go Mr. Morgan on Survivorships. 



"~ 7 „, , r ui i e-f.o.a'" , it — o.e—f.a—J + a"-\-a" 



n — o . e — j . a'" -\- n — o ■fa'"-\ J - -\ - J — 



-f a '". of +11 — o f . a — a' -\- a" -f- a"' + c — e . n — o . a!" -f 



a' + a" . c—e . n — o . b — n . c—e . a"' -, • j .% T f 



j , and so on in the other years. It 



these several fractions be expanded, they will form nineteen 

 different series, whose sum may be found = S into -— - x 



V— ABC - -£±! - *£ + *£ + AB + — x AK+BK— 2ABK 



2 2 r ' ' 2 c ' 



g. AF— AFC . m d . i + APT 



2 I zbr c ■ 



If B be the oldest of the three lives, let n denote the probability 

 that B dies after C,* then will the value of S, after the extinc- 

 tion of the life of B, be = ' *' q x r -^- L — :L — •, and the whole 



value of the reversion will be = S into x V — ABC — 



A'+B A'C'+BC . AT3 |3.AF_AFC 



+ AB - p '" , r " 4- — x A' K' + BK - 



zr ' 2 b ' 2 c 



Tabk + 4- x d ' I+APT - mTap + ^4- x 7=1 . t^a* 



1 2 o r c ' ' ar x 



. . . . q, A', A'C, &c. denoting the same quantities as in the 

 former part of the preceding problem. 



If C be the oldest of the three lives, let the symbols be changed 

 as in the preceding problem, and the value of the given sum 



will be = S into — x V — ABC — i^+B' 



r 2 I 



2 " T •* 2 b 



^EESEl _ j" xThTnpc - ac+bc +A'B'+ -4- x 



2 a a or ■ 2r ' »2or 



TarpcTH — x i 4- NC After the decease of C, the 



* By the Table, page 229, Phil. Trans, for the year 1794. 



