20G Opsonic Index — "Mathematical Error and Functional Error"" 
Slide T. A. No. T. which gave rise to a count of 1000 and compared it with 
Greenwood and White's Slide B — selected purely at random because a 1000 
count had been made from it. The results were as follows: 
Number of Bacilli. 
0 
1 
2 
3 
If 
5 
6 
V 
8 
9 
10 
11 
12 
13 
U 
15 
16 
Totals 
Fleming 
54 
99 
184 
189 
156 
121 
84 
48 
29 
13 
9 
4 
4 
1 
2 
1 
2 
1000 
Greenwood I 
and White | 
71 
131 
197 
162 
137 
111 
58 
47 
32 
22 
13 
11 
2 
2 
2 
1 
1 
1000 
The actual constants of the distributions were as follows : 
Fleming Greenwood and White 
Mean 372 361 
Mode 2-67 1-94 
Standard Deviation 2-40 2*59 
Hi ... 5-747 6-699 
M:i ... 15-474 18-945 
^ 4 ... 180-740 202-477 
Theoretical Range Infinite 463 
ft ... 1-262 1-194 
(3 2 ... 5-472 4-512 
logy = 27-785,8387 „=i7q-r4 fi 4 - x Y™' 
+ 21 -6550 log(.r- 5-2705) -40-2546 log ^ y V 2-4541/ \ 43-8558/ 
Origin at - 8'7417 bacilli. Origin at mode. 
The graphs of these results are given in Diagrams I and II. It seems wholly 
unreasonable, either from mere inspection of the graphs or from any consideration 
of the constants of the distributions as given above, to suppose one of these 
frequencies to be due to " functional errors " and the other to be something quite 
different. Either both show " enormous functional errors," or else both exhibit 
the variations which occur in a population of this kind whether it be prepared 
in or outside Sir Almroth's Laboratory. The standard deviation measure of 
variability is slightly greater for Greenwood and White than for Fleming, 2'59 
as against 2 - 40; but this difference is not beyond what we find in two slides 
prepared by the same individual ; and if it were needful to account for it — 
which it is not — all that has to be noted would be that our observers are 
dealing with the serums of different individuals. 
On the basis of these samples it seems to me that a population prepared and 
counted in Sir Almroth Wright's own laboratory gives sensibly the same range 
of variation as a population prepared and counted elsewhere, and that until this 
is demonstrated to be erroneous, it is wide of the mark to talk about critics 
showing enormous working errors in opsonic estimations and to assert that 
such are really only measures of the critics' own " functional errors." 
