508 
Miscellanea 
I have next endeavoured to form an estimate of the distribution of severity in the oases of 
smallpox, and the only method of doing this seemed to be to form a frequency distribution for 
the intervals which elapse between either (a) onset or {b) eruption and the first bath. This may 
be taken in a rough sort of way as a measure of the severity of the attack. Unluckily any 
character which depends on time usually gives a skew frequency distribution and the present 
case is no exception to the rule. But I do not think that the resulting distributions can be in 
any way described as curtailed normal curves. Dr John Brownlee kindly provided me with the 
particuliirs of between 800 and 900 cases. I could distinguish no sensible differences in the male 
and female distributions. Further, the vaccinated cases formed a very large proportion of the 
total, for example 779, as against 55 un vaccinated and 21 doubtful. Hence, taking into account 
that what Dr Turner is dealing with is the distribution of cases in all classes, vaccinated or 
unvaccinated, I have clubbed all groups together to get my distribution of severity. There 
were 57 deaths, which must of course be excluded, from a time to bath test of severity, they 
occurred with rather an erratic distribution at a mean interval of 10'4 days after onset or 7'6 
days after beginning of the eruption. Thus the interval between onset and eruption in the fatal 
cases is about 2'8 days, while in the recoveries it is 3"1 days, so that there may, when more 
material is forthcoming, be found to be a sensible difference in this interval for the two classes of 
cases. 
The following table gives the distribution of severity of attack as measured by the two tests 
of days (i) from onset to bath and (ii) from eruption to bath. _ 
Days 
1 
1 
1 
1 
J, 
<-( 
1 
1 
1 
®< 
1 
1 
1 
f 
1 
so 
BO 
1 
1 
so 
1 
so 
1 
T 
Totals 
o 
00 
®! 
Co 
3^ 
eo 
■a 
so 
00 
so 
Onset to Bath ... 
2 
13 
40 
131 
192 
152 
99 
73 
40 
24 
13 
17 
10 
6 
4 
6 
2 
1 
1 
826 
Eruption to Bath 
lu 
55 
164 
174 
156 
96 
71 
39 
26 
13 
21 
6 
8 
2 
7 
3 
3 
1 
855 
Neither of these distributions can be considered as a curtailed normal curve. They must, I think, 
be looked upon as significantly skew distributions of the usual type such as in practice almost 
invariably arise, when time is the variate to which we plot frequency. They do not appear to 
me to give any support to Dr Turner's view exjjressed on p. 496 above as (2), or to the sugges- 
tion on p. 497, that the mildest cases ai;o more frequent than those more severe ; the different 
degrees of severity do not diminish without exception as the degree increases, and since the bulk 
of our cases are all vaccinated, it is not possible to suppose that the actual frequency curve 
among the vaccinated is of the type suggested by Dr Turner. The modal frequency corresponds 
to a sensible degree of severity of attack, i.e. to about 13 days from onset to first bath, while the 
mildest cases correspond to only 4 days. It seems therefore quite impossible to suppose, as 
Dr Turner does on p. 502, that the severity frequency distribution is half a normal curve of all 
exposed to risk. The distribution of the attacked ver}' considerably passes the mode, and on 
the assumption made by Dr Turner, those exposed to risk and escaping must be a very small 
fraction indeed of the total population exposed to risk. Indeed the above distributions show 
that the severity of the attack rises from zero to a maximum, and then falls, in the usual skew 
frequency fashion, at a slower rate to zero. The constants of the above distributions have been 
worked out ; it will suffice here to give, however : 
Onset to Bath ft = 2-3229, i32 = 6-2466. 
Eruption to Bath = 2-606, /32 = 6-3664. 
Thus both distributions are sensibly non-Gaussian. 
