John Spencer 
53 
mentioned above in introducing the element of mortality. It gives ^1 - -yj as the 
force of sickness at age x and leads to the result 
colog (^^^=A,,^-B.,c.?. 
The material which formed the subject of my investigation is embodied in 
Mr A. W. Watson's important work on the Sickness and Mortality Experience of 
the Manchester Unity Friendly Society for the five years 1893-1897*. The magni- 
tude of the data there dealt with — embracing as they do no fewer than 39,000 
deaths in the quinquennium and the record of upwards of 7,000,000 weeks of sick- 
ness — and the care and accuracy witli which the observations have been analyzed 
and tabulated entitle the results disclosed in the volume to a degree of authority 
to which no previous investigation of the same character can lay claim. Mr 
Watson's exhaustive enquiry led him to deal with his voluminous data upon novel 
lines, and we find tabulated the mortality experience of various sections of the 
Society grouped according to geographical situation, while as regards Sickness the 
element of occupation was the factor which determined the classification, the 
experience of each of the four following groups of trades being published : — 
(a) Agricultural and General (Normal) occupations ; 
{h) Building Trades, Railway, Seafaring and Outdoor Labouring Occupations ; 
(c) Quarry Workers, Iron, Steel and Chemical Workers, &c. ; and 
(d) Mining Occupations. 
The first of these groups is the one to which the following notes relate. It 
consists, broadly speaking, of persons engaged in occupations involving no special 
hazard, and comprises nearly 80 per cent, of the membership of the Society. These 
lives were during the quinquennium exposed to risk of sickness for 2,352,099 years, 
while they experienced in the aggregate 5,289,586 weeks of sickness in the 
period. 
Throughout the investigation in determining the quantity " Exposed to Risk 
of Sickness" it was assumed, with a particular object in view, that lives dying in 
any calendar year during the period of observation were at risk until the middle of 
the year. In consequence of this assumption the ungraduated rates of sickness 
which were obtained by dividing the number of weeks' sickness experienced during 
the year by persons of a particular age by the quantity "Exposed to Risk" at that 
age differ from the rates of sickness ordinarily tabulated. They represent rather 
what might be termed central rates of sickness, or, approximately speaking, values 
of the force of sickness at the middle of the year. The latter consideration enables 
us on the hypothesis which I am discussing to write the tabulated rate of sickness 
in the form A -\- Bc'^+i and suggests a simple method of deducing the values of 
the constants. Having for reasons which will appear presently come to the 
* London : C. and E. Layton. 1903. 
