( 6x ) 
After the fame manner may the difference of the faid two 
Logarithms be very fitly applyed to find the Logarithms of 
Prithe Numbers.having the Logarithms of the two next Num- 
bers above and below them : For the difference of thQ ratio of 
a to\z. and of |«» to h is the ratio of a h to \ and the 
half of that ratio is that oi V ab to {Zj or of the Geometri- 
cal Mean to the Arithmetical. And confequendy the Loga- 
rithm thereof will be the half difference of the Logarithms 
of thofe rationes^ viz. 
Which is a Theorem of good difpatch to find the Logarithm 
of ^ z,. But the fame is yet much more advantageoufly per- 
formed by a Rule derived from the foregoing, and beyond 
which in my Opinion nothing better can be hoped. For the 
ratioof a h to \zz, ov \aa'\-\ah ^\hh^ has the difference 
of its terms ^ ^ ^ — | ^ ^ + ^ ^ or the Square of |- ^ — i b=i x x, 
which in the prefent cafe of finding the Logarithms of Prime 
Numbers is always Unity, and calling the Sum of the terms 
\z z,-\-a h:=^y y, the Logarithm of the ratio oiVabto^ a-^ \ h 
or z, will be found 
which converges very much failer than any Theorem hither- 
to publifhed for this purpofe. 
Here note that ^ is all along applyed to adapt thefe Rules 
to all forts of Logarithms. If m be loooo &c. it tmy be r>eg- 
lecStcd, and you will hn^ Nafeir'^s LogarithmSj as was hinted 
before; but if you defire Bnggs's Logarithms^ which ar^now 
generally received^ you muit divide your Series by 
2,302585092994045684017991454684364207601 ioi48S62S77i97^o33328 
or multiply it by the reciprocal thereof, zfiz,. 
0,434294481903251827651128918916605082294397005803666566114454 
IBuc to fave fo operofe a Multiplication (which is n;ore 
than all the refiof the Work) ic is expedient to Divkk tilis 
Multiplicator by the Powers of 2s or / continually, accord- 
ing to the dire^ion of the Theorem^ efpecially wliere x is 
fmall and Integer, referving the proper Quotes to be added 
together, when you have produced your Logarithm to as 
many 
