27 0 Mr, Gompertz's analysis .applicable to the 
as m is less than p , ; if the whole assurance be required : and 
L 
observing that when a; is equal to, or greater than that — g X 
a 
. fluent of — — ^ is = o ; and that fluent of . —r~ 
c b C a 
will be = — g ; if — g is its value when x = p, we shall find 
the contingency after that term, that is when x is greater 
L b 
than [a, = constant — g — '■ ; and • the remainder of the 
L b 
r 
assurance will be — g . p b to be added. I do not state the 
m — 
case of B’s being the oldest, because it is only necessary to 
write a for b in the last case to have this. 
If we should not be satisfied with the approximation de- 
duced, by assuming the equality of chance above named, 
during a long period, we have only to divide the period in 
shorter periods to attain any accuracy, being careful pro- 
perly to correct the fluents. 
The theorem I have just given for a solution to the pro- 
blem in question, is so much more simple than the solutions 
I have seen to this problem, that I think it proper to inform 
the reader, that the cause will be understood from Art. 6, 
Section 3 ; and that no fear may be left in using the Theo- 
rem, I shall point out the connection between this solution and 
that given by Mr. Baily, and 1 shall for the easier comparison 
denote L fl , L b , L., by#, b, c; L^ +w , L. +n by a , b, c 
and L a , +n+l , L b+n+lt L e+M+1 by a ,, i b , [,c"\ and as the con- 
tingency, that the event takes place before the expiration of 
7 ? 4* years will be found by writing n for x in the formula. 
