2 66 
L 
Mr. Gompertz's analysis applicable to the 
( 
c+x 
+ 
x+x 
zL 
x : a, c 
of 
/ L , 
/ ^ +■ ^ 
C + x 
+ 
c 
L 
= correction 
i .L , 
o + x c+x 
TTTl 
o c 
zL 
x:b,c 
J b,c 
~‘x:a,b 
l-t 
a, o 
'« + x 
— fluent 
zL. 
x:a,c 
a, c 
J Z>+x\ 
~T~J ’ an< ^ assurance on the contingency may evidently 
bear the form in which Mr. Baily has put it. 
Example 9. On the death of the last survivor of A, B and 
C ; provided that should be either A or B : this contingency 
in a similar manner from the proper interpretations of K" and 
K'", is found immediately = — fluent of (1 
J b+X 
. 1 - 
C + X 
"fl + X 
f 1 
a + x 
. 1 
C + X ^ + x'\ rj n C + X 
— ■ -lT = ~ fluent of 1 - — 
C 0 / c 
X ( 1 
^6 + x ^a+x . ^"x + x ^5 + x\ ^ c -\-x 
l -+ 1 — • -£-j=fluentoti- T — 
b a a b / c 
(■ - -ir7 
C + X 
Of 
c+x 
(1 
J b+x 
fl+X 
. 1 — _£±i _|_ fluent 
Hence the assurance on 
this contingency, will be equal to the assurance on the longest 
of the three lives ; — the assurance of C’s life, provided that 
he be the last which fails. See Example 3. This in fact is 
almost evident at first sight. 
Example 10. On the death of the first of the two A and B, 
provided it be the first or second which fails. This, as Mr. 
Morgan, &c. observe, is on the extinction of the joint lives 
A and B only, &c. 
