EXPLANATION OF MENDELIAN RESULTS 199 



will always remain in the hybrid condition and will continue 

 to split up as before in the characteristic Mendelian proportions. 

 We see, then, from Mendel's experiments, that in the case of 

 peas, where one of the two contrasted characters is dominant 

 over the other, the offspring of the first hybrid appear in the 

 proportion of three apparent dominants to one recessive, but that 

 further analysis shows that the real proportion is 



1 D : 2 D (K) : 1 K. 1 



This proportion has since been observed not only in peas but 

 in a large number of other cases, including animals as well as 

 plants. It is evidently a phenomenon of very common 

 occurrence, though we cannot as yet say that it occurs 

 universally whenever two forms with contrasted characters are 

 crossed. Moreover, as we have already noticed, the phenomenon 

 of dominance is not always shown, and the hybrid may exhibit 

 a character intermediate between those of the two parents or 

 different from either. The occurrence of Mendelian propor- 

 tions, however, is sufficiently frequent to demand explanation 

 and this explanation we must now seek. 



Suppose we take a large number of black and an equal number 

 of white counters, all alike in shape, size and weight, and after 

 shaking them up thoroughly in a bag, draw them out two at a 

 time, and one on top of the other, without looking. Each pair 

 that we draw out may consist of white over white, black over white, 

 white over black, or black over black. If we draw out a sufficiently 

 large number of pairs entirely at random in this way and then count 

 them, we shall find that they occur in the proportion : 1 W W : 

 1 B W : 1 W B : 1 B B, or, since B W and W B may be looked 

 upon as the same, 1 W W : 2 W B : 1 B B, or one all white, two 

 white and black, and one all black ; this being, of course, only 

 what is to be expected in accordance with the mathematical law 

 of probability. This is also the same as the simple Mendelian 

 proportion, and at once suggests that the latter may, perhaps, be 

 explained in a similar way as the result of random union of 

 characters in accordance with the laws of chance. 



We know that each individual plant or animal produced by. 

 sexual reproduction is formed by the union of two germ cells or 

 gametes. Now these gametes are formed in very large numbers 



l This is sometimes written more fully 1 D D : 2 D (R) : 1 R R. The reason 

 for so doing will be obvious from what follows. 



