Using the foniiiila 



K. Pkahson and A. JjKk 393 



= -5585 (r„ >•, ,• + ?v,. )•,,) (x ), 



I lind tlic lolliiw iiiLf nsiills givi'ii in 'raLlc XI 11. The agivcincnt dt' tiiu 

 obscrvcd iuul calcnlati'd icsnlts is not as close as in the j>ri'vioii.s ca.se ot' cross- 

 parcntal lieredily, but the sorii's t'roni wliicli the ubseived vahies ari^ dctcrniined 

 are not lialt' as large. l'urthcr, the ealciilated vahies depend on tlie coeHicientH 

 of dircct collateial inlieritance, aiid in wniking out thesc \ve luivi; always coITolated 

 eider with younger brotlier. On the uther band it did not seeni worth while in 

 ealcuhiting the eross-coetticients to separate our rather sinall ainount ol' niaterial 

 up into two groups and distinguish betvveen the rehitionship of, say, stature of 

 clder brother to spaii of younger brothor, and again, stature of younger bi'other 

 to spaa of eider brother. This ditierence of treatnient is no doubt a source of some 

 of the observed irreguhirity, but the bulk of it is due to the smalluess of our group 

 of brothers. 



The nieau error of the results froin (vii) is 'OIO and from (x) is ■020, but (vii) 

 has errors of '043, '043 and •039 larger than the niaxiniuni '034 reached by (x). 

 The first formula gives seven vakies greater and five less, the second forniula gives 

 six greater and six less than the corresponding probable errors in Table XII. Thus 

 on the whole Formula (x) is .slightly the better, but the advantage is .so small 

 tliat for practieal convenience (vii) niight be well used for both. I do not see 

 why the nunierical factors in (x) and (vii) should necessarily be equai or nearly 

 ecpial ; still less is there any reason why the faetur.s in these blood relationship 

 forniulae shoiild be nearly equal to tlie value of the factoi- in (iü), the einpirieal 

 fornuila for assortative niating. But it is worth noting that for most practieal 

 purposes a connnon formula with a mean nunierical factt)r of ■55,") will give results 

 quite within the limits of the probable errors of our material. 



It thus appears that my original proposition as to cross-heredity, based on the 

 assumptions of equality ol all inheritance-coefficients and of the corresponding 

 organic correlations in the pair of relatives, is not correet ; the factor of '5 in the 

 original proposition has in the case of man to be replaced by a value lying 

 betweeu "5 and "G, the mean value being ■öö.'J. We have not at preseut material 

 enough to test how far this number has any validity beyoud cross-heredit}- in 

 man*. The cases I have data for, however, do show an excess over '5 of the 

 same order as we find in the case of man, and I hojoe shortly to publish fnrther 

 results for cross-heredity, closely bearing on this poiut. 



(xi) General Cuncliisiuns. 



If readers of the present paper feel that on certain points it is inconclusive, 

 I think this niust be largely attributed to the inherent difficulties of the subject. 

 The further we advance, the rnore comjjlex the problem becomes, and the -wider 



* A Short series in Apliis has been dealt witli by Dr Wanen: see Hii^metrika, Vol. i. p, 14'i. The 

 value of the factor there given is '5 for one character and '(58 for the secoud, giving a mean ixtreiilal 

 factor of ■.5U for Apliis as against '06 for man. 



