346 Mr. Morgan 
joint lives differ from each other in a greater or lefs degree than 
they have been given in thofe Tables. But by comparing the 
values of the reverfions when the ages are equal (in which cafe 
Mr. Simpson gives the true rule) it will be feen , that the 
values of the joint lives are fufficiently correct for the purpofe ; 
and in order to put this matter out of all doubt, I have com- 
puted the values by the foregoing rule from the exadl values of 
the joint lives by the Northampton Table, and alfo from thofe 
values which have been deduced from Dr. Price’s Tables, and 
I have found them to agree exceedingly well *. 
It may be perceived, that in all the cafes of equal lives I 
have computed the values of the furvivorfhips by the preceding 
rule. This has only been done to prove its accuracy by com- 
paring it with Mr. Simpson’s rule, which is in this particu- 
lar cafe, as I have already obferved, perfe&ly right ; for when 
the ages are equal, the chance of furvivorfhip mud alfo be 
equal, and therefore half the value of the reverlion after the 
extinction of the joint lives will be the true value of the 
given Turn payable on the death of either or B, fubjeft to 
the contingency of his being furvived by the other life. The • 
truth of this rule is felf-evident ; nor does it at all feem to 
depend on IVlr. Simpson’s folution in his Seledt Exercifes. 
That it is capable, .however, of being deduced from the fore- 
going feries, may be demonftrated in the following manner. By 
* I (hall juft mention the following inftances. When the age of B is 20 and 
that of A is 2 years, the value, by taking the joint lives from Dr. Price’s Table, 
and approximating to the real values of thofe lives in the manner directed by 
him, Vol. II. p. 75. of his Treatife, is 29.59. When the ages of B and A are 
40 and 2, 50 and 20, 60 and 2, and 70 and 10, the refpedlive values are 26.93, 
18 78, 21.57, and 7.08, which being compared with the values in p. 344. will 
be found to agree almofl exa£tly with them. 
reafoning 
