﻿428 Sir W. Thomson on Approach caused by Vibration. 



gions of greater fluid motion or of less fluid motion (that is to 

 say, is attracted towards the vibrator or repelled from it) accord- 

 ingly as the density is greater or less than that of the fluid. 



I have worked out this theory in detail for a perfectly rigid 

 spherical solid left to itself in an incompressible liquid disturbed 

 by a single spherical body moviug to and fro with a simple har- 

 monic motion through a short space in a line with the free 

 sphere, the radius of one at least of the two spheres being so 

 small that there is no sensible disturbance of the fluid in the 

 neighbourhood of the free sphere due to the influence of this 

 body itself reflected back to the vibrator. When the density of 

 the free sphere differs from that of the liquid, I suppose there to 

 be no force of gravity. In illustrative experiments, when the 

 force of gravity is sensible, it may be readily balanced by means 

 of a thread properly applied to support the body or to prevent 

 it from rising, as the case may be, in general without sensibly 

 interfering* with the to-and-fro motion of the sphere. The 

 range of the vibration may be of any magnitude relatively to its 

 own diameter, but must be small relatively to the distance of the 

 nearest point of the free globe. A very simple application of 

 the method of images sufiices for the problem. I intend to give 

 the details in the continuation of my paper on u Vortex-motion." 

 One chief result is this : when the density of the free globe is 

 less than that of the fluid, it is repelled or attracted, according 

 to whether its radius is less or greater than 



/V'-v"-^ 



where p denotes the density of the free globe, and / its distance 

 from the vibrator (the density of the fluid being taken as unity) . 

 From this it follows that the free globe, if of great diameter in 

 comparison with that of the vibrator, is repelled when placed in 

 the line of the vibration at any distance greater than 



and is attracted when placed at any distance less than this cri- 



* [Note added April 13th, 1871.] Not so readily as I believed when 

 writing the above. Even a rough approximation to this condition is not 

 very " readily " attained ; and on this account experimental verification of 

 the theoretical conclusion is somewhat difficult. I have, however, obtained 

 more or less imperfect illustrations of it readily enough by using the hand 

 or a round wooden bar to produce vibratory motions in the neighbourhood 

 of wooden balls or other light rigid globes anchored by very thin threads, 

 allowing them to float near the surface of water in a vat about 6 feet dee p. 

 — W. T. 



