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XLVII. Of Logarithns^ hy the late William 
Jones, Efq\ F, R. S. Communicated hy 
John Robertfon, Lib, R, S, 
Read Dec. ^ | i H E following paper on the nature 
^771* Jl^ conftrudion of Logarithms, 
was communicated to me many years fince, by that 
eminent Mathematician the late William Jones, Efq. 
. The familiar manner in which he explains their na- 
ture, and the great art with which he obtains the 
modes of computation, not being exceeded, if 
equaled, by any writer on this fubjedt, may claim a 
place in the Philofophical Tranfadions, to be pre- 
lerved among the multitude of excellent papers, of 
which that mod invaluable work is a fafe repo^ 
fitory. 
Of Logarithms. 
I. Any number may be exprefled by fome Angle 
power of the fame radical number. . 
For every number whatever is placed fomewhere 
in a fcaleof the feveral powers of fome radical num- 
ber r, whofe indices are m—iy m— 2 y m — &c. 
where not only the numbers r”, 5 ^ 0 . 
are exprefled j but alfo .any intermediate number x 
is reprefen ted by r, with a proper index z, 
VoL. LXI. - M m m 4 
The 
