(> OX A GENERALISED THEORY OF ALTERNATIVE INHERITANCE, ETC. 



or not with the biometric observations on such populations. If they are consistent, it 

 shows their possibility, but does not prove their necessity. If they are not, it shows 

 they are inadequate. The present investigation shows that in the theory of the pure 

 gamete there is nothing in essential opposition to the broad features of linear 

 regression, skew distribution, the geometric law of ancestral correlation, etc., of the 

 biometric description of inheritance in populations. But it does show that the 

 generalised theory here dealt with is not elastic enough to account for the numerical 

 values of the constants of heredity hitherto observed. 



It will be time enough to consider other more or less general Mendelian formulae 

 when there is far better evidence than exists at present that they cover a real range 

 of observation, and have not been solely invented to describe isolated experiences, the 

 numerical results of which are not in complete accordance with simple Mendelianism. 

 Given such neo-Mendelian formula?, there is a perfectly straightforward mathematical 

 method of applying them to randomly mating populations, but that method is 

 excessively laborious, and the biometrician may well hesitate to undertake the task 

 of their investigation. A few minutes suffice to invent a Mendelian formula, but 

 weeks of labour may be involved in testing whether it leads to legitimate results 

 when applied to sexually crossing races. Let us therefore have a few simple general 

 principles stated which embrace rill the i'acts deducible from the hybridisation 

 experiments of the Mendelians; these can form the basis of a new mathematical 

 investigation, but it is idle to undertake such an investigation so long as Mendelian 

 Principles remain in a state of flux. 



Any combination of the theory of pure gametes here discussed with homogamy, or 

 with fertility correlated with homogamy, or again with prepotency of individual or of 

 type, would emphasise the correlations which we have found above to be too low; 

 but such hypotheses would involve a fundamental alteration in the formula 



(ft + a') (A + A') = A + A' + ' A' + AA'. 



Such a formula would then give the j>oxsil>ilitiex of the cross, but the proportions of 

 these possibilities actually occurring would be quite different* 



Such loading of the possibilities not only of the individual couplet but very 

 probably of associated couplets in the constitution might conceivably enable us to 

 deduce better values for the ancestral and collateral correlations. But it would 

 abolish not only the simplicity of the fundamental Mendelian formula, it would also 

 involve lengthy preliminary studies on homogamy, fertility, and prepotency before 

 any effective formula could be propounded. 



> Toss two pennies, and the result of 4n tossings will closely approximate to the distribution 

 n (HH + 2HT + TT). Load one or both coins, and the possible variations will still be HH, HT or TT, but 

 their proportions will be far from n : 2ft : n. 



