OF FLUIDS ON THE MOTION OF PENDULUMS. 



[77] 



the whole apparatus which is given in Plate I., and by a comparison of figs. 2 and S, Plate 

 II., it must have been very small, that is to say, a small fraction of the radius of the sphere*. 

 If so, although the exact calculation of the correction for confined space would form a problem 

 of extreme difficulty, it may be shewn from theoretical considerations that the correction would 

 be by no means insensible, so that it might wholly or in part account for the difference + - 13Q 

 between the results of theory and observation. It is, however, not improbable, for a reason 

 which has been already mentioned, that the theoretical correction for the wire is not quite 

 exact. 



64. The experiments performed by Bessel on a sphere vibrating in water will be more 

 conveniently considered after the discussion of some experiments of Coulomb's, to which I now 

 proceed. These experiments are contained in a memoir entitled Experiences destinies a deter- 

 miner la coherence des Jluides et les lois de leur resistance dans les mouvements tres-lents, 

 which will be found in the 3rd Volume of the Memoires de VInstitut, p. 246. The experi- 

 ments which I shall first consider are those which relate to the oscillations of disks suspended 

 in water with their planes horizontal. In these experiments the disk operated upon was attached 

 to the lower extremity of a vertical cylinder of copper, not quite half an inch in diameter, the 

 axis of which passed through the centre of the disk. The cylinder was suspended by a fine 

 wire attached to its upper extremity. The under portion of the cylinder, together with the 

 attached disk, were immersed in water, the disk at the bottom of the cylinder being immersed 

 to the depth of 4 or 5 centimetres below the surface. The upper portion carried a horizontal 

 metallic graduated disk, by means of which the arc of oscillation could be read off, and which, 

 on account of its size and weight, mainly determined the inertia of the system, so that the time 

 of oscillation in the different experiments was nearly the same. The observations were taken 

 as follows. The whole system was turned very slowly round by applying the hands of the 

 graduated disk, taking care not to derange the vertical position of the suspending wire. The 

 arc through which the system had been turned was read by means of the graduation, or rather 

 the system was turned through an arc previously fixed on ; the system was then left to itself, 

 and the arc again read off to a certain number of oscillations. Thus it was the decrement 

 of the arc of oscillation that was observed ; the time of oscillation was indeed also observed, 

 but only approximately, for the sake of determining a subsidiary quantity required in the cal- 

 culation. Indeed, it will be easily seen that the experiments were not adapted to determine the 

 effect of the fluid on the time of oscillation. The decrement of arc so determined had to be 

 corrected for the effect of the imperfect elasticity of the wire, and of the resistance of the air 

 against the graduated disk, and of the water against the portion of the copper cylinder 

 immersed. The amount of the correction was determined by repeating the observation when 

 the lower disk had been removed. 



It appeared from the experiments, first, that with the same disk immersed, the successive 



* The measurement of either of Bessel's figures, figs. 5 or 6, 

 Plate II. gives I'd inch for the distance of the centre of the 

 sphere from the surface of the broad iron bar which formed the 

 back of the frame, the surface of the bar being supposed truly 



vertical ; and the measurement of fig. 2 giving 2*06 inches for 

 the diameter of the sphere, it appears that the distance of the 

 surface of the sphere from the surface of the bar was barely 

 equal to half the radius of the sphere. 



