Septembee 13, 1895.] 



SCIENCE. 



345 



a certain age lie between narrow limits are 

 treated alone, the variability of the series in- 

 creases steadily until the adult stage is reached, 

 and that furthermore this increase in variabil- 

 ity is the less the nearer the initial point ap- 

 proaches the adult stage. It appears at the 

 same time that each of these series approaches 

 the middle values as time elapses from the ini- 

 tial age. 



Another important phenomenon which is 

 brought out in this paper is that tall boys of 16 

 years grow much less than short boys, because 

 they are nearer the adult stage. As the ta- 

 ble which Dr. Beyer gives is rather complex 

 and not quite clear, I have computed it again 

 and give it here in a modified form. I have 

 compensated the series and find that among 

 each 100 boys the following amounts of total 

 growth occur : 



typical value of that class. For the 17th year 

 I obtained the following distribution and ap- 

 proximate typical values of growth from the 

 17th to the 22d year of age : 



These figures show that the typical amount 

 of growth of the 16-year-old boy who is 62 or 63 

 inches tall is about 4.4 inches ; of the boy who is 

 64 or 65 inches tall 2.4 inches, and of those from 

 66 to 69 inches only 1.8 inches. It also shows 

 that the boys grow more uniformly the taller 

 they are, and this is probably the cause of the 

 more rapid approach of the lower grades to- 

 wards the middle values. The curves showing 

 the total amount of growth are necessarily very 

 assymetrical and the assymetry effects the aver- 

 ages of the statures of the boys who originally 

 belong to the same grade. Therefore these 

 averages which were used by Dr. Beyer in fol- 

 lowing the growth of a certain group of individ- 

 uals are only very rough approximations to the 



This consideration cannot be carried on, be- 

 cause the selection made by the author of indi- 

 viduals of equal stature of 16 years of age in- 

 fluences the distribution of measurements taken 

 during the later years too much. 



It appears from these tables that it would be 

 an easy matter to determine in this manner, 

 how many individuals of each class are adult at 

 a certain age, and this is one of the fundamental 

 points required for a better understanding of 

 the laws of growth. But it would have been 

 much better to start with individuals who as 

 adults have the same measurements and to inves- 

 tigate how these measurements are distributed 

 in earlier years. This is the only means by 

 Avhich the difficulties arising from the irregular 

 distribution of the period of growth in different 

 individuals can be overcome. 



The investigation suffers greatly from the fact 

 that only a selection — and not a very systematic 

 selection — of data from the rich material has 

 been utilized. The author deserves our special 

 thanks for having given these data in an una- 

 bridged form. They are contained in Tables 

 XIV. to XVI., which represent the heights of 63 

 tall, 71 middle-sized, and 52 short individuals, 

 measured mostly annually from their 16th to 

 their 22d year, but the measurements for the 

 21st year are missing in most cases. The group- 

 ing, however, is not favorable, the limits of the 

 lowest and highest classes being too wide. The 

 shortest class contains individuals of from 60.5 



