530 
ME. B. GOMPEETZ ON THE SCIENCE 
cc. 
Carlisle. 
Milne. 
37, 
Carlisle. 
Milne. 
X. 
Carlisle. 
Milne. 
ar. 
Carlisle. 
Milne. 
The 
formula 
gives XLj.. 
XL,. 
The 
formula 
gives XL,. 
XL,. 
The 
formula 
gives XL,. 
The 
formula 
gives XL,. 
XL,. 
10 
3-81323 
3-8102 
28 
3-75759 
3-75952 
46 
3-67106 
3-66811 
64 
3-48635 
3-49734 
11 
3-81113 
3-80823 
29 
3-75397 
3-75557 
47 
3-66569 
3-66162 
65 
3-47298 
3-47972 
12 
3-80809 
3-80618 
30 
3-75619 
3-75143 
48 
3-65771 
3-65523 
66 
3-45128 
3-46150 
13 
3-80564 
3-80400 
31 
3-74623 
3-74702 
49 
3-65051 
3-64915 
67 
3-43176 
3-44264 
14 
3-80237 
3-80175 
32 
3-74222 
3-74257 
50 
3-64309 
3-64316 
68 
3-41090 
3-42292 
15 
3-80089 
3-79934 
33 
3-73870 
3-73815 
51 
3-6.3513 
3-63729 
69 
3-38863 
3-40226 
16 
3-79694 
3-79664 
34 
3-73398 
3-73376 
52 
3-62707 
3-63104 
70 
3-36540 
3-38039 
17 
3-79354 
3-79373 
35 
3-72957 
3-72933 
53 
3-61853 
3-62439 
71 
3-33865 
3-35776 
18 
3-79070 
3-79071 
36 
3-72548 
3-72485 
54 
3-60917 
3-61731 
72 
3-32065 
3-33102 
19 
3-78792 
3-78767 
37 
3-71984 
3-72024 
55 
3-59321 
3-60991 
73 
3-27909 
3-30038 
20 
3-78454 
3-78462 
38 
3-71501 
3-71550 
56~ 
3-59022 
3-60206 
74 
3-24834 
3-26505 
21 
3-78145 
3-78154 
39 
3-71112 
3-71063 
57 
3-58953 
3-59373 
75 
3-21177 
3-22401 
22 
3-77822 
3-77851 
40 
3-70380 
3-70544 
58 
3-56774 
3-58456 
76 
3-20301 
3-18041 
23 
3-77501 
3-77546 
41 
3-69939 
3-69975 
59 
3-55672 
3-57392 
77 
3-12399 
3-13322 
24 
3-77167 
3-77240 
42 
3-69491 
3-69373 
60 
3-54427 
3-56146 
78 
3-08460 
3-08386 
25 
3-76828 
3-76930 
43 
3-68929 
3-68744 
61 
3-53269 
3-54667 
79 
3-06272 
3-03383 
26 
3-76483 
3-76612 
44 
3-68313 
3-68106 
62 
3-51806 
3-53084 
80 
2-97895 
2-97909 
27 
3-76125 
3-76290 
45 
3-67643 
3-67459 
63 
3-50241 
3-51428 
Art. 13. The very near coincidence of the result of the formula 
A.Xg'o} 
with Mr. Milne’s Table, from the age 10 years to the age 80, that is to say, for seventy 
years in continuance, appears strongly demonstrative of the near proximity of the above 
formula to the law of mortality ; and from the uniformity of the progression being evident, 
which uniformity in Milne’s Table does not equally appear, gives reason for a preference 
for the number deduced from the law, to those of Milne’s Table, for adoption. But it will 
appear that notwithstanding this agreement of the result of the formula whose constants 
C, S, e, h, ^0 are obtained, the first two of them from the values of in the two formula 
—^qic 
in my paper of 1825, which treats of the formula 'L^:^d.g\ , the one being obtained by 
the vital rule of three, by the selection of the three ages 20, 40, 60, the other by the 
selection 60, 80, 100, and the other three constants, namely e, h, g'o? by help of those 
constants C, €, by only three selected ages at thirty years’ distance from each other, 
namely the ages 20, 50, 80 ; and though the vital rule of three is here constructed on a 
more recondite analysis than the former ; still that uniformity and that interesting coin- 
cidence does not subsist with ages less than 10, nor with ages above 80, and especially 
for ages from birth to the age of a few months ; because the more correct formula seems 
to require three additional terms discoverable by investigation. These I find to be of the 
form Jet'', gjf, where Jc, s, /li, v are all constant quantities, and of such peculiarly 
interesting values, that I feel it proper to draw the reader’s attention to their values, 
their effects, and the mode of the discovery of them. The effect of the first, com- 
mences at birth in its greatest value, but at the expiration of one month sinks to com- 
parative insignificance, and before the end of one year leaves no appreciable signs of its 
existence ; the second, Jef, arises in its effect with birth, but continually decreases in 
