Karl Pearson and David Heron 
161 
is not only unfair to Perozzo, but to one of us, whom Mr Yule was directly attacking. 
Pearson's memoir on "Skew Variation in Homogeneous Material" was sent to 
the Royal Society on December 19, 1894. Mr Yule's memoir on Association 
was presented on October 20, 1899. He had previously attended the statistical 
lectures of Pearson and been an assistant to him during a period when nearly 
the whole work of the statistical laboratory turned on non-Gaussian distributions. 
A collection was then made of non-Gaussian material with a view to dealing with 
the correlation surfaces of continuous non-Gaussian variates. Among the material 
especially selected as providing extreme cases were (i) barometric heights (memoir 
presented 1897) and (ii) ages of husband and wife; of the latter the laboratory 
still possesses the contour lines drawn by Mr Yule under Pearson's direction to 
indicate extreme cases of what the latter has termed skew variation, or wide 
deviation from the normal surface. Another illustration of marked skewness is 
that of the contour lines of the correlation between the numbers of a particular- 
suit in two partners' hands at whist. These latter curves were published by one of 
us in 1894, and at that time* it was distinctly stated that the contour curves for 
ages of husband and wife differed widely from the Gaussian type. It is singular 
that Mr Yule in the paper we are about to discuss should have made use of two of 
the extreme types of non-Gaussian frequency with which he was very familiar when 
he was an assistant in the University College Department of Applied Mathematics, 
and yet have allowed such a statement as that of Mr Sanger's to remain uncon- 
tradicted. The fact is that the promise made in 1894 f to deal with skew 
correlation surfaces only remained unfulfilled because the differential equations to 
the surfaces obtained in that year have so far defied integration. Undoubtedly for 
continuous variates a generalised correlation surface should be the starting-point 
for attacking the problem of association |. That it has remained unsolved shows 
only the extreme difficulty of the problem ; it does not indicate that all 
statisticians before Mr Yule had " this passion for the normal curve." 
And here we will at once emphasise the fundamental difference between 
Mr Yule and ourselves. Mr Yule, as we will indicate later, does not stop to discuss 
whether his attributes are really continuous or are discrete, or hide under discrete 
terminology true continuous variates. We see under such class-indices as 'death' 
or 'recovery,' 'employment' or 'non-employment' of mother, only measures of 
continuous variates — which of course are not a priori and necessarily Gaussian. 
Mr Greenwood in the discussion on Mr Yule's paper referred to the jibe§ about 
* Phil. Trans. Vol. 186 A, p. 411. 
t Ibid. p. 411. 
X Such a surface, however, involves 5, 7, or more independent constants, not the three of the 
Gaussian surface, and as the fourfold table has, apart from its total, only three available constants, we 
could not hope to determine such a surface for & fourfold table without some additional knowledge or 
hypothesis, other than conveyed by the table itself, as to the nature of the frequency. 
§ "We are considering," writes Mr Yule, " simply the performance as against the non-performance 
of the operation of vaccination. Similarly all those who have died of small-pox are equally dead: no 
one of them is more dead or less dead than another, and the dead are quite distinct from the survivors " 
Biometrika ix 21 
