Page:Philosophical Transactions - Volume 053.djvu/331

 As we are informed, that there are two vulcanoes opened, I am in great hopes thee will prove a ufficient vent to dicharge all the remaining ulphurous matter in the bowels of thee countries, and put a top to any further earthquakes here; at leat 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. F the following obervations do not eem to you to be too minute, I hould eteem it as a favour, if you would pleae to communicate them to the Royal Society.

It has been aerted by ome eminent mathematicians, that the um 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 whoe radius is unity. And it is true that this expreion will very nearly approach to the value of that fum when z is large, and you take in only a proper number of the firt terms of the foregoing eries: but the whole eries can never properly ex-