i4 2 
Mr. Morgan on Survivorships. 
*' + »’ + = 
cr + 
ff . i 
cr* + : 
x + 3 d, &c. years will be 
„ t _ jlI. . . . &c. But the series -±2 x ^r+7 
C _"C' — AC — A'C, and 
cr* + 3 cr x + 
£+£±i' x _C_ + &c. is 
, . - .* , _L &C is=7r.C— C, the whole va- 
the series +7^ + ac - , 
lue of the annuity therefore, when B is the eldest, will be - 
„ C— A'C' BC-ABC_ T .crTc'. 
C — 2 2 
COROLLARY. 
If the solution of either of these two problems be given, 
the solution of the other problem may be immediately d 
rived from it; for the value of the reversion in one is no more 
than the difference between the value ofthe— ^ 
other and the value of an annuity on the life of C 
In other words, let the value found by either o t ese pro- 
blems be called Q, and the required value of the reversion m 
the other problem, aup^ing^^ ^ 
the same in both, will be C >d , .« 
is self-evident, and if applied to any of the foregoing rules w 
be found to confirm the truth of the solution. 
PROBLEM III. 
To find the value of a given sum payable on the death of 
A Ind C, provided B should survive one file in particular 
(A). 
