A. Barrington, a. Lee and K. Pearson 
253 
(d) contained all dogs with wliite or black, but no red or fawn of any kind, 
(e') contained all red or white dogs or the mixture of these colours with fawn. 
We are now not at all certain that (d'} does not really contain more of black than 
(c'). We worked out afresh a certain number of tables in which {d') was placed 
before (c) but without real modification of result. The fourfold division of the 
red pigment inheritance table was made between (h) and (c), and of the black 
pigment table between (c') and {d') for the first set of cases, and after (b') when 
(d') was placed above (c'). We shall cite these methods as Red A, Black B 
and Black G, respectively. In contingency we took a 36-fold table as our 
standard, choosing the groupings R., Bd., W., F., P. Bk. and M. Bk. used as in 
Tables I and II. We shall speak of this method as Contingency 1). In order to 
compare the fourfold method with contingency methods, 16-fold tables and 25-fold 
tables were worked out to compare with the fourfold tables adopted for the 
inheritance of red and black pigment respectively. These we shall refer to as 
Contingency E, and Contingency F. Further, in order to familiarise ourselves 
thoroughly with the scope and limitations of the new method of contingency, 
beside the investigations by mean square contingency adopted in D, E, F, we 
(a) determined a number of results by mean contingency*; and (6) worked out 
the mean square contingency in a few cases by 144-fold and 400-fold tables. The 
object of the latter was to test on a large scale the exaggerating effect of isolated 
units. The amount of arithmetical calculation involved in this investigation is 
thus not at all represented in the pages of the present memoir, but we believe 
it has been of advantage in enabling us to foi'm just appreciations of the scope 
of the new method of contingency. In future it is likely that all our work on 
colour inheritance will be done by the use of method D, i.e. the application of 
mean squared contingency to groups sufficiently large not to be sensibly influenced 
by unit difficulties. Even with our 36-fold table the smallness of the white 
entries is to some extent a difficulty, but the Contingency F method shows us 
that the separation of the small unit groups of white has not seriously modified 
our results. The results deduced by Contingency D method are singularly uniform 
and steady as compared with those of the fourfold-table methods, and we believe 
if it be adopted generally for such pigmentation problems, it will not only free 
us from any question of pigmentation scale, but afford a good result on a not 
excessive expenditure of calculating energy. At the same time we can hardly 
over- emphasise the need for caution when isolated units are scattered over a 
table divided into a very large number of small classes f. As illustration of this 
we cite the following results for the correlation between siblings — dog and 
bitch — born in different litters of the same parents. 
It will be seen that while the contingency result only increases from '49 
to "51 when we pass from 16 to 36 groups, agreeing well with fourfold table 
results, we spring up to "76 as we increase to 400 groups. In fact, the personal 
* Drapcr^s Research Memoirs I. " Mathematical Contributions to the Theory of Evolution : XIII. On 
the Mathematical Theory of Contingency," p. 31 (Dulau and Co., Soho Square, London), 
f Memoir on contingency, loc. cit. pp. IC and 35. 
