[ 458 ] 
7 . Putting ^ <UJ N=r -. 
Then z~ log. of :v, or the log. of g + Vy will be 
= + &c. x/> 
q .iq—^q 4 ? 5 ^ 
:= +N- |N^+ iN^+4N’-^N^&C.y/. 
For .i = L, AT = L, 5^ + -i; = 7 'x — = /x 
iv <v V* d/ 
-q q" ~ q^ - q^ 
j See. X J • 
8. In three quantities p, g, r, increafing by equal 
differences, the logarithm of any one of them being 
given, the logarithms of the other two are alio given. 
Forj \zt v — q —p—r — q\ ; 
q q q 
P, Q^, R, the logarithms of />, y, r. 
q 
I. L=?=(L,-^=)(i-Pz=/xN + |N^+;-N^-f 
For L, — ^ — =/ X 
q — V q ' — V 
II. L,r=:(L/-^=)R— Q=/x N-iN'+^-N'— i N-+,N',fcc. =/X. 
For L. l±Z=fy. 
q q V 
,IM.L,:=:2/xV4-X = R-P-2/xN -^-;N^_}-.'N^ + -;-N/+^-N^6CC.=:z 2/Z. 
Where N ^ ^ 
Or, I. 
r + p 
L, t±f = R _ p 
For I 
p q—V 
q V 
2/Z. , 
V 
2 / 
q 'V 
q q — V V 
9. Hence, 
