122 NATURAL INHERITANCE. cHAr,

connected by the law of Frequency of Error. But though the system of y values and that of y' 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 premature 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=the number of individuals who have the stature P±x, counting those who have the stature P, as 1.

y'=the number of times in which P±x is the most favoured stature, counting those in which P is the most favoured, as 1.

Then yy'=the number of times that individuals of the stature P±x are selected, counting those in which individuals of the stature P are selected, as 1.

As the relation between y and x, and between y' and x are severally governed by the law of Frequency of Error, it follows directly from the formula by which