Mi fcettanea Cur to fa . 4. 1 



dex m may be taken at pleafure, the feveral 

 Scales of Logarithms to fuch Indices will be as 



■—-or reciprocally as the Indices. And if the 



Index be taken 10000, &c as in the cafe of 

 Nafeirh Logarithms, they will be limply q—i 



Again, if the Logarithm of a decreafing ra- 

 tio be fought, the infinite Root of 1— q or 

 1 



&c whence the decrement of the 



* 6m l 



firft of our infinite Number of Proportionals 

 will be 4 into f+l f^^if 4 *^^!^ &c. 



which therefore will be as the Logarithm of 

 the ratio of Unity to 1— q. But if m be put 

 i 0 ooo, &c. then the faid Logarithm will be 



Hence the terms of any ratio^hting a and 



b-——& 



q becomes — - — or the difference divided by 



the lefler term, when 'tis an increafing ratio ; 



or^"^ a when 'tis decreafing, or as b to a. 



Whence the Logarithm of the lame ratio may 

 be doubly expreft, for putting x for the diffe- 

 rence of the terms ^and it will be either 



-into T+Ty^— +jp+ 5 TT" f 6ir &c - or 



I . x x r . x* . X? x* 



—into ~~ — h— - 5 ^ 6*F &c ' 



But 



