[ 269 ] 
As we are informed, that there are two vulcanoes 
opened, I am in great hopes thefe will prove a fuf- 
ficient vent to difcharge all the remaining fulphurous 
matter in the bowels of thefe countries, and put a 
flop to any further earthquakes here; at lead 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. 
S I R, 
Read Nov. 24, 'T' F the following obfervations do not 
17 3 ‘ X f eem t0 you to be too minute, I fhould 
efteem it as a favour, if you would pleafe to commu- 
nicate them to the Royal Society. 
It has been afferted by fome eminent mathemati- 
cians, that the fum of the logarithms of the num- 
bers 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 ^ c denote the circumference of 
a circle whofe radius is unity. And it is true that this 
expreffion will very nearly approach to the value of 
that fum when z is large, and you take in only a 
proper number of the firft terms of the foregoing 
feries : but the whole feries can never properly ex- 
prefs 
