272 Sir W. Thomson on Approach caused by Vibration. [Jan. 26, 



card than on the remote portions of the vibrating surface. Your theoreti- 

 cal observation, 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 towards the tuning-fork, and there 

 were not an equal and opposite 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 velocityinthe direction 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 suffices to put down 

 such an argument, and elementary mathematical theory, especially the 

 theory of momentum in hydro-kinetics explained in my article on " Vor- 

 tex-motion," negatives 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 speci- 

 fied by the application of a principle explained in a short article communi- 

 cated to the Royal Society of Edinburgh in February last, as an abstract 

 of an intended continuation 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 hydro-kinetic 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 opposite mag- 

 netization back through zero to the primitive magnetization, and so on 

 periodically. The resultant of fluid pressure on the disk is not at each in- 

 stant equal and opposite to the magnetic force at the corresponding in- 

 stant, but the average resultant 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 magnetization, 

 it follows that the average resultant of the fluid pressure is an attraction 

 on the whole towards the tuning-fork into whatever position the tuning- 

 fork be turned relatively to it. 



Your seventh experiment * has interested me even more than any of 

 the others. It illustrates the elementary law of pressure in hydro-kinetics, 

 not by showing effects of fluid pressure on portions of a solid bounding 



* Experiment 7 in Proceedings Koy. Soe. vol. xix. p. 38, or experiment 10, Phil. 

 Mag. Nov. 1870. — F. G. 



