Mr. Morgan on Survivorships. 41 



in my first Paper, on the contingency of C's dying after A) * 

 This general rule gives the true value of the reversion, when B 

 is the oldest of the three lives. But, when C is the oldest of the 



three lives, the general rule will be = S into 1 —^- x BC — B' 



ztabc + JE- - ££■ + -f- x T+-.VP' - i-i±^I - 



2C 



BK — ABK + R + ^ ' ? 7 r 1 , + y~ Bjr * — x denoting the difference 



between the ages of C and of the oldest person in the table; p the 

 number of persons living at the age of B after x years ; B', A'B', 

 and A'P', the values of annuities on those single and joint lives 

 for x years ; and p the probability that C dies after A.-f 



When A is the oldest of the three lives, let the symbols be 

 changed as in the solution of the preceding problem, and the 



S b' h" 



whole value of the given sum will be = -—^- % — - -| 1- -j- 



b m c -> ; S cb' , db" , el)'" r -, , S- d if , 



— > &c - + 7b7 * — ± — + — ® c - + TbTT x ~ + 



*-«+ y 1 &c £ x -^-4-— 4-^4- & c - — x 



il . /j[±*l . &?, L x -f^lj_ s _i:_Liil4, Aft r; 



2 a 6 c 



sc6' , dtb" , g«fr" , «, S gig , eu.b'+b" 



» J > jaoc r ■ r ■ r 37 ' zab c r r * 



r x t»^ -T zabc x r T r* T. r* T» «** +77177 







* Phil. Trans. Vol. LXXVIII. page 347. 

 f Phil. Trans, for the year 17941 table, in page 229, 

 MDCCC. G» 



