286 
Mr. Gompertz’s analysis applicable to the 
value of the expression ^ — . n 
m 
a, b—p 
J a—p P 
-7 . n 
a, b—p , and 
the like ; see Art. 3. Section 4,. I observe if — be a whole 
number, andy> small, from Art. 1 of this Scholium, that n \ s , t 
ml 
r 
, r" . L , + r m L , p 
__ />— ? n: g,b m: g,b ? 
2q ‘ L - ' — P ; 
g, 
r 
. } b . — ; therefore — ^ — ? 
f 
. 72 
m 
a, b—t 
—a 9 
a—q 
m 
b > a —? 2^ ? T • ( rW • + 
• L m ; — /*" . L„ . a b — 7 . ; a q t b) 
a, b — q 
~‘b—q P_ 
L * ‘ * 
L. fl p 
a——q, b • — - • But L x • a> b—q L x : b , a—q == 
L a * 
L x+a x (L K+ b + -y (L y .+h~p — L*+i)) — L h+ 5 x (L x+a -f- 
~ (L x+a __£ — , L* +a )) nearly under the hypothesis of q and p 
being small intervals ; and this by an evident reduction is sim- 
ply J (L« ; a, b—p — L *:h,a—p)\ and in the same way it is 
shown that L* ; j — — L x . 3, q — ~p (L* ; 5—^ ~ ~ Lc . a—p] 
nearly. Moreover « 
m 
^b-q P 
a, b — q . — j- — n 
m 
a—q, b 
a —V 
L “ 
„ : a, b—q ^“n-.b, a—q , n+p ^ n+p:a,b — q ^n-\-p:a — q,b , 0 
r . - l 7 T r * ITT r Kc * 
a, b a, b 
= from above, nearly -L |r*. — 
^ a, 3— ^ : b, a — p 
J a, b 
+ 
