510 
Miscellanea 
therefore very unreliable*. We find, however^ that the correlation = — '238 with a probable 
error of about + -Oo. In other words within the limits defined by the probable errors, we get a 
correlation sensibly equal to the actual value —•174. I think accordingly that we may assume 
that the skewness of our severity test would not materially alter the condition of affairs. 
I conclude as follows : 
(i) There is no reason a priori for supposing that the distribution of severity of attack 
in smallpox follows a curtailed normal curve. Such curves are contrary to any existing 
experience of the distribution of frequency in selected groups. In particular they do not occur 
in the case of soldiers suggested by Dr Turner. 
(ii) The only tests I have been able to apply to the frequency distribution of severity 
is that of length tif period from onset or eruption to bath. These both give a continuous and 
not a curtailed curve. The curves are skew, as we are accustomed almost invariably to find 
them when time is the variate. 
(iii) This skewness, due to the time as variate, may not really be characteristic of the 
distribution of smalli^ox severity ; this could only be determined if we chose a variate other 
than time to measure severity. But if it were characteristic, it does not appear that a fourfold 
division taken so far towards the tail as occurs when we divide severity at death would seriously 
affect the result. It is shewn that within the limits of probable error the product moment 
method of calculating the coefficient of correlation and the fourfold division method lead to 
sensibly the same results, even when we have a skewness in the distribution as great as 
is indicated in the eruption to bath test of severity. 
II. On the Mean Duration of Life of Individuals Dying within a 
Year after Birthf. 
By RAYMOND PEARL, Ph.D. 
The usual custom in tabulating census returns of mortality at different ages is to use a five 
year base unit for ages above 5, and below that age a one-year unit. This method of tabulation 
makes the finding of the moments of the frequency distribution somewhat less simple than would 
be the case if all the base elements were equal. Furthermore, the age distribution of the heavy 
mortality of the first year of life is not given at all. It becomes a very important matter to know, 
at least apjjroximately, this first year distribution when one attempts to find the moments for the 
whole material, because the frequency in this element must be centred at some point before one 
can proceed with the calculations. The mean age at death of those dying under one year must 
be known. In connection with some work on vital statistics which is being carried on in the 
Zoological Laboratory of the University of Michigan, it became necessary to have as exact 
a determination of the centering point of this first year mortality as it was possible to get. 
It is the purpose of this note to present the results obtained. 
* Dr Turner's Tables XIV. and XV. contain only 8 and 2 cases in their fourth quadrants and the 
probable errors of the resulting coefficients are very considerable. I think Dr Brownlee's figures 
(Biometrika, Vol. iv. p. 325 ; Journal of Hygiene, Vol. v. pp. 533 — 4) may be safely taken as giving a 
reasonable measure of the reduction •with time of vaccination protection. 
t Contributions from the Zoological Laboratory, University of Michigan, No. 88. 
