[ 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 1.2.3.4. &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-