Modds of the Aethtr. 315 



If a thin ring, for which the circulation is zero, is introduced 

 into the fluid, it will experience no ponderomotive forces ; but 

 if a ring initially carrying no current is introduced into a 

 magnetic field, it will experience ponderomotive forces, owing 

 to the electric currents induced in it by its motion, 



Imperfect though the analogy is, it is not without interest. 

 A bar-magnet, being equivalent to a current circulating in a wire 

 wound round it, may be compared (as W. Thomson remarked) 

 to a straight tube immersed in a perfect fluid, the fluid entering 

 at one end and flowing out by the other, so that the particles 

 of fluid follow the lines of magnetic force. If two such tubes 

 are presented with like ends to each other, they attract ; with 

 unlike ends, they repeL The forces are thus diametrically 

 opposite in direction to those of magnets ; but in other respects 

 the laws of mutual action between these tubes and between 

 magnets are precisely the same.* 



* The mathematical analysis in this ease is very simple. A narrow rube through 

 which water is flowing may be regarded as equivalent to a source at one end of the 

 tube and a sink at the other; and the problem may therefore be reduced to the 

 consideration of sinks in an unlimited fluid, If there are two sinks in sneh a fluid, 

 of strengths m and */, the Telocity-potential is 



at/r + m*//, 



where r and i" denote distance from the sinks. The kinetic energy per unit 

 of the fluid is 



thedensiryof the fluid; whence it is easily seen that the total 

 energy of the fluid, when the two sinks are at a dtBtance I apart, exceeds the total 

 cneigy when they are at an infinite distance apart by an amount 



0*i*ae*i*+^ld^&m^Mmt1to+k&lm*at1i*> 

 small spheres *, /, surrounding the sinks. By Green's 

 reduces at once to 



where the integration is taken over * and ", and m 



or '. The integral taken over *' vanishe 



hare 



of the fluid is therefore greater when sinks of strengths at, at* are at a 



