502 Sir Oliver Lodge on the 



© 



limit), and replace lines of force by lines of motion of the liquid, 

 its velocity to everywhere correspond to the magnetic force." 



" The liquid within the cylindrical space corresponding to the 

 wire is rotating, every particle of it, with the same angular velocity. 

 The motion of the liquid outside the vortex, however, although the 

 lines of motion are circles about the vortex, is differentially 

 irrotational 



"Current direction corresponds to the axis of a vortex, current- 

 density to twice the angular velocity ; vortex lines and tubes, 

 analogous to current lines and tubes, are always re-entrant; 

 the line-integral of magnetic force about a current, measuring the 

 amount of current, corresponds to the circulation of liquid about a 

 vortex, being proportional to the angular velocity of the latter, etc. 



"But, not to go into details, we will merely note, further, the 

 analogue of the identity 



[p. 244 ante]. Here, B z being the magnetic force of current C v 

 whose potential is A ]? we have two expressions for the quantity 

 that there is reason to believe is the kinetic energy of the system 

 of magnetic force. Now, let B } be the velocity of a perfect liquid 

 of unit density, then 2|B X 2 is really the kinetic energy of the whole 

 motion (sum of mass of each elementary portion X \ square of its 

 velocity). We have then the remarkable result that the kinetic 

 energy of the moving liquid can be expressed in terms of its angular 

 velocity in those places where the motion is rotational, and of the 

 corresponding vector-potential.'' 



"Further, since if C 1 = everywhere, making 2A 1 C 1 = 0, it 

 follows that 2B £ 2 = 0, which (being the sum of squares) involves 

 B x = everywhere. That is to say, if there is no rotation there can 

 be no motion of the liquid [except a uniform motion not vanishing 

 at infinity]. Hence, if the liquid fills all space, its motion, what- 

 ever it may be, cannot be everywhere irrotational." .... 



" Wa 3 is in fact the whole energy in the case of the moving 

 liquid, including that of the sphere of same density." 



30. But going still further back, to a time 35 years ago, Lord 

 Kelvin's representation of a magnetic field as a fluid-flow may be 

 illustrated by the following quotations from a paper of his published 

 in 1872; which is where we got the name 'permeability' from. 

 See his ' Papers on Electrostatics and Magnetism,' pp. 581 and 568. 



"It is convenient to attribute to the supposed liquid such a 

 density that A-k times the kinetic energy of liquid permeating a 

 solid of unit permeability, reckoned per unit volume of the whole 

 space occupied by porous solid and liquid, shall be equal to half the 

 square of the ' flux ' ; the word flux being borrowed from .Fourier's 

 theory of the conduction of heat and adapted to the use we have to 

 make of it." 



" The whole strength of current in each circuit, reckoned in 

 absolute electro-magnetic measure, is to be equal to the circulation 



