53 
Mr % Morgan on Survivor flips. 
TABLE III. 
Value of the fame reverfion by Simp- 
True value o 
Common Age. 
son’s rule, when the ages of the 
three lives are equal. 
fame reverfion. 
70 
1 
0 
M 
1 
1 
12.00 
75 
1 
1 
1—4 
vb 
00 
1 
I 2.94 
80 
16.58 
13.84 
85 
17,86 
14-45. 
By comparing the values in the preceding tables* Mr. Simp- 
son’s rule appears In almoft every in fiance to be exceedingly 
incorrect Even when the lives are equal (in which cafe it 
might have been expected to be fufficiently accurate) it feems 
to deviate, in old age at leaf:, fo widely from the truth as to 
be unfit for ufe. When C or B are eldeft (which, however., 
is a cafe that does not often occur), the refults fometimes 
exceed the truth one-half, and generally by more than one - 
third of the real value. When A is the oldeft of the three 
lives (which is the molt common cafe) thefe refults are erro- 
neous in nearly an equal degree. Nay, in fome cafes, Mr. 
Simpson’s rule is not only wrong but abfurd. Thus, in the 
laft example in the fecond table, the value of £. ioo. payable 
on the contingency of C aged 18 furviving B aged 78 
after A aged 78, is by this rule ~ /. 37*554* The value, 
therefore, of the fame fum on the contingency of C’s furviv- 
ing A after B is alfo 37.554. Hence the value of £ . ioo. 
on the contingency of C’s furviving A and B (without the 
reftridlion of one dying before the other) is 2x37.5 54 = 
£. 75.108*. By another rule of Mr. Simpson the value 
* See Simpson’s Selt£t Exercife% Prob, 39. f Ibid. Prob. 32. 
of 
