Mtfcettanea Curiofa. 43 



plied to find the Logarithms of Prime Num- 

 bers, having the Logarithms of the two next 

 Numbers above and below them : For the dif- 

 ference of the ratio of a to | z. and of \ z, to b 

 is the ratio of a b to | and the half of that 

 ratio ^ is that of V a b to \ z,, or of the Geo- 

 metrical Mean to the Arithmetical. And 

 confequently the Logarithm thereof will be the 

 half difference of the Logarithms of thofe rati* 

 oneSy viz*. 



1 . • XX \ X t ~\ x* 1 x 3 « 



Which is a Theorem of good difpatch to .find 

 the Logarithm of I z.. But the fame is yet much 

 more advantageoufly performed by a Rule de- 

 rived from the foregoing, and beyond which, 

 in my Opinion, nothing better can be hoped. 

 For the ratio of a b toi ' .zx. or 4 aa + \ ab'Ar \ 

 b b, has the difference of its terms * aa—k ab*\~ 

 % bb 7 or the Square of i a — \ b=% x which 

 in the prefent cafe of finding the Logarithms 

 of Prime Numbers^ is always Unity, and cal- 

 ling tbe Sum of the terms %z.z,*\-a b=yy^ the 

 Logarithm of the ratio of^/abto \a-\kb or | 

 % will be found 



JLin-i J^l-^J-^'^J^ &c .. 

 m yy 1 3/ > 5> 1 V 5 9^ 



which converges very much fafter than any 

 Theorem hitherto publifhed for this purpofe. 



Here note — is all alone; applied to adapt theft 



