412 



Scientific Proceedings, Royal Dublin Society. 



site effect will, of course, take place on stopping the primary 

 current. 



I have thus shown how the states of the ether, that Clerk- 

 Maxwell assumes, in order to explain electrical and magnetic phe- 

 nomena can be illustrated by my model. It is not difficult either 

 to show that the energy of the ether can be represented by equa- 

 tions exactly the same as those by which Clerk-Maxwell expresses 

 it. We must, however, bear in mind that my model is only a one 

 dimensional one, and would require to be supplemented by two 

 others in planes at right angles to itself to represent a space full 

 of ether. To consider, then, what the energy of the electro-mag- 

 netic field become in one dimension, I will deal with the form 

 to which I reduced it in my Paper on the " Electro-magnetic 

 Theory of the Eeflexion and Refraction of Light" (R. S. Trans. 

 vol. ii. 1880); The potential energy in an isotropic medium is, 



W=- 



K 



32 r 

 while the kinetic energy is 



dX, dr)V /dl d(^V /(h _ d^ 

 dy d%) \d% dx j \dx dy 



dx dy dz 



T = 



$7 



I'-^n'+'C 



dx dy dz. 



Now with only one of the three coordinate planes existing, we 



must evidently make ? = 0, rj = ; and if we suppose t to be the 

 angular velocity of the wheels, we evidently obtain the right form 



for the kinetic energy. The potential energy depends on the 



d^ d^ 



squares of + — and - — . Observe that E, is the angle through 



d^ . 

 which any wheel has rotated ; then it is evident that -- is the 

 •^ dy 



rate of change of this angle along y, and is proportional to the 



difference of stretching of the indiarubber bands in this direction, 



i. e. to what I have compared with electric displacement in the x 



direction ; and manifestly, if the bands obey the usual laws of 



elasticity, their potential energy is proportional to the square of 



. . . d^ 

 the stretching. We see similarly that the y polarisation is - — . 



It is further evident that, with three systems of planes at right 

 angles to one another, we must make the potential energy depend 



