-258 Mr. Morgan on 
When the lives are all equal, the above expreftion will be- 
changed into - x r - t * V - (j g- v ~ ccc _ V _ m — s • r ~ t 
r 3 
* -j-; or “ one-third the value of the abfolute reverfion after 
“ the extindion of the longeft of the three lives.” This is 
known from l'elfievident principles to be the true value, and 
therefore the foregoing folution is corred. The fame rule may 
allb be obtained immediately from the feries ; for the value in. 
this cafe for the firft year will be = - x 1 - _ f nr 
r 3 ' « 3 -r 3 ’ 
the fecond yeai—-^ x 
the remaining years. 
3c 2 3,3 cc * r c ■ CC "" C 
Hence the whole value 
, and fo on for 
of the reverfion* 
will be = — x L + - 
3 r 2 
x 
. Q^E. D. 
? R.O B L E M IV. 
To determine the value of a given fum payable on the ex- 
tindion of the lives of A and B, fhould they be the firjl that 
fail of the three lives A, B, and C, 
SOMTT ION. 
The given fum pay be received in the firft year, either on 
the extinction of the three lives, C having died laft; or on 
the extindion of only the two lives A and B, C having fur- 
vived the year. In the fecond and following years, the given 
fum may be received, provided either of fix events fhould 
happen, ift. If the three lives fhould become extind in the 
year, C having been the laft that failed, adly. If A only 
Ihould 
