estimation of the value of life contingencies. 243 
mencement of the period. But the mode of analysis pursued 
by those gentlemen, have led them to divide their periods 
continually into two, the one a period generally of several 
years, and the other a period of one year only, and they have 
calculated for the two periods separately, and added the re- 
sult of the two. This mode would be given from the first of 
the two forms of this article, which is extremely more com- 
plex than the second form, and apparently with very little, if 
any advantage; for if the decrements were accurately i-n a 
constant proportion to the time from the commencement, 
they would be perfectly of equal value ; though the one pos- 
sesses so much more simple a form than the other ; and when 
they are each but approximations, there will be but little 
choice to be made between them, in point of proximity, in 
the use they are to be made of in those problems ; though 
there will be a vast difference in the degree of simplicity in 
the resulting formula. 
Art. 7. Hence the value of L p + x x (fluent of L q+x . L,. +x 
commencing with x equal to 0) will form Article 3, when 
X — 71- j-£, be L p-\-n+£ x V « +# ^r+X 2 ^q 4 - n > r + nJ "f" 
~L/>+« + £, q + n, r + n + e ~ L p + n + t, g + w + e, r + M + 
-7 L p+n+t, q + n+ e , r+n+, ; and when * becomes fl-f-g + e', sup- 
posing the uniform decrement to last through the whole 
L q+x L r + x 
period s-fis', the fluent will be Lp +M+£+E 'xl 0 , 
~£ Lg 4. n , r 4. k] "h ~ + n + s -j- /, q + n, r + n + £ + s' 
2 + n + £ + 9 + w + e ~h £, > 2 > q-\-n 
