212 Opsonic Index — "Mathematical Error and Functioned Error ' 1 
The current theory of random sampling supposes, however, that in actual counting 
we draw from the leucocytes on the slide our sample of 50 or 100 precisely as 
we should draw balls from a bag. Now this is not exactly the method which 
can be followed in a count of thousands. A mechanical stage has to be used 
in order to prevent any danger of counting the same leucocyte several times. 
Both Strangeways and White used such a stage. I am not aware whether or 
no Dr Fleming did. But in using such a stage we count along a line, drawn 
as it were across the slide, and are liable in doing this to traverse somewhat 
heterogeneous areas. On the other hand, if the 50 or 100 leucocytes for the 
mean count are taken at random from the slide, we may tend to even out 
these heterogeneous areas and so obtain less variation in the distribution of 
means, while the frequency of bacilli in the leucocyte population remains absolutely 
the same. 
To test possibilities in this direction I took (i) the 1000 count of Dr Fleming, 
which provided 20 means of 50 and therefore 19 pairs of successive means; 
(ii) Slide IV of Strangeways' 2000 count, giving me 39 pairs of successive means ; 
and finally (iii) Slide B of Greenwood and White's big 20,000 count giving 19 
pairs of successive means. Of course 19 and 39 are very small numbers of pairs 
to base any really definite conclusions on, but the results may show whether 
there is very high correlation between successive pairs*. The following are the 
numerical values obtained : 
Strangeways Greenwood 
Fleming _ j. . and White 
Without With 
clumps (40) clumps (60) 
Mean Number of bacilli 3 714 1-696 1-723 3-605 
Standard Deviation ... -2779 -2560 -2635 -3086 
^^teofsT 0688 " 6 ! -064±-154 + "097±-107 + -013±OB8 -319±;139 
Clearly the correlation between successive means of both Fleming and 
Strangeways is insignificant. Greenwood and White obtain a larger result, 
but not of any great importance considering its probable error. It is further 
negative, or the successive means tend in opposite directions on this slide. It 
seemed worth while testing whether the negative correlation obtained from 
one slide (B) of Greenwood and White's big count would be maintained if 
the whole series of these authors' data was considered. We were not able to 
obtain 400 successive means, as this would have involved passing from one 
slide to a second. A first sample of 193 and then all available 386 successive 
means were taken; there resulted: 
First sample of 193 Whole material 386 
Mean Number of Bacilli 3-679 3'684 
Standard Deviation -2644 -2575 
Correlation of successive counts of 50 + -259 + -045 + - 245 ± -032 
* Dr Strangeways writes: "The cells were counted in successive rows and so far as it was humanly 
possible every cell was counted and no cell was counted twice... every set of 25 came from the same part 
of the slide and from a very small area of it as the leucocytes were very plentiful." Letter to Dr 
Greenwood. 13/2/11. 
