256 Mr. Gompertz’s analysis applicable to the 
P 
for the sum of them all — * n 
2 „ 
z,b + -L 
J b-i 
a, l — p 
L a-p P 
a—p,s. This is the same in fact as Mr. Milne's 
form, excepting something more general ; in as much as 
it refers to the case if the assurance be temporary, and 
transferred at the same time, and that the interval p is not 
necessarily one year, and that it refers also to insurances 
when the contingencies are taken momentarily ; but it must 
be remarked, that in this case p being infinitely small 
i 
T “l 
r r 
T >w 
b—p P\ i a-p p 
~ n la, b — p * 
T ft 
b m * 2 a m 
a-p,b will have the appearance 
to some readers of being equal to o ; whereas that is not neces- 
sarily the case ; it is true that the ratio of 
J b—p P 
a, b—p to 
h p 
a—p r 
—[ — " • n 
^ a rn 
a—p, i will differ infinitely little from the ratio of equa- 
lity ; but as they will be each of them infinite, their difference 
may be finite. See how to calculate this value in the Scholium 
Art. 3. 
Article 4. A correct notation of the value in the last article 
P 
is in conformity with our plan — «—/> 
m — p 
r n+P 
L~~ X * 
• a, b it-\-p 
+ x • ^b+x. 
And if for L . we write L — L , , it will express the value 
a + x a a + x 1 r 
of the assurance on the death of B, provided A be dead at that 
time, other things remaining the same. And because w 
if +p 
