[ 4^0 ] 
ro. In three quantities'/^', q, r, increafing by equal 
differences, the logarithms of any two of them being 
given, the'Iogarithm of the third is alfo given. ' 
I. For L, ii = 2/xV — X = 2Q^^F4-R 
&e: = 2/Y. 
Where N = I^. 
r + p 
Or L, --if— = 2 /Y — 2Ci~P4n?^ 
pr qq — VV ^ ^ ‘ 
Becaufe L, — ^- 1 — 2 fx — — — 
qq — VV qq — vv 
II. Putting N = = (where ‘um) — - — ; 
qq+pr qq + rp ^ 
A=/N} B=r:AN^ 6cc. 
Then L, ”=2S=:2Q-’R^; Or 0_i±Z=S. 
pr I ^ ^ 
For fince vv — qq — pr ■=. i ; put qq for r y pr for y. 
Then r — pz=.qq — pr — vv=. \ 1 r-\-pz=.qq-\-pr» 
III. Putting N=-=:A, &CC. a—\. 
And M=^A-f 6cc.; S=|R-f-P; A=:|R-P, 
Then Qj= 2 + ^ 
For — P— yv — a; R — Pzrr2jfZ=:2A; ' 
but I -j- M 1 = p > Therefore, 6cc.* 
2 2 
II. Any 
