On thé Mean Dénsily of the Earth. I 
The last column shows the numbers for the required density, 
resulting from the calculation by the foregoing theorem, being 
all a little above 5, excepting the third number, which is a little 
below 5. And immediately after, is the following remark, show- 
ing the author’s doubt of their accuracy; viz. ‘* From this table 
it appears, that though the experiments agree pretty well to- 
gether, yet the difference between them, both in the quantity of 
motion of the arm, and in the time of vibration, is greater than 
can proceed merely from the error of observation. As to the 
difference in the motion of the arm, it may very well be accounted 
for from the current of air produced by the difference of ternpe- 
rature ; but whether this can account for the difference in the 
time of vibration, is doubtful. If the current of air was regular 
and of the same swiftness in all parts of the vibration of the ball, 
I think it could not; but as there will most likely be much irre- 
gularity in the current, it may very likely be sufficient to account 
for the difference.” [t then proceeds: ‘* By a mean of the ex- 
periments made with the wire first used,”’ [viz. the first six num- 
bers or experiments] “‘ the density of the earth comes out 5-48 
times greater than that of water; and by a mean of those made 
with the latter wire, it comes out the same,” &c. 
. Now, though the former list of errata were but small in quan- 
tity, yet here is one of a considerable magnitude, viz. in the me- 
dium of the first six experiments, said to be 5°48, which is very 
erroneous, the true medium being only 5°31; and it is rather 
curious that that medium 5:46 has been obtained, by taking the 
third experiment as 5°88 instead of 4°88, through mere oversight 
or carelessness. If this were the only error, it might perhaps be 
excused as a single accident; but the whole will make a very dif- 
ferent appearance, when we have shown that many small errors 
exist in almost all the numbers in the last column of the table, 
as resulting from erroneous calculations, in the use of the general 
theorem before mentioned, and evinced by a comparison of the 
numbers in the foregoing table, with those of the following one, 
derived by our calculation from the same data, and by the same 
theorem when corrected. 
B2 The 
