Qgo Mr. Knight on the construction 
L . «'+(«— i)L . *"+ ^“~ a) L . «"'= r 3 ) + L. iZ "+ 
(■) 
(w— 2)L.«"' = r 2) 
O 
If L . a."" had been used, we must have made L.«"+L.«"' 
= r , and have proceeded as before. 
( 4 ) 
The substitutions above being made equations ( e ) become 
L . .r=L(.r— i)-|-L . « 
( Lr— J- 1 )=L . tT -}-La-|-La — L . jr-{-r=L . x r 
L( .r-f-a) — L ( a:-f- 1 ) + r 4 "L • a/ +L . =L( 1 ) -}- 
r , =L(j:+i)+r+ r 
{') 
L( ) == L( -T-j-a ) -J"^ -|-r L . 
( l ) 
r ,; =L(a:+2 r ' 
(') 
L(x-f* 4 ) == L(a:-{-’ 3 ) +^ /# -j- ? / "t*L . a/'-l-aL . « //, =L ( ^ -j- 3 ) ~h 
I 1 ) 
r / "=L(.z+ 3 ) 4 _r ”+ r" 
C) 
L( a: 5 ) =L( a:-j-4 ) . a!'-\-£L . a ,,, ==L 4)-}- 
(*) 
r ,,/ '=L(jr+4)+r /,, -f-r' // 
(*) 
&c. &c. 
Where it is plain that each logarithm is found by four addi- 
tions r', r", r &c. being got by two each. 
0 0 ( l > 
Prop. V. 
11. To construct a Table of Logarithms by means of interpolation 
from the converging expressions L . s, L . s', L . s", &c. 
If we consider the formation of equations ( d ), we easily 
perceive that the terms of L(<r-f -n) observe the same law. 
