414 
Book Notes and Bibliography 
a larger work the Lectures in their published form appear a little disjointed. This is unfortunate 
as it gives an impression of hurry which is enhanced by the fact that there is neither an index 
nor list of contents ! 
To biometricians Mr Hardy's treatment of frequency curves will not we think pass without a 
certain amount of criticism. On p. 39 the differential equation from which the Pearson-type 
curves are evolved is given as 
1 Jy^_ 
1/ ' dx " a —h.v+c.v^^ 
which does not seem to lead to Type I, while the curves have been renumbered simply according 
to range which seems unsatisfactory, as, if we are to give up a numbering to which we are 
accustomed, it is well to adopt one which will not call for revision. This could have been done 
either according to the number of terms in the denominator of the right-hand side of the funda- 
mental equation or according to the number of moments required, e.g. the curves requiring two 
moments numbered II a, II b, etc., and then further curves could be added if for any class of 
statistics a further term had to be included in the differential equation. 
There are one or two other details with which we find it hard to agree ; for example, on p. 46, 
Type III should we think have been used to fit the binomial series, while we find it hard to 
follow Mr Hardy's statement that Types III and IV are not specially useful to Actuaries, the 
I'eason given is hardly convincing, and we have found both curves in not a few cases from actuarial 
data. 
To most people interested in graduation however the part of Mr Hardy's book which will be 
most attractive will certainly be his account of his own gradvxation of the select tables (i.e. tables 
giving the effect of medical selection) based on the new British Offices experience. Prior to this 
graduation there had we believe been no published graduation of a select table by any curve- 
fitting process, and though the two diagrams (pp. 74 and 75) do not betoken a very close fit it 
must be borne in mind that it is on the sum of the two curves that the agreement really depends, 
and little fault can be found with the resulting graduation. But apart from this one cannot 
expect a perfect method of graduation to be reached immediately, and Mr Hardy has probably 
done far more in actuarial circles for scientific graduation than most actuaries realise. 
Our disagreement with some of the remarks made in Mr Hardy's book does not obscure but 
rather tends to accentuate in our minds the value of many of his actuarial suggestions, while we 
hope his work will stimulate other Actuaries to a study of general curve-fitting, so that the old 
methods which have been used so freely in the past may be displaced by those which Mr Hardy 
more than any other actuary has brought before the notice of his profession. 
W. P. E. 
BIBLIOGRAPHY. 
(1) Albrecht, K. Die Fehlerwahrscheinlichkoitsrechnung und ihre Anwendung auf die 
PflanzenzUchtung. Fiihlings Laudw. Ztg., pp. 577 — 585. 1908. 
(2) Allegea, G. T. Sul peso dell' encefalo umano e delle sue parti nei Messinesi. Ann. di 
nevroL, Napoli, Vol. xxv, pp. 300—357. 1907. 
(3) Anthbaume, a. and Vurpas, C. La transmission her^ditaire ; enquete sur une famille 
de gymnasiarques vieille de plus que trois cents ans. Rev. scient., Paris, Ser. 5, 
T. X, pp. 523—527. 1908. 
(4) Baines, Sir .J. A. The peradventures of an Indian life-table. Jour. Roy. Statist. Soc, 
Loud., Vol. Lxxi, pij. 291—318, 1908, 
