MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
105 
If we examine this table we see that the error in r) amounts to from ‘02 to '025 
when we have upwards of 1000 tabulated cases, but can amount to ’035 when we 
have as few as 700 to 750 tabulated cases. An examination of the values of rj in 
Table VII. shows us that most of our differences with probable errors taken on this 
scale are very sensible. A comparison with Table VIII. shows us that the probable 
error of the median is always greater than the probable error of rj, and accordingly 
the former, being much easier of calculation, may be taken as a maximum limit. The 
probable errors of £, i.e. , the ratio of oy to ay, are more considerable, amounting to about 
•04 for our longer series, and even to '077 in the case of the short series of grand¬ 
mother and granddaughter, but in this case £ actually takes its maximum value 
of 1*291, so that the error is under 6 per cent. ; in the longer series it is under 5 per 
cent. Again, we see that in most cases our differences in the ratio of variabilities are 
quite sensible. It must be admitted, however, that the ratio of variabilities as based 
on the grey blue-green range of eye-colour is not as satisfactory as that based on the 
bay range of coat-colour in horses. In the latter case, one-half of the horses fall into 
the bay range, but only about a quarter of mankind fall into the grey blue-green 
range of eye-colour, and, further, the appreciation of eye-colour seems to me by no 
means so satisfactory as that of coat-colour in horses. 
I have tried a further series of values for the ratio of the variabilities by measuring 
the ranges occupied not only by the tints grey blue-green, but by the whole range of 
tints 3, 4, 5, and 6 of Mr. Galton’s classification (see p. 87). Lastly, I have taken 
a third method of appreciating the relative variabilities, namely, by using the method 
of column and row excesses, E L and E 3 , discussed in Part VII. of this series. While 
this method has the advantage of using all and not part of the observations to deter¬ 
mine the ratio of oy to oy, and so naturally agrees better with the results based on 
the four than the one tint ranges, it suffers from the evil that these excesses can only 
be found by interpolation methods, which are not very satisfactory when our classes 
are, as in this case, so few and so disproportionate. On the whole, this investigation 
of relative variability is the least satisfactory part of our eye-colour inquiry, and I 
attribute this to two sources :— 
(i.) The vagueness in appreciation of eye-colour when no colour scale accompanies 
the directions for observation ( cf. p. 103, (c) ). 
(ii.) A possible deviation from true normality in the factor upon which eye-colour 
really depends (cf p. 80, (ii) 80). 
Lastly, we may note that the probable error in the correlation amounts in most 
cases to less than ‘03, rising only somewhat above this value for grandparental 
inheritance, where our series are somewhat short—650 to 750 instead of 1000. Here 
again most of the divergences are quite sensible. 
Allowing accordingly for the comparative largeness of our probable errors, we 
shall do best to base conclusions on the general average of series ; to insist oil general 
inequalities rather than on exact quantitative differences, and to emphasise the 
VOL. GXCV.—A. 
P 
