-490 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1692-3. 



to N the number of the younger age; AC, BD, &c. proportional to n; and 

 AG, CE, &c. proportional to the number of the elder, or n : then the whole 

 parallel opipedon will be as the product Nwk, or our whole number of chances. 

 Let BP be as R, and AP as Y ; let CL be as r, and Ln as y, and GN as f, 

 and N A as u ; and let the plane PRea be made parallel to the plane ACGE, 

 the plane NV^Y parallel to A BCD, and the plane LXTQ parallel to the 

 plane ABGH; then our first product Rrj will be as the solid STWIFZe/^; 

 the 2d, or r^y, will be as the solid EYZeQSMI; the 3d, Rf?/, as the solid 

 RHOVWIST; and the 4th, Rru, as the solid ZaZ^DWXIK ; 5th. fiy, as 

 the solid GQRSIMNO; 6th, rYu, asIKLMGYZA; 7 th, Ryu, as the solid 

 IKPOBXVW ; and lastly, AIKLMNOP will be as the product of the three 

 numbers of persons dead, or Yyv. I shall not apply this in all its cases, for 

 brevity sake, but only show in one how all the rest may be performed ; let it be 

 demanded what is the value of the reversion of the younger life after the two 

 elder proposed. The proportion is, as the whole number of chances, orNwc, 

 to the product Ryu, so is the certain present value of the sum payable after any 

 term proposed, to the value due to such chances, as the younger person has to 

 bury both the elder, by the term proposed ; which therefore he is to pay for. 

 Here it is to be noted, that the first term of all these proportions, is the same 

 throughout, viz. Nni-; the second changing yearly according to the decrease 

 of R, r, f, and increase of Y, y, u ; and the third are successively the present 

 values of money, payable after one, two, three, &c. years, according to the 

 rate of interest agreed on. These numbers, which are in all cases of annuities of 

 necessary use, I have set in the following table, being the decimal values of one 

 pound payable after the number of years in the margin, at the rate of 6 per Cent. 



