js.s MR. G. UDNY YULE ON THE ASSOCIATION 



Ssj = 2 8/, = 2 (8<, + 8<^) 



/ 1 .T Oo I ^^~ i I 2 I >JL ^/i ft* *9* /4\ *4* 



OCpi . Ou)."> O(Dn OQ)"* I 



u)i <p . 



X r y^ |\ / - |\ I | flflfl 



= 0. 

 Therefore 



(17), 



that is to say, there is no correlation between errors in association and errors in 

 surplus. Although we were to select out of the whole population a particular group 

 with an abnormally large surplus ratio for any one attribute, we would not expect 

 any definite divergence from the normal in the associations of that attribute observed 

 within the group. 



Of course all the expressions we have given above are for standard errors ; the 

 values of the probable errors will be obtained by multiplying them by the constant 

 674489. . . . 



V. ILLUSTRATIONS. 

 A. Miscellaneous. 



(1.) Small-pox attack rate and vaccination. 



(2.) Examples from Mr. GALTON'S " Natural Inheritance" : 



Assortative mating according to temper. 



Association of temper in fraternities. 



Inheritance of artistic faculty. 



Assortative mating according to stature. 

 (3.) Examples from DARWIN'S " Cross and Self Fertilisation " : 



Cross fertilisation of parentage and tallness of offspring. 



Pure self fertilisation and crossing of flowers on same plant. 



(A). Miscellaneous. 



44. (1.) Small -pox and vaccination. 



At the very commencement of this paper death-rates, with and without the adminis- 

 tration of an antitoxin, were suggested as affording suitable examples of " association." 

 Death-rates by small-pox amongst the vaccinated and unvaccinated would form such 



