484 THE GRAMMAR OF SCIENCE 



character H^ who had mediocre mid-parents for further 

 ancestry, i.e. Ho = H3 = H^ = ... =0. Actually mid- 

 parents with positive deviation H^ are likely to have 

 had ancestry above the mediocre. Now let us see what 

 happens to our .5H1 offspring, if we do not again select 

 out of them those of character H^. Their offspring will 

 have a mid-parent .5 H^ and a mid-grandparent of Ho = H^ ; 

 all the ancestry further back will be of zero deviation, 

 i.e. mediocre. Thus by the law of ancestral heredity 



or the offspring are like their parents, i.e. The stock will 

 now breed true to one-Jialf the selected character. 



The reader will now be able to grasp the meaning of 

 our second column. Thus, after four generations of select- 

 ing Hj, the offspring will have .9375 of the character, 

 and will, without further selection, now breed true to this 

 extent. After six generations of selection the offspring 

 will, selection being suspended, breed true to under 2 per 

 cent divergence from the previously selected type. 



In the third column are given the variabilities of the 

 offspring after each selection,^ and we see that if selection 

 were to have gone on for an indefinite number of genera- 

 tions, the variability would not have been reduced by 

 more than some i i per cent. Selection, however long 

 continued, cannot reduce the original variation of the race 

 by more than this amount. This is the solid fact to be 

 met by those who assert an indefinitely great variability 

 at any earlier stage of selection (p. 475). But even this 

 reduction is not admissible in selection in nature, it is 

 only a theoretical maximum limit. For in nature we do 

 not find only individuals with one definite value of a 

 given character survive ; nature aims at a type, i.e. selects 

 round it, the surviving individuals having a definite 

 variability about this type. With this, the essential 

 feature of natural selection, it may be shown that our 

 second column giving the change~of type still holds, but 



1 All the ratios of variability are equal, because to assume all the back 

 ancestry to be mediocre is really a form of selection carried on indefinitely. 



