542 TRANSMISSION 



to mate without selection. In this treatment we shall assume 

 mediocrity in this back ancestry of the n selected generations 

 of ancestry. 



As was seen on page 539, the character is established in the 



amount given by 1 1 ) H\ , and we shall now show that if 



this offspring be allowed to breed without further selection it 

 will breed true to I of the selected character. 



2" 



In the first generation of offspring after no selection we 

 should have 



of the character H^ in question. 

 This series may be written as 



i/ i\ i/i i 



- i -+-(- + - 



2\ 2" / 2\2 2 2 



i i i i i i 



, =~ h ~+~ * ~~ =i ~ 



2" 2 2" 2 2 n 2" 



The amount of the character present is therefore unchanged. 

 In the second generation of offspring after no selection we 

 should have 



so that the amount of the character present is again unchanged. 



The method here used can be extended to any number of 



generations. We may show that if it be true for the rth genera- 



tion of offspring bred without selection, it will be true for the 



(r+ i)th generation. If i -- - of the character has appeared in 



r generations, then in the next generation the amount of the 

 character should be given by 



