On the Mean Density of the Earth. § 
the extent and time of each vibration. Then, from these spaces 
and times, the density of the earth is to be calculated, by peculiar 
theorems, as compared with the vibrations of common pendulums, 
that are produced by the attractions of the earth. 
All these effects were so minute, and produced by machinery 
so complex, and the results calculated by theorems derived from 
intricate mathematical investigations, that it is impossible at first, 
for ordinary readers, to conceive how any accurate results can be 
deduced from them, and even for the more judicious reader to 
place confidence in them, except chiefly on account of the high 
character of the experimenter himself. From the nature of the 
machinery I could therefore derive no confidence in the results, 
nor compare them with the mountain experiment, without re- 
peating the whole of the calculations. But, after a long life spent 
in almost daily abstruse investigations, from the tenth year of my 
age, and now being at 84, and oppressed with distressing illness, 
1 thought I might be excused from such atask. But after urging 
more than one mathematical friend, without being able to in- 
terest them sufficiently to engage in so severe an operation, my 
anxiety to accomplish the business induced me to make an ex- 
ertion to effect it myself; especially as the learned experimenter 
informs us, that he availed himself of the assistance of the then 
Clerk of the Society, who he says made some of the experiments, 
and who doubtless made most of the arithmetical computations ; 
operations, of both kinds, in which I remember he was also much 
employed by Sir Charles Blagden, and other gentlemen, in pre- 
paring their papers for the Royal Society. 1 have therefore re- 
computed all the experiments, and have traced the investigations 
of all the theorems ; and have found that my labour has not been 
in vain ; but, on the contrary, has been rewarded with the follow- 
ing copious list of errata, some of which are large or important. 
In the following instances it is to be noted, that the refer- 
ences are made to Mr. Cavendish’s paper, as printed in my edi- 
tion of the Phil. Trans., as I am not now possessed of a set of 
the original edition, but with which, however, I have had my own 
set compared and verified. 
Some of the Errata in Mr, Cavenpisn’s Paper. 
In page 399, line 10 from the bottom, for 8739000, read 
8740000. 
Ditto, line 6 b, or from the bottom, for 8739000, read 8740000. 
The same also in line 5 b. 
Ib. line 4 b, for 10683, read 10685. 
The same also in line 1 b. 
Page 403, lines 12 and 13, for 8739000, read 8740000. 
Ib, line 13, for 10844, read 10847. 
Vol, 58, No, 279, July 1821. B Page 
