POPULATION OF THE UNITED STATES 3S5 



These observation equations follow : 



1 3.9 = £ + + 7 23.2 = S + QT+ 36J7 



2 5.3 = £ + T+ U 8 31.4 = £ + IT + 49*7 



3 7.2 = iS + 2T + 4E7 9 38.6 = £ + 8T + 6417 



4 9.6 = ,8 + 37/ + 9C/ 10 50.2 = £ + 97/ + Sit/ 



5 12.9=& + 47/ + 1617 11 62.6 = S + 107/ + 10017 



6 17.1 = -ST + 52' + 25C7 12 76.3 = 8 + 117/ + 12117 



Normal equations for each constant are formed from these obser- 

 vation equations by multiplying each equation by the coefficient of the 

 constant concerned in the equation and adding. This gives us three 

 equations containing three unknown quantities. These unknown quan- 

 tities are determined by any method and substituted in the general 

 formula for S, T and U , respectively. For example, in 1900, before 

 the census returns for that year were available, the process above out- 

 lined yielded the following equations : 



261.7= 1LS+ 447/ + 286Z7 



1669.5= 44£ + 2867/ + 2026E7 



12324.1 = 286/Sf + 20267/ + 15334C7 



When these equations are solved, it is found that 



fir = 6.08, T = 0.690, U = 0.622. 



If we substitute these in the formula, we get 



P = 6.08 + 6.9 + 62.2, or P = 75.2 millions, 



which is the forecast for 1900. 



(It should be observed that in this work the year 1790 was con- 

 sidered — 1, and 1800 was taken as the origin.) 



This estimate proved somewhat low, as the census returns reported 

 76.3 millions for 1900. This indicates that the population of the 

 country is growing a little more rapidly than would be indicated from 

 its past history. 



While the government authorities are at work on the census for 

 1910, it will be interesting to try this method of forecasting, and to see 

 how well our results will compare with those to be announced later on. 

 I have made a number of equations which are supposed to represent 

 empirically the growth of the population of our country. These have 

 been made in various ways, but all depend upon the parabolic formula, 

 and the method outlined above. 



A. P = 5.13 + 0.358X + 0.666X 2 D. P = 5.30— 0.20Z + 0.73Z 2 



B. P = 5.30 + 0.49X + 0.65X 2 E. P= 5.40+ 0.12Z + 0.70Z 2 



C. P = 4.90 + 0.45Z + 0.66X 2 F. P = 39.1 + 10.45Z + 0.65Z 2 



The equations yield the following values for the census of 1910: 



