PIUTCHETT FORMULA FOR POPULATION". 605 



the law expressed by equation (2) very accurately, and also that 

 this rate of growth was more rapid than that of later decades. 

 Had this rate of growth continued to 1S70, the population would 

 have amounted at that time to 41,877,100. The diminution dur- 

 ing the decade due to those actually killed, to lessened immigra- 

 tion and decreased birth-rate, cannot be stated with exactness, 

 but probably approximates 1,700.000. After deducting this loss 

 it does not seem possible that the population in 1S70 could have 

 been less than 40,000,000, a result entirely in accordance with the 

 conclusions arrived at by the last two Superintendents of the 

 Census. 



Had the population continued to grow after 1S60 at the same 

 rate as before, we should have had in 1S90 a population of over 

 71 millions, about nine millions more than we really have. It is 

 scarcfely possible that the whole of this difference is chargeable 

 to the war, but is probably due in part to a diminishing birth- 

 rate. 



PROBABLE ERROR. 



Assuming the formula correct, there results for the probable 

 error of a single determination of the population ± 0-367, ex- 

 pressed as a fraction of a million. 



This error contains, of course, both the error of the formula 

 and the error of the census enumeration. Assuming A, B, C and 

 D as independent quantities, we obtain for their probable errors 

 the following values : 



Probable error of A = :i; o-i79 

 Probable error of B = ± 0.127 

 Probable error of C ^ ± 0.017S 

 Probable error of D = ^t 0.0066 



From these values, expressing, P as a function of A, B, C and 

 D its probable error may be computed at any time. This pro- 

 bable error would remain a small percent of the computed popu- 

 lation. 



