Hemarhs on the Theory of Anthropometry, 19 



great, and each form must have a limited amount of varia- 

 bility onl}'. A concrete case of this kind is found in the 

 anthropometry of the half-blood race of Indian and white 

 parentage. Generally speaking, the ancestry of a people 

 will be such that a number of forms which do not differ very 

 much among themselves enter into its composition. The 

 greater the number of forms, the nearer the curve of meas- 

 urements will conform to a probability curve ; but, neverthe- 

 less, it must be borne in mind that the mixture may be such 

 that constant deviations from such a curve are found which 

 are not due to accident. Our conclusion from these consid- 

 erations is that anthropometric measurements do not, as a 

 rule, follow the laws of chance, and that a careful examina- 

 tion of the curves is necessary in each case. We cannot 

 expect that in all cases a classification of the material will 

 lead to curves which follow the laws of chance more closely, 

 as the laws of heredity are such that they do not necessitate 

 an arrangement of this character. These facts must make 

 us very careful in the use of the average considered as the 

 type of a series. It will be necessary to investigate each 

 series in order to ascertain if there are any deviations from 

 the law of chance which seem to be due to constant causes, 

 not to accident. 



Besides these biological considerations, we must consider 

 a number of other factors which may cause deviations from 

 the probability curve. If a series of measurements is dis- 

 tributed according to the laws of chance, and the measure- 

 ments of the whole series are changing, deviations will occur 

 whenever the rate of change is not uniform. Such changes 

 occur during the period of growth, and this is the cause of 

 the asymmetry of distribution of measurements of children 

 to wiiicli Dr. Bowditcli called attention. Similar changes 

 may occur when the conditions of life of a community are 

 changing, or when one form is gaining preponderance over 

 another form. In all such cases the computation of the 

 average, of the mean, and of the most frequent value have no 



