418 
Miscellatiea 
Thus since p' vanishes with r, 
If we used ranks instead of grades, we should have a^^ for arg^ and consequently 
Tlius finally 
»•= ^^//= 1-0233 p', 
or '-=^^7 — l-0233p". 
It will be clear from this that the correlation p' between rank and quantitative variate can 
never be " perfect," for it cannot exceed the value '9772, otherwise the correlation r would exceed 
unity. It will be seen that for practical purposes /• is very close to p', but still from the 
theoretical standpoint, it is not without interest to discover that the correlation between 
ranks and a quantitative variate can never be perfect. For examj^le, it is impossible to have 
perfect correlation between place in class and examination test, even if the boys were in the 
same order in class and examination. The defect, however, will be very slight. 
Case (ii). Let the subscript C refer to any "broad" class and let r; be found from either 
of the formulae 
12 
the first applying to grades and the second to ranks ; then 
or = 1 -0233 ^Y^S {n, {v, - vf], 
according as grades or ranks are used. In actual practice the values of ?y' or rj" should be 
correct for number of classes and for " broad " categories. See Biometrika, Vol. viii. p. 256 and 
Vol. IX. p. 118. 
Numerical illustrations will bo provided later. 
III. Correction of a Misstatement by Mr Major Greenwood, Junior. 
In a recent paper by Mr ilajor Greenwood and Mrs Frances Wood " On changes in the 
Recorded Mortality from Cancer and tlieir Possible Interpretation*" occur the following words : 
" The case is evidently analogous to that studied by Professor Karl Pearson in his pamphlet, 
The Fight against Tuberculosis and the Death-rate from Phthisis (Dulau and Co.). Professor 
Pearson published three diagrams : («) the general death-rate of England and Wales ; (b) the 
phthisis death-rate ; (c) the ratio of phthisis deaths to all deaths. The original figures seem to 
have been the crude rate for males and females separately from 1835 onwards." The " evident 
analogy " with what appears to me the wholly fallacious treatment of the authors in their paper 
above cited I do not now stay to discuss, but I wish to draw attention to the words: "The 
* Koyal Society of Medicine, Procecdinris, Vol. vii. Section of Epidemiology, pp. 79 — 170. 
March 27, 1914. 
