[ 94 ] 
This pei lod In joint lives, 1 have obferved, is nevtf 
ordinalcs are 
and ax'ii x.— The Jiuent of this expreflion, 
X 
or X is the fum itfelf for the time x\ and this, when x—ti. 
becomes and gives the expeSfation of the afligned life, or the 
fum of all the probabilities juft mentioned for its whole poflible 
duration. In like manner : Since 
is the probability that 
two equal joint lives will continue x time x x will be the 
Jiuxion of the fum of the probabilities. The fluent is 
A--— — I ;> which when werA-is— the expectation of two 
» 3 
^"^X 2 X 
— X — is the proba- 
n n 
bility that there will be a furvivor of two equal joint lives at the 
fl^^X ^ X ^ 
end of .V time, x — \x will be the fluxion of the fum of 
* tj 
equal joint lives.- 
-Again : Since 
2 X ■ 
the probabilities } .and the^w^’w/, or — — is (when x=.n) 
«, or the expeoiation of furvivorfhip between two equal lives, 
which therefore appears to be equal to the expediation of their 
joint continuance. The expectation of two unequal joint lives 
found in the fame way is m being the complemetjt of 
the oldeft life, and n the complement of the ydungeft. The whole 
• r r • n - • ^ ^ o 
expeflation of furvivorlnip is - — ^ — f . The expectation 
m ' 
of furvivorlhip on the part of the oldeft is, , and the ex- 
pectation on the part of the youngeft is, ^ It is 
eafy to apply this inveftigation to any number of joint lives, and 
to all cafes of furvivorftiip. 
I have above endeavoured to fliew diftinCtly how the rAr/)^(f7<7- 
tions of ftngle lives may be found, agreeably to any Table of Ob- 
fervations, without having recourfe to any principles, except (uch 
as are plain and common. 
the 
