estimation of the value of life contingencies. 
2 59 
No. 6. n 
y_ 
(k K r «' 
V X X „ 
K" k™) will denote the portion of 
chance due to the time between n and m, that K shall dis- 
continue during the continuance of K', on the condition that 
previously to that event taking place, K'" shall after the time 
n' have discontinued during the continuance of K". 
And thus we might proceed to an infinite variety of cases 
with regard to the limits in time, with regard to the number 
of events, &c. ; and however compounded and numerous the 
signs of fluentization and summation may be, and if this 
mode of enunciation be duly considered, it will be found that 
the meaning of the more compound cases is much easier to 
express and to understand, in this analytical language, than 
by a more elaborate phraseology ; and that this mode ena- 
bles us as soon as the meaning of the question is under- 
stood, granting the theory of summations and fluentizations , to 
solve it. 
No. 7. By way of illustration I shall only add here, that 
the nature of the events to which K, K', K ,f See. may refer, 
is unlimited ; they may refer to single lives only, to joint 
lives, to joint lives connected with other joint lives, to 
joint lives connected with deaths, &c. And that more com- 
pounded cases may be understood, I also mention that 
P 
— ”—p 
m — p 
ir + p - . 
X 
o 
V 
+p 
K" Kp expresses the assurance of one 
pound to be received at the first of the equal periods^), after 
the time n — p, that shall happen after the discontinuance of 
K'"; provided that that discontinuance happens during the 
