220 Opsonic Index — "Mathematical Error and Functional Error" 
in his frequency of bacilli per leucocyte, and a rather greater scatter in his 20 
independent means than Greenwood and White in their 400 independent means, 
he yet records his results in some manner which leads to less variation in the 
dependent means, i.e. when we take 400 means of samples of 50, starting with 
the first, second, third, etc. entry in his record. I think the explanation will be 
found in the fact that Fleming's record of his count was not obtained by working 
backwards and forwards across the slide with a mechanical stage. 
This is the only point where the variation in result of workers inside and 
outside Sir Almroth Wright's Laboratory appears to me on the present data 
appreciably different, and it concerns the nature of the record, rather than the 
actual contents of a slide or the results of counting the bacilli per leucocyte. 
(8) Conclusions. 
Counts of at least 1000 leucocytes have been considered in this paper when : 
(a) the slide was prepared and recorded by a member of Sir Almroth 
Wright's staff. 
(b) the slide was prepared by an " internal," but recorded by an " external," 
investigator. I 
(c) the slide was both prepared and counted by an " external " investigator. 
The three slides all refer to sera mixed with tubercle bacilli, and have not 
been specially selected by me, beyond imposing the condition that a 1000 
leucocytes at least should have been dealt with. Before the reduction of the 
numbers I had no idea what would arise from them. 
I find that: 
(i) The same degree of variation in the opsonic index of an individual tested 
against himself arises when external investigators count slides prepared inside or 
outside Sir Almroth Wright's Laboratory. It seems improbable therefore that 
" enormous working errors " are functional ei'rors due to the defective preparation 
of the slide. 
(ii) The same degree of variation in the bacilli per leucocyte arises when the 
slides are prepared and counted (a) inside or (b) outside Sir Almroth's Laboratory. 
The population of a slide therefore shows the same high degree of variation under 
both conditions. 
(iii) The variation of twenty independent means of 50 from the same in- 
dividual is of the same order in the case of internal and external workers. The 
variation of the opsonic index of the same patient tested against himself is as 
great for the slides tested whether they be of internal or external origin. 
(iv) There is a difference in the nature of the written record of the counts. 
The " external " counters worked backwards and forwards across the slide, re- 
cording continuously by aid of a mechanical stage. I have no knowledge of how 
Dr Fleming's record was entered but, while it exhibits the same order of variation 
