158 On the Theories of Multiple and Partial Contingency 
Hence it would follow that 
or the first factor is approximately unity. The value of Xo' then becomes 
a quantity which I have shown elsewhere * has an important relation to the question 
of the significant difference of corrected death rates. 
It is obvious that the present method is of wide generality and I propose to 
illustrate it later by considering whether the general death distributions of various 
national groups allowing for age distribution, occupation distribution and character 
of mortality are or are not significantly different. 
Meanwhile (xxxix) provides us with a formula which enables us readily in the 
case of districts, special diseases or class groups to assert whether mortality 
experiences corrected for age distribution are or are not significantly different. 
As far as I can see (xxxix) and its extensions to occupation groups provide the 
proper means of ascertaining whether the populations at risk in various insurance 
offices or friendly societies are or are not materially different in character. It 
should be a guide to the actuary also as to which classes of the population it 
is most desirable to cater for. 
I have to thank my friends Mr H. E. Soper and Mr A. W. Young for 
suggestions and help at several points. In the following paper numerical 
illustrations of (xl) are provided. 
VP' \P) \p + p'J' 
* See Biomdriha, Vol. xi. p. 164. 
