( "5 )

rkhm of ehe Ratio of « the leiser, to b the greater Terrn, b wouid bc dse'Pro-duft of a into i - 4 * L — L 1 -P — L t, See. < 4 (tL H—^ < L 1

-1- i- a L \ See. But is b were given, n wouid be = b — b L -f t L T

— ~ b L *, 8cc. Whence by the help of the Cbiliads , the Number apper-

taining to any Logarirhm will be exactly had to the utmost extent of theTables. If you feek the nearest next Logarithm, whether greater or leiser,and call its Number a if leiser, or b if greater, then the given L, and the diffe-rence thereof from the said nearest Logarithm you call l ; it will follow thatthe Number anfivering to the Logarithm L will be either a into i -+■ L

-j- — / 1 - 4 - -—/? H-/ 4 H- [S &c. or eile b into i — / ■+ 1 / 1

2 6 24 120 a

—. / 3 -4- ^ / 4 — / 5, &c. wherein as l is leß the Series will converge

the Iwiftcr. And if the first zoooo Logarithms be given to 14 places, thereis rarely occasign for the three first steps of this Series to find the Number toas many places. But for Vlacqs great Canon of 100000 Logarithms, whichis made but to ten places, there is soarce ever need for more than the firststep a ■+ a /, or <1 -+ m a l in one Cafe, or elfe b — b /, or b — mb l in theother, to have the Number true to as many Figures as those Logarithmsconsist of.

There is another Series, which is not indeed so simple and uniform, yet the firststep thereof is most Commodious for Practice, and exact enough for Tables not

a l b l

exceeding 14 Places. It is thus • a -+--—, or b -will be the Num-

x — f / 1 -P i /

ber anlwering to the Logarithm given, differing from the truth but by one( half oi the third step ofthe former Series. But that which rendersit yet moreeligible is, that with equal facility it ferves for Briggs ’s or any other fort of

Logarithms, with the only Variation of Writing — instead of 1 , that is

tn

* -P

a l

■,and b —

bl

— <*-+5/4 -b—itb

or

-i l

m

and

m

m

-u

—P J /

m

-, which

are eafity resolved into Analogies, v>\.

As 43429 See. — 1043429 -P 4 /

Or As 43429 kc. ~P i l .1043429 — 1 /

ES# to die Number sought.

0 .x

tf