Karl Pearson 
211 
point, fertile of differences in technique, produces practically little differentiation 
in the resulting variation of the index. 
It seems to me — as a quite unprejudiced outsider — that a claim to special 
monopoly of technique in placing the film on the slide or in preparing it in 
any way needs further justification. In taking a large population, the "enormous 
working errors in opsonic estimation " appear equally in slides prepared and 
counted in Sir Almroth Wright's Laboratory, in slides prepared there and counted 
elsewhere, and in slides both prepared and counted elsewhere. Hence these 
"enormous working errors" are either variations of random sampling, or are 
peculiar to the method of counting of both internal and external microscopists*. 
(5) To the purely theoretical statistician the subject might now, for the 
time being, appear exhausted. If the slide population of leucocytes presents 
in the above three cases the same range of bacilli-frequency, then if we are 
seeking the distribution of the opsonic index of the individual as against himself 
on the basis of a count of 50 or 100 leucocytes, all we have to do is to follow 
a purely mathematical process, i.e. to determine every mean of possible groups of 
the given number and divide by every other mean. We shall thus reach the 
final distribution of possible opsonic indices of the individual tested against 
himself, each index appearing with the frequency of a random distribution. 
Now given any frequency of a variate, the frequency of a random sample 
of the means of 50 or 100 of these variate values is perfectly well known. If 
/3i and /3 2 be the fundamental frequency-constants of the primitive frequency 
then 
5 1 = /8 1 /n and B 2 - 3 = (& - 3)/n 
are the fundamental frequency constantsf of the derived frequency of the means 
of n variates at a time, such means being selected out of this primitive population 
by a purely random process. The population of means should thus tend to 
become rapidly Gaussian. Now Dr Greenwood has shown that the means of 
25, 50, or 100 leucocyte results — as obtained in a particular manner from the 
slide population — do not follow this rule, but give far more skew distributions^. 
This point is one of extraordinary importance, for it suggests, if it may not yet 
be said to demonstrate, that the 50 or 100 leucocytes counted from the population 
on the slide is not a random sample of the contents of the slide as more nearly 
measured when 1000 to 3000 leucocytes are counted. "Student" in a most 
interesting note§ on Greenwood and White's paper has suggested that the result 
is due to " homotyposis," i.e. to a certain degree of likeness in consecutive counts. 
* In any further discussion of this subject, it is essentially important that the slides and the counts 
used should be those made by both parties to the discussion, before the present issues as to " functional 
errors " and " errors of method " were raised. 
t The mean of the means is the mean of the primitive population and the standard deviation, the 
only other constant needed, = aj^Jn. 
X Biometrika, Vol. vi. p. 400 and Graph 16. 
§ Biometrika, Vol. vn. p. 210. 
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