two Persons of 18 and 35 are proposed, and after 8 Years these Chances are required. The Numbers for 18 and 35, are 610 and 490; and there are 50 of the First Age dead in 8 Years, and 73 of the Elder Age. There are in all 610 × 490, or 298900 Chances; of these there are 50 × 73, or 3650, that they are both dead. And as 298900, to 298900 - 3650, or 295250: So is the present Value of a Sum of Money to be paid after 8 Years, to the present Value of a Sum to be paid, if either of the two live. And as 560 × 73, so are the Chances that the Elder is dead, leaving the Younger; and as 417 × 50, so are the Chances that the Younger is dead, leaving the Elder. Wherefore as 610 × 490 to 560 × 73, so is the present Value of a Sum to be paid at 8 Years end, to the Sum to be paid for the Chance of the Younger's Survivance; and as 610 × 490 to 417 × 50, so is the same present Value to the Sum to be paid for the Chance of the Elder's Survivance. This possibly may be yet better explained, by expounding these Products by Rectangular Parallelograms, as in _Fig. 7._ wherein _AB_ or _CD_ represents the number of Persons of the younger Age, and _DE_, _BH_ those remaining alive after a certain Term of Years; whence _CE_ will answer the number of those dead in that time: So _AC_, _BD_ may represent the number of the elder Age; _AF_, _BI_ the Survivors after the same Term; and _CF_, _DI_, those of that Age that are dead at that time. Then shall the whole Parallelogram _ABCD_ be _Nn_, or the Product of the two Numbers of Persons, representing such a number of Persons of the two Ages given; and by what was said before, after the Term proposed, the Rectangle _HD_ shall be as the number of Persons of the younger Age that survive, and the Rectangle _AE_ as the number of those that die. So likewise the Rectangles _AI_, _FD_ shall be as the Numbers, living and dead, of the other Age. Hence the Rectangle _HI_ shall be as an equal number of both Ages surviving. The Rectangle _FE_ being the Product of the Deceased, or _Yy_, an equal number of both dead. The Rectangle _GD_ or _Ry_, a number living of the younger Age, and dead of the elder: And the Rectangle _AG_ or _rY_ a number living of the elder Age, but dead of the younger. This being understood, it is obvious, that as the whole Rectangle _AD_ or _Nn_ is to the _Gnomon FABDEG_ or _Nn - Yy_, so is the whole number of Persons or Chances, to the number of Chances that one of the two Persons is living: And as _AD_ or _Nn_ is to _FE_ or _Yy_, so are all the Chances, to the Chances that both are dead; whereby may be computed the Value of the Reversion after both Lives. And as _AD_ to _GD_ or _Ry_, so the whole number of Chances, to the Chances that the younger is living, and the other dead; whereby may be cast up what Value ought to be paid for the Reversion of one Life after another, as in the Case of providing for Clergy-men's Widows, and others, by such Reversions. And as _AD_ to _AG_, or _rY_, so are all the Chances, to