president's address. SECTION Gl. 511 



purely scientific statistics, demanded considerable specialisation for 

 practical reasons. The failures of inadequately equipped institutions, 

 and the arguments of Laplace, Baily, Lacroix, and Littrow — viz., that 

 to be sound the foundation of insurance business must rest upon strict 

 mathematical deductions derived from systematised experience — led 

 to the founding of actuarial method. 



6. First Effect of Elimination of Various Elements. — The initial 

 effect on statistics, of the elimination of these various subjects, was 

 that the whole system declined, and was little more than a tabular 

 statement of various important facts. As a university study, it lost 

 its pride of place, and doubt even arose as to whether scientific 

 statistics was a jiossibility. But it was not long before it became 

 evident that answers to quite simple questions relating to population 

 and its various features, or to industry, &c., required special returns, 

 and demanded well-ordered investigations, involving occasionally 

 highly specialised ti'eatment. This fact gave rise to a more critical 

 study of the matter of statistics, and ultimately to the creation of the 

 various official bureaux, and was responsible for the development of a 

 clearer recognition of the proper nature of statistical science. 



7. Illustration of the Evolution of Scientific Idea of Statistics. — 

 Given sufficient ignorance of the subject, statistics will probably appear 

 to be little more than a series of tabulations based upon more or less 

 well-organised schemes of inquiiy. That such a vieAV is quite inade- 

 quate will, however, appear from a very simple case. Consider for a 

 moment a series of tabulations of an increasing population, say, corre- 

 sponding to the tenuinations of a series of years. The absolute in- 

 crease year by year is, of course, immediately apparent,* but not the 

 rate of such increase. If this absolute annual increase proved on 

 examination to be in each instance the same fraction of the popula- 

 tion, let us suppose, of the population at the end of the preceding year, 

 we should then recognise the fact that the ajinual rate of increase^ was 

 constant. This increase, however, might be regarded as continuous 

 throughout each instant during that year; hence, through that assump- 

 tion, we should reach the idea of an instantaneous rate of increase^ 

 On the other hand, the rate itself may, and, as a matter of fact, always 

 does change. It is not the same from instant to instant; hence an 

 approximate and useful study would be the nature of such changes of 

 rate. We see, then, that it is in the progressive unfolding of the 

 meaning of the rough data, or in the subsuming the crude results 

 under some general conception, that the science of statistics is con- 

 stituted. 



8. Statistical Prediction. — Here one may digress somewhat to 

 remark that the value of statistics lies chiefly in its scientific elements 

 — viz., those that belong to systematised knowledge^ — and by way of 

 illustration it may be pointed out that the history of the subject con- 

 tains a remarkable example of the application of the idea of §" rate of 



* Po. - Px 



t (P., - P^) / Pi = r, a constant— I.e., the constant annual rate of increase. 



pt 

 J Pj / Pi= e in which p is the instantaneous rate of increase. 



§P/P„ = c„0(<) 



