540 
On the Constants of Tndex-Distributiom 
modal or most probable value of the opsonic index of an individual tested by 
himself is less than unity and his average value greater than unity. 
If we actually suppose the distributions normal and varying round the means 
with the standard deviations given above we have the following results: 
Significance laid on an event 
wiiich will not happen more 
frequently than 
Number of Counts 
25 
50 
100 
Once in ten trials 
Once in eight trials 
Once in six trials 
•58—1-48 
-61—1-46 
•65—1-42 
•68— 1-36 
•70— 1-34 
•73—1-31 
•75—1-27 
-77—1-25 
■80—1-23 
This table is to be read in the following sense : If an opsonic index were based 
on a count of 50 cells, then once in eight trials an individual tested against himself 
would have an index lying outside the limits '70 to r34<. Or, again, with 100 
counts once in six trials an individual tested against himself would have an index 
lying outside the limits •SO to 1'23. It may be added that for most of the purposes 
of practical life or of exact science we should not consider an "improbability" 
which could happen once in ten trials as marking a significant differentiation. 
Much greater degrees of improbability would be required. In the case of medicine, 
however, much less certainty may be demanded of a judgment, and probably no 
weight would be given to an isolated opsonic determination in diagnosis. Still 
the matter gives ground for pause, the opsonic index of the same material tested 
by itself has a very wide range round uuity. 
The following table will sliow how closely Greenwood and White's experimental 
determinations agree with our theoretical evaluation of the constants : 
Constant of 
Distribution 
Samples of 25 
Sample 
s of 50 
Samples of 100 
G. +W. 
P. 
G.+W. 
P. 
G. + W.* 
P. 
Mean 
1-0362 
1-0356 
V0205 
V0205 
1-0120 
1-0116 
Mode 
-9432 
-9330 
■9536 
•9611 
•9689 
-9774 
Standard Deviation 
•2585 
•2776 
-2204 
•2072 
-1553 
•1562 
/3i 
■7099 
•7060 
•6952 
•4837 
-3654 
•3132 
^■2 
4-3914 
4^3088 
4^8945 
4^1022 
3-7138 
3-9472 
The only substantial divergences are in Greenwood and White's values for /3i 
and ^2 ill the case of samples of 50. I have been through my results again and 
can find no error. Dr Gi'eenwood has been through his figures and finds slight 
* They have used the boundary curve Type V in the case of samples of 100. 
