472 



GROWTH 



certain \'ariations in the rate of growth which may be correlated 

 with alterations in the conditions to which the subjects are 

 subjected. 



1. Phase Differences. 



(ft) Individual. Quetelet found that, under normal conditions, 

 the variations in the rate of growth of man were just what might 

 be predicted from the application of the mathematical law of 

 probability. This law is represented by the equation 



y = —r- • ^ . 



where <r and y are rectangular co-ordinates and h — parameter 

 of the curve. Riedel tabulated the heights of nearly 4,000 school- 

 boys of various ages, and found that the variations in height 

 observed for each age were, for all intents and purposes, just what 

 the mathematician predicted. Other investigators have con- 

 firmed this and have extended the scope of the equation, applying 

 it to variations in weight, chest measurement, etc. 



The index of variability, or standard deviation denoted by the 

 letter a, is equivalent to a determination of the point on the actual 

 frequency curve, where it changes its curvature on either side of 

 the mean. For example, if the curve showing the number of 

 individuals of a certain age having a certain height, for instance, 

 be plotted it will cut the theoretical curve at various points. 

 CT is a measure of this divergence. 



The coefficient of variability (Table LXXXIV.) is obtained by 

 dividing a by the mean and, for convenience, multiplying by 100, 



I.e. 



C 



M 



X 100. 



TABLE LXXXIV 



Coefficient of Variability in Man at Various Ages 



From this, we see that the coefficient of variability tends to 

 decrease when the rate of growth decreases and tends to increase 

 again when rapid growth restarts in the " teens." 



