548 
Miscellanea 
dull to go and of the dull to stay at difierent ages. If we now give the higher values to the 
correlations produced by these tendencies in elementary schools, we find on correction not that 
they have tended to disguise the real value of the " general intelligence " character by giving it 
a spurious high intensity, but that they have tended to lower its true importance. Those who 
complain of the different percentages of the divers grades of intelligence of the children in the 
di&erent standards of the same elementary school often seem unaware that the same sample does 
not pass through all standards, at one stage there is a rejection of the very dull and at another 
the retention of the dull class. The main facts brought out are the substantial correlation 
between teacher's estimate of general capacity and examination test, and the fact that extreme 
allowance for age and standard tends to emphasise this relationship rather than to shew that 
the teacher's estimate is of little value. These observations were not made ad hoc, but they 
have been confirmed by other observations made on far larger numbers with additional safeguards 
for accuracy. The results of these will shortly be published, but it seems worth while indicating 
at a time when hasty criticisms are being made of the value of "general intelligence" estimates 
that the teachei-'s appreciation of mental capacity does mean something, and has a very direct 
and practical value, when properly registered and handled. 
K. P. 
II. Note on the Separate Inheritance of Quantity and Quality 
in Cows' Milk. 
By KARL PEARSON, F.R.S. 
Under the above title Professor James Wilson, of the Royal College of Science, Dublin, read 
a paper in May, 1910, which is published in Vol. xii. pp. 470 — 479, of the Scientific Proceedings 
of the Royal Dublin Society. 
He states that : " It is a very general opinion that the milk of high-yielding cows is usually 
poorer and that of low-yielding cows richer in quality " (p. 470), and again he writes : 
" If we group together all the low-yielding cows, and find their milk invariably high in quality, we 
may infer that low yield and high quality are of the nature of concomitant variations. If we group the 
high-yielding cows together, and find their milk invariably of low quality, we may infer that high yield 
and low quality run together. But if we take these groups and any other groups we can form, and find 
that the quality varies the same way in them all — that is that there are low qualities, high qualities, and 
medium qualities in every one of them — then we are justified in inferring that the quantity and quality 
of the milk are independent of each other. And this is what we do find " (p. 471). 
The italics are mine. It would be difficult to find a paragraph containing more fallacies in as 
many words. Two qualities may be associated together, even closely correlated, and yet one will 
not be invariably accompanied by the other. High, low and medium values of one character 
may occur with any given value of a second and yet there be high correlation between them. 
The whole problem turns on the extent of the variation of the first character for a given value of 
the second, and not the invariable appearance of one with the other. The author may have 
some conception of correlation other than absolute association, but neither this paragraph, nor 
his general treatment of the subject, shews any signs of it. 
Professor Wilson's material is involved in the table below. 
Now there can be no doubt of the value of such returns and of tabling them, although we 
regret the clubbing together of the tail frequencies, that common error of the non-statistical 
trained mind, which renders determination of the true correlation so difficult. 
