Mathematical Contributions to the Theory of Evolution. 497 



Tabulating the corresponding quantities for the other sex we 

 find 



2 Skeletons. Number = 22 to 24. Measurements in centimetres. 



Femur, F : m , = 38'075, a, = T494, Vl = 3'924. 



Tibia, T : m 2 = 29'800, <r 2 = T576, v z 5'289. 



Humerus, H : m 3 = 27'565, <r 3 = 1-109, v 5 = 4'022. 



r n = 0-8457. 



r 13 = 0-8922. 



r 23 = 0-7277. 



i n = 127-90, 2 12 = 3'8937, V 12 = 3'0444. 



t 13 = 138-37, 2 13 = 2-6930, V 13 = T9462. 



in = 108-36, 2 23 = 4-1022, V^ = 3'7857. 



p = 0-6006. 

 p = 0-3904. 



Femur and tibia : 

 Femur and humerns : 

 Tibia and humerus : 

 Index, F/T : 

 Index, F/H : 

 Index, T/H : 



Hence we may conclude as follows : 



(i) The absolute lengths of the long bones differ from those of the 

 skull in being very closely correlated. 



(ii) The use of indices for the long bones would appear to mini- 

 mise, rather than, as in the case of the skull, to exaggerate this 

 correlation. 



(iii) If we measure, however, organic correlation of the indices by 

 ppoi we shall find index correlation less than absolute length corre- 

 lation for both long bones and skull, and in both cases the former 

 comparatively small as compared with the latter. 



(iv) The results for the 24 female skeletons, although based on 

 but few data, serve on the whole to confirm the male results.* 



(6.) From the above examples it will be seen that the method, 

 which judges of the intensity of organic correlation by the reduction 

 of all absolute measures to indices, the denominators of which are 

 some one absolute measurement, is not free from obscurity ; for this 

 method would give the major portion of the observed index corre- 

 lation had the parts of the animal been thrown together entirely at 

 random, i.e., if there were no organic correlation at all. The follow- 

 ing additional remarks may be of interest. The results (iv) (vi) 

 show us that the correlation coefficients of indices are functions, not 

 only of the correlation coefficients of absolute measurements, but also 

 of the coefficients of variation of the latter measurements. Hence, 



* The fact that the male is more variable in height-sitting, in femur, and in 

 tibia tban the female, while she appears to be more vai-iable than he is in stature, 

 led me to prophesy, in my paper on " Variation in Man and Woman," that the 

 female would be found to be more closely correlated in the bones forming stature 

 than the male. This appears to be the case for the femur and tibia of Ainos. 

 VOL. LX. 2 P 



