6o2 



TRANS. ST. LOUIS ACAD. SCIENCE. 



How accurately this formula represents the observed values of 

 the population will be seen from the graphical representation 

 of the computed curve which follows. In this plat the axis of Y 

 is the time axis, and the abscissas represent the population ex- 

 pressed in millions. The observed values of the population for 

 each decade are represented by the black dots, and the black-line 

 curve is furnished by formula (i). With the exception of the 

 values for iS6o and 1S70, it will be noted that the curve fits the 

 observations with great exactness. 



tSQOr 



00 millions. 



Substituting the values of A, B, C and D into the equations 

 of condition, there result the residuals given in the column head- 

 ed "z>." An examination of these residuals brings out several 

 interesting facts. 



The smallnessof the residuals, and the consequent close agree- 

 ment of the formula with the observations, establishes the fact 

 that the general growth of the population has been in the main a 

 regular and orderly one. 



