estimation of the value of life contingencies . 
265 
death A and B, provided that that be the first or last which 
dies of the three A, B, C. Here I first take K" = 
A x-.b,c 
J b , c 
and 
K'"= _£±f ; and then take K"= 
a 
X : a, C 
a , c 
and K"'= 
J b + x 
; and 
L L„ . r 
I find the contingency = — fluent of ( - j* -■ . - — [- 
J b + x 
x: a, c 
a. c 
— — fluent of 
L , ,L 
c + x 
te‘)= 
correction — * 
J x : a,b, c 
a, 0, c 
L x-a b + x 
-f- fluent of -r~— • -f - . Note, the word correction might 
b c 
have been omitted by considering it implicitly contained in 
the word fluent. Hence the assurance on the first of the 
deaths of A and B, provided it be the first to fail of the three 
A, B, C, is equal to the absolute assurance on the three joint 
lives, less the assurance on C's life, provided he dies first : 
the same as Mr. Baily makes it in a note at page 240 ; by 
comparing the result of his solution with a former solution ; 
but I should observe there is a typographical error in the note, 
by inserting -f- ABC instead of — ABC. 
Example 8. If the first of the deaths of A and B, is to be 
~h± - 
the second of the three; in this case taking first K'== 1 — ~~-- 
c+x 
+ 1 t~ • — r +1 and and then K"= 1 
c+x 
+ 1 
L . 
c+x a+x 
b 1 g 
and K y// = —j- — , we get the contingency 
L 
a + x 
L 
= — fluent of 
{¥( 
L . L, , 2 L . 
c+x , b + x x:b,c 
T "T ~T L “ 
c b by c 
+ 
J b+x 
