Karl Pearson and David Heron 
257 
moment correlation. This method has been used from the " earliest times " by 
biometricians, e.g. in dealing with the teeth on the carapace of prawns, the 
prickles on holly leaves, stigmatic bands on poppies, veins on leaves, etc., etc. 
There is absolutely nothing new in the Yulean method of pseudo-ranks applied to 
these data, the rank is the true measure of the variate in such cases. But the 
method is wholly false when applied to continuous variates in such cases as 
Mr Yule applies it. It is wholly false in particular when applied to fourfold 
tables, unless the difference between the two classes is a measurable unit. Tbis, 
as we have indicated, is not the case in the Mendelian results of actual practice ; 
it is not the case in the vaccination data or in any one of the cases to which 
Mr Yule has applied his coefficients. In no cases is he dealing with discrete unit 
differences. The nearest approach to a discrete difference is possibly in the case 
Diagrams XIV and XV. Regression of Intensity of Vaccination upon Severity of Small-pox. 
{A) Original data. (B) Vaccinated made 50% and haemorrhagie and confluent 50°/ o 
(Yule's Hypothesis). Intensity of Vaccination and Severity of Attack treated by Gaussian 
Methods. 
(i) Assuming "severity" has a Gaussian distribution after the change of frequencies. 
(ii) Assuming the eentroids of each severity group unaltered by the change of frequencies. 
Diagram XIV. 
(i) 
0-10 
10-25 
25-45 
Oi 
45 
Means 
- < 
Haemorrhagie. 
Biometrika ix 
Confluent. Abundant. 
Severity of Attack. 
Sparse. Very Sparse. 
33 
