32 Mr. W. Steadman Alclis. On the Numerical 



difference in stature was found to be 2*751 inches, and the standard 

 deviation of its distribution 2 '070 inches. The correlation between 

 difference in stature and size of family was - 0*0236, or greater fer- 

 tility appears associated with small differences. The observations, 

 however, are so few (205) that the probable error of the correlation is 

 0'0471, and thus no stress can be laid on this result. If the reader 

 asks why is not the result in § 7 conclusive, the answer must be, it 

 would be conclusive, if the means of the husbands and wives weighted 

 with their fertility were the same as when they were unweighted ; 

 increased correlation would then necessarily connote that fertility was 

 associated with homogamy. Actually the fact that absolutely taller 

 mothers are the more fertile alters the centre of the correlation table, 

 and somewhat obscures the issue as to whether the whole increase of 

 correlation is really due to homogamy being correlated with fertility. 



That in man, whether from conscious or unconscious sexual selection, 

 there is far more homogamy than has hitherto been supposed, my family 

 data cards amply demonstrate. If in man, then with great probability 

 we can consider it to exist in other forms of life. But the existence of 

 such homogamy is of immense importance for the problem of differen- 

 tiation. The present statistics do not enable us to say whether 

 homogamy in man is definitely correlated with fertility ; they do show 

 that fertility is not a random character, but depends upon the relative 

 size of husband and wife, and thus bring evidence in favour of genetic 

 selection. I can conceive no more valuable investigation than a series 

 of experiments or measurements directed to ascertaining whether 

 homogamy is or is not correlated with fertility, but such investigation,, 

 bearing in mind Darwin's conclusions, should carefully distinguish 

 between exogamous and endogamous homogamy. 



" On the JiTumerical Computation of the Functions Go(ic), Q^ix), 

 and J,.(^cv'^)." By W. Steadman Aldis, M.A. Communi- 

 cated by Professor J. J. Thomson, F.E.S. Eeceived and 

 Bead June 15, 1899. 



1. The complete solution of the equation 



may be written 



y ^ AI,(.j)-fBK4.;), 



where 



on(r) . n(ft+>-) 



(1); 



