Page:Philosophical Transactions - Volume 053.djvu/331

This page needs to be proofread.

[ 269 ]

As we are informed, that there are two vulcanoes opened, I am in great hopes theſe will prove a ſufficient vent to diſcharge all the remaining ſulphurous matter in the bowels of theſe countries, and put a ſtop to any further earthquakes here; at leaſt for many years to come.

XLIII. A Letter from the late Reverend Mr. Thomas Bayes, F. R. S. to John Canton, M. A, and F. R. S.

SIR, Read Nov. 24, 1763. IF the following obſervations do not ſeem to you to be too minute, I ſhould eſteem it as a favour, if you would pleaſe to communicate them to the Royal Society.

It has been aſſerted by ſome eminent mathematicians, that the ſum of the logarithms of the numbers &c. to z, is equal to 4. log. c--z--l. x log. 2; leffened by the feries -4-k- 1 — 1 J J j I2Z~36o Z 3 I26oz 5 ^ -rr — 7 if c denote the circumference of a circle whoſe radius is unity. And it is true that this expreſſion will very nearly approach to the value of that fum when z is large, and you take in only a proper number of the firſt terms of the foregoing ſeries: but the whole ſeries can never properly ex-