Ethel M. Elderton and Karl Pearson 
563 
Turning now to our measure of the prosperity of the district, we find that it 
has no influence on the attack-rate, that it sensibly, but not very intensely affects 
the mortality, the higher death-rate occurring in the poorer districts, and that 
isolation is associated quite significantly with the prosperity of the district, i.e. the 
more well-to-do the district the more isolation is practised*. 
Variates Correlated 
Number of Domestic Servants and Attack-rate . 
Number of Domestic Servants and Death-rate 
Number of Domestic Servants and Isolation -rate 
First Period 
1901-1908 
-f- 095±-076 
- -219 ± -073 
+ -437 ± -062 
Second Period 
1909-1912 
-f -024 ±-075 
- -308 ± -068 
+ -363 ± -065 
We conclude therefore that the more prosperous and generally healthier 
districts are associated with fuller isolation, and that the more prosperous, but 
not necessarily the more healthy districts, have the less diphtheria death-rate. 
On the other hand the incidence of the disease seems independent of the prosperity 
or density of population of the district and to be somewhat greater in those towns 
where the sanitary conditions as judged by infant death-rate and overcrowding are 
betterf. 
Thus as far as our measures go, we must conclude that diphtheria is not to be 
considered as a disease of markedly urban districts, of overcrowded or of insanitary 
districts J. It would appear that the more prosperous and healthy districts have 
the greater isolation and that these are subject to somewhat the greater incidence. 
* Of course this may largely mean that the more prosperous towns introduce isolation to remove 
the supposed danger of infection when servants of the families of the well-to-do are attacked. 
t In order to ascertain whether the variates persons per acre (p^) and overcrowding (O) were merely 
measures of the size of the town population (P) we correlated P with and with 0 and found : 
rp^^= +-404±-064 (1904-8), = 4- -402 ± -063 (1909-12), 
j-po= -(-•091 ±-07(3 (1904-8),= + -074 ±-075 (1909-12). 
Thus overcrowding has no relation to the size of the town, the larger towns do not show more over- 
crowding. There is, however, a considerable association of persons per acre with total population, 
the larger towns having more persons per acre without exhibiting any more significant overcrowding. 
Making the population constant we find : 
First Period 1904-1908 
' Second Period 1909-1912 
[ 
Total Correlation 
Partial Correlation 
Total Correlation 
Partial Correlation 
r^^^= -h-165± -075 
rj= - -153 ±-075 
r?> _= -f •122±-076 
p)-.v„"= - -167 ±-075 
r^„^= +-043±-075 
--136 ±-074 
= -^•023±-075 
pr^,/= -•140±-074 
Thus correcting for population only makes the relation between persons per acre and incidence still 
more insignificant, while the relation between incidence and less overcrowding becomes slightly greater, 
without rising to any real importance. 
X This result must not offhand be extended to subdistricts of our towns, it is an inter-urban and not 
intra-urban statement. 
Biometrika x 72 
