496 Prof. Karl Pearson. 



cephalic indices, for no less than 0'4008 of this would remain, if we 

 destroyed all organic relationship between the lengths on which these 

 indices are based. 



Example (d). To find the spurious correlation lettueen the indices 

 femur jliumerus and femurj tibia. 



The following results have been calculated* from measurements 

 made by Koganei on Aino skeletons. (See ' Mittheilungen aus der 

 medicinischenFacultat der K. J. Universitat, Tokio,' Bd. I. Tables.) 



I have kept the sexes apart although there are but few of each. 



3 Skeletons. Number = 40 to 44. Measurements in centimetres. 



Femur, F : m l = 40'845, <TJ = 1'957, Vi = 4792. 



Tibia, T : r^ = 31'740, <r z = T577, v z = 4'970. 



Humerus, H : ma = 29'593, <r 3 = 1*337, V 3 = 4-517. 



The following coefficients of coiTelation were calculated directly : 



Femur and tibia : r 12 ='0'8266. 

 Femur and humerus : r^ = 0'8585. 

 Tibia and humerus : r^ = 0'7447. 



From these were deduced by the formulae of this paperf : 



Index, F/T : t w = 128'75, 2 12 = 3*7075, V 18 = 2*8795. 

 Index, F/H : z ls = 137'92, 2 13 = 3'4084, V 13 = 2'4714. 

 Index, T/H: i 23 = 107'02, 223 = 3-6675, Y 23 = 3'4271. 



Hence we find for the correlation of the indices F/H and T/H : 



p = 0*5644. 



But the spurious correlation, if the bones had been grouped at 

 random would have been 



Q = 0-4557. 



* I have to thank Miss Alice Lee for a considerable part of the arithmetic work 

 of this example. 



f The values for the indices are not in absolute agreement with those to be 

 deduced from the lengths, for it was not always possible to use the same skeleton 

 for femur and humerus as for tibia and humerus, i.e., sometimes one or other bone 

 was missing. For the same reason, the constants for the absolute lengths do not 

 agree entirely with those given for Ainos in my paper on " Yariation in Man and 

 Woman" in 'The Chances of Death and other Studies in Evolution/ vol. 1, 

 p. 303), for the simple reason that I there used every available bone, and not every 

 available pair, as here. 



