0(3 Graduation of a Siclmess Table hij Maliehani's Hypothesis 
Ifc will be seen that on the whole my graduated rates run very closely to the 
unadjusted values until about age 55. Above that age the agreement is not 
invariably so marked and from age 75, as might have been anticipated, the two 
series diverge rapidly. Obviously the graduation fails to fit the raw data above 
age 80 and, apart from this circumstance, the fact that after a certain point the 
value of the force of sickness would exceed unity, or 52^ weeks per annum, forms 
a theoretical objection to the hypothesis as applied to the final ages in the table. 
Makeham's own theory of sickness avoids the latter difficulty, though, after 
investigation, I conclude that it fails satisfactorily to represent the sickness after 
age 80 in the table under examination. 
To show the extent to which the graduated rates of sickness reproduce the 
actual sickness experienced when multiplied at each age by the number " Exposed 
to Risk " I now give the following comparison : — 
Age 
Group 
Expected weeks 
of Sickness 
Actual weeks 
of Sickness 
Excess of 
Expected over 
Actual 
Ratio per cent, 
of Excess to 
Actual 
16—29 
659,739 
658,029 
+ 1,710 
+ -3 
30—89 
645,877 
652,620 
- 6,743 
-10 
JfO-49 
700,681 
715,141 
-14,460 
-2-0 
50—59 
938,759 
924,705 
+ 14,054 
+ 1-5 
60—69 
1,035,598 
1,046,278 
- 10,680 
-1-0 
70—79 
1,009,216 
1,005,771 
+ 3,445 
+ -3 
Totals 
4,989,870 
5,002,544 
-12,674 
- -25 
As a final test of the graduation I append the values at 3% interest of a 
benefit of £1 per week during sickness throughout life as compared with those 
published officially, the mortality assumed in each case being that exhibited by the 
members of the Society in Non-Manufacturing Districts, designated Area 1 in 
Mr Watson's volume. For the purpose of calculating the former values it was 
necessary to deal with the sickness above age 79 and I made the convenient 
assumption of a constant rate of sickness from age 80 onwards of 34"634 weeks per 
annum, this being the value of A + Bc^" given by my constants. The average rate 
of sickness at these ages according to the observations is only 32"724' weeks per 
annum, but the adoption of the higher value not only avoids the assumption of a 
diminishing rate of sickness but introduces a factor which compensates for the 
deficiency of Expected Sickness up to age 79. Strictly speaking perhaps I should 
have worked out monetary values from the unadjusted data for comparison with 
those now calculated, but since the graduation upon which the official values are 
based is in effect a smoothing-down process which reproduces the prominent 
characteristics of the rough data, the published values may coufidently be employed 
as a standard of comparison. 
