434 
Miscellanea 
distribution of cases. Dr Law Webb's data provide sufficient evidence to justify a demand for a 
thorough investigation of the subject, such as is not feasible in the case of the individual medical 
man. They do not finally demonstrate that cancer is more frequent in one house than a second, 
but they do justify a complete inquiry into the possibility that "cancer-houses" are not wholly 
a myth, in other words, that immediate environment is in the long run a factor of the frequency 
of cancer. What is needed is a record of the houses in which cancer has occurred, say for the 
last 50 or 60 years in (i) a practically fully developed urban district, (ii) a completely agri- 
cultural district, and (iii) an industrial area such as occurs frequently in Lancashire or 
Yorkshire, etc., with relatively small factories, mines or works spread out over a rural district. 
The examination of the certificates of death of such districts, the careful preparation of " spot 
maps," and the record of occupations and relationships ought to be a perfectly straight-forward 
matter, and if it be carried out, — whether it justifies the inference to be drawn from the present 
data, or does not, — I think Dr Law Webb must be considered as a pioneer in the inquiry. 
Experiment. It occurred to me on reading this paper through after completion, that the im- 
probability of multiple cases as measured by the P derived from x 2 , however much it may appeal 
to the statistician, might not sufficiently impress the medical mind as demonstrating the non- 
random character of this cancer distribution. Above all a medical man thinking of cancer as a 
common disease might fail to appreciate, on reading the individual details of the multiple cases, 
their extreme improbability taken as a whole. 
Accordingly, at the suggestion of my colleague, Dr David Heron, I arranged for the drawing 
at random of 377 cases out of 2000 possibilities. What we want is something equivalent to 
drawing 377 times at random a ball out of 2000 balls numbered 1 to 2000 in a bag, each 
ball being replaced after drawing. 
The experiment was arranged in the following manner. A series of numbers of four figures 
having no exact square root, cube root or reciprocal was taken, and the figures in the 
seventh decimal place of the first and second and in the tenth decimal place of the third were 
written down. These formed the last three figures of the numbers. To obtain the first figure 
in the number, in one case the last figure of the cube, i.e. the twelfth was taken, and in three 
other cases, the tenth figure of the cube. The whole series of 377 numbers were thus taken 
directly from tables of cubes, square roots, cube roots and reciprocals (Barlow's). Out of the 
numbers thus obtained, those beginning with 0, 1, 2, 3, 4 were reckoned as belonging to the 
first thousand, and those beginning with 5, 6, 7, 8 and 9 to the second thousand ; 0000 
counted however as 2000. Thus : 3004 = 0004 = 4, but 5004 = 1004. We thus had equal chances 
for every number from ] to 2000, provided there be no bias in taking numbers consecutively * 
out of such tables. 
The results were as follows : 
Theory 
1st 
Experiment 
2nd 
Experiment 
3rd 
Experiment 
4th 
Experiment 
Pi ■■■ 
313 
315 
321 
333 
321 
Pi ... 
29 
31 
28 
22 
28 
Ps ■■■ 
2 
0 
0 
0 
0 
pi 
0 
0 
0 
0 
0 
The absence of triplets led me to suppose some bias in the tables tending in favour of more 
uniform distribution than a mere random drawing provides. Accordingly a fifth experiment 
* Subject to the omission of numbers with perfect square or cube roots etc., as stated above. 
