NATURfi OF LOGARITHMS. 245 



tjiose, which are to be found at present, in mo-st of the^ 

 common tables of logarithms. 



The distinguishing mark of this system of logarithms 

 is, that the index or logarithm of 10 is I j that of 100 is 

 2 ; tliat of 1000 is 3, &c. And, in decimals, the logar- 

 ithm of 'I is -—I 5 that of 'pi is — 2-5 that of 'ooi is 

 . — 3, &c. the logarithm of i being o in every system. 



Whence it follows, that the logarithm of any number 

 between i and 10 must be o and some fractional parts ; 

 and that of a number between 10 and 100, i and some 

 fractional parts ; and so on, for any other number what- 

 ever. 



And since the integral part of a logarithm, thus readily 

 found, shews the highest place of the corresponding num- 

 ber, it is called the hia'ex, or characteristic, and is common- 

 ly omitted in the tables ; being left to be supplied by the 

 person, who uses them, as occasion requires. , 



Another definition of logarithms is, that the logarithm 

 of any number is the index of that power of some other 

 number, which is equal to the given number. So if there 

 be JVzzr", then n is the log. of N \ where n rriay be either 

 positive or negative, or nothing, and the root r any num- 

 ber whatever, according to the different systems of log- 

 arithms. 



When n\s zro, then AT is zri, whatever t\\Q value p£ 

 r is ; which shews, that the logarithm of i is always o, in 

 every system of logarithms. 



When n is :=i, then AT is rzr ; so that the radix r is 

 always that number, whose logarithm is i in every system. 



When the radix r is zr2'7 1828 1828459, Sec. the in- 

 dices n are the hyperbolic or Napier's logarithm of the 

 numbers N ; so that n is always the hyperbolic logarithm 



of the number A^ or 2*7 18, &c.| . 



But when the radix r Is zzio, then the index n becomes 

 lj:e common or Briggs' logarithm of the number N ; so 



that 



