PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 297 
second term might be ^ to while, for values of the order ‘7 in the correlation 
coefficients, it would be a much more important term than the first, i.e., heredity 
would completely obscure the general correlation between intensity and age. 
Similar remarks apply, of course, to the formula 
and the modification of its k by the factor 
, , v (v + e) 
1 + i 0 ' 2 ’ 
While the above discussion has been adapted particularly to the problem of morbid 
inheritance, it should be noted that the general formulae for triple correlation apply 
to a number of interesting problems on the inheritance of two faculties by the 
offspring from the parent. In particular, the above special formulae in 77, e, and k 
apply without modification to any case when (a) the two faculties are correlated in 
like manner ( k ) in jiarent and offspring, ( b ) the two faculties are each directly 
inherited (77 and e), (c) there is an insensible or zero amount of cross heredity. I do 
not stay to develop the formulae at present, because I hope to return to them when 
I have more ample statistics to illustrate the properties of cross heredity from. 
( d .) On the Skeiuness of Disease Curves. —There is one qualifying remark which 
must, however, be made before we leave the topic of morbid inheritance. We have 
assumed that the frequency surface for intensity and age of appearance of disease is a 
normal correlation surface. This, however, is only an approximation. If we add 
together all the intensities for each age, we shall have a frequency with age curve for 
the disease, and if the correlation surface were a true normal surface, this would be a 
true normal curve. In many diseases, possibly in all, it is however, a distinctly skew 
curve, and this whether we take the case-frequency or the mortality-frequency. This 
has been illustrated in “ Contributions to Mathematical Theory of Evolution, II.” 
(‘Phil. Trans.,’ vol. 186 , A.), Plate 12, for enteric fever.* The following statistics 
illustrate the same skewness for a disease more distinctly associated with heredity! :— 
Phthisis : 2000 cases with History of Parental Phthisis. 
Age. . . 
1 
10 15 
20 
25 
30 
35 
40 
45 
50 
1 
55 
i 
60 
Frequency 
26 
I 
100 436 
549 
392 
217 
149 
65 
27 
6 
1 
9 
4 
* It is, I think, true for all fevers, some of which, however, have k positive and others k negative, 
f R. E. Thomson, ‘ Family Phthisis,’ p. 22, London, 1884. 
MDCCCXCVI.—A. 2 Q 
