MENDEL'S LAW. 277 



tion of its progeny would then be, supposing the primed characters to 

 be recessive : 



Aa' Bb' Cc' AV ( ABC N, ABC Nn', ABC A 7 ', etc. 



(hybrid.) \ (progeny.) 



The total number of types occurring in the progeny is 3"; the 

 number of fixed types (homozygote) is 2". The number of types 

 with r latent characters is nCr2 n ~ r , where nCr is the number of com- 

 binations of n things taken r at a time. Only one type, namely, 

 A'B'C N', consisting entirely of recessive characters, could be 

 selected out without getting with it one or more heterozygote types. 

 But by saving the seed of each tree of this generation separately, and 

 observing which, with close fertilization, would reproduce true to type, 

 we could at once secure, in fixed from, all the 2 homozygote types. 



If the tree happened to be of the type VgSb, discussed above, in 

 which all the characters of its original parents are present, the above 

 process of analysis would give, not only all its original parents, but 

 all possible combinations of them, and each in a form that would 

 reproduce true to seed, if self-fertilized. If it were of the type VgB, 

 in which some of the parent characters are missing, it would give all 

 the original parents whose characters are all present, together with 

 all their combinations with characters that are present from other 

 parents, some of whose characters are missing. Since apples are con- 

 fessedly many times multihybrids, it is probable that a very large 

 number of seed would have to be used to secure all the types capable 

 of resulting from combinations of the N pairs of characters. 



Suppose we neglect all but essential characters; we might, in the 

 case of the apple, reduce the number of types to a point which would 

 make the task a possible one. If this were done, it would mean much 

 to the plant breeder. Having a large number of fixed varieties of 

 apples, supposing, of course, that Mendel's law holds, we could select 

 parents with a view to producing any combination of characters we 

 desire. Did not Downing, many years ago, assert that much better 

 results could be secured in producing new seedling apples by using 

 seed from strains that had already been propagated several genera- 

 tions from seed? And why? Possibly because the continuous prop- 

 agation from seed tends to produce pure strains. If the seed used 

 were always produced by self-pollination, there certainly would be a 

 tendency to pure strains if Mendel's law applies. This problem is 

 worth working out, both from practical and from theoretical grounds. 

 It could be done more easily with strawberries, or with some of the 

 common ornamentals that do not reproduce true to seed. This 

 method of analysis is one way of testing Mendel's law in such groups. 



This subject is too new to permit of any useful generalizations 



