202 
Mr. Gompertz’s analysis applicable to the 
'‘a—p, b—\p, c—\p P 
■ — jy~ ' - X n 
a, l,c m 
a—p, h—\p, c~\p — 
hr H 
b, c m 
a, l — \p. c — \p 
This is on the supposition that we have neglected the value 
due to the part - r’ +f x — ' + ’ r 
12 1 ■ 
L 3-f 9T4-A 
X T £ X 
C ~hvF~\~ p 
3 as being extremely small when p is small, 
c 
such for instance as one year. But I observe that a near ap- 
proximation of its value in this case is one twelfth of the in- 
come certain for the term multiplied by the chance of all three 
dying between the intervals n and n-\-p ; and as an example 
ofy>=i n= l, and the corresponding assurance for the whole 
possible joint existence be required from the Northampton 
Tables, for three lives at the age of 30, at the interest of 3 per 
cent. ; considering the last income possibly to be received, to 
be at the age 95, the term will be 65, and the approximative 
value of this neglected part, if the assurance be on ,£1000. to 
be paid for in one payment; will be 1000 x ~ 
= about - ^ 3 * 5 oo of one pound, which is less than three pence. 
If we use Article 10, Section 3, we shall obtain the same 
portions of the contingencies as has been used by Messrs. 
Morgan and Baily, whence &c. 
“ Note. I may observe that if the contingencies were as in 
<c this example with the exception that A is to die before any 
‘‘ of the lives B, G, D, F, &c. the value would be 
te 
J a — p ,b — |j>, c — \p, d — \p, &c. , P 
J a, b , c, d , & c. 
a — p > b — Ip, c — d — \p, &c. 
