206 
J. p. LOTSY. 
„remain pure, so that half of ail the progeny are still homozygotes on 
^jthis accouut. Tlie hétérozygotes of course agaiii break up, in the way 
„already set forth, one half into x, the other half remaining ?/. Since ^ 
„included half of ail, this will give 7^ of (= 'j, of ail) as 'j., of 
.//•i (= V4 ail) as^. 
„So the total proportion for the homozygotes becomes after the 
„second fertilisation : 
„This process is repeated after each fertilisation , so that if there are 
„n fertilisations in succession, the total number of homozygotes w be- 
^ = ^ + (D ' + G) ' • • • • *° CD" 
2" — 1 
„This expression reduces to x = , where u is the number of 
^fertilisations. 
„For the hétérozygotes ^, on the other hand, the formule is simply 
„These then are the formulae in case we deal with but one pair of 
,_,characters. Tliey express : 
„1) the proportion of ail the organisms that will be homozygotic (or 
„heterozygotic as the case may be), after a given number n of fertilisations. 
„2) also they of course express the relative probability for a given 
„case as to whether it shall be homozygotic or heterozygotic. 
„2. When we are to deal with two or more pairs of characters, the 
„problem may be attacked in two ways. One is by the gênerai principles 
„of probabilities, the other is by analysing the case of two or more cha- 
„racters in the way exemplified above. The two methods give the same 
„results. The first method is by far the simpler. It is merely an appli- 
„cation of the principle that when we know the probability for each of 
„two or more things separately, the probability that ail of them shall 
„happen is the product of the separate probabilities for each. Now we 
„know that the probability x for the homozygotic condition with respect 
„to one character is : 
