208 Opsonic Index — "Mathematical Error and Functional Error" 
in that laboratory and counted by Strange ways. In the case of Slide IV he 
had counted 2000 single cells; this gave me 40 samples of 50*. He had also 
counted 3000 clumped and single cells from the same slide, thus giving me 
60 samples of 50 by a different method of counting. In the one case I had 
1600, in the other 3600 possible opsonic indices of the individual patient tested 
against himself. I was thus able to appreciate the sort of effect that differences 
of functioning in counting produced in the variation of the opsonic index. Against 
these two sets of Strangeways' results, I was able to place Greenwood and 
Diagram II. (Greenwood and White.) 
200 
150 
100 
-1 0 1 
3-4 5 .6 7 8 9 10 11 12 13 14 15 16 
Bacilli per Leucocyte. 
White's 400 samples of 50 counts. The latter has already been considered by me 
in a previous paper-f*. Strangeways' two series were reduced in precisely the 
same manner as that indicated in the paper just referred to. The following are 
the constants for the three distributions, and the resulting three curves are 
plotted, reduced to the scale of 1000 indices, in Diagram III. 
* Each sample of 50 was taken in the precise order of counting, 
f See Biometrika, Vol. vn. pp. 536, 537. 
