estimation of the value of life contingencies. 263 
a L b—\p, c — \p, d — \p. Sec. x P 
J b, c, d, &e. 
b — ip, c — ~p, d—±p, &c. very nearly.” 
Note also, that if the lives be all equal, and there be q 
of them in number, the contingency of one in particular dying 
~ L >/— 1 . 
before the rest will be — fluent of -J lf- L a+X = (if it 
L Yl 
commences with x — o) —(1 — 
rf-fx 
and the assurance on 
that contingency will be -1-x the assurance on the joint lives. 
Example 2. In a similar manner from Art. 2. No. 5, of this 
l 
c-\-x 
section, writing — •. 1 
and 
J b+x 
+ 1 
L , L, , 
C-J-X o + x 
for K", 
■jg— for K"', we have the contingency that A is the se- 
rf 
cond which fails of the three lives A, B, C= ~ fluent of 
( b - ± *L bt * + Vf ' L ‘+* - = chance of 
\ L C, a L b, a rf, b, c ) 
A’s dying before C + that of A’s dying before B — twice the 
chance of A’s dying before B and A ; and the assurance is in 
a similar manner made up of the assurances on the like con- 
tingencies as Messrs. Morgan, &c. have shown. 
Example 3. If K" be put 
L_ . _ ’ L 
J 6-|-x 
X 1 — 
c + x 
that is 
c+x ^b + x . L /i+x* L c + x J v// . L rf+x . . 
i~ j- 2 — — , and K'"=z — — , in the same 
c b 0, c ^ a 
article No. 2 ; we shall have the contingency of A’s being 
/l . 
the last which fails of the three lives = — fluent oft L — 
