at the Summit of Fujiyama, Japan. 101 
to these conditions they were all reduced after being corrected 
for arc, chronometer rate, &c. Finally the mean of all is re- 
duced to the Tokio conditions as to temperature and pressure. 
The coefficient of expansion of the bar has not been deter- 
mined, but it has been assumed to be ‘00000187 for 1° C. This 
is a commonly accepted coefficient for brass, and a comparison 
of the vibration periods of the pendulum, under different tem- 
peratures, indicates that it cannot be far from correct. The 
correction for difference of barometric height is the most diffi- 
cult to determine. Were it possible to vibrate the pendulum 
at the same place under pressures wide iffering, it might be 
determined experimentally. Lacking this, I was, fortunately, 
able to refer to a recent elaborate and exhaustive discussion of 
the whole subject, from an experimental as well as from a 
theoretical standpoint, by C. S. Peirce, Esq., of the U. S. 
Coast Survey.* In this valuable memoir Mr. Peirce gives a 
graphical representation of the periods of vibration of his pen- 
dulum, under various pressures, from 80 inches of mercury 
down to what is practically a vacuum. By interpolation the 
period for any pressure between these limits can be very closely 
ascertained, as also the correction in going from one pressure to 
another. There are important differences between the pendu- 
lum used by Mr. Peirce and that in use here, the principal 
one being the difference in shape of the cylindrical weights, and 
the fact that in our pendulum only one cylinder was carried. 
Nevertheless, a fair approximation to the correction may be 
taken from his curve showing the results with “heavy end 
lums are such as to make the correction for our pendulums 
considerably less than that of the Coast Survey. In this way, 
y considering these differences the correction used in the re- 
duction was determined. After it had been established, I was 
fortunate in getting possession of the complete memoir of Mr. 
form and dimensions, resembles ours quite closely, and the re- 
sults of his experiments with it confirm the accuracy of the 
to a vacuum. It is thought, therefore, that the correction ap- 
ee 18 not far wrong. The corrected time, then, appears to 
as follows: ; 
pee Measurements of Gravity at Initial Stations in America and Europe. Appen- 
No. 15, U. 8. Coast Survey. - Report for 1876. 
