APEIL 9, 1897.] 



SCIENCE. 



571 



This table shows that young children 

 grow more uniformly than older children. 

 The increasing variability is very great dur- 

 ing the years of adolescence. After this 

 period it must necessarily fall. It disap- 

 pears as soon as all the individuals have 

 ceased growing. This increase in varia- 

 bility must be considered due to the 

 effect of retardation and acceleration of 

 growth. During the period preceding pu- 

 berty some individuals will have reached 

 their full growth, while others are still 

 growing at a very rapid rate. As 

 the rate of growth during the early 

 years of childhood does not vary very 

 much, retardation and acceleration will 

 not have any effect of this sort. For the 

 same reason the distribution of amounts of 

 growth during the years preceding puberty 

 is very asymmetrical and must be more so 

 for the years from 17 to 20, for which I have 

 no observations. It will be noticed that 

 ^ihe growth of girls is more variable than 

 that of boys. 



I have furthermore divided the series for 

 each year in two equal halves, the one em- 

 bracing the tall children, the other embra- 

 cing the short children. The average an- 

 nual increases of these two groups are as 

 follows : 



are throughout their period of growth re- 

 tarded in development, and smallness at 

 any given period as compared to the aver- 

 age must in most cases be interpreted as due 

 to slowness of development. During early 

 life slowness of development which has 

 manifested itself is likely to continue, while 

 some of the effects of retardation will be 

 made good during the period of adolescence, 

 which is liable to be longer than in children 

 who develop rapidly in early life. 



We will call the average stature at the 

 age t A,; the amount of growth of an indi- 

 vidual whose stature at that period is J., + a; 

 may be called d^. "We assume that the re- 

 lation between the actual size of an indi- 

 vidual and the average amount of its annual 

 growth be expressed by the simple relation 



d^= d + ax 

 where a is a constant. 



Furthermore we will assume that the vari- 

 ability of d^ will be the same for all values 

 of X. Then it can easily be proved that 



-J^ 



where ii. and [i^ the variabilities of stature 

 at the periods t and t^ and where m the 

 variability of the amount of growth during 

 the period t^-t. 



Average Increase in Stature Between the Following Years: 



It appears that during the early years of 

 •childhood short children grow more slowly 

 than tall children, that is to say their gen- 

 eral development continues to be slow. 

 Later on, during the period of adolescence, 

 they continue to grow while tall children 

 have more nearly reached their full de- 

 velopment. That is to say, small children 



From these data the following values of 

 a have been computed: 



