SIMPLE-HAKMONIC WAVES. DIFFRACTION 231 



since t enters only through U. Substituting we find 



(9) 



The remarkable point here is that the force is independent 

 of the velocity, and depends only on the acceleration of the 

 sphere. If the mass of the sphere be M, and if it be subject to 

 other extraneous force X, its equation of motion will be 



(10) 



or (*+f/^~Z ................... (11) 



This is the same as if the fluid were abolished, and the inertia 

 of the sphere were increased by Trpa 3 , i.e. by half that of the 

 fluid which it displaces. It was shewn by Stokes (1843) that 

 this conclusion is accurate even when the restriction to small 

 motions is abandoned. 



There is, as we shall see ( 79), nothing peculiar to the 

 sphere in the general character of the above result, but the 

 apparent addition to the inertia will vary of course with the 

 shape as well as the size of the solid, and will usually be 

 different for different directions of motion, as e.g. in the case of 

 an ellipsoid. The theory here touched upon has had a great 

 influence on recent physical speculations, and is responsible 

 ultimately for the suggestion that the apparent inertia of 

 ordinary matter may be partly or even wholly due to that of a 

 surrounding aetherial medium. 



Turning now to the acoustical problem, let the velocity of 

 the sphere be expressed symbolically by 



U = Ae int ...................... (12) 



The surface-condition will have the same form (1) as before. 

 The velocity-potential of a double source Ce in * at is 



by 76 (21), the time-factor e int being omitted. The ratio of C 

 to A is then determined by (1). 



