OF FLUIDS ON THE MOTION OF PENDULUMS. 



[87] 



have caused the oscillations to subside if an extraneous force had not frequently been 

 applied. 



71. In Dubuat's experiments on spheres oscillating in air, the lightness of the fluid was 

 compensated by the extreme lightness of the spheres, which were composed, the first two of 

 paper, and the third of gold-beater's skin. In the following table the diameter 2 a of the 

 sphere is expressed in French inches. The value of ^/p employed in the reduction is the 

 same as was before used in the reduction of observations made in air, namely 0.1 16 inch 

 English, or 0.1088 inch French. 



Dubuat's experiments on light spheres oscillating in air. 



The differences certainly appear very small when the delicacy of the experiments and the 

 simplicity of the apparatus employed are considered. 



72. The only comparison yet made in this section between theory and observation in the 

 case of pendulum experiments, consists in comparing the observed times of vibration with the 

 results calculated with an assumed value of \Z/u'. But according to theory we ought to be 

 able, without assigning a particular value to any new disposable constant, to calculate the rate 

 of decrease of the arc of vibration. I have not met with any experiments made with a view of 

 investigating the decrease in the arc of vibration in the case of extremely small vibrations, such 

 as those employed in pendulum experiments. The experiments of Newton and others, in which 

 the arc of vibration was so large that the resistance depended mainly on the square of the 

 velocity, would be quite useless for my purpose. The pendulum experiments of Bessel and 

 Baily contain however the requisite information, or at least some portion of it, for the arcs are 

 registered for the sake of giving the data for calculating the small reduction to indefinitely 

 small vibrations. 



In Bessel's experiments the arc is registered for the end of equal intervals of time during 

 the motion. The number of such registrations in one experiment amounts in some cases to 

 eleven, and is never less than three. So far the observations are just what are wanted; but 

 there are other causes which prevent an exact comparison between theory and experiment. In 

 the first place the spheres were swung so close to the back of the frame that the increase of 

 resistance due to the confinement of the air must have been very sensible. In the second 

 place the effect of the wire must have been very sensible, especially in the case of the long 

 pendulum. For the table of Section III. Part I., shews that for the wire (for which tit is very 

 small) the value of U is much larger than that of k, whereas for spheres of the size of those 

 employed, when the time of oscillation is only one or two seconds, k' is a good deal smaller 



