Correlation and Application of Statistics to Problems of Heredity 75 



of lung trouble. In 413 cases where information as to the father was 

 given, he was definitely phthisical in 7 '02 / o arid 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 funda- 

 mental 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 

 justifiable, 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 distribu- 

 tion 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— - 9945cr is the level of immunity at which con- 

 sumption begins its ravages, and the mean immunity of those who die from 

 consumption is M— r5207o\ But, if we accept Galton's figures for stature, 

 the parental regression (and correlation) is |, or the marriage in which only 

 one parent is consumptive gives rise to a "co-fraternity" (modern "array") 

 of mean M — ^ x r5207o- = J/— -5069cr, with a variability or standard devia- 

 tion of 2 = owl — ^ = a x - 9428. Accordingly the centre of this array is at a 

 distance - 4876cr 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 °/ o . Galton, disregarding the 

 fact that by choosing his regression, he has ipso facto chosen the variability 

 of his array, tries values for it which he thinks reasonable and which give 

 him 31 °/ o , 29 °/ and 27 °/ c of consumptives in the offspring of a consumptive 

 parent. These are not far from the value 30 °/ o we have obtained. Galton 

 by his different methods obtained 26 °/ o 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 

 18-207 o were suspected; but of the 410 parents of male subjects only 5-127„ were definitely 

 phthisical and 12-68 °/ o 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. 



10—2 



