estimation of the value of life contingencies. 
261 
L 
'a-\-vr 
— L 
q+n+p f , very nearly: as the other 
7T+p:b,c J J 
simply 
L 
'a, b, c 
2 
part will be comparatively with this extremely small ; as an in- 
stance, i { p answered to one year ; a~\- 7 r, 6+7t, c-J-tt , each to 34 
years, and the Northampton Tables be used: the error caused 
by neglecting the part in question, will not amount to the thirty 
three thousandth part of the real value. The error towards 
the very commencement of life, or towards the end, is c.r- 
tainly greater; thus if the values of a-\- 7 r, b- J-tt, c-\- 7 t were 
all go ; the error with the same tables, and on the same hypo- 
thesis of decrement, would bear a nearer proportion to the 
real value ; but would not amount to the one hundred and thir- 
tieth part of the real value ; and it should be observed in these 
extreme cases, the hypothesis itself is defective. Moreover, 
the present value of one pound to be received at the end of 
the time tt ~fp, if the event should take place between the 
times 7r and 7 will be the said expression x r”+P ; and the 
sum of all the values produced by interpreting 7 r, by n — p , n , 
n+p, &c. to m — p, will be the present value of the assurance 
of one pound on the contingency. If we wish to calculate 
this from tables of the values of periodic incomes ; as the 
part due to the interval between 7 r and 7 r + P, may be ex- 
pressed by neglecting the small part above alluded to, 
r 
L / 
a , b, e 
or its equal 
r 
L tt: a-j-p, b + \p, c+\p _ 
L a> k—\p> c—\p 
assurance equal to 
; and therefore we have the value of the 
MDCCCXX. 
M m 
