264 The Proposed Pendulum Operations for India. [No. 4, 
feet in front of the pendulum, and between the two, the object glass 
of a telescope was adjusted to form an image of the detached pendulum 
in the plane of the clock pendulum, to enable them both to be seen 
simultaneously through the observing telescope, which was set up at a 
distance of about 15 feet. On the wire of the detached pendulum 
was fixed a small brass cylinder, painted black and called the coinci- 
dence cylinder; it weighed something under 4 grains, and could be 
brought exactly opposite the scale for measuring the are of vibration. 
On this scale a black streak was painted, in the middle of which a 
space was left white, equal to the diameter of the coincidence cylinder, 
so that when the pendulum was at rest, the cylinder exactly covered it. 
Again, to the bottom of the clock pendulum a piece of blackened 
paper was attached, in which a hole had been cut of such a size that 
when both pendulums were at rest, it exactly coincided with the image 
of the white space on the black streak: hence when the pendulums 
were moving in coincidence, the coincidence cylinder was visible 
through the hole, and completely eclipsed the white space. Bessel’s 
result was expressed in lines of the toise of Peru, the standard used in 
the measurement of the Peruvian are. 
In publishing these experiments, M. Bessel pointed out the true 
correction for buoyancy, which he had investigated by swinging in air 
two spheres of equal diameters, but of different densities, one being of 
brass and the other of ivory, suspended by a fine steel wire; and again 
by swinging the same brass sphere first in air and then in water. 
These experiments showed that the old formula for reducing observ- 
ations in air to a vacuum gave too small a correction, and that it should 
be multiplied by a factor. 
Mr. Francis Baily made a long series of experiments on the cor- 
rection for buoyancy, which were published in the Philosophical 
Transactions for 1832. He used about 80 pendulums, all differing in 
form, weight, and mode of suspension. From these experiments he 
deduced factors for pendulums of almost every description that have — 
ever been used, and computed also the weight of the air adhering to 
each, in other words deduced the vibrating specific* gravity of the — 
* “The vibrating specific gravity of a compound pendulum is ordinarily found 
“as follows; Let d’, d’ d’”’ ...denote the distance of the centre of gravity of each — 
“body respectively from the axis of suspension: w’, w”, w’”, ...the weight (in air) — 
“of each body: s’, s’, s’’, ...the specific gravity of each body determined in the 

