642 
ME. B. aOMPEETZ ON THE SCIENCE 
and supposing a to be constant, that is to say, supposing the chcumstance of speciality 
to cause a constant instantaneity of effect, we shall have 
and therefore if N represent the number whose Napierian logarithm is 1, that is, if 
be put for <=-1, then, because Mo=La, we have 
If a were very small, which would be the case if the speciality depended on the risk of 
death by shipwreck, which might be but 1 or 2 per cent, per annum to a sailor either 
always at sea or occasionally at sea, then the above expression would give the 
number out of living who would be living in x years 
Art. 23. No. 1. This Table of Napierian Logarithms of persons living at every Age 
according to Milne’s Carlisle Mortality will be found useful ; I have therefore given it. 
X Age. 
X Age. 
X Age. 
0 
9-21034 
34 
8-59739 
68 
7-88156 
1 
9-04322 
35 
8-58709 
69 
7-83400 
2 
8-95854 
36 
8-57678 
70 
7-78344 
3 
8-89206 
37 
8-56617 
71 
7-73061 
4 
8-85338 
38 
8-55526 
72 
7-66996 
5 
8-82434 
39 
8-54403 
73 
7-59940 
6 
8-80627 
40 
8-53208 
74 
7-51806 
7 
8-79392 
41 
8-51899 
75 
7-42357 
8 
8-78508 
42 
8-50512 
76 
7-32317 
9 
8-77848 
43 
8-49064 
-77 
7-21450 
10 
8-77338 
44 
8-47595 
78 
7-10085 
11 
8-76889 
45 
8-46105 
79 
6-98564 
12 
8-76405 
46 
8-44613 
80 
6-85961 
13 
8-75904 
47 
8-43120 
81 
6-72982 
14 
8-75385 
48 
8-41649 
82 
6-62274 
15 
8-74830 
49 
8-40479 
83 
6-43455 
16 
8-74219 
50 
8-38868 
84 
6-27019 
17 
8-73536 
51 
8-37526 
85 
6-09807 
18 
8-72847 
52 
8-36077 
86 
5-90536 
19 
8-72144 
53 
8-34555 
87 
5-69036 
20 
8-71440 
54 
8-32918 
88 
5-44674 
21 
8-70738 
55 
8-31214 
89 
5-19850 
oo 
8-70025 
56 
8-29405 
90 
4-95583 
23 
8-69333 
57 
8-27487 
91 
4-65396 
24 
8-68626 
58 
8-25375 
92 
4-31749 
25 
8-67914 
59 
8-22924 
93 
3-98809 
26 
8-67180 
60 
8-20056 
94 
3-68888 
27 
8-66441 
61 
8-16650 
95 
3-40129 
28 
8-65661 
62 
8-13006 
96 
3-13549 
29 
8-64788 
63 
8-09193 
97 
2-89037 
30 
8-63799 
64 
8-05293 
98 
2-63906 
31 
8-62784 
65 
8-01235 
99 
2-39790 
32 
8-61758 
66 
7-97039 
100 
2-19722 
33 
8-60749 
67 
7-92696 
