of Logarithmic Tables, 231 
with respect to those of L(x-f -n — 1), which we observed in 
equations (c) ; we have therefore by a similar elimination, 
L . x =L( x — 2 ) -f L . s 
L(x+i)=L(.r — i)-j-L. 5 + L . s 1 
L(x+2)=L.x +L.5+2L./+ L . s" 
L( jc-j -3 )=L( )-f-L . 5-^-3^ • 5 , -j~3L • . s' 1 ' 
L(x+ n ) = L(x+rc— 2) +L .s+nL. s'+“-^=^L . j"+ 
which in order that the logarithms may be got from one ano- 
ther by addition, must be transformed as in the last propo- 
sition by the assumption of p, p, ", &c. ; p, p', p", &c. ; 
P>P) p) 
p, p/ p," &c. : thus if the case only requires us to use L.s, L .s’, 
p)p) P) 
and L . s", make 
L . 5-}- L . s’ = p 
L . s -j— 2 L . L . s" — p -f L • .P-f- L . s tr p 
L . 5-^-3^ • P-j-3^-* • ~~ P "f*L • 5 # -|-2L . s" “ p ,r 
&c. &c. &c. 
by substituting which our equations become 
L.x =L(a? ■— 2) 
L(a?+i) = L(j:— 1) -f-L . s + L . s' — L(x-i)-| -p 
)=L . x ~j“ p -f L . P-j— L . s" L . x "f"p , 
h(^ , + 3 )“L(a:-|-i )-J- p'+L . s'- J-2L . s " ~L( )~hp // 
&c. &c. &c. 
If now we put successively o, 1, 2 for 7z in the value of 
L . s" ”, given in Art. 7, we find 
L.<=L(£ih L. S "=L(g^);°r 
L.s= 
mdcccxvii. H h 
