Data for the Froblem of Evolution in Man. 319 



when the two organs bear a certain ratio to each other. For example, 

 we hardly mean by a homogamous union in man and woman with 

 regard to stature, a case of husband and wife of equal height, but 

 rather a case of their being relatively of equal height, or, say, the ratio of 

 their statures = 1-08.* 

 For this reason I put 



and asked Mr. L. N. G. Filon, M.A., to work out for me the constants 

 of the correlation surface, whose ordinate is ^' = ^ x n. He has kindly 

 provided me with the following results, the analysis being straight- 

 forward but lengthy. 



Let nil + hi, m2 + h2 be the mean values of the organs in the parents, 

 each parent being repeated for each of his or her offspring, ms + h^ = 

 mean value of offspring's organ, or hs be the progression in the character 

 due to the influence of homogamy. 



2i, ^2, the standard deviations of the parents' organs, these being, as 

 in the case of hi and ho, weighted with their fertility. 



^3 = standard deviation in offspring's organ, or i'3 - 0-3 is the change 

 in variability due to the homogamous influence. 



Psh P32 = the correlations between parent and offspring when we 

 take all, and not a single offspring from each union. 



P12 the coefficient of assortative mating when we take each pair as 

 many times as there are offspring of the union. 



We have : 



_ ^ _ {Pl^l -P20-2) (Pim -P2m.2) /-x 



(Tl 0*2 S'^ + (piO-i - P2(T9^'^ ' " " 



h _ rzi + r32 {pi(Ti -P20-2) (pim -P2m2) ^ ^^^y 



0*3 1 + ri2 S'^ + (piO-i -P'2(T2Y 



This last result may be written 



[h _ ^'31 - ^•i-2?'32 h rs2 - ri2? 31 h /-\ 



0-3 1 - 7i2- O-j 1 - ri2-' 0-2 

 V 2 o _ {piO-l - ri2p2^2f \ 



\ s^^pW-\-p'^^^-'lri2pip2^i(T^j 



V = [\ - {n2PlCri-p20-2f \ /^x 



\ 52 +^i2o-i2 +^2 W - 2ri2^lj?20"lO-2/ 



232 = 0-3^ /l - {ri^Pl^i-r2iP2^2f \ /^iy 



+ +^2W - 2ri2^1^20-l0'2/ 



* This is how I have looked at the matter in " Data for the Problem of Evolu- 

 tion in Man. Ill," ' Eoy. Soc» Proc.,' vol. 66, p. 31. 



