for computing Logarithms . 
SCHOLIUM. 
Neither the number a, nor the fraction is chofen 
as the moft advantageous to begin with in computing a 
table of logarithms; but they are taken as fome of the 
firft that occurred, to fhow the ufe of thefe theorems. 
Perhaps there are other inftances in which they would 
be fhown to much more advantage ; but I hope their ufe 
will appear from the few examples given. They may 
indeed be transformed fo as to be more commodious in 
particular cafes, and there may be fome others derived 
from them, one or two of which I will here put down. 
called theorem 3. 
Again, this equation may be thus exprefled : log. 
and, by tranfpofition, 2 log. ip+q- log. 2p+2q+ log.’ 2 p 
+ log. which may be called theorem 4. And 
this is, in effect, one of the theorems given by Dr. hal- 
Vol. LXX. 
U u 
LEY 
