K. Pearson 303 
were based on the range 17 to 88 and therefore are not strictly comparable with 
mine based on a different range. 
Life Table (L^ = log Ix). 
Calculated differences* 
Calculated differences 
Age 
Observed 
By moments 
By averages 
Age 
Observed 
By moments 
By averages 
25 
3-96833 
+ 
•00184 
+ 
•00043 
56 
3^81354 
+ 
•00046 
+ 
•00039 
26 
•96609 
+ 
83 
— 
45 
57 
•80339 
75 
+ 
59 
27 
•96307 
+ 
56 
- 
59 
58 
•79289 
4- 
71 
+ 
44 
28 
•96025 
+ 
5 
- 
97 
59 
•78184 
+ 
47 
+ 
09 
29 
•95684 
+ 
8 
— 
81 
60 
•77069 
— 
50 
— 
100 
30 
•95363 
- 
13 
— 
91 
61 
•75695 
+ 
21 
- 
41 
31 
•95003 
- 
1 
— 
67 
62 
•74259 
+ 
55 
- 
20 
32 
•94682 
— 
34 
— 
89 
63 
•72729 
+ 
73 
- 
15 
33 
•94319 
32 
— 
76 
64 
•71075 
+ 
95 
6 
SJf 
•93957 
37 
72 
65 
•69294 
+ 
112 
— 
2 
35 
•93578 
34 
59 
66 
•67359 
+ 
138 
+ 
13 
36 
•93219 
60 
76 
67 
•65281 
+ 
148 
+ 
12 
37 
•92833 
68 
76 
68 
•63099 
+ 
87 
57 
OO 
56 
56 
A'Q 
Oif 
+ 
123 
27 
39 
•91967 
23 
16 
70 
•57894 
+ 
212 
+ 
58 
40 
•91503 
+ 
12 
+ 
25 
71 
•55390 
161 
314 
41 
42 
•91072 
0 
+ 
19 
72 
•52602 
504 
652 
•90615 
1 
+ 
22 
73 
•48994 
306 
443 
43 
•90147 
8 
+ 
19 
74 
•45432 
460 
579 
44 
•89685 
40 
9 
75 
•40598 
+ 
321 
+ 
229 
45 
•89169 
38 
5 
76 
•36295 
+ 
202 
+ 
147 
46 
•88629 
34 
0 
77 
•31403 
+ 
266 
+ 
261 
47 
•88082 
48 
13 
78 
•26403 
7 
+ 
51 
48 
•87463 
16 
+ 
18 
79 
•20713 
80 
59 
49 
•86847 
18 
+ 
15 
80 
•14362 
29 
+ 
210 
50 
•86179 
+ 
1 
+ 
31 
81 
■07776 
332 
+ 
29 
51 
•85456 
+ 
39 
+ 
65 
82 
•00212 
306 
+ 
205 
52 
•84693 
+ 
77 
+ 
99 
83 
2'92001 
343 
+ 
348 
53 
•83947 
+ 
56 
+ 
72 
84 
•81934 
+ 
694 
+ 
1600 
54 
•83194 
5 
+ 
4 
85 
•73319 
578 
+ 
584 
55 
•82363 
40 
38 
* Calculated less observed values. 
By the method of moments the mean difference is 00116 and by the method 
of averages it is "00126. The improvement is not vei-y sensible, but the method 
of fitting being brought under a general rule is an advantage of great importance. 
The actuaries have adopted Makeham's formula to express the life-table, but it 
cannot be considered to give good results for the down slope of old age, say 68 
onwards. From the mathematical standpoint better results would be obtained by 
the choice of other functions. I have selected Makeham's solely with a view of 
illustrating the application of my general method to a somewhat complex arith- 
metical problem. 
{To he continued.) 
