estimation of the value of life contingencies. 2 57 
^a + x * ^~“b+x ^-^l + vr+tr ^ + 
.0 
IT 
ir+p 
J I 
* ^L+x’ 
and n —P 
m — p 
*+p L 5+n+p~ L 6+p 
tu 
therefore the value 
of this contingency is » 
m 
i — that of the last article. 
Article 5. No. 1. If there may be a continuance of certain 
independent events, denominated for the sake of distinction 
K, K', K", K'", &c. ; and the chances of their continuing the 
times zv, x, y, z, Sec., be denoted by K , K ; , K", See. re- 
spectively, then will 1 — K w , 1 — K^, &c. denote the corre- 
sponding chances of their not continuing during those 
times ; K , K'^, K", Sec. will express the fluxions of the 
chances of those events continuing ; and if these fluxions be 
taken with regard to the respective under written letters 
w, x, y, Sec., they will be the chances of continuance of those 
respective events due to the finite times w, x,y , Sec. respec- 
tively, on the consideration that at the terms zv, 30, y, Sec. the 
causes, if any, perturbating the proportionality to the times 
of the discontinuance vanishes. And under the like hypo- 
thesis would — K , — K' , — K", which are the fluxions of 
the chances of discontinuance, express the chances of the 
discontinuance taking place during the times w, x,y, Sec. 
No. 2. Hence we see that — K" K'" is the fluxion of the 
X X 
chance of the event K 7 " discontinuing, whilst K" continues ; 
and 
m- 
K" . K"' is the chance, that between the times n" 
