220 
Mr. Gompertz’s analysis applicable to the 
c+z 
&c. considered independently of each other ; and the chance 
~c 
that the event shall take place conjointly, that is, that every one 
of all the events shall take place is 
a + x 
J b+y 
c+z 
&C. 
or b+y ’ andify,z,&c. are each equal tox,the ex- 
b, e, Sec. 
pression may be further abbreviated thus, ^ a,b,c ’ Note, 
a, b, c, See. 
that one year is considered the unite of time. 
And if r be the present worth of one pound due in one 
L x-a b c Sec 
year certain , r •- jf ' "*’ ’ c ' will be the present worth of one 
a, b, c. See. 
pound to be received in the time x in case nominated persons 
of the ages a , b, c , d, &c. should be all living at that time. 
Corollary. Hence, n 1 r m . ~- a,b ’ c> w jH denote the pre- 
sent value of a periodic income of one pound, payable at equal 
intervals p of time, the first payment being to be made in the 
time n , and the last in the time m, on the contingency of the 
persons whose present ages are a , b, c, & c. being jointly liv- 
ing at those intervals ; interest being reckoned at the rate 
per cent, which makes the present value of one pound certain 
due in one year equal to r; and if there be no danger of 
mistaking the variable radical, we omit it in the prefixed 
symbol, and would write the last expression n r" . / 
and this we would write still shorter when a more developed 
expression is not necessary, thus « 
m 
a, b t c y &c. to signify as 
