estimation of the value of life contingencies. 
287 
r n +P L n+P ■ 1 —P L n+p : b, a—p ^ | | , 
J a,h 
N-' 
J h—p P 

m 
a, b — p 
u a—p p 
L * M 
b, a—p 
r t . A L “-? 
Hence we get —r — • « L b— q — l 
b m I a 
1 P—q *"* ' : a, b — p ^n: b, a—p) r : a, b — p m\b,a — -p ) 
b a — a nearly — — — * f 
1 J 2 P lj a, b 
+ 
±± 
1 1 
a, /5 — p — 
— p 
b, a—p , when - is a whole 
1 
number. 
Article 4. It is proper to observe, that what refers to the 
fluents of the expressions x L r+X , ^p+ x x 1^+* x L r+X » 
&c. of Section 3, equally apply whether L in the different ex- 
pressions L ?+a; , L ~ +x , &c. is, mutatis mutandis , the same, or a 
different functional characteristic, whether when they refer to 
life contingencies, if L in the one part refers to one given con- 
stitution, and in the other part it refers to another constitu- 
tion or not ; for instance, if in the expression x L r+jV , 
L ?+je refers to the Northampton lives, and L r+Jr to the Swe- 
dish lives, or whether they both refer to the same lives, &c. 
Whether they refer to the number of living at the ages q- \-x 
and r-j-jr, or whether they refer with respect to the variable 
time x to expressions compounded of the number of living 
and dead. But instead of resuming the characteristic L here, 
I shall, with a view to better distinction, consider the value 
IT 
V+P 
M x N x . And I observe, similarly to what is done in Sec- 
