﻿424 Sir W. Thomson on Approach caused by Vibration, 



that the square of the average velocity must be greater on the 

 surfaces of the tuning-fork next to the card than on the remote 

 portions of the vibrating surface. Your theoretical observa- 

 tion, however, that the attraction must be mutual, is beyond 

 doubt valid, as we may convince ourselves by imagining the 

 stand which bears the tuning-fork and the card to be perfectly 

 free to move through the fluid. If the card were attracted to- 

 wards the tuning-fork, and there were not an equal and oppo- 

 site force on the remainder of the whole surface of the tuning- 

 fork and support, the whole system would commence moving, 

 and continue moving with an accelerated velocity in the direc- 

 tion of the force acting on the card — an impossible result. It 

 might, indeed, be argued that this result is not impossible, as it 

 might be said that the kinetic energy of the vibrations could 

 gradually transform itself into kinetic energy of the solid mass 

 moving through the fluid, and of the fluid escaping before and 

 closing up behind the solid. But " common sense" almost suf- 

 fices to put down such an argument, and elementary mathema- 

 tical theory, especially the theory of momentum in hydro- 

 kinetics explained in my article on " Vortex-motion," nega- 

 tives it. 



The law of the attraction which you observed agrees perfectly 

 with the law of magnetic attraction in a certain ideal case which 

 may be fully specified by the application of a principle explained 

 in a short article communicated to the Royal Society of Edin- 

 burgh in February last, as an abstract of an intended continua- 

 tion of my paper on " Vortex- motion." Thus, if we take as an 

 ideal tuning-fork two globes or disks moving rapidly to and fro 

 in the line joining their centres, the corresponding magnet will 

 be a bar with poles of the same name as its two ends and a 

 double opposite pole in its middle. Again, the analogue of 

 your paper disk is an equal and similar diamagnetic of infinite 

 diamagnetic inductive capacity. The mutual force between the 

 magnet and the diamagnetic will be equal and opposite to the 

 corresponding hydrokinetic force at each instant. To apply the 

 analogy, we must suppose the magnet to gradually vary from 

 maximum magnetization to zero, then through an equal and op- 

 posite magnetization back through zero to the primitive mag- 

 netization, and so on periodically. The resultant of fluid pres- 

 sure on the disk is not at each instant equal and opposite to the 

 magnetic force at the corresponding instant, but the average re- 

 sultant of the fluid pressure is equal to the average resultant of 

 the magnetic force. Inasmuch as the force on the diamagnetic 

 is generally repulsion from the magnet, however the magnet be 

 held, and is unaltered in amount by the reversal of the magnet- 

 ization, it follows that the average resultant of the fluid pressure 



