248 Mr. Morgan on 
V, denotes the perpetuity. 
W, denotes the value of S on the contingency of C's dying 
after A (by my 3d prob. Vol. LXXV 1 II). 
a and a denote the number of perfons living in a table of 
obfervations at the ages of H and A. 
/, u y Wy &c. denote the number of perfons living at the 
end of the ift, 2d, 3d, &c. years from the age of A. 
jG and by denote the number of perfons living at the ages of 
F and B. 
m, n, 0, py See. denote the number of perfons living at the 
end of the ift, 2d, 3d, &c. years from the age of B, 
k and c denote the number of perfons living at the ages of 
K and C. 
dy Cy f, gy Sec . denote th e number of perfons living at the 
end of the ift, 2d, 3d, & c. years from the age of C. 
denote the decrements of life at the end 
of the 1 ft, 2d, 3d, &c. years from the 
Cy c " , c /y/ y See. J refpeilive ages of A, B, and C. 
r, denotes the value of £. 1 increafed by its intereft for a 
year. 
The combinations of two or three of the feveral letters A, 
By Cy Fy H, &c. denote the values of annuities on the joint 
continuance of two or three of thofe refpedtive lives. 
// 
a 
/// 
&c. 
b'y b"y b'"y SCC. 
See. 
PROBLEM I. 
To determine the value of a given fum, payable if A (hould 
be the JirJi that fails of the three lives A, B, and C. 
solution. 
In order to receive the given fum in the firft year, it is 
neceffary that one or other of four events ihould happen, ift, 
That 
