Balanced Crosses 305 



seven differentiating marks 16,384 individuals 

 are required for a complete series. And in 

 this set the group with the seven attributes all 

 in a latent condition would contain only a 

 single individual. 



Unfortunately the practical value of these 

 calculations is not very great. They indicate 

 the size of the cultures required to get all the 

 possible combinations, and show that in ordi- 

 nary cases many thousands of individuals have 

 to be cultivated, in order to exhaust the whole 

 range of possibilities. They further show that 

 among all these thousands, only very few are 

 constant in all their characters ; in fact, it may 

 easily be seen that with seven differentiating 

 points among the 16,384 named above, only one 

 individual will have all the seven qualities in 

 pure active, and only one will have them all in a 

 purely dormant condition. Then there will be 

 some with some attributes active and others 

 latent, but their numbers will also be very small. 

 All others will split up in the succeeding genera- 

 tion in regard to one or more of their appar- 

 ently active marks. And since only in very 

 rare cases the stable hybrids can be distin- 

 guished by external characters from the un- 

 stable ones, the stability of each individual 

 bearing a desired combination of characters 

 would have to be established by experiment 



