Remarks on the Theory of Anthropometry. 21 



chance. The average length of liead would be 193 mm., the 

 average breadth of head 155 mm. According to the method 

 under consideration, this would be the typical combination. 

 When the tribes are properly subdivided in an eastern and a 

 western group, it will be found tliat the length of head is 

 195 mm. in the west, 191 iu the east, and that 193 does not 

 represent the type of any one tribe. These people speak 

 the same language, and miglit be gathered on one reserva- 

 tion. In that case a subdivision would be impossible, and 

 an erroneous result would ])e obtained. Therefore, a critical 

 study of distributions must precede the establishment of the 

 type. The theory of statistics points to a clear way for this 

 study, but unfortunately it has never been applied up to 

 this time. The study must be based on a comparison of the 

 variabilities of measurements. Whenever tlie variability of 

 a measurement that is correlated to another one is abnor- 

 mally increased we must suppose that there is an intermixt- 

 ure of types. 



I must add a few words regarding the subject of correla- 

 tions. 



The admirable investigations of Mr. Alphonse Bertillon 

 and those of Soren-Hansen, Bischoff, and others have proved 

 that with increasing height all other measurements increase 

 not proportionally, but at a slower rate. This law may be 

 given a wider meaning by saying that whenever a group of 

 people are arranged according to one measurement, with the 

 increase of this measurement all others increase at a slower 

 rate, the rate being the slower the slighter the correlation. 

 This law leads us to establish the fact that we must consider 

 each measurement as a function of a number of variable 

 factors which rei)resent the laws of heredit}^ and environ- 

 ment. The correlation of two measurements will be close 

 when they depend largely upon the same factor, slight wlien 

 they depend largely upon distinct factors. This difference 

 in the degree of correlation, which is a well-established fact, 

 proves that the system which is applied in many of our 



