486 On Napier s Logarithms. 



bla? = 101 °T^= 10101 ^©- 



And Napier's final form is, of course, 



nl^ = 10 l0 B log 10 ^. 



Biirgi's Arithmetische und Geometrisclie Progress Tabulen 

 also come under the same law. If the terms in the Arith- 

 metical Progression are taken as the logarithms of the terms 

 in the Geometrical Progression, and Blzc stands for what I 

 may call Biirgi's logarithm of x s we have 



for 



^ffl =101o g ,(•), 

 ,=10»(l + ^J, 



5 being any positive integer. 

 Finally, treating Napier's series 



0, 1, 2, 



10 > H 1 -^ H'-M' 



in the same way, and denoting this logarithm by Nl#, 

 we have 



log.(^f) , 



1A< A 



log.(l- "- 4 



ioV 



-io 7 (i- iy, 



5 being any positive integer. 

 Sydney, August 1916. 



