Mr. Morgan on Survivorships. 
227 
And in like manner when their ages are 91 and 81, the three 
terms — + y x 1 - &c. form a part of the series which denotes 
the probability between two persons, aged 92 and 82. By pro- 
ceeding with these operations, a table may be formed for all 
lives, whose common difference of age is the same, with little 
more trouble than in the single case of the two youngest lives. 
If a table of the probabilities of survivorship be already formed 
(such as that to which I have referred in my first paper), the 
operations in the present case may be exceedingly abridged ; 
and it will not perhaps be improper here to explain the man- 
ner in which this is effected. By exchanging the symbols c , 
d, e, &c. in the solution in my first paper, for their equals m, 
n, 0, &c. in the present solution, the series expressing the pro- 
bability of B's surviving A will become =— x h ' a ' I m ' a ' +a " 1 
n . a " -f a"’ , z . a* , . ^ 
2 T —> winch exceeds the series expressing the 
probability of B's dying after A by A. x~a' + a"+a'" . . 7 ~. . -f fl 
(or supposing s, as in the Northampton Table, to be = 1) by 
nearI y- Ir " therefore, the given probability of B J s surviv- 
ing A be denoted by Y, the probability of B's dying after A 
will be — Y— ~, and the probability of A J s dying after B 
will be a i . The following table has been computed 
in this manner, excepting the first and the two last divisions, 
where the difference of age between the two lives is 10, 80, 
and 90 years. In these cases, the probabilities have been de- 
duced from the series in this lemma, and chiefly with the view 
of proving the accuracy of the table in my first paper. It is 
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