CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
197 
straight, add ‘32 centim. for male and ‘33 centim. for female to the length before 
using the above formulse. 
(ii.) If the tibia has been measured with, and not without, the spine, subtract 
•96 centim. for male and '87 centim. for female from the length before using the above 
formulae. 
(iii.) The above formulae have been determined from the right members; a small 
error, of the second order as a rule, arises when the left is used. The following 
numbers are determined from Rollet’s measurements; they give the amount to be 
added to a left bone when it is used in the formulae :— 
Femur. 
Hnmerus. 
Tibia. 
Radius. 
Male.. 
-•04 
+ •42 
+ •18 
+ •28 
Female. 
+ •03 
+ •51 
+ •09 
+ •19 
The femur change is insignificant. In most statements of lengths the rightness or 
leftness of the bone is not given, and hence, no correction can generally be made for 
an individual. The error will, however, be hardly sensible except in the case of the 
humerus and radius. If a considerable number of bones have been averaefed, 
probably half may be looked upon as right and half left, and in this case half the 
above corrections may be added to the average. In any case, it is probably only the 
estimate based on the humerus and radius which need to be corrected in this manner. 
Even here it is a problem how far there is a racial character in this right and left¬ 
sideness. Results due to Callender, Roberts, Garson, Harting, and Raymondaud 
are cited by Rollet (Joe. cit., pp. 53-60), but being based either on very few cases, 
on measurements on the living, or on unsexed material, they are not of much service 
for our present purpose. Results of much greater value for racial comparison have 
been given by Dr. Warren for the Naqada race (‘Phil. Trans.,’ B, vol. 189, p. 135 
et seq.). He finds :— 
Femur. 
Humerus. 
Tibia. 
Radius. 
Male. 
-11 
+ •34 
-•08 
+ •20 
Female. 
-•16 
+ •57 
-•105 
+ •305 
Dr. Warren’s results are for the oblique femur, and from centre to centre of the 
articulate surfaces in the case of tibia and radius. Thus they are not directly com¬ 
parable with the results for the French, On the whole, if the bone is stated to be 
left, we may add '45 for the humerus and ‘25 for the radius, leaving the femur and 
tibia unaltered. These additions are approximately the same for both sexes. 
