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



The first edition does not contain the experiments in question. Dubuat justly remarked that 

 the time of oscillation of a pendulum oscillating in a fluid is greater than it would be in vacuum, 

 not only on account of the buoyancy of the fluid, which diminishes the moving force, but also on 

 account of the mass of fluid which must be regarded as accompanying the pendulum in its 

 motion ; and even determined experimentally the mass of fluid which must be regarded as 

 carried by the oscillating body in the case of spheres and of several other solids. Thus 

 Dubuat anticipated by about forty years the discovery of Bessel ; but it was not until after 

 the appearance of Bessel's memoir that Dubuat's labours relating to the same subject attracted 

 attention. 



Dubuat's method was as follows. Imagine a body suspended by a fine thread or wire and 

 swung in vacuum, and let a be the length of the pendulum, reckoned from the centre of sus- 

 pension to the centre of oscillation. Now imagine the same body swung in a fluid, in which 

 its apparent weight is p, so that if P denote the weight of fluid displaced, the true weight of 

 the body will be p + P. Since the moving force is diminished in the ratio of p + P to p, if 

 the inertia of the body were all that had to be overcome, it would be necessary to diminish the 

 length of the pendulum in the same ratio, in order to preserve the same time of oscillation. 

 But since the mass in motion consists not only of the mass of the body itself, but also of that 

 of the fluid which it carries with it, the pendulum must be shortened still more, in order that 

 the time of oscillation may be unaltered. Let I be the length of the pendulum so shortened, 

 and ft (which for the same reason as before I write instead of Dubuat's n,) a factor greater 

 than unity, such that p + TIP is the weight of the mass in motion ; then 



uu , p (a \ 



— , whence n = ^ I- - ll • . . . (167) 



ap 



Dubuat's experiments on this subject consist of 44 experiments on spheres oscillating in 

 water, (Tom. 11. p. 236) ; 31 experiments on other solids oscillating in water, (p. 246) ; and 

 3 experiments on spheres oscillating in air, (p. 283). The following table contains a compa- 

 rison of the formula (148) with Dubuat's results for spheres oscillating in water. The value 

 of \Zfi employed in the calculation is 0.0564 inch English, or 0.05291 inch French. 



