Mr. Gompertz’s analysis applicable to the 
292 
when M , M' do not contain either x or y , 0 
ir ir J ’ n 
M' M = 0 
x x n 
M'M 
y y 
and therefore N = M' M 
y y y 
This form is put down for the 
purpose of reducing double fluents at once, such as occur in 
Section 4. In a similar manner may the immediate reduction 
of analogous triple fluents be shown; and I may remark, that 
in the double fluents of Section 4, the case of the question 
may not always require them both to commence with the 
same value of x. 
r 
The application of the symbol ° n 
m 
to all 
cases of definite and indefinite fluents, and of simple, double 
&c. fluents, might be entered on perhaps with advantage to 
other branches of the mathematics; but this is not my pre- 
sent object. 
Art. 6. If in the room of of Art. 4, of this Scholium, we 
put r" M x , still being put to represent the chance that the 
said certain circumstance shall exist in the time x, we shall 
have the present value of one pound to be received immedi- 
ately on the failure of the second circumstance, provided it 
takes place during the existence of the first circumstance, and 
between the times n — p and m , merely by making that sub- 
stitution in the expression 
P 
n—p 
m — p 
( N „ 
N 
7t+p 
M 
*+\P 
) by 
which means it will become p 
n—p 
m — p 
(N — N 
V 7T 
V+P 
r «+lP v M \ 
; x M n +lp) 
or its equal . Q ; O being put for the value of the con- 
tingency as in Article 4 of this Scholium; namely, when the 
payment is to be made at the first of the equal periods n> n-\-p , 
