that the notation adopted 
for some of the actuarial functions is unfortunate. In 
certain types of mathematical work a multiple-suffix 
notation is helpful, but such symbols as 
(on) 1 (on) 
Ais: ral! ates Dm? tH £V¥ tx] 
present considerable difficulties to both printer and 
a hen > 
