74 PROFESSOE K. PEARSON ON A GENERALISED THEORY OF ALTERNATIVE 



to be learnt from the present investigation is, however, that there is no essential 

 repugnance between any of the main results of the biometric school and a theory of 

 the pure gamete, but, on the contrary, it is perfectly possible to test such theories by 

 biometric methods. We may fairly ask anyone who propounds in future a Mendelian 

 or pure gamete formula as a general theory of heredity, to remember that it involves 

 in itself definite laws regulating the reproduction of a population mating at random, 

 and that it is incumbent on the propounder to test whether or not such laws are 

 consistent with what we already know of the inheritance statistics of such popula- 

 tions. When we remember that deducing all the effects of such a formula within the 

 whole field of inheritance will almost always form a very laborious piece of 

 mathematical analysis, there seems a touch of scientific irresponsibility in propounding 

 an immense variety of formulae to suit one or other special case, and the modifying or 

 withdrawing them when they are found to fail in another. 



(10.) PROPOSITION VIII. To find tlic Per/region and Correlation of Brethren 

 on the Theory developed in thix Paper. 



We shall suppose the group of brethren to consist of 4^ members, or any pair of 

 parents to have a family of 4^. 



Consider first parents of one couplet only, the offspring of the 16 possible pairs are 

 nveii in the table below : 



Father. 



<i 4- a. 



. + A. 



4 X 



A + a. 



A + A. 



Now let us take every pair of brothers out of eacli of these 1G families and form a 

 correlation table of brothers. The following table gives the distribution of the 

 various types : 



