270 Mr. Morgan on 
fhould both die In the year, and C live. 5thly, If B only 
fhould die In the year, A having died before the beginning, and 
C lived to the end of it. 6thly, If A only fhould die in the 
year, B having died before the beginning, and C lived to the 
end of it. ythly, If C fhould die after A in the year, B hav- 
ing died in either of the foregoing years. 8thly, If C fhould 
die after B in the year, A having died in either of the 
foregoing years. 9thly, If A and B fhould both die in the 
year, C having died in either of the preceding years. lothly, 
If B only fhould die in the year, C having died before the 
beginning, and A lived to the end of it. And, laftly, if A 
only fhould die in the year, C having died before the begin- 
ning, and B lived to the end of it. 1 he feveral fra&ions de- 
noting thefe contingencies in each year being added together will 
become = i- x + ® x — 
r r abc r r 1 
abc 
+ 4_ x i±l + y : a ; + < + &c. 
* abc r r 
abc 
r r J 
X 
4S 
3 at,c 
1 S bda' . mea' 
— X h— p 
%abc r r 
-(- &c. x 
$abc r 
+ &C. — 
n iri + & c . - A. x + n j£ + 
t 3 3 .be r r z r ■* 
+- &c. — 
S b — m.c m — n . d —o.e 
2bc * r r 3 
&CC.--X pl+ n ^l 
2bc r r * r 3 
+ &C. +— X 
ab r 
ma f n . a' + a" Q S ba' , 
b — -P— + &c. - T X — + 
r ab r 
m . a a 
+ &C. + 
4- x-+^ + ~ + &c. + * ’^+!^L + !=! + &c. + 
ab r r z r* b r r z r 3 
S ca' da" , ea'" , - , S .da' , ea" % fa"' , * r „ ~ 
— x — + — + -T-Hr &c. + — x b — + y -r + &c. Let O 
r r 2 acr r x r 3 x 
20 C 
denote the value of S by the firft rule in the eighth problem, 
and the firft ten feries will be=£- 2Q. The four next feries 
3 are 
