504 Proceedings of the Royal Society of Edinburgh. [Sess. 
Returning now to the mating of red and white we have the red parentage 
a (R, R) + A (R, W); 
and the white parentage 
(a + h) (W, W) 
should give 
bh(a + h) (W, W). 
In this case (a + A ) 2 — 135, so that 1’45 white cattle should occur. When 
red mates with roan in like manner about sixteen white calves should occur 
though only four are found. 
These figures are, of course, based on the first group, and if all the 
groups were given equal weight the number of white to be expected in 
groups two and three would be less, but then likewise also the numbers 
of roan in group one. 
Two more matings require to be considered, roan and roan, and roan and 
white. In both these cases it is to be noted that only about half the white 
turns up which might be expected. This is in line with what has been 
observed as regards expected whites. It is not necessarily against 
Mendelism. Many extracted races are comparatively sterile, and if such 
be proved with regard to white shorthorns it would explain not only the 
defect in expected whites but also their unpopularity from a breeder s point 
of view. 
Apart altogether from refined theories the general aspect can be 
explained roughly on a Mendelian basis, and if it is so then the correlation 
coefficients may be calculated on the principles already enunciated. As 
the hybrid is distinct the correlation should be (par. 6) *5. Several 
factors, however, lower this ; the dominant is greatly in excess and the 
recessive in defect (par. 30). This makes a marked difference. Also the 
recessive only appears in half the number expected when roan and roan, 
etc., are mated ; this also lowers the correlation. For let the population be 
2 (a, a), 4 (a, b), 2 (b, b), and let the recessive only appear only in half 
numbers, and we get a correlation table : — 
Parents. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
(a, a) . 
8 
8 
(a, b) . 
8 
16 
8 
(b, b) . 
4 
4 
Which gives r = '454 instead of r = '5. 
