280 Mr R. F. Gwyther, On the solution of the [May 25, 



May 25, 1885. 

 Prof. Foster, President, in the Chair. 

 Prof. K. Pearson was elected a fellow of the Society. 



The following communications were made to the Society: — 



(1) On the solution of the equations of vibrations of the ether 

 and the stresses and strains in a light wave. By R. F. Gwyther, 

 M.A. Communicated by Prof. J. J. Thomson, M.A. 



In the first part of this paper I develop a solution of the equa- 

 tions relating to a light disturbance in a series of periodic terms 

 with coefficients expressed in a manner comparable with the 



geometric series — . -$ , etc., and am thus able to get a simple ap- 

 proximate form of solution suitable for distances from the source of 

 light large compared with a wave length. 



From this it follows that 



d^/dx = x/ra : . d%/dt, etc., 



so that the elements of the strain are proportional to the velocity 

 of the displacement, and that at any particular place and time the 

 kinetic and potential energies are equal, and their sum is variable. 

 In this particular the disturbance is not analogous to a pendulum 

 vibration. 



At the same time, I find to what degree of accuracy the equa- 

 tion of continuity demands that the vibration shall be in the wave 

 front. 



In the next part of the paper I calculate the stresses of a 

 second order in the medium due to the disturbance (the stresses 

 of the first order being of a circular harmonic type do not con- 

 tribute at all to the mean stresses). From this consideration 

 I prove that, except near the point source, the mean stresses are 

 such that P xy = P yx , et cetera. I find the expressions for the actual 

 stresses and they turn out to be those required by Maxwell's 

 Theory of the Electro-magnetic nature of light, that is they are 

 of the same form as the stresses in the Electro-magnetic field. I 

 also obtain Maxwell's Equations of Electro-magnetic force. Finally 

 it would follow from this investigation that in a wave of plane 

 polarised light the displacement is in the direction of the magnetic 

 force. 



I also discuss in the last part certain analogies which are of 

 interest but do not satisfy the conditions developed in this paper. 



