DE. EAEB ON THE CONSTEHCTION OE LIFE-TABLES. 
853 
reduced to zero, and is therefore omitted. The first given term being let the second 
be the Ath from and iiy be the yth, the ;sth from Wo- Here x<y<z. Then the 
following equations give the differences*: — 
{y-x){{z-\)[ 2 - 2 )-{^-l){y- 2 )}-{z-y){{y-l){y- 2 )-{x-l){x- 2 )] ' ^ ’ 
5’=y4s{^-7-{&-l)&-2)-(*-lX*-2)}|} (14.) 
(15.) 
By making y — 2x, and z — ?>x, these equations assume the same forms as equations (3.), 
(4.), (6.), with the term struck out. 
Putting .r=4, y = 9, and 2 = 17, the three preceding equations become those which 
were actually used in constructing the series to is reduced to zero and is not 
used. 
45 ^ 17 - 22 1^ 9 + 306 2/4 
13260 
^2 4M9 — 92/4 — 3008 ^ 
' 90 ' 
(17.) 
2/4 — 68® — 48® 
~ 4 
Checking equation. 
w,.=W4-|-17S‘ + 136a^-f680S^ 
(18.) 
(19.) 
* A useful Table in applying the above formulae. 
X. 
(a?-l)(x-2). 
X. 
{ x — l)(.r— 2). 
X, 
{w— 1)(^ — 2). 
X, 
(x — l){x — 2). 
20 
342 
30 
812 
40 
1482 
50 
2352 
21 
380 
! 31 
870 
41 
1560 
51 
2450 
22 
420 
1 32 
930 
42 
1640 
52 
2550 
23 
462 
! 33 
992 
43 
1722 
53 
2652 
24 
506 
34 
1056 
44 
1806 
54 
25 
552 
35 
1122 
45 
1892 
55 
2862 
26 
600 
36 
1190 
46 
1980 
56 
2970 
27 
650 
37 
1260 
47 
2070 
57 
3080 
28 
702 
38 
1332 
48 
2162 
58 
3192 
29 
756 
39 
1406 
49 
2256 
59 
3306 
5 u 
MDCCCLIX. 
