SOCIETY OF THE UNIVERSITY OF ABERDEEN. H7 



use of ratios or indices. Among those recommended as characteristic 

 may be mentioned the nasal index, the facial index and the ratio of 

 height to length of head, and there are many others in use. 



Anthropologists of the empirical school usually consider the 

 absolute dimensions to be of very little importance, except for the 

 purpose of calculating an index or ratio. For example, Livi, in his 

 report on the measurements of the Italian conscripts, publishes no 

 absolute dimensions of the head, but only the cephalic indices. 

 Gustav Retzius ' and Ammoy have both recently emphasised the 

 superiority of the cephalic index to absolute measurements of length 

 and breadth of head. 



Stature appears to be the only important absolute dimension of 

 the human body which has escaped the tendency of the empirical 

 school to reduce all dimensions to ratios. Nobody yet, as far as I 

 know, has recommended an index to represent the ratio of the breadth 

 of the body to its length. 



Angles such as the facial angle are also measured by the empiri- 

 cists, and it is by means of these that prognathism or orthognathism 

 is determined. Angles, as every mathematician knows, are also funda- 

 mentally equivalent to ratios. 



The analysis of anthropometric statistics by the empirical method 

 becomes in view of what has been said comparatively simple. Calculate 

 the cephalic and other indices for each individual, and find the average 

 or mean index for the whole group of people measured. The highest 

 and lowest index is also usually stated with the view of indicating the 

 range of variation on each side of the mean. In the case of stature 

 the mean and extreme values of the absolute dimensions are usually 

 calculated. 



It is difficult to understand on what experimental data the belief 

 of the empirical school in the value of indices is based. The range of 

 variation of the cephalic index is usually quite as great as the range 

 of variation of the absolute dimensions. The cephalic indices of the 



1 Eetzius u. Ki'rst, Anthropologia Sueica, 1902, p. 116. 



