of Logarithmic Tables. 229 
L( x-\~ 2 ) — L( .t’ 4 ~ 1 ) -\~r -J-L . a ! - |-L . a!' =L( x -\- 1 )-| -r' 
L(o:-|-3 ) =L(jc+2) -\-r' +L . ol-\- 2L . a." =L( j:+2)-f r" 
L(x+4) =L(x+3) 4 - 1 " +L . a-\-fL . a" =L (^4"3)+ ^,/, 
&c. &c. &c. 
If, in the value of L,a"—« (Art. 6), we put successively o, 1, 2 
for n , we have 
f— ] 
|. T r' T /(*— 1 ) (J?+l)] 
1 ■ T /y" T 1 
I (X+2)X 3 | 
U — i / 
1 , . ex. lq x2 j 
1 , . ce. — iq 
l(*— 0 {x+l)*/ 
L . %=■. 
or 
L.« = -J +y(sb) +1 
L ' a/ =~2M{^ I +7(^br) +7(^=7) 4 -} 
l-"= ^j^ ^_ i + |( ^: 3 t^ -) 3 4 -} 
These are the most converging values, I shall show pre- 
sently how to expand them into series of monomials. 
10. If the intended number of decimal places should re- 
quire L . a!" also to be retained, make, first 
L . « 4- L . <x! — r 
L.«4-2L.ct , 4- L.al* =r 4-L./4" L .a!' — y f 
L . a 4 ” 3 L • a/ 4"3L • «'+ L. a //, =r / 4-L. a / 4-2L. a / '4- L 
L . . oc -\- 6 L» a. / 4”4^- J • ^"—r"+L . a! 4“3^ • a”4“3L • a 7 ” — r ,rt 
l . «+«l . »■+ 7 =^ l . *"+ l . a '" =r “....(»- 2) + 
L/+(«_1 )L L . 
Next make 
L . a.' 4~ L a” = r 
(*) 
L . a / 4 ~ 2 L . a 11 4~ L . a!" = r 4-L . a”4"L . ol'" =: r ; 
L . a '+3L . «"+ 3 L . = V' +L «"+sL.'" = V " 
!■) Cl 
