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A Formula for Predicting the Population of the 

 United States. 



By H. S. Pritchett. 



It is often desired to represent by a mathematical equation the 

 law connecting a series of observations for which theory gives 

 no explanation. In such a case ignorance of the physical cause 

 of the phenomena observed does not diminish the accuracy of the 

 computed formula for purposes of prediction, provided the obser- 

 vations are accurate and there are enough of them, and provided 

 the same causes continue to operate. 



As the forces giving rise to a series of phenomena become 

 more complicated, the equation which would represent the law 

 connecting the phenomena would generally be correspondingly 

 complicated. When such observed quantities result from a few 

 general causes modified by factors varying among themselves in 

 magnitude and direction, it may be possible to represent the ob- 

 servations fairly well by a comparatively simple equation. 



The problem of deriving an equation to represent the law of 

 growth of population in the United States is such a case. The 

 factors entering into this growth, such as birth-rate and death- 

 rate, immigration and emigration, &c., are more numerous and 



