W. F. Harvey and A. M^Kendeick 
73 
also we observe, on the same basis, the following expectations regarding the 
normality of more limited ranges : 
Limits 
•83 to -89 
•89 to ^95 
•95 to l^Ol 
rOl to 1^07 
1-07 to M3 
M3 to M9 
2^95 7, 
7- 87 7„ 
22^95 7 
31-64 7„ 
22-46 7„ 
8- 69 7, 
Total 
96-56 7„ 
Now how do these percentages compare with those found amongst test sera ? 
If our "test" sera indices had all referred to the first examinations of patients, we 
should then have been in a position to say how frequently any given index occurred 
with the serum obtained from an individual suspected of being tubercular. With 
such data -we should also have been able to state definitely what were the prob- 
abilities for and against a given index being normal or abnormal. This point has 
been treated of by Noon and Fleming*. The figures given above are unfortunately 
not those of patients examined only for the first time. They are simply the 
indices of patients examined I'rom day to day, irrespective of whether they liad 
presented themselves for the first time, were under inoculation treatment, or had 
received some such special treatment as massage, exercise, Bier's bandage and so 
on, in order to bring out more distinctly the normality or abnormality of their 
condition. Indeed a large proportion must have been under treatment at the 
time of the examinations here recorded. We should therefore expect that a great 
number of those who were originally subnormal were being maintained at normal 
by the inoculations, whereas, owing to the well recognised difficulty of maintaining 
a hypernormal index in tuberculosis, those amongst the originally normal who 
passed over into the category of the hypernormal were not so numerous. Still 
the figures as they stand give us a considerable amount of information. They 
show the much greater extent to which test sera vary as compared with normal 
sera, and how in spite of the selection implied by the inclusion of an excess of 
normal individuals there still remains a much greater deviation of indices from the 
mean than with viormal sera. A comparison of the two distributions will also give 
us some idea of the extreme limits within which a serum can be called normal. 
It will show us too the relative frequency with which given indices occur in 
normal and abnormal cases — always remembering that in this comparison the 
proportions, for the reason given, are likely to be overlaid with odds in favour of 
normality. With this qualification we set down the figures. 
Biometrika vii 
* Lancet, April 25, 1908. 
10 
