122 NATURAL INHERITANCE. [CHAP. 



connected by the law of Frequency of Error. But 

 though the system of y values and that of i/ values 

 may be both subject to the law, it is not for a moment 

 to be supposed that their Q values are necessarily 

 the same. 



We have now to show how a large population of 

 animals becomes reduced by the action of natural 

 selection to a smaller one, in which the M value of the 

 statures is unchanged, while the Q value is decreased. 



To do this we must first consider the population to 

 have grown up entirely shielded from causes of pre- 

 mature mortality ; call their number N. Then suppose 

 them to be assailed by all the lethal influences that have 

 no reference to stature. These would reduce their 

 number to N', but by the hypothesis, the values of 

 M and of Q would remain unaffected. Next let the 

 influences that act selectively on stature, further reduce 

 the numbers to S ; these being the final survivors. 

 We have seen that : 



y = ihe number of individuals who have the stature 

 Px, counting those who have the stature P, as 1. 



2/'=:the number of times in which Pcc is the most 

 favoured stature, counting those in which P is the 

 most favoured, as 1. 



Then yy' = ihQ number of times that individuals of 

 the stature Px are selected, counting those in which 

 individuals of the stature P are selected, as 1. 



As the relation between y and x, and between if and 

 x are severally governed by the law of Frequency of 

 Error, it follows directly from the formula by which 



