378 On the Frequency Distributions of Phagocytic Counts 
This brief description is perhaps enough to establish the statements as to the 
essentially statistical nature of the problem advanced above. Since the funda- 
mental point is whether and how far the character of the cells counted (a sample 
liable to the full error of random sampling) describes fairly that of the whole popu- 
lation of cells from which it is drawn, the question can only be adequately treated 
by a statistician. It is equally clear that the problem is complex because it 
involves several variables, no one of which is exactly known. 
In the first place, the thickness of the bacillary emulsion, i.e. the number of 
bacilli per unit volume of emulsion, is necessarily different from day to day, because 
no satisfactory method of standardisation has yet been discovered. For instance, 
if on one occasion the emulsion contained a bacilli per unit volume, then it is 
impossible to insure that in subsequent determinations the emulsion will be of the 
same strength. Such variations are often large. 
This difficulty is met by the assumption that if, with an emulsion of concentra- 
tion a bacilli per unit, cells in normal serum ingest A bacilli per leucocyte and 
cells in pathological serum B bacilli per leucocyte, then with an emulsion of 
concentration n.a, the average cell contents will be respectively k.A and k.B where 
h is some constant. 
It will be noticed that this assumption involves two distinct assertions, viz. : — 
(1) that the normal opsonic power is constant: (2) that given (1) nothing is 
changed relatively when the number of bacteria to be ingested is altered. 
These questions have recently been discussed by Dr Alexander Fleming*, to 
whose statements we shall briefly refer. 
In the first place, Dr Fleming cites the results of Dr Bulloch -f, who estimated 
the indices of 84 apparently normal persons in terms of his own serum. 75 were 
between 0"9 and I'l, the other 9 falling within the extreme limits of 1'2 and 0"8. 
But a constant ratio, i.e. a constant opsonic index, would be found if the opsonic 
content of each serum varied from day to day in the same direction. The criticism 
is perhaps of little importance, but the point must be remembered. 
A somewhat different process has been used in Sir Almroth Wright's laboratory 
and we quote Dr Fleming's description of it J. 
" Id the routine work of the laboratory, the controls used in connection with the estimation 
of the tuberculo-opsonic indices of our patients are furnished by the various workers in the 
laboratory, or, it may be, by interested visitors and students, and these are used in the propor- 
tion of one control to every eight or ten patients' sera. Thus, in each day's work, there are three 
or four normal sera used, and each observer who engages in counting any of the slides, counts at 
least two, but even three or more of these controls. 
* " Some Observations on the Opsonic Index with Special Eeference to the Accuracy of the Method 
and to some of the Sources of Error" by Alexander Fleming (Practitioner, 1908, Vol. 80, pp. 607—634). 
t W. Bulloch, Trans. Path. Soc. 1905, Vol. 56, p. 334. 
+ Fleming, ojJ. cit. p. 608. 
