of Logarithmic Tables. 
225 
this we may remember had x first changed into .r-— 1, and 
afterwards into .r-J-i , so that it receives no alteration. Finally 
there is to be added L .«"•••(« + 2). 
7. Cor. 2. Change x into x — 1 in equations (b), and let 
the new values of ct , x" , &c. be jG, jG', jG", &c., and there 
arises the following series of equations, 
i=z(x— 2 ) x a 
x =(.r— 1) x 0 x/3' 
.r+i=.rx — x/3' x /3" 
X+2=(X+1 ) X X fcL^±l> x /3"x r 
&c. &c. 
which being multiplied by equations (6), the first by the 
first, the second by the second, and so on, factor by factor, 
and putting a x /3 == a'x jG a"xjG"=s", and so on, give 
x=(x—q) x s 
X-\-l — {X — l ) X 5 X s' 
I Jf+ I I If 
X+2— X X — XS Xi" 
£+2 (jr+2) (x— 1 ) w p// 
(•*+>)•* 
&C. 
-£-f-3=(- r + 1 ) X ~ X v ;_T rr r ' x 5'x tr 
& c. 
which, being put into logarithms, give 
L° — L -fL .s 
U =L+L.s+L.s' (d) 
L" =L°+(L / -L)+L . /-f L.s" 
I 
L'"=L' + ( L" — L°) + ( L"— L'-U+L) + L.s"+L . 
L" (« + 0=L" («- 0+ ( L"-«— 
