680 REPORT— 1893. 



and this is proportional to the electric force. Moreover, its convergence measures 

 the quantity of electricity present per unit volume; but we have no certain 

 mechanical conception of electric displacement or quantity of electricity, we 

 have no satisfactory mechanical theory of the electromagnetic field. The first 

 edition of the ' Electricity and Magnetism ' appeared twenty years ago. In it 

 Maxwell says : ' It must be carefully borne in mind that we have made only one 

 step in the theory of the action of the medium. We have supposed it to be in a 

 state of stress, but we have not in any way accounted for this stress or explained 

 how it is maintained. This step, however, appears to me to be an important one, 

 as it explains by the action of consecutive parts of the medium phenomena which 

 were foj'merly supposed to be explicable only by direcc action at a distance. I 

 have not been able to make the next step, namely, to account by mechanical con- 

 siderations for these stresses in the dielectric' And these words are true still. 



But, for all this, I think it may be useful to press the theory of the quasi- labile 

 ether as far as it will go, and endeavour to see what the consequences must be. 



The analogy between the equations of the electromagnetic field and those of 

 an elastic solid has been discussed by many writers. In a most interesting paper 

 on the theory of dimensions, read recently before the Physical Society, Mr. Williams 

 has called attention to the fact that two only of these analogies have throughout a 

 simple mechanical interpretation. These two have been developed at some length 

 by Mr. Heaviside in his paper in the ' Electrician ' for January 23, 1891. To one 

 of them Lord Kelvin had previously called attention (' Collected Papers,' vol. iii. 

 p. 450.) 



Starting with a quasi-labile ether, then, we may suppose that fi, the magnetic 

 permeability of the medium, is 47rp,' where p is the density, and that K, the in- 

 ductive capacity, is l/4rrB, B being the rigidity, or the quasi-rigidity conferred by 

 the rotation. 



The kinetic energy of such a medium is | p (i" + fj'^ + ^•), where ^, fj, f are the 

 components of the displacement. Let us identity this with the electromagnetic 

 energy (a^ + jS^ + ■y'^jSTr, a, ^, y being components of the magnetic force, so that 

 a = i, fi = fj,y = ^. Then the components of the electric displacement, assuming 

 them to be zero initially, are given by 



' 47r \dy dz/' ' 



that is, the electric displacement ® multiplied by iw is equal to the rotation in 

 the medium. Denote this by Q. 



The potential energy due to the strain is 



i BQ^ or ^167r-B2)-, 



and on substituting for B this becomes 



which is Maxwell's expression for the electrostatic energy of the field. 



Thus so far, but no farther, the analogy is complete ; the kinetic energy of the 

 medium measures the magnetic energy, the potential energy measures the electro- 

 static energy. The stresses in the ether, however, are not those given by Max- 

 well's theory. 



la the other form of the analogy we are to take the inductive capacity as 

 47rp and the magnetic permeability as l/47rB. The velocity measiu-es the electric 

 force, and the rotation the magnetic force, so that electrostatic energy is kinetic, 

 and magnetic energy potential. Such an arrangement is not so easy to grasp as 

 the other. Optical experiments, however, show us that in all probability it is p, 

 and not B, which varies, while from our electrical measurements we know that K is 

 variable and ft constant ; hence this is a reason for adopting the second form. 



• If we adopted Mr. Heaviside's rational system of units the 4ir would disappear. 



