





















262 The Proposed Pendulum Operations for India. [No. 4, 
Captain Sabine was not at first aware of the strict expression for the 
reduction to a vacuum, but after the publication of Bessel’s observ- 
ations in 1828, he had an apparatus specially constructed, and ascer- 
tained the proper correction practically, by swinging his pendulums 
in air, and in vacuo. 
The error from this cause, however, proved to be trifling, owing to 
his observations being strictly differential, so that only the differences 
between the corrections by the old and new formule entered. 
The most widely differing buoyancy corrections at any of his or 
Captain Kater’s stations of observation, computed by the old formula 
were + 5.75 vibrations at Sierra Leone, and + 6.27 vibrations at 
Spitzbergen, in amean solar day. These corrections, multiplied by 
the proper factor, 1.65, to reduce them to the new formula, became ++ 
9.52 and + 10.38 vibrations, so that the number of vibrations in a 
mean solar day at Sierra Leone required to be increased by (9.52—5.75) 
3.77, and at Spitzbergen by (10.88—6.27) 4.11 vibrations. But the 
acceleration between the stations would only be wcreased by the — 
difference between these numbers, or by 0.44 vibrations. It so happened, 
however, that even this difference was too large, for in the deduction 
of the temperature correction, the old buoyancy formula had of course 
been used; on applying a correction on this account, the above dif- 
ference required to be reduced by 0.36 vibrations, so that the whole 
error on the acceleration of the pendulum between Sierra Leone and 
Spitzbergen was only -++ .08 vibrations. 
Captain Sabine subsequently determined the difference in the 
number of vibrations made by an invariable pendulum between London 
and Paris, London and Greenwich, and London and Altona. He also 
detormined the true buoyancy correction for Kater’s convertible 
pendulum. 
In 1825 M. Bessel made his experiments for determining the length 
of the seconds’ pendulum at Kénigsberg, with an apparatus constructed 
and partly designed by Repsold, the celebrated artist of Hamburg. 
The apparatus was contrived so as to avoid any uncertainty in the 
centre of oscillation of the pendulum, as well as any error in the 
measure of its length, by observing the times of vibration of a pen- 
dulum ball suspended alternately by two wires, whose difference in 
length was known. 
