A. Barrington and K. Pearson 
443 
Rose crossed by Earl Clarence 2nd (R) gave the white cow calf Minnette *. Such 
cases may be very rare indeed but, if authentic, reduce the Mendelian formula 
to a rough empirical statement of a statistical ratio ; they are inconsistent with 
any theory of a pure gamete. 
If we pass from the question of purity in the supposed homozygous elements 
to the first hybrid generation, we find in the Tables II. and III. of our random 
samples 90 cases of (RR) x (IFW^), and the result is (Ro) the assumed hybrid in 
85 cases or in 94'5 per cent, of cases, but particoloured (RW) has occurred in two 
cases, white marking in one case and whole red in a third ; while travelling 
beyond the field of our working sample {RR)x( WW) is actually recorded to 
have given (ITTF). Crossing the hybrid generation together, we should expect: 
(Ro) X (Ro) = (RR) + 2 (Ro) + ( WW). 
Our actual numbers on the random samples are : 
514 (Ro) X (Ro) - 86 (RR)^ + 31 (RLW) + 35 (RW) + 278 {Ro) + 84 ( WW), 
as against the Mendelian formula : 
= 128-5 (RR) + 257 {Ro) + 128-5 ( WW). 
The (Ro) is thus seen to be, like (RR) and (IFir), a non-homogeneous group ; 
we are compelled to suppose that some (Ro) have white marking and others parti- 
colour determinants latent in them. If we cross the hybrid (Ro) by the original 
stocks, we have : 
656 (Ro) X (RR) = 243 (RR) + 46 (RL W) + 39 (R W) + 324 (Ro) + 4>iWW), 
as against the Mendelian formula : 
= d28 (RR) (Ro). 
The close approximation to the Mendelian number of (Ro) is noteworthy, but 
the appearance of 4(lFir) is again impossible unless some of the reds are to be 
treated as heterozygous. The latent white marking and particolour determinants 
are again manifestly needed. 
Lastly, we take the case of (Ro) x(WW): 
74 (Ro) X ( WW) = 1 (RR) + 1 (RL W) + 1 (R W) + 47 (Ro) + 24 ( WW), 
as against the Mendelian formula : 
'37 (Ro)+S7(WW). 
Here again we are compelled to assert a heterozygous white, or if we treat the 
individual instances of (RR), (RLW), and (RW) as heterozygotes and club them 
with the (Ro), the proportion 50 to 24 is very far from the Mendelian equality. 
Of course the same process could not then be applied to explain the anomalies in 
the crosses (Ro)x(Ro) and (Ro)x(RR). The anomalous cases in these crosses can 
* Coates' Herdhoolc, Vol. xxxviii. p. 231. 
t No attempt is made to express anything but (RR) and {WW) in Mendelian form, the constitution 
of the other individuals being unknown. 
56—2 
