164: Lord Kelvin on Ether and 



at every instant is (as has been pointed out to me by Professor 

 Stokes) half kinetic energy of the revolving particles and half 

 potential energy of the distortion kept up in the luminiferous 

 medium ; and, therefore, v being now taken to denote the 

 constant velocity of motion of each particle, double the pre- 

 ceding expression gives the mechanical value of the whole 

 disturbance in a unit of volume in the present case. 



§ 5. Hence it is clear that for any elliptically polarized 

 light the mechanical value of the disturbance in a unit of 

 volume will be between ^pv~ and pv 2 , if v still denote the 

 greatest velocity of the vibrating particles. The mechanical 

 value of the disturbance kept up by a number o£ coexisting 

 series of waves of different periods, polarized in the same plane, 

 is the sum of the mechanical values due to each homogeneous 

 series separately, and the greatest velocity that can possibly 

 be acquired by any vibrating particle is the sum of the sepa- 

 rate velocities due to the different series. Exactly the same 

 remark applies to coexistent series of circularly polarized 

 waves of different periods. Hence the mechanical value is 

 certainly less than half the mass multiplied into the square of 

 the greatest velocity acquired by a particle, when the dis- 

 turbance consists in the superposition of different series of 

 plane polarized waves ; and we may conclude, for every kind 

 of radiation of light or heat except a series of homogeneous 

 circularly polarized waves, that the mechanical value of the dis- 

 turbance kept up in any space is less than the product of the 

 ■mass into the square of the greatest velocity acquired by a 

 vibrating particle in the varying phases of its motion, How 

 much less in such a complex radiation as that of sunlight and 

 heat we cannot tell, because we do not know how much the 

 velocity of a particle may mount up, perhaps even to a con- 

 siderable value in comparison with the velocity of propagation, 

 at some instant by the superposition of different motions 

 chancing to agree ; but we may be sure that the product of 

 the mass into the square of an ordinary maximum velocity, or 

 of the mean of a great many successive maximum velocities 

 of a vibrating particle, cannot exceed in any great ratio the 

 true mechanical value of the disturbance. 



§ 6. Recurring, however, to the definite expression for the 

 mechanical value of the disturbance in the case of homo- 

 geneous circularly polarized light, the only case in which the 

 velocities of all particles are constant and the same, we may 

 define the mean velocity of vibration in any case as such a 

 velocity that the product of its square into the mass of the 

 vibrating particles is equal to the whole mechanical value, in 

 kinetic and potential energy, of the disturbance in a certain 



