INHERITANCE, WITH SPECIAL REFERENCE TO MENDEL'S LAWS. 55 



for (ii.) ; it can only do so satisfactorily, however, if it does not contradict the results 

 of (i.). Hence arises the present attempt to develop in one direction a generalised 

 theory of the action of the germ-cell. 



As we have frequently had to assert, the laws investigated under (i.) have nothing 

 whatever to do with any physiological hypothesis. That a physiological hypothesis 

 leads to them is not much test of its validity it is a necessary, but riot sufficient, 

 criterion of its correctness. If, however, it contradicts them, we are bound to 

 discard it, and seek for its modification or replacement. The present study is an 

 attempt to see how far one generalised pure gamete theory leads to results in 

 accordance with the law of regression and the known nature of the distributions of 

 offspring in populations. 



('2.) Nature of Hypothesis adopted. 



'We start with a zygote consisting not of a single protogenic pair AA, but built 

 up of n such pairs, 



AjAj -|- A.iA.i -|- A 3 A 3 -f- . . . -j- A,,A,,. 



We suppose this to produce gametes which unite with those of a similar allogenic 

 zygote 



%! + 3 a 2 + a 3 3 + . . . + . 



Any element of the protogenic gamete must unite with the corresponding element 

 of the allogenic gamete, i.e., A,, with a r , and by the fundamental principle (i.) above, 

 this gives rise to the four possibilities 



A,.a r , 



A,a, , 

 a r A,. , 



which are all of the same constitution. The result is the hybrid group, symbolised by 



a^ + j,A 3 + 3 A 3 -(-...+ ,,A, 



the perfect multiple heterozygote. 



The population will now be supposed to consist of any number of such perfect 

 heterozygotes, which we shall suppose to again cross. We shall now have 



a r A,. X a,A r = r a r a r 

 a r A. r 



lA,A r , 



