Ethel M. Elderton and Karl Pearson 
565 
early periods had most isolation in the later period, and whether the towns with 
most rapid increase of isolation -rate in the earlier periods had most incidence in 
the later period. We found : 
,. ; J = - -004 + -077, 
rf = + -085 + -077. 
-'2-1 -'':! 
Thus there is no significant relation whatever between either increase of attack- 
rate or increase of isolation-rate in the first periods, and the isolation or the 
incidence in the following period. 
As criticism of this result it might, perhaps, be suggested that the correlation 
of A2-1 and I3 will be influenced by what has been the course of / in the periods 
and and the nature of A in T. ; we have accordingly, in order to test this, 
made the isolation-rate constant in the first two periods and the attack-rate 
constant in the third period and find 
ri J = + -147 + -076. 
-'1+2 ^3 "^2-1 ':i — 
This is still of no real significance, although the sign appears to indicate that 
where the isolation-rate has been constant then increasing attack-rate in the 
earlier period is followed by very slightly more isolation in the third period, even 
if the attack-rate in that period be itself constant. 
Similarly we determined : 
rj , = + -077 + -077. 
^1+2 ■'3 -'2-1 '^3 
This coefficient shows that towns which have increased their isolation-rate during 
a period of constant attack are not liable to sensibly heavier attack in the 
following period. 
It would thus seem that our first two problems are both to be answered in the 
negative. Towns which increase their isolation are not those which in the fol- 
lowing period have most incidence, nor are those which have increasing incidence 
markedly those of most isolation in the following period. Attack and isolation 
appear to have no causative relation, and the association we have found between 
more isolation and more incidence seems to be contemporaneous rather than 
successional. We are, it seems, compelled to search for something in the environ- 
ment, which favours incidence and at the same time isolation. The only common 
factor that we have been able to reach at present is the prosperity and general 
healthy condition of the town. Under these circumstances there appears to be 
economic possibility of greater isolation, but why should there be greater incidence ? 
Is it possible that in the more prosperous towns there is greater consumption of 
some easily contaminated commodities, which may act as carriers of the disease, 
or more concourse of those of susceptible ages at places of public amusement or 
instruction ? 
(8) Test of the "organic" nature of the correlation of Isolation- and Attack- 
rates by the method of Variate Differences. If the suggestion made at the end 
of the last section be correct we should anticipate that by the use of the method 
72—2 
