208 
J. p. LOTSY. 
„lABAB + lAbAb-\-laBaB-^lahah + ?.ABah+9.AbaB-{- 
„2 ABAh + 2 ABaB + 2 Abab + 2 aB ab = 16. 
„It will be observed that of the entire 16, the first four are purehomo- 
„zygotes , the second four are imre hétérozygotes (heterozygotic with 
„ respect to both characters) while the last are mixed (honiozygotic with 
^respect to one character, heterozygotic witli regard to the other). 
„Letting x = pure homozygotes, ?j = pure hétérozygotes, z — mixed, 
„we find thus that : 
- = l.. = i. . = !.-.... 
,_,Now, by an analysis of the sort already given, it will be found that 
„at the next self-fertilisation x remains x, y breaks up, '/4 of thèse be- 
^,coming x, ^2 becoming z and ^4 remaining^/; z breaks up, ^2 of thèse 
,,becoming x, ^2 remaining z. Now, when we recall that before the se- 
„cond fertilisation x was ^li^i y = 74 ^ — V2 of ail, we see from 
„the above, that after the second fertilisation: 
^ = (i X i) = rê = GT" 
^=0/.xvO + Gx^)-| 
" Î6 "~ V 2'^ ) 
„These are the same formulae for x and y that were obtained by the 
„other method (since here n and m are each 2). This metliod however 
ogives in addition a direct formula for z. 
„It is easy to verify the formulae for three pairs of characters, though 
„of course the conditions become here somewhat more complex. We may 
„now summarise our formulae, and show the results they give in certain 
„examples. 
„Let X — the proportional number of organisms that are pure homo- 
„ zygotes (with respect to ail the characters considered), 
„y — the proportion that are heterozygotic with respect to ail the 
„characters considered, 
,yZ = the proportion that are mixed, 
„v = the proportion that have any heterozygotic characters. 
