Mtfcellanea Cur to fa. 4 9 



ftrated by a like Procefs, from the fame gene- 

 neral Theorem of Mr. Newton : For as the Lo- 

 garithm of the ratio of i toi-b? was proved to be 

 1 



^f^ m —i, and that of the ratio of i to 1—7 to 



be j— 1 — -Cj \ m *. fo the Logarithm, which we 

 will from henceforth call £, being given, i^L; 



will be equal to rF^l * in the one cafe ; and 



1 



\ — L will be equal to iZ^\ m in the other: Con- 



fequently 7^X| W will be .equal to r!^, and 



"^Zi\ m to 1—7; that is, according to Mr. 



Newt on* $ faid Rule, i^-mL^m % LVjf^^V^ 

 i 7 w4L«~h-Uw 5 L' &c. will befei^V? and 1 — 

 L'L * L' L A + *$m*L*^J 9 -th< V &c. 

 will be equal to 1— ^ being any infinite In- 

 dex whatfoever, which is a full and general 

 Propofition from the Logarithm given to find 

 the Number, be the Species' of Logarithm what 

 it will. But if Napeir\ Logarithm be given, 

 the Multiplication by m is faved (which Mul- 

 tiplication is indeed no other than the redu- 

 cing the other Species to his) and the Series will 

 be more fnnple, viz.: i-| L-j iLL-|4 L^ r 4L ? -|- 

 ,WL 5 &c. or i-L-|-fLL-iL s H -^L + - r £ 5 L' . 

 &c. This Series, efpecially in great Numbers 

 converges To flowly, that.it were to be wilhed 

 it could be contracted. 



If 



