70 THE EVOLUTION OF LIVING BEINGS, 



while 



„This process is repeated after each fertilization, 

 „so that if there are n fertilizations in succession, 

 „the total number of homozygotes x, becomes 

 »^ = i+a)2 + {i)'.... up to a)». 



„This expression reduces to ;« = ^" — ^ where n 



2" 



„is the number of fertilizations. 



„For the heterozygotes, y, on the other hand the 



..formula is simply 



y = (i) • 

 ..These then are the formulae in case we deal with 

 „but one pair of characters. They express: 

 i) the proportion of aU the organisms that will be 

 homozygotic (or heterozygotic as the case may 

 be), after a given number of n fertilizations. 

 2) also they of course express the relative proba- 

 bility for a given case, as to whether it shall be 

 homozygotic or heterozygotic. 

 2) „ When we are to deal with two or more pairs ofcharac- 

 „ters, the problem may be attacked in two ways. 

 ..One is by the general principles of probabiUties ; 

 ..the other is by analyzing the case of two or more 

 ..characters, in the way exempUfied above. 

 „The two methods give the same results. 

 ..The first method is by far the simpler. It is 

 ..merely an appUcation of the principle that when 

 ..we know the probability for each of two or more 

 ..things separately, the probability that all of them 



