212 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



Method II. Not having in a given case the material to do this, owing to tlie absence of one of 

 the necessary bones, we use the calculated average length of the missing bone in place of the factor 

 which the pecuUar length of it would constitute if it were present. For instance, suppose we 

 desire to calculate the atitibrachial index for a limb of whicli the radius is missing, we multiply the 

 average length of all the radii by 100 and divide the product by the length of the humerus; and if 

 the humerus, instead of the radius, is missing, we multiply the length of the radius by 100 and 

 divide the product by the average length of the humeri. Relatively corresponding formulae are 

 used for the posterior limb. 



Thus we obtain two sets of figures, one which definitely states the relations of the bones in 

 a given in dividual to whose skeleton both bones belonged, and one which states that a bone of a 

 certain individual bears such and such a relation to the general average of certain related bones, 

 whatever they may be, of his race. 



In the synopsis (Table Lii) giving the average osteometric indices the results obtained from 

 the complete limbs by method i are given first, then those obtained by method ii, namely, by the 

 lengths of the bones compared to the averages. These two groups of figures, which sum up with 

 very little diflerence, are then combined to give a general average for the race. In each of these 

 groups of indices there are three subdivisions, one for the right side, one for the left, and one for 

 the total of both sides. The figures found at the bottouis of the columns of indiviiliial indices are 

 the totals obtained from both methods. They reappear in the synopsis. 



The extremes of the indices obtained by method ii are preposterous and should be allowed 

 no weight in discussing the variations in relative length of the segments of the limbs. The cause 

 of the great variation in question is almost self evident. They are from those cases where the 

 individual was much above or much below the normal stature of the race. The cases where the 

 index upon one side of a skeleton is calculated from two of its own proper bones, while upon 

 the other side it is calculated from the relation of a bone's length to the average, often gives a 

 startling difference between the right index and the left index, for which the above explanation 

 accounts; but when we come to the average indices all these difficulties disappear and the figures 

 obtained by method ii come close to those obtained by method i. This we regard as sufficient 

 justification for the adoption of method ii as a means of increasing the number of individuals 

 with whom our figures deal. 



The reader is liable to think that he finds some obscurity with regard to the number of indi- 

 viduals concerned in the combined right aud left or total index obtained by method ii, and the 

 same index obtained by methods 1 aud ii combined. Taking the antibrachial index as an instance, 

 however (see Synopsis <>/ Indices, Table lii), the cross line beginning with the words " computed 

 by method ii" and giving the number of total indices as 15 must not be read as if it ought to 

 mean that there are 15 indices of each .side combined to form a total of 15 indices of both sides 

 but that the index derived from combining the aggregate of each side represents the average of 

 a sum which consi.sts of 30 factors. 



A reference to the tables of antibrachial aud tibiofemoral indices in Topinard's Anthropology* 

 will show that the variation per cent of these indices is small. His minimum and maximum of the 

 antibrachial index are 69.8 in a male Eskimo and 81.7 in a female Andamanese, respectively; hence 

 only 11.9 per cent — this, be it noted, between individuals, not between racial averages. The tibio- 

 femoral index varies from 78.6 in 9 male Esthouians to 89.0 in 1 female Negrito, or 10.4 per cent. 



The maximum and minimum of series which contain five or more (individuals or limbs?)t are 

 as follows: For the antibrachial index the maximum is 79.0 in 32 male African Negroes, the mini- 

 mum is 72.4 in 26 female Europeans. For the tibiofemoral index the maximum is 84.4 in 10 African 

 Negresses, the minimum is 80.2 in 5 male Chinese. 



Continuing our study of Dr. Topinard's tables, we find that the sexual differences with regard 

 to these indices are not great. As to the antibrachial index, the sexual difference ranges from 

 0.1 in Europeans to 3.0 in South Americans, the males having the higher index in each case. As 

 to the tibiofemoral index, the sexual difference ranges from 0.3 in Europeans to 1.5 in negroes, the 



"ToPiNAUD, op. cit., pp. 1043-1045. 



tProbably individuals. (Seo Topinard, op. cit., pp. 1043-1045.) 



