410 



Prof. Karl Pearson. 



from single pairs, are given in the table below. This case, which 

 offers some striking applications of Galton's law, I postpone for the 

 present. 



Collateral Heredity according to Galton's Law. 



Eelationship. 



Correlation. 





'4000 





-1500 





-0625 





-0750 





-0344 





-0172 



Second cousins once removed. . . . 



-0082 





-0041 



Had we regarded second cousins as grandchildren of brethren, we 

 should have found 0'0090 instead of 0*0172 for example, showing 

 the degree of approximation of the incomplete theory. 



(12) On Gross Heredity. — In my memoir on heredity cf 1895, I 

 have defined cross heredity as the correlation between different organs 

 in any two relations.* If we consider Galton's law of ancestral 

 heredity to be applicable to the inheritance of any character or 

 quality whatsoever, then we can obtain from it a solution of the whole 

 problem, of cross heredity. This solution seems so simple and 

 plausible that it deserves careful consideration, and I hope shortly 

 to be able to test it by the measurements in my possession. 



Let A and B be any two relatives ; 1 and 3 represent any two 

 organs in A, 2 and 4 the same organs in JB. 



Now suppose we investigate the manner in which the index 1 to 3 

 is inherited by B, i.e., let us find the correlation between the indices 

 1 to 3 and 2 to 4. Let p be the coefficient of heredity between the 

 degrees of blood A and B, and suppose it by Galton's law to take 

 the same value for all qualities and characters, then r will be the 

 correlation not only between 1 and 2, and 3 and 4, but also between 

 the indices 1 to 3 and 2 to 4. The value of this correlation was given 

 by me in ' Roy. Soc. Proc.,' vol. 60, p. 493, Equation iv, and is 



P Vvi+v-i— 2r iz v l v z *Jv£ + Vi — 2r 2 4^4 



where v h v 2 , v d , v± are the coefficients of variation of the four organs, 

 and the r's are their coefficients of correlation. 



Now if there be no secular selection v x — v 2 , v 3 = and r 13 = r 2 i ; 



* < Phil. Trans.,' A, vol. 187, p. 259. 



