534 



HUMAN BIOLOGY 



present writer and his colleague, Lowell J. Reed, without 

 any knowledge of Verhulst's prior work, independently hit 

 upon the same equation. 



Fig. 4. Logistic curve and its first derivative. 



Verhulst called his curve "logistic." This usage we shall 

 follow. The characteristic appearance, and some of the 

 mathematical properties of the logistic curve are shown in 

 Figure 4. The equation to the simple logistic used by Verhulst 

 is: 



y = 



I +e 



a-\-hx 



The generahzed logistic, developed by the writer and 

 Reed, has the form 



k 



y 



J _!_ pa<s + <iiX-'ratx'^-\- , . .Onx" 



