[12] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



at Oxford in 1847, and are noticed in the volume of reports for that year, but they have 

 not yet been published in detail. 



The preceding are all the investigations that have fallen under my notice, of which the 

 object was to calculate from hydrodynamics the resistance to a body of given form oscillating 

 as a pendulum. They all proceed on the ordinary equations of the motion of fluids. They 

 all fail to account for one leading feature of the experimental results, namely, the increase 

 of the factor n with a decrease in the dimensions of the body. They recognize no distinction 

 between the action of different fluids, except what arises from their difference of density. 



In a conversation with Dr Robinson about seven or eight years ago on the subject of the 

 application of theory to pendulums, he noticed the discrepancy which existed between the 

 results of theory and experiment relating to a ball pendulum, and expressed to me his con- 

 viction that the discrepancy in question arose from the adoption of the ordinary theory of 

 fluid motion, in which the pressure is supposed to be equal in all directions. He also de- 

 scribed to me a remarkable experiment of Sir James South's which he had witnessed. This 

 experiment has nojt been published, but Sir James South has kindly allowed me to mention 

 it. When a pendulum is in motion, one would naturally have supposed that the air near the 

 moving body glided past the surface, or the surface past it, which comes to the same thing 

 if the relative motion only be considered, with a velocity comparable with the absolute velocity 

 of the surface itself. But on attaching a piece of gold leaf to the bottom of a pendulum, so 

 as to stick out in a direction perpendicular to the surface, and then setting the pendulum in 

 motion, Sir James South found that the gold leaf retained its perpendicular position just as 

 if the pendulum had been at rest ; and it was not till the gold leaf carried by the pendulum 

 had been removed to some distance from the surface, that it began to lag behind. This 

 experiment shews clearly the existence of a tangential action between the pendulum and the 

 air, and between one layer of air and another. The existence of a similar action in water is 

 clearly exhibited in some experiments of Coulomb's which will be mentioned in the second 

 part of this paper, and indeed might be concluded from several very ordinary phenomena. 

 Moreover Dubuat, in discussing the results of his experiments on the oscillations of spheres 

 in water, notices a slight increase in the effect of the water corresponding to an increase in 

 the time of vibration, and expressly attributes it to the viscosity of the fluid. 



Having afterwards occupied myself with the theory of the friction of fluids, and arrived 

 at general equations of motion, the same in essential points as those which had been pre- 

 viously obtained in a totally different manner by others, of which, however, I was not at 

 the time aware, I was desirous of applying, if possible, these equations to the calculation 

 of the motion of some kind of pendulum. The difficulty of the problem is of course 

 materially increased by the introduction of internal friction, but as I felt great confidence in 

 the essential parts of the theory, I thought that labour would not be ill-bestowed on the 

 subject. I first tried a long cylinder, because the solution of the problem appeared likely 

 to be simpler than in the case of a sphere. But after having proceeded a good way towards 

 the result, I was stopped by a difficulty relating to the determination of the arbitrary con- 

 stants, which appeared as the coefficients of certain infinite series by which the integral of a 

 certain differential equation was expressed. Having failed in the case of a cylinder, I tried 



