REVIEWS 



MATHEMATICS 



The Mathematical Theory of Population applied to the Data of Australian 

 Population Statistics. Appendix A. Vol.1. By G. H. Knibbs, C.M.G., 

 F.S.S., F.R.A.S., Commonwealth Statistician. [Pp. xvi + 466.] (Mel- 

 bourne : McCarron, Bird & Co., 191 7.) 



This volume comprises a very detailed consideration of the Australian Census 

 Statistics, the work being, as far as possible, in mathematical form. 



The first seven sections deal entirely with the theory of the formulae, the types 

 of curves which fit a special series of points, the determination of constants to 

 a sufficient degree of accuracy, etc. ; the remaining eleven sections give their 

 application to the actual census returns. 



An immense amount of detailed work has been done, especially on the subject 

 of the birthrate, which is considered from many points of view, such as the ages 

 and differences of age of the parents, the number of months between marriage and 

 first confinement, the probability of triplets, etc. ; graphs are given not only in a 

 plane, but also of three dimensions, and account is taken of such complexities as 

 the probability of misstatement of age and the varying position of Easter. 



Considering the enormous mass of statistics and formulae, it is not always 

 possible to give the reasons for using any particular equation, and considerable 

 knowledge of actuarial theory is assumed. 



The author is careful to point out that mathematical formulae need using with 

 common sense, that they may appear to give a precision far beyond that which 

 the data can furnish, their computation may be too laborious for practical use, and 

 results need testing by a priori judgments. 



This work deals essentially with the mathematical representations of statistics 

 and not with theories or deductions from them ; indeed, it is pointed out how 

 vague any deductions must be owing to the inevitable omission of some untabulated 

 circumstance, and the lack of corresponding statistics for different countries. 



On the assumption that the present rate of increase of the world's population 

 would exhaust the sources of energy within at most seven centuries, we need 

 international statistics in order to regulate the expansion of mankind, and the 

 present work aims at supplying some means whereby mathematical reasoning can 

 be used to interpret tables of figures when they are compiled. 



Minor criticisms may be passed on the mathematical language, e.g. "the pro- 

 portion is about 133" (p. 7 footnote), meaning the ratio is about 133:100; the 

 introduction of symbols without explanation ; the wrong use of the sign = (p. 66) ; 

 and several inaccuracies probably due to printer's errors. 



Authorities may differ in their judgments as to whether the particular formulae 

 used are the best and soundest possible with our present knowledge ; but the 

 author has rendered great service in suggesting lines on which exact reasoning 

 may be applied to this branch of study, and in calling attention to the care needed 

 in handling the subject. 



W. M. Hudson. 

 Sis 



