IMPORTANCE OF STATISTICAL IDEAS. 119 



Here the birth-rates, to begin with, are not so high as in Australasia, 

 and presumably in the United States, and the excess of births over 

 deaths, though it has declined a good deal since 1871-81, when it was 

 highest, has been by comparison fairly well maintained, being still 11 

 per 1,000, as compared with 12.2 in 1851. 



We have thus on one side a manifest decline in the rate of growth 

 of population in three large groups of population, coupled with a large 

 decline of birth-rates in England and Australasia where the facts are 

 known, and a smaller decline in the rate of the excess of births over 

 deaths, this decline in England as yet being comparatively small. Such 

 facts cannot but excite inquiry, and it is an excellent result of the use 

 of continuous statistical records that the questions involved can be so 

 definitely raised. 



As I have stated, it would be foreign to the object of this paper to 

 discuss fully the various questions thus brought up for discussion, but 

 one or two observations may be made having regard to some inferences 

 which are somewhat hastily drawn. 



1. The rate of growth of population of the communities may still 

 be very considerable, even if it is no higher than it has been in the 

 last few years. A growth of 16, 15, or even 12 per cent, in ten years, 

 owing to the excess of births over deaths, is a very considerable growth, 

 though it is much less than the larger figures which existed in some 

 parts forty or fifty years ago. What has happened in the United King- 

 dom is well worth observing in this connection. Since 1840 the popu- 

 lation of the United Kingdom as a whole has increased nearly 60 per 

 cent., although the increase in most of the decades hardly ever exceeded 

 8 per cent., and in 1840-50 was no more than 2i/^ per cent. The 

 increase, it must be remembered, goes on at a compound ratio, and in. 

 a few decades an enormous change is apparent. The increase from 

 about 170 to 510 millions in the course of the last century among Eu- 

 ropean people generally, though it includes the enormous growth of the 

 United States in those decades, when the rate of growth was at the 

 highest, also includes the slower growth of other periods, and the slower 

 growths of other countries. An addition of even 10 per cent, only as 

 the average every ten years would far more than double the 500 millions 

 in a century, and an increase to at least 1,500 millions during the cen- 

 tury now beginning, unless some great change should occur, would 

 accordingly appear not improbable. 



2. Some of the rates of growth of population from which there has 

 been a falling off of late years were obviously quite abnormal. I refer 

 especially to the growth in Australasia between 1850 and 1880, and 

 the growth in the United States prior to 1860. They were largely due 

 to the indirect effect of immigration which has been already referred to. 



The population to which immigrants are largely added in a few 



