r 4 Q 3 1 
periods, the probability of the furvivor’s living is 
above exhibited ; and, confequently, the probabilities 
of the furvivorfhip’ s taking place, in thofe times, will 
be feverally reprefented by the above products. 
Now the fum of 36 terms of this feries of pro- 
ducts, will, upon computation, appear to be 7-! 5 which 
is, therefore, the probability of the furvivorfhip re- 
quired. 
But if, inftead of requiring, as above, the probabi- 
lity of the elder perfon’s furviving the younger, it 
were required to find the probability of the younger 
perfon’s furviving the elder ; then, fince it is almoft a 
certainty, that both of them will not die in the fame 
moment of time ; we may, by denoting that certainty 
by unity (agreeable to another principle eftablifhed in 
the doCtrine of chances) determine the probability re- 
quired to be f 1 — or) vf: The algebraic invefti- 
gation of each of thefe cafes is annexed, to which I 
beg leave to refer, for a farther ill u fixation ; and fhall 
only oblerve, farther, that the above two refults will, 
upon comparifon with thofe given, upon a fluxional 
procefs by Mr. De Moivre, in his treatife of annuities 
on lives, appear to coincide with them exactly. 
The probability of any order of furvivorfhip, that 
can happen among three pcrfons, and, confequently, 
that of one perfon’s furviving two others, may, like- 
wife, be inveftigated upon fimilar principles, without 
the afliftance of fluxions ; but as this problem admits 
of flx cafes, and the algebraic procefs is of a length, 
too great for the defigned limits of this eflay, I beg 
leave to poftpone it. 
Si com- 
