366 Philosophical Transactions of the 
- mass of the body over that: of an equal bulk of air, by the mass of 
the body itself, and all the reductions of a pendulum’s motion in air, 
to that which would take place in a vacuum, are made upon the same 
principle. Bessel, the celebrated astronomer of Konigsberg, was the 
first to suspect the truth of this principle, which allows for simple 
buoyancy alone, without taking into view the force necessary to com- 
municate motion to the particles of the air that are successively dis- 
placed. He established conclusively, that his suspicion was correct, 
and found that, when the oscillations of a pendulum take place in 
rare media, such as the air of our atmosphere, this retarding force, 
which has hitherto been neglected, is at least equal in amount to the 
simple buoyancy. ‘The apparatus of Bessel, was a modification of 
that by which he had determined the length of the pendulum. It 
differs from the methods of Borda and Kater, and approaches more 
nearly than they do to the more ancient plan used by Whitehurst. 
The pendulum is composed of a sphere, suspended by a wire of 
steel, in such ‘a manner that it may be made to vibrate either, from 
the upper or lower end of a scale, of known length. ‘There are 
thus in fact two pendulums, the difference of whose lengths is a 
known quantity, and hence when their respective times of oscillation 
are known, the absolute length may be calculated. ‘To apply this 
apparatus to the investigation of the air’s resistance, the bulbs are 
made of materials of very different densities, but of the same size and 
shape. Sabine, on the other hand, employed an invariable pendu- 
lum, made upon Kater’s plan, and the investigation of the resistance 
of the air was made directly, by causing the pendulum to vibrate al- 
ternately in air, and in the exhausted receiver of an air pump. ‘The 
experiments of Sabine have fully confirmed those of Bessel, and a 
similar result has been found, by causing the pendulum to vibrate in 
hydrogen. In this gas, as well as in common air, a resistance, grow- 
ing out of the necessity of displacing the particles, has been detected. 
This result is the more important, in as much as it shews, that the 
method of Kater is liable to an objection, in consequence of the 
pendulum with convertible axes being unequally affected by the fluid 
» It-seems that every new improvement in the apparatus, by which 
the length of the second pendulum is ascertained, tends to. the dis- 
covery of new, although slight, causes of disturbance, and although 
for all mere practical purposes the measures of Kater and Biot may 
_ be taken as sufficient, corrections never before employed, must now 
be introduced, whe trict scientific accuracy is desired. 
