198 Prof. F. Y. Edgeworth on 



cubit and stature being here, as for the most part they must 

 be, identical with those used for the simpler calculation (at 

 p. 193). 



Table III. 



Height of knee 

 (above 20-5). 



Statures, 

 (above 67'2). 



Corresponding 

 cubit. 



22-9 



21-4 



21-6 



21 



21-7 



22 



21-1 



206 



21-6 



21-4 



20-6 



20-8 



21 



22-3 



21-4 



72-4 



71*9 



71-5 



70 



70-3 



72-2 



69 



68 



716 



68-4 



68-3 



68-4 



70-2 



71-1 



68-3 



19-3 



18-7 



18-8 



18-4 



18-6 



19-6 



18-4 



18-3 



19-3 



18-2 



18-1 



18-7 



18 



194 



18-8 



321-4 



1051-6 



280-6 



The mean deviations of cubit and of stature are as before 

 (in units of the quartiles) 1*17 and 1-66. The mean deviation 



of knee-height is ( — tt 20*5 W '8 (20*5 in. being the mean 



and '8 in. the quartile for the height of knee ; Galton, Proc. 

 Boy. Soc. 1888, Co-relations, Table I.) = 1'16. According to 

 theory the sum of the mean positive deviations of the stature 

 and knee-height divided into the corresponding mean devia- 

 tion of cubit should yield a quotient '42. In fact 



l-17-*-(l"16 + l-66)=-415. 



This consilience between fact and theory will appear all 

 the more striking when it is mentioned that the anthro- 

 pometrical observations from which Mr. Galton educed his 

 coefficients *8, '9, and *8 were not coincident with those by 

 which I have verified the theory built upon those coefficients. 

 This theory is readily extended to the case of many variables. 

 One way of looking at the whole matter is as follows : — 

 Beginning with the case of three variables — the familiar 

 x } y, z — let us suppose that w, the probability of particular 

 values of x, y, z concurring, = Je~ n dxdydz, where R=a^ 2 

 + fo/ 2 + cz 2 + 2fyz + tyxz 4- 2hxy ; and let us inquire how, 



