263 Mr. Morgan on 
The above rule gives the exa£t value when C is the oldeft 
of the three lives, But if A be the oldeft, the fymbols 
muft be changed as in fome of the foregoing problems, 
and the value in this cafe will be exprefled by the feries 
2S abc' wise" ntc" c S amc' , nsc" otc'" 0 
3 abc r r z r 6 babe r 1 r* 
S bsc' , mtc" n 
X p — +- 
babe r r 
+ &c. - + 
abc 
&c. + 
i.x ^+^+4+ &c. - 4 * — + 4 +-^ + & c . - 
ab r r r * * 3 ab r r x r 3 * 
S abc' . ms . c' c" Q S msc' , rd . c'A-c" „ 
X — + j— — + &c. -j — - x — j- _r_ + & c . From 
abc r r abc rr 
thefe feveral feries, the general rule exprefling the value 
of the reverfion will be found = S into — 1 ~ AJ t— * 
3 a 
x 
& . HF-HFC , HB ■— HBC 0 . AF— AFC , 2 . r- i . AB — ABC 
4- ZT + : + 
6 b 
3 r 
m . AP-APC , S ^ BN-BNC , m . PN-PNC 
”^3 ar a b 
bbr 
When the lives are all equal, the firft rule becomes = 
r^7 . V^CC . 2 . r^ T . CC-CCC , X* . KK-CKK , * . CK — CCK' 
2 r ' 
3 r 
6 cc 
6 c 
d . CT — CCT dd . Tf-CTT 
6 cr 
6 ccr 
, and the fecond rule = 
r - I . V— CC 
- a . r— i . CC-CCC _ ** . KK-CKK y . KC-CCK f d. CT-CCT 
3 r ’ 3 CC 3 C + 3^ - 
+. ~* J 1 ' " » I11 the one cafe the four laft fractions arer^ 
y C r 
r— I . V-CC 
6 r 
r- 1 > V — CC 
3 r 
„ 2>S,r-l 
3 r 
; and in the other cafe thofe fractions arez= -4 
; therefore, in both cafes the general rule becomes 
x V — CCC, which is known to be the true value 
from 
