Miscellanea 
431 
There appear to be very few large houses in the district, most being by their descriptions of 
the cottage type. Certainly those in which multiple cases of cancer have occurred are often 
quite small. It is not very easy to determine from the maps the exact number of inhabited 
houses, but it appears to be about 2865*. Twelve cases of cancer appeared to be living in the 
district at the date of the return ; these are not included in our number of cases. Taking 377 
death cases in all and supposing these to be distributed at random among the 2865 houses we 
should anticipate according to the formulae of my article (Biometrika, Vol. vin. p. 410). 
330'6 houses with one case, in round numbers 331 
21 - 7 houses with two cases, ,, ,, 22 
■95 houses with three cases, „ ,, 1 
■03 houses with four cases, „ ,, 0 
A total is thus obtained of 354 houses with 377 cases and there will be 2511 houses with no 
cases. 
The actually recorded numbers appear to be as follows : 2523 houses with no cases, 315 
houses with one case ; 20 houses with two cases ; six houses with three cases ; and one house 
with four cases. The identification of the houses is not always quite clear, but 1 think I have 
erred, if at all, on the side of reducing the multiple houses, e.g. I have supposed nine cases in 
which the house was not known to have occurred in non-multiple houses. On the other hand, 
when the sufferer lived in a house up to death, going perhaps to a general hospital or the work- 
house just before death, I have reckoned the cancer as developed in that house. 
If we now substitute in the general formula 
c , , (16) 2 4x(2) 2 9x(5) 2 16x(-97) 2 
we find v 2 = ^ — - + ^ -4 -{ >- — - 
x 331 22 1 -03 
= about 727. 
The probability P is therefore infinitesimal, being widely outside any existing tables for x 2 
and P. We may therefore say that if these numbers be correct the distribution cannot possibly 
be a random one. Six houses with three cases each and one with four are wholly beyond the 
bounds of the possible, assuming cancer to be distributed at random among the houses. 
I have made a second estimate of this improbability. I have assumed that Dr Law Webb's 
district actually coincides with the Madeley subregistration district and that a count of houses 
on the Ordnance Map is likely to be defective t. 
The 1841 Census gives the number of houses as 1802 and the population as 8732. The 1851 
Census gives 2006 houses and a population of 9848 ; the 1861 Census provides 2154 houses and 
a population of 10,733. In 1871 we have 2291 houses and a population of 10,535. In 1881 the 
numbers are 2359 houses and 10,026 persons. In 1891 we have 2228 houses and 8825 persons. 
In 1901, 9129 persons and 2196 houses. But it is not quite certain that the boundaries 
remained absolutely the same. In 1911 the population was 8859 and the inhabited houses 2037. 
I take 2000 as an average number of houses, and if 9000 to 10,000 be the average population 
then 4 - 5 to 5'0 are the average number of inhabitants per house. 
* Taking about eight cancer deaths a year for the last three decades, this suggests an average 
recognised duration of the disease of about eighteen months. 
t The estimate of houses must be very elastic, many houses in the period have come into being, 
large numbers have ceased to be : the 2865 is a maximum limit. 
