166 Mr Larmor, On a mechanical representation of a [May 4, 



It is also a well-known relation, and forms in many respects 

 the simplest and most symmetrical mathematical specification 

 of the connexions of the electric field on Maxwell's scheme, that 

 the magnetic induction (abc) is represented by the vorticity of 

 the electric force (PQR), and the electric force by the vorticity 

 of the magnetic induction, according to the equations 



dQ dR _ da 

 dz dy dt ' 

 db dc . ( 7r d \ D 



n -T y =- *"* r j t + v p - ■••■•••■ 



In the dielectric, a is zero, and the electric displacement (fgh) is 

 proportional to the electric force according to the relation 



K d 

 Thus the vorticity of the electric displacement is — -j- of the 



magnetic induction ; and the time integrals of (fgh) represent 

 on Sir W. Thomson's analogy the displacements of the elastic 



medium multiplied by the factor ^— • 



Or we may, as in the following sections, take the electric dis- 

 placement to represent the actual displacement of the elastic 

 medium, and then the magnetic induction will be equal to the 



8-7T 



time integral of its vorticity multiplied by ~r ; and the electric 

 current will be equal to the time integral of the impressed 



4*7T 



forcive multiplied by -^- . This forcive must on Maxwell's 



scheme be circuital, that is, circulating in ideal channels in the 

 manner of the velocity system of an incompressible fluid. 



These considerations thus present a mechanical view of the 

 electric propagation in dielectrics, with the exception that the 

 current on the wire must be imitated by an applied forcive of 

 some kind. If the media are magnetic, differences in rigidity 

 or of density must be introduced between them. 



For an electrical vibrator we can however complete the me- 

 chanical analogy, provided the wave-length of the undulations 

 is not smaller than a few centimetres in the case when the 

 vibrator is made of an ordinary conducting metal. For ex- 

 perimental types of Hertzian vibrators the analogy will therefore 

 be practically exact. 



To do this we have to examine the conditions as regards electric 

 displacement that must be satisfied at the surface of a conductor. 



