2 03* THE EFFECT OF THE INTERNAL FBICTION OF FLUIDS
correction for buoyancy is easily calculated from the first principles of hydrostatics, and formed for a considerable time the^ only correction which it was thought necessary to make for reduction to a vacuum. But in the year 1828 Bessel, in a very important memoir in which he determined by a new method the length of the seconds' pendulum, pointed out from theoretical considerations the necessity of taking account of the inertia of the air as well as of its buoyancy. The numerical calculation of the effect of the inertia forms a problem of hydrodynamics which Bessel did not attack; but he concluded from general principles that a fluid, or at any rate a fluid of small density, has no other effect on the time of very small vibrations of a pendulum than that it diminishes its gravity and increases its moment of inertia. In the case of a body of which the dimensions are small compared with the length of the suspending wire, Bessel represented the increase of inertia -by that of a mass equal to k times the mass of the fluid displaced, which must be supposed'to be added to the inertia of the body itself. This factor k he determined experimentally "for a sphere a little more than two inches in diameter, swung in air and in water. The result for air, obtained in a rather indirect way, was k = 0*9459, which value Bessel in a subsequent paper increased to 0*956. A brass sphere of the above size having been swung in water with two different lengths of wire in succession gave two values of Jc, differing a little from each other, and equal to only about two-thirds of the value obtained for air.
The attention of the scientific world having been called to the subject by the publication of Bessel'a memoiry fresh researches both theoretical and experimental soon appeared. In order to examine the effect of the air by a more direct method than that employed by Bessel, a large vacuum apparatus was erected at the expense of the Board of Longitude, and by means of this apparatus Captain (now Colonel) Sabine- determined the effect of the air on the time of vibration of a particular invariable pendulum. The results of the experiments are contained in a memoir read before the Royal Society in March 1829, and printed in the Philosophical Transactions for that year. The mean of eight very consistent experiments gave 1/655 as the factor by which for that pendulum the old correction for buoyancy must be multiplied in order to give the whole correction on account of the air. A very remarkable fact was discovered in the course of these experiments. While