W. F. Harvey and A. M^Kendrici^ 
89 
imagine that those who invented the opsonic index and initiated vaccino-therapy 
would prefer to have their names more closely associated with the latter than with 
the former. 
Let us take up the discussion, however, on the minor point as to whether an 
improvement could be made on the method of estimation of the opsonic index. 
The average is, as we have already stated, but a rough measure of an opsonic 
frequency distribution. The suggestion has emanated from America that in place 
of the ratio of averages we should take the ratio of the percentages of leucocytes 
which have failed to phagocytose at all. The objection which will occur to every 
one is that this may very likely include a certain number of dead leucocytes. 
Again, it is a cardinal point in determining the best measure for expressing the 
features of a frequency distribution that it should be based on the whole number 
of observations. This the "zero index" — as we may call it — is not. At tlie 
same time it must be conceded that the "zero index" is more rapidly determinable 
than the " average index," and so would allow of the errors associated with its 
determination being lessened by affording more time to increase the number of 
observations. It would be specially of advantage where the emulsions used were 
at all concentrated and where consequently the strain and difficulty of counting 
the numerous bacteria ingested become very great. It might be of use also in 
cases where it is not easy to obtain uniform emulsions, and where the leucocytes 
may contain chains or clumps of bacteria. On the other hand, with concentrated 
emulsions the number of leucocytes containing no bacteria becomes greatly 
diminished, and may in fact simply come to represent those which are actually 
dead. In this case, instead of taking these leucocytes as our gauge of phagocytic 
power, we might take those containing only one bacterium instead. I have made 
a small number of observations on the degree of correspondence of the two indices 
in the case of B. tuher'culosis. The slides from which the two indices were deter- 
mined were those which had served for the routine estimations of the laboratory. 
All the indices were calculated from countings done by myself alone. The distri- 
butions of 'the two were as follows : — 
Average 
Indices 
■3 
■4 
■5 
•6 
•7 
■8 
•9 
1-0 
1-2 
1-3 
1■J^ 
1-5 
1-6 
Mean 
S.D. 
Frequency 
0 
1 
5 
4 
6 
17 
17 
12 
17 
13 
1 
3 
2 
2 
•96 ±-02 
■24 
Zero Indices 
■3 
■A 
■5 
•6 
•7 
■8 
10 
■9 
1-0 
1-1 
1-2 
1-3 
1-5 
1-6 
Mean 
S.D. 
Frequency 
6 
5 
6 
5 
10 
16 
10 
7 
8 
5 
6 
3 
3 
•91 ±-02 
•35 
We note at once a marked difference between the distributions. The "average 
index " shows a greater concentration about the mean than the " zero index." In 
fact the zero index shows a greater variability than the other, a result which we 
should have expected from the fact that the zero index is based on only one 
observation whereas the other is based on the total number of observations. The 
Biometrika vii 12 
