408 CALCULATIONS OF POPULATION IN JUNE, 1900 



from the time of landing to the end of the decade. If allowance 

 were made for such increase, it would result in a slightly smaller 

 estimated population for the first day of June next. The cor- 

 rection is here neglected for four reasons : (1) its uncertainty — 

 for the assumption that an immigrant population, immediately 

 after arrival, will increase at the same rate as natives is only 

 approximately true, and there is no trustworthy way of tracing 

 this element of the population from census to census ; (2) the 

 smallness of the amount involved — no reasonable estimate of 

 the increase in question for any decade, even that beginning 

 with 1880, would reach half a million, by but a very small frac- 

 tion of which amount the final result for 1900 could be affected, 

 a fraction insignificant when compared with errors unavoidably 

 entering ; (3) the desirability of simplicity in the calculation, as 

 well as defmiteness ; (4) the probability that the discordance 

 between the 1880 and 1890 census figures, brought out by the 

 application in the formulae herewith to be shown, is due more to 

 deficiency of the latter rather than to excess of the former, so 

 that any treatment which, using the figures as they stand, leads 

 to a lower final result for 1900 is to be avoided. The " natural 

 increase," therefore, as here understood, is the total increase 

 during the decade by census record, diminished only by the ac- 

 cession from immigration in that time. 



Law of Natural Increase. — In a newly occupied territory the 

 tendency of a population is to grow in a geometrical progression ; 

 the percentage of increase is in that case constant for a constant 

 interval, and the total population equal to some fixed quantity 

 raised to a power represented by the time. After a period, 

 longer or shorter, according to the capacity of the population to 

 support itself on the land, the percentage of increase falls off 

 and grows lower as the population grows greater. The law of 

 this falling off in the ratio is one which, in the present state of 

 our knowledge, has to be decided empirically. The following 

 formula is used, with some modifications to be explained, in 

 these calculations : 



A V — — i t i 2 ' 



where p denotes the population, Ap its natural increase in ten 

 years, and e,f, g positive constants to be found by calculation. 

 It will be seen that this formula would give a geometrical pro- 

 gression if /and g were zero; that it gives a near approach to 

 such a progression for small values of p; that Ap would contin- 



