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 

 resistance. 



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, whenever strict scientific accuracy is desired. 



