Correlation and Application of Statistics to Problems of Heredity 75
jof lung trouble. In 413 cases where information as to the father was given, he was definitely phthisical in 7.02 °/o and there were suspicions of phthisis in 17.19 °/o. In 420 cases of mother the corresponding numbers were 6'90 °/o and 13.81°/°. Thus Galton's view of the greater influence of the mother, whether by infection or by heredity, is not confirmed on large numbers*. Notwithstanding Galton's suggestion as to the fundamental part played by infecting mothers he proceeds on pp. 181-185 to discuss consumption on the basis of heredity. Although we may not feel this ustifiable, his method is so suggestive and generally applicable that it must be discussed here. He starts by assuming that the distribution of resistance or immunity in the population may be supposed to have a normal distribution of mean M and-to use modern notation-a standard deviation a-. Now according to Galton's data 16 °/o of the deaths of his general population were from consumption, hence M- *9945a- is the level of immunity at which consumption begins its ravages, and the mean immunity of those who die from consumption is M-1.5207o-. But, if we accept Galton's figures for stature, the parental regression (and correlation) is 3, or the marriage in which only one parent is consumptive gives rise to a "co-fraternity" (modern "array") of mean M- 3 x 1'5207v = M- -5069o-, with a variability or standard devia
tion of Y. = a,/1 - s = a- x -9428. Accordingly the centre of this array is at a distance •4876o- from the limit to immunity and the ratio of this to the standard deviation of the array ='5172. The table of the Probability Integral shows that this is only very slightly over 30 °/a. Galton, disregarding the fact that by choosing his regression, he has ipso facto chosen the variability of his array, tries values for it which be thinks reasonable and which give him 31 °/o, 29 °/o and 27 °/, of consumptives in the offspring of a consumptive parent. These are not far from the value 30 °/° we have obtained. Galton by his different methods obtained 26'/. and 28 °/o of consumptive offspring of a consumptive parent, but this is only a minimum limit, as it does not appear that he confined himself to families all the members of which . were already dead, or had passed practically through the age zone of really lethal tuberculosis. Of course the method supposes that within reasonable limits the degree of immunity of each individual remains constant, and that, within reasonable limits again, this degree of immunity is not affected by the size of the dose.
The importance of the method is greater than that of its application, which is rendered doubtful by the use of the special values, not confirmed, for stature, and by the fact that Galton had already attributed much of the result to infection. What, however, the method indicates is, that if we know the frequency of a particular type of disease in the community and its
* One curious result does seem to flow from my data. If we divide our patients into male and female, then of the 423 parents of the female subjects 8.75'/° were definitely phthisical and 18.20 °/° were suspected ; but of the 410 parents of male subjects only 5.12 °/° were definitely phthisical and 12.68'/° suspected of phthisis. This suggests either that the parentage was more
influential in the case of the female, or that women knew more or were less reserved than the men about the diseases of their parents.