568 Mr. Gompertz on the nature of the function 
TABLE VI. — Accommodated annual ratio for an unlimited period for every age a 
1 , 05 "^ 1 , 05 -* 
Xr=X i‘l£_X«ll + X 1,05. 
-1 
^ r Carlisle, 
*».rDeparcieux. ? 
r Northampton. 
a 
Carlisle. 
^ 1’ Deparcieux. 
Xr Northampton. 
0 
7,98665 
— 
— 
52 
1,98390 
1,98216 
1,97950 
1 
1^99121 
— 
*>98517 
53 
1,98305 
1,98240 
1,97878 
2 
*>99313 
— 
*>98997- 
54 
1,98212 
1,98156 
1,97802 
3 
1,99458 
*>99399 
*> 99 * 5 * 
55 
1,981 12 
*,98073 
1,97721 
4 
1,99528 
*>99446 
*,99244 
56 
1,98005 
1,97982 
^^97^35 
5 
1,99577 
*>99473 
1,99284 
57 
1,97887 
1,97882 
*>97542 
6 
1,99599 
*>99493 
1,99324 
58 
*>97763 
1,97780 
*>97445 
7 
1,99606 
I >99505 
1,99346 
59 
*,97637 
1,97668 
*>97341 
8 
1,99606 
*> 995*3 
1,99357 
60 
*> 975*4 
*>97545 
1,97230 
9 
f, 99600 
*> 995*9 
1,99354 
61 
1,97400 
1,97408 
1,971 1 1 
10 
1,99529 
*> 995*9 
1,99341 
62 
1,97281 
*>97254 
*>96983 
1 1 
1,99576 
*>99514 
1,99323 
63 
*>97154 
1,97093 
*>96843 
12 
1,99563 
1,99503 
*,99304 
64 
1,97014 
1,96912 
*,96693 
*3 
1,99549 
*>99491 
1,99284 
65 
1,96858 
1,96707 
1,96526 
*>99535 
*>99478 
1,99262 
66 
1,96685 
1,96489 
1,96346 
15 
1,99522 
*,99464 
1,99240 
67 
1,96491 
1,96250 
1,96150 
16 
*>99509 
1,99450 
1,99213 
68 
1,96273 
1,96009 
1,95936 
17 
*,99487 
1,99438 
1,99190 
69 
1,96029 
*>95750 
*>95703 
18 
1,99484 
*>99425 
1,99167 
70 
*>95755 
1,95480 
*,95448 
19 
1,9947* 
*>99413 
*,99*45 
7 * 
*>95440 
£,95181 
*>95*71 
20 
*>99455 
*>99398 
1,99124 
72 
1,951 1 1 
1,94870 
1,94869 
21 
*,99442 
1,99388 
1 .99106 
73 
*>94784 
1,94542 
*>94541 
22 
*,99425 
*>99375 
1,99088 
74 
*>94467 
£,94180 
1,94186 
23 
1,99408 
*>99364 
1,99070 
75 
1,94185 
*,93790 
1,93812 
24 
*>99390 
*,99350 
1,99051 
76 
1,93888 
^>93330 
1,93423 
25 
*>99370 
*>99338 
1,99030 
77 
*> 9359 * 
£>92833 
1,92994 
26 
*>99349 
*>99323 
1,99009 
78 
£,93265 
1,92314 
*>92503 
27 
1,99328 
*,99308 
1,98988 
79 
1,92863 
*>91715 
1,91916 
28 
7,99306 
*,99293 
1,98965 
80 
1,92461 
1,91 124 
1,91246 
29 
1,99290 
1,99277 
*>98943 
81 
1,91891 
*,90493 
1,90509 
30 
7,99265 
*>99259 
1,98917 
82 
1,91491 
1,89856 
1,89697 
3 * 
*>99245 
1,90241 
1,98892 
83 
*>90939 
1,89069 
1,88844 
32 
1,99224 
*>99223 
1,98865 
84 
*,90344 
i,88co5 
1,881 10 
33 
1,99201 
1,99202 
*,98837 
85 
1,89657 
1,86782 
1,87361 
34 
7,99176 
1,99181 
1,98808 
86 
1,88978 
1,85416 
1,86599 
35 
1,99149 
1,99158 
*,98777 
87 
1,88369 
1,8401 1 
1,85803 
36 
1,991 10 
*> 99*34 
*,98745 
88 
1,87972 
1,81788 
1,85069 
37 
38 
7,99090 
1,99058 
£,99109 
*>99077 
£,98811 
1,98675 
89 
90 
1,87481 
1,86660 
1,78941 
*>75223 
£>85454 
1,82243 
39 
1,99025 
*,99043 
i>98637 
9 * 
1,86560 
1,70265 
1,79303 
40 
1,98991 
1,99006 
*,98597 
92 
1,87056 
1,63694 
*>74992 
4 » 
1,98958 
1,98967 
1,98556 
93 
£,87595 
*>52971 
*>67376 
42 
43 
1,98924 
1,98890 
1,98924 
1,98878 
1 >985 1 3 
1,98469 
94 
95 
1,87840 
1,87967 
— 
*>55753 
*>30505 
44 
*,98853 
1,98828 
1,98423 
96 
*>77774 
— 
45 
1,98814 
*>98771 
*>98375 
97 
*,77140 
— - 
— 
46 
*>98771 
1,98714 
*>98323 
98 
£>76333 
— 
• 
47 
*>98725 
1,98655 
1,98270 
99 
1,84829 
— 
— 
48 
1,98673 
1,98590 
1 ,98209 
100 
1,81282 
- - 
— 
49 
1,98612 
1,98526 
1,98148 
loi 
*,75663 
— 

50 
7,98546 
7,98456 
1,98083 
102 
1,65421 
— 
— 
51 
1,98471 
1,98386 
1,98017 
103 
1,40266 
