2 JI 
are 
Survhorjhips . 
^ ’ r ~ I ■ - V ; and the two laft feries are=:D; the 
whole value of the reverfion, therefore (when C is the oldeft 
of the three lives), — -~ -f D -f S - 2Q. 
When A is the oldeft of the three lives, the different feries, by 
changing the fymbols, as in fome of the foregoing problems, will 
, 2 S abc' . ms.c' + c' n 2S msc' nt.c' + c " Q 
become = , x 4- &c. x — + — 4- &c. - 
abc r r cib t r r z 
AS abc ' , msc" , nt*c" , « , 2S ms . c* nt . c r oh . 
— X — + — + — - + &C.+ -r x — — + &C. 
%abc r 
%abc 
_ amt m t at , Q , b bsc ttltC ' 72 UC ' ' ~ 
+ — r x — H — r'! — r + &c. + — r x - + _ - + -r- + &c. - 
r r r 5 yibc r r >■$ 
S be' , m . 7 + 7 ' J S »' J 
X + + &C. + — X -{ --j + ,&C. + 
be r r be r 
S be . m " . ne"’ . „ S 
4- X “ + 2j- + CL. + &C. - ~ X — + 
2 be r r r 3 2^ r r 
S 
4 - &c. - 
ac' , J . , a , S , t . /-pc' ^ 
x h — - 4- &c. + — x ■ — + —a— + &c. 4- 
acr r ac r r* 
_x_ + — 4 
2 tf£ - r r r 
c S tc" , w"' Q 
f- &C. x 1 — - + — — + &c. -f- 
s' r r r 3 
S £ — 02 , m—n , »-(? . « S o-m. > m- n.l n~o . u « 
x — 4 " -a 4 “ -T- + ~ ~7 X — — 4 2 + 1 + &C. 
hr r r 3 ab r r z r* 
S b—m . s . m — n.t 
+ -— X _ T 
r 
&c. Let Q reprefent the value of S 
by the fecond rule in the eighth problem, O and A the values 
of the fame fum on the contingency of B’s dying after C, 
and on the contingency of A’s dying after C refpedlively * ; then 
will the general rule in this cafe become = — - — - ~~ ~~ — -—^5 
— 2Q — n 4- A, or, becaufe D 4- 2 are = 
r — 1 . 2V — B — A 
* See my 3d Prob* in Phil. Tranf. Vol. LXXYIII* 
f See my 2d and 3d Prob. Vol. LXXVXIL 
n4 -At ? 
It 
