364 Miscellanea 
Fitting lineally by Least Squares (weighted with the number of observatio,,,?) the means 
uf the groups to the corresponding death-rates, we have if x be the abscissa of normal curve 
Death-rate = 51 -3 + 25-7.r/o-. 
This gives : 
Death-rate 
Sparse 
Abundant 
Confluent 
Haemorrhagic 
Range ... 
Value at Mean of Class 
0 to 15-0 
3-4 
15-0 -47-2 
33-5 
47 -2 -97 -9 
66-7 
9 7 '9 upwards 
108-0* 
Observed Value ... 
ll-l±7-2 
29-3±4-8 
68-9±4-4 
100 ±9-8? 
These results are well within the errors of the samples given. The death-iute at the mean 
amount of pocking is 51-3. Thus, if we assume the amount of severity as given by pocking to 
follow a normal curve, the scale of severity obtained fits well the severity of the classes as 
found by a death-rate standard. It is further clear that the modal value lies in the confluent 
class and does not coincide with the slightest cases. Further there is a very high correlation 
between severity as measured by a normal scale of pock-marking, and severity as measured by 
death-rate in the case of no acquired innaunity. 
If an investigation similar to the present on cases vaccinated, — say within ten years — should 
show that a normal distribution of pock-markings fits in well there also with the death-rate 
severity scale, it would indicate that Dr Turner's severity skewness is due to a mixture of vacci- 
nated and unvaccinated in his returns. Dr Brownlee's view that the disea.'^e is physiologically 
different in the two classes would thus be confirmed. The discussion having turned on the 
distribution of severity in disease, has got somewhat far from the original point, as to whether 
the case population, recovering and dying, could be represented by a normal curve. But clearly 
death on such a scale marks a certain intensity of the disease relative to the individual con- 
stitution ; a scale of pock-marking cannot, we see from the above statistics, be equivalent 
to this scale ; for deaths occur with all classes of pocking, and death cannot accordingly be 
made to correspond to a definite intensity of severity on a pocking scale. In .short "power 
to resist disease when acquired " might obey a normal distribution although pocking did not, 
for failure to recover is not a fi.xed point on the scale of number of pocks. 
If we have to dismiss entirely Dr Turner's suggestion of a curtailed normal curve, I cannot 
dismiss his severity statistics in the easy way in which he appears to dismiss mine. The bath 
test appears to me quite as valid as the pock test. It is further in accordance with a very 
considerable range of statistics for various diseases which have recently been published by 
Dr John Brownleet, and which all go to show that the severity in other diseases is not such that 
the ma.ximum frequency occurs at the minimum sex'erity, but that the mean severity is 
approximately modal with milder and severer cases on either side. 
It will thus be seen that the matter really demands further statistics. Is smallpox an 
exceptional disease for which the absolutely mildest cases are the most frequent? Or, may it 
not be that there is some method of reconciling the pock test of severity with the bath test of 
severity for which smallpox falls into line with other diseases ] It appears to me that there are 
many other factors highly correlated with time and contributing to severity which may be 
largely overlooked by the nvunerical estimate of pocking as the sole test of severity and take 
their proper place and influence in the bath test, or what for our present purposes is more 
important than either, in a "power of resistance" test. 
' This is no impossible value, for the severity might be more than sufficient to kill the whole number 
of haemorrhagic cases. 
t Royal Phil. Soc. Glastjow Proceedings, November 7, 1906. 
