210 Opsonic Index — "Mathematical Error and Functional Error" 
Distribution of Opsonic Indices. Samples of 50. 
Mean Index 
Mode 
Standard Deviation 
ft 
a, 
Origin at Index ... 
I. Strangeways' 
2000 single cells 
1-0202 
■9852 
•2083 
•00510 
•00906 
•3184 
4-8122 
■8481 
II. Strangeways' 
3000 clumped 
and single cells 
1-0221 
■9734 
•2181 
•00567 
•00892 
•2985 
3-9401 
•6002 
III. Greenwood 
and White's 
20,000 cells 
1-0205 
•9611 
•2072 
•00619 
•00757 
•4837 
4-1022 
•3409 
I. 
II. 
III. 
O? \ -4-9268 2-6106 tan-i (ar/-5175) 
y = 15614 (l + .-^-l e 
The equations to the curves, reduced to a total of 1000, are 
y = 20-88 (l + ■ 
y = 1061 (l + 
•5418 
x" 
•3911 
- 9-0480 9-1837 tan" 1 (x/-7360) 
11-4301 22-6704 tan- 1 (x/-6254) 
e 
Now it will be clear from an examination of this table of constants that there 
is no significant difference in the variation of these three series ; no one of them 
can be described as having " enormous working errors " compared with another ; 
they show, for arguments about the range of variation of the opsonic index, practi- 
cally equivalent results; one of Strangeways' series lying on the one side, and the 
other upon the other side of Greenwood and White's series. The only conclusion 
that anyone examining Diagram III, or the above analytical constants of the 
curves, can reach, is that : If the countings are done by different microscopists, 
not members of Sir Almroth Wright's Laboratory, the variation in the opsonic 
index of an individual reckoned against himself shows the same magnitude of 
range, and this whether the slide was prepared or not in Sir Almroth's Laboratory. 
We have now, as far as our data extend, reached two or three interesting 
results : 
(i) The preparation of a slide inside or outside Sir Almroth Wright's 
laboratory makes very little difference in the population presented by it. 
(ii) In counting a large population, say 1000 to 2000 leucocytes, no sub- 
stantial difference arises according to whether the counter be a member or 
not of Sir Almroth Wright's staff*. 
(iii) The counting or not of clumped cells, when a large population, 2000 
to 3000 cells, is being dealt with, has little effect on the range of opsonic index 
which results when an individual is tested against himself. In other words a 
* The assumption of course made is that the counter is really a trained microscopist and does 
his work conscientiously. 
