258 Mr. Gompertz’s analysis applicable to the 
and m " , K"' discontinues during the time of K"'s continuing : 
And if y be either a constant quantity or a function of x, 
K" K' 1 ' will denote the chance due to the time between 
m" y x 
n” and m'", that is whilst x becomes from n" to be equal to 
m"; that whatever x may be, at the time of K'^’s disconti- 
nuance, that K" shall be in continuance at the corresponding 
time y. 
X 
No. q. — K' ( » K" K'") will denote the chance that the 
° y\yxx' 
event K' continues during the time y ; with the proviso, that 
the event K'" shall fail some time between the times n andy; 
but on the condition that whenever that event shall take place, 
the event K" shall not yet have discontinued. 
iL 
No. 4. And — K' ( » 
y \ y 
1 — K" . kp will express the similar 
chance, except that the discontinuance instead of the con- 
tinuance of K'" is to take place after the discontinuance of K". 
No. 5. 
(K 
y y 
K' k" 1 ) will denote the portion of the 
X X ' 
chance due to the time between n and m; of K discontinuing 
after the event has taken place of K"’s having discontinued 
during the continuance of K' ; if that super-continuance of K' 
should not take place before the time n'. And if in the above 
expression 1— K^. be written for K'^ every thing will be the 
same ; with the exception that that part which referred to the 
continuance of K', will now refer to the discontinuance of K* 
having taken place. 
