58o Mr. Gompertz o?i the nature of the function 
taken equal to i ,we shall have from the equation L ^ 
^i-i: a,b,c,8cc.'^ 
— and this would be the real 
n-i‘.a,h,Ct See. 
value which should be taken for tt, if the geometrical pro- 
gression coincided perfectly with the fact ; and it would be 
indifferent whether we made it equal to 6,c,&c ^ 
n-'i-\-t\a,biC,Scc. 
* ct f) c Sc c 
' ’ ’ — as the two would be the same; but this not 
n-i:a, b, c. Sec. 
being the case, there will be a preference ; and generally, if 
not always, tt should be taken an intermediate value between 
the two ; and when the term is not very long, it v/ill answer 
a good purpose to take it about the middle between them, 
inclining generally, though perhaps not always, rather 
nearer the last than the first, as the first terms are generally 
of more consequence than the last. If the said assurance be 
not deferred, and instead of being paid for immediately, be 
to be paid for by equal periodic payments, at an unite of 
time from each other, up to the time m—i inclusive, and the 
first payment be to be made immediately, then will the 
present value of such periodic payment be and 
consequently each payment, from what is shown above, is 
r r 
equal to m • — ( i — tt). r. From whence 
we may draw an inference worthy of remark, namely ; when 
an assurance of joint lives is meant to commence immedi- 
ately, and to continue for a term of t years, which is not 
large, and to be paid for by t annual payments, that those 
payments will not differ much with the increase of the time 
ti provided, as I have said, that t be not large, and the ages 
