184 THE ANGORA GOAT, 
mathematicians tell us that the chance of an event 
happening when the operating or controlling circum- 
stances as far as we can know them are given, is always 
susceptible of an accurate evaluation, and a numerical 
measure can be determined of the degree of the defect 
from absolute certainty. This theory is called the 
Doctrine of Chances or Probabilities. This doctrine 
has its origin in our want of knowledge of all the 
causes operating to produce certain effects, and would 
not exist were these causes fully known to us. Let us 
apply this theory to the question of breeding by 
selection. 
If each ancestor of any pair going back for thirty 
generations, has been carefully selected to one type, the 
progeny of this pair must "throw back" thirty-one 
generations, if any variation from that selected type 
takes place. If we calculate the number of ancestors 
that an individual can have in thirty generations, 
which is a problem in geometrical progression, and by the 
algebraic formula for ascertaining the sum of the series, 
we find that they reach the enormous number of 2,147 
millions, and according to the doctrine of probabilities, 
the chances are 2,147 millions to one that no departure 
from the selected type will occur. But the chances are 
in a still greater proportion in favour of the selected 
individual remaining true to the desired type, because 
out of the 2,147 millions of ancestors, some of the 
same individuals would probably be repeated over and 
over again in the pedigree, as we see in the pedigrees 
of pure short-horn cattle, and thorough-bred horses. 
All carefully selected stock are of necessity closely 
bred, the best individuals being usually selected for 
continuing the breed. In most cases in-and-in breeding 
