estimation of the value of life contingencies. 
239 
M, 
M. , „ or 
p+z 
X 
p 
n—p 
m — p 
M 
p + x. 
>+«■ and also = M » + *_ 
This last is also evident from above. 
Art. 3. It may be proper to state that the symbol ”] is not 
necessarily written with the letters x,p, n , in ; but that with 
other letters it will, mutatis mutandis, have a similar meaning: 
the first or highest letter within the symbol expressing the 
constant increment of the variable quantity above the symbol ; 
the second, the value of that variable quantity at the com- 
mencement ; and the last or lowest letter the value thereof at 
the end. If this letter be infinite, we omit its notation and 
■X I 
write the symbol thus n j. If p, or the first letter within be 
infinitely small, or 0 comparatively with finites, then the 
symbol will stand « 
and will express the integral of a differ- 
ential expression of ac between the limits n and m of a?, and 
will be the same as the fluent of a fluxional expression 
between the same limits, mutatis mutandis. 
Art. 4. L a , Lfr, L,, &c. are put to denote the number of 
persons living at the ages a, b, c, &c. in a given table of mor- 
tality, and L is put for an abbreviation of L x L, x L 
fly Oy Cy OCC» Cl t) ™ 
x : a, b, c, &c 
&c. also L „ is put for an abbreviation ofL , x L 
c ■ 
b -f x 
a - \-x ) 
xL c+J L (»: a,b, ctcc.) &c. for anabbreviationol L +J xL s+t 
x L c-m & c ' x h d x b x L / &c ' 
He nee the chances of nominated persons of the ages a , b,c, 
&c. living respectively, the times w,y- t z t &c. are 
L. , 
a-rx o+y 
TT " 3 l> 3 
