78 
THE PRINCIPLES OF BREEDING. 
will result from the employment of two individuals of different 
breeds. They understand that, by the coupling of a horse of 
pure blood with an ordinary or indigenous mare, the progeny will 
be half-bred ; they believe that, by the union of this half-bred 
mare with the same father they will have a progeny three-quarters 
bi‘ed; but they cannot comprehend how it is that they have not 
pure blood in the third generation. There is a great deal of 
roguery about these different gradations of blood : interested or 
dishonest dealers talk loudly of J and of blood, but few seem 
to comprehend the real proportion of pure blood which exists in 
a horse that has any deviation from absolute purity. 
It may be therefore received as a principle, that, from the union 
of two individuals of different breeds, a half-bred progeny is pro¬ 
duced ; i. e. containing half of the father and half of the mother. 
Then it is easy to draw up a kind of scale by which we may 
easily determine the degree of pure blood that any generation, 
however distant, may possess; or the proportional quantity of 
pure and common blood which flows in the veins of any horse 
whose progeny is known. 
A recourse to figures is here necessary, in order clearly to ex¬ 
press the proportional transmission of pure blood to races of infe¬ 
rior value. Let us call the horse of pure blood Regeneratrix, or 
express him by the letter R, and he shall be equal in value to 1. 
The mare shall be called Degenereej expressed by the letter D, 
and her value 0. Then the progeny which may result from the 
union may be characterized by the letter A, Amtliore, and it is 
composed of half of the father and half of the mother, and thus 
decimally expressed = 0.50, or 
Then we suppose that this progeny, being a mare, is covered 
by another thorough-bred horse, and the calculation will stand 
thus,— or ^ zz .75, or three parts pure blood. 
We carry it on to another'generation. The progeny shall 
again be a mare, and be covered by another thorough-bred horse, 
and the result is -- or ^ zz .875 z: J pure blood. 
The fourth generation will thus stand, ^ — or = .9375, 
or 44 . 
The tenth generation would give, as the reader may work out 
if he pleases, 4§||: pure blood : and the twentieth would possess 
of pure blood; thus we should constantly approach nearer 
and nearer to the unit expressing the value of the father, but we 
should never quite arrive at it. The deficiency would be so 
slight as not, to any extent worth consideration, depreciating the 
value of the offspring, but the pure blood would never be abso¬ 
lutely reproduced. 
