1910-11.] The Mono-Molecular Reaction and Life- Processes. 631 
TABLE IY. 
Table showing the Case Mortality for Small-pox among the Vaccinated, 
Gloucester, 1895-6. 
Age 
Period. 
Cases. 
Deaths. 
Case Mortality. 
Actual. 
Theor. 
20-30 
367 
23 
6-2 
8T* 
30-40 
272 
29 
106 
10*6 
40-50 
142 
21 
14-8 
13-8 
50-60 
63 
12 
19-8 
18-0 
(50-70 
34 
8 
23-5 
23-6 
70-80 
13 
4 
30-8 
30-8 
* Age when the law does not hold. 
For all ages = 2 - 4 P = *62. 
For ages above 30 )(= '3 P = '91. 
With regard to small-pox, Table IV., the’ Gloucester figures show a very 
good agreement between fact and theory. From 30 upwards the concord- 
ance is exact. The theoretical figures were fitted to the mortality rates for 
the latter years, and that for the age period 20-30 thence calculated. When 
the whole series thus obtained is considered, the value of P is not specially 
high, but for the period above 30 years the fit is exceptionally good. 
3. Gompertz ’ Law . — This law is the product of an earlier science, 
and has almost been forgotten. Briefly expressed, it is to the effect that 
the liability to death increases in a geometrical progression with age. Its 
truth is undoubted for all ages above 50 for both sexes. In this law 
Makeham made a change which rendered it much more convenient to 
actuaries, but which obscured the biological significance of the original 
statement. The following figures from the Registrar- General’s tables for 
England sufficiently explain the facts : — 
\ 
TABLE Y. 
Showing the Average Death-rate in Males and Females at Ages 55 and 
Upwards for the Period 1858-1901. 
Age Period. 
Males. 
Females. 
55-65 
333 
28 1 
65-75 
68-3 
60-0 
75-85 
147-4 
133-3 
85- 
308 6 
281-9 
The death-rate thus approximately doubles itself every ten years. 
