210 Opsonic Index — "Mathematical Error and Functional Error'' 
(see Diagrams I and II), and the independent means have much the same 
range (see footnote \, p. 213), yet for these records the small and large numbers 
of bacilli much more closely alternate in Fleming's counts than in Strangeways' 
or White's returns. If any slide does not really contain a "random distribution" 
of leucocytes, but is " patchy," then it is conceivable that working with a 
mechanical stage and crossing the slide along a line, we might in counting our 
50 leucocytes cover patches of various degrees of density, and so reach a mean, 
subject to much the same variation of bacilli, as if we drew from a bag the 
leucocytes at random ; but if we worked back for the next 50 across the slide 
on a parallel line, thus : 
First Line 
-> 
A 
G 
B 
A' 
C 
B' 
Second Line 
<r 
the means of 50 leucocytes along AB or B'A' may not show the same variation 
as if we worked from GB for 25 and then from B'C for the second 25 of the 50. 
For in the latter case the leucocytes are chosen from a more concentrated portion 
of the slide. This illustration is of course purely arbitrary, but it may indicate 
how heterogeneity on the slide may produce in the frequency of means obtained 
by mechanical stage counting a differentiation from what is to be expected from 
pure random sampling. 
To test the methods of counting I took 400 means from Fleming's record, 
by starting with one leucocyte less at the beginning and one leucocyte more 
at the end of the 50 sample each time. It soon became obvious that the 
non-independent means thus found gave very different ranges of variation in 
the Fleming and the White series. Both are fairly irregular (see Diagrams VI 
and VII), but the Greenwood-White series is 30 °/ 0 more variable than the 
Fleming. The analytical constants of the two distributions are as follows : 
Fleming Greenwood and White 
Mean 3723 3609 
Mode ... 3-758 3718 
Standard Deviation ... "2609 "3394 
ft -0461 -1957 
0 2 2-763 2-836 
/ x \ 9-3628 / x \5-4454 . . / x \ 6-4159 / x \ 2-3288 
14*067) - 8-3288-) ' *=^(l + ll ^) (l " g^) . 
The test for goodness of fit gave P — '09 for Fleming and P = *14 for Green- 
wood and White, no great difference*, but what there is lies to the advantage of 
Greenwood and White. 
* For the bacilli per leucocyte (see Diagrams I and II) P=-36 for Fleming, and -33 for Greenwood 
and White, i.e. both have quite reasonable and practically equal goodness of fit. 
