estimation of the value of life contingencies. 22 g 
By the prefixed symbols A, A 2 , A 3 , &c., I mean the first, 
X 8 X t X % 
second, and third differences of the function to which it is 
prefixed, arising from the series formed by writing x, x-\-e, 
x-f-2£, x- f-3£, &c. in the place of x in that function. Hence 
from the method of differences we have 
r r r r 
a-\-oi — n 
m 
Cl • n 
a s m 
+ -xi_‘.A*S 
• f -7 
a s m 
a+a,, b, c, & c.= n 
m 
i a a P \ I a. c a i P 
j, b. c, Sec. -j ZA n a , b, c. Sec. “p A « 
— ‘ aim £ 2 aim 
a -j- &c. 
a, b, c. Sec. -j- &C. 
a+u,b + @,c,Scc. = n 
— ■ ■■ ■ - m 
a P 
a, bj c, Sec. -f- — A n 
— 6 a s m 
+ « 
— • 
-A 2 B 
a E 772 
a, b, c, Sec. , SCC. 
TT 
anm 
■ a jS » » P 
a, b, c, Sec. -p — • — /\ /\ n 
a t b it m 
l_i - 
+ £a_a*. „ 
7r 2 b n m 
a , 6 , c, &c. j &C. 
a, d, c. Sec. 5 &C. 
And in a similar manner are other expressions written. It 
may be often of advantage, where the text is sufficiently ex- 
plicit, to use the differencing symbols and omit the others, 
leaving them to be understood, and to write, for instance, 
b + 0, c, Se c. — 
P 
n 
m 
u b, c, 4* T : + -p ' 
— 1 
A : -j" & c - 
a e 
a £ 
+ - A : - A A: 4- &c. 
a £ 
A 
ST ’ 2 
— ! 
A • “j” 
H h 
MDCCCXX. 
