W. F. Harvfa'' and a. M^Kendrick 
77 
We may ask ourselves what are the probabilities that the distributions corre- 
sponding to Test Serum I and Test Serum II are significantly different from that 
of the Normal Serum here used and regarded as a type ? Let us understand 
thoroughly what is meant by the use of the expression " significantly different." 
Had we made a large number of counts of lOU for this normal serum, we should 
have found that no two of them would be alike. If then we counted at random a 
large number of such lOO's, what are tlie probabilities that in the long run we 
should get a distribution like that given in the case of Serum I or Serum II? 
Put in another form the problem is :— How many successive lOO's should we on 
the average expect to have to count from the slide representing normal serum 
before we should get a distribution like either of those given by the test sera. 
Now for distributions like the above, if they contain a sufficiently large number of 
observations, and still better if they have had an ideal frequency curve fitted to 
them, the probabilities for and against the chance here referred to can be calculated. 
In the case we are considering the numbers are much too small for an accurate 
determination, but they will serve to give us a rough idea of the order of the signifi- 
cance or absence of significance of the differences exhibited by the distributions. 
Test Serum I works out as significantly different (P = '002) from the normal 
serum here utilised in 998 cases out of 1000, and Test Serum II (P = "005) in 995 
cases out of 1000 ; in other words for this case it would be safe to the extent 
named to say that we are dealing with sera producing a different degree of phago- 
cytosis from a normal serum. Let me repeat that owing to the small number of 
observations the figures are only rough approximations to the order of the chances 
for and against. Further be it noticed that I limit my comparison to this 
particular normal serum assumed to be a type, as it would not be safe to state the 
matter any more strongly without a reference to the degree of variability of normal 
sera. Now as all work on the subject goes to show that opsonic activity is a 
specific character, our finding may be said to amount to this : that a diagnosis that 
the serum of these patients was associated with the presence of tubercular disease 
or the subjection to treatment with a tubercular vaccine would be correct in some 
99 cases out of 100. 
I have adverted to the point that the selection of the tuberculo-opsonic index 
as a test case for the reliability of the inferences which are based upon its 
estimation, was scarcely a fair one, if the point were generalised to the extent 
of saying that the adverse findings for this particular index applied to the indices 
obtained with other bacteria. Take the case of the bacillus of glanders, of which — 
through the kindness of Dr Fleming — I can afford an instance which was only one 
of similar results continuing in the particular case for week after week. Indeed, 
the diagnosis of glanders was based upon the results of opsonic index determinations 
many months before the actual isolation of the organism set all doubts at rest — 
if there could be any possible doubt in such a case. At the time of taking the 
serum, which gave the following phagocytic result, the patient was receiving 
a glanders vaccine. 
