Karl Pearson 
403 
The whole of the labour of measurement is due to him, and this is, perhaps, the 
most important part of the work. I have to thank my late colleague and assistant, 
Dr Alice Lee, and my present assistant. Miss Julia Bell, for most of the arith- 
metical work. My own task has been that of suggesting the nature of the statistical 
reductions to be made, and drawing from them possibly disputable conclusions. 
Foremost among these I take to be the point raised by Dr Warren himself in 
1903, that in many cases an intimate relation exists between the size of the body 
and the size of the cell*. In the case of Daphnia magna the cell was a constituent 
part of the body length ; in the present case we have to deal with a related but 
detached cell. I cannot avoid making the suggestion that the field for inquiry here 
is not only very wide, but exceedingly important. 
The second difficulty that arises in the homotyposis of cellular characters is the 
practical difficulty of obtaining and measuring a sufficiently large sample of a cell 
population. The whole theory of " small " samples is only at present owing to the 
labours of von Bortkewitschf , "Student "J and others, in course of development. 
But it is easy to see that the general effect of " small " sampling is to increase the 
apparent variability of the means of the sub-populations by terms depending on 
the error of random sampling and thus to make the variability of an array larger, 
and consequently the correlation, or in the special case the homotyposis, smaller 
than it should be as a result of " large " sampling. It is needful accordingly to 
bear in mind the double possibility (a) that cell size is correlated with the growth 
of the individual, and (h) that "small" sampling has considerable influence on these 
intercellular correlations. 
(2) Dr Warren's material was collected at Hendon. The total length from 
tip of tail to head, and the body length from head to anus were measured. The 
end of the tail being removed, the maximum length and breadth of 25 corpuscles 
from a drop of blood from the wound were measured with an ocular micrometer. 
In the present paper, if the characters of rather more than 25 corpuscles were 
determined in a few cases by Dr Warren, I have dealt only with the first 25. 
In the first place I shall consider the relation of cell length to body length, 
choosing this instead of total length as the length of the tail is much influenced 
by the changing state of development. Table A (see p. 412) gives the actual 
measurement of 25 blood corpuscles of 71 tadpoles, cell length against body length. 
In Diagram I. I have represented the same result graphically, taking the means 
of the lengths from the table below. 
The correlation coefficient between cell and body length is r = — '25, and the 
correlation ratio — not very widely removed from it in value, and thus indicating 
approximately linear regression — is 7; = '28, with a probable error of about '02. 
Thus there can be no doubt from this result that the size of the blood corpuscle of 
* Biometrika, Vol. 11. p. 255. 
t Das Gesetz der kleinen Zahleit, Leipzig, 1898. 
J Biometrika, Vol. vi. p. 1. and Vol. vi. p. 302. 
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