K. 1'eakson 



225 



that «3-1 = 0-0=0-.,= ... =o-„ is iiol true, und lurthor tliat hp^Jip,, l>p,--- üi'C measured 

 froni different mcans, \ve have no ä priori right to suppo.so it ought to be satisfied. 



(8) It is not witluiut intercst to follow iij) wliat woiild happcii in man and 

 horsc if, with oiir present imnibers, we .siipposed the condilious for a stable popula- 

 tioii to be rcally satisfied. Let us select aboiit the deviation h from thc common 

 mcan for s generations, thcu the otfspring would have a probable'deviatiou from 

 that mean of 



l-p 



If we then ceased to select, bat bred tho offspring among themselves for t 

 generations, the offspring of tho ith generation wouhl havo a probable deviation 

 ii'om the mean of 



e.lr^ .(\/2ryh. 

 l-p 



Lot US turn these results into numbers, remembering that e = '6244 and 

 p=-3184. 



Result of sclecting all ancestry for one generation = '62h 



„ „ „ two generations = ■82/t 



„ „ „ three „ ='89Ä 



„ „ „ innumerable ,, = '92h. 



In other words indefinitely long selection would only rai.se us to '92 of the 

 desired character. We should therefore not get the whole of the desired character 

 withont selecting bejjond it. But on the other band by merely selecting for two 

 generations we should get within ten, and for three generations withia four per 

 Cent, of the possible maximum of indefinitely protracted selection. Hence selec- 

 tion for a very few generations would raise the selection rapidly to within a small 

 percentage of the maximum result. 



Generations ufter which selection is stopped and simple hreeding-in of seleded 



stock follows. 



Next let US suppose selection stopped and the stock to breed-in or mate with 

 its likes. The above table shows how it would slowly degeneratc. The essential 

 Biometrika n 29 



