38 Prof. W. Thomson on the Possible Density of the 



quantity of vibrating matter contained in a certain space, a 

 space of unit volume for instance, the whole mechanical value of 

 all the energy, both actual and potential, of the disturbance 

 within that space at any time is ^pv 2 . The mechanical energy of 

 circularly-polarized light at every instance is (as has been pointed 

 out to me by Professor Stokes) half actual 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 preceding expression gives the mechanical value of the whole 

 disturbance in a unit of volume in the present case. 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 2 and pv 2 , if v still denote the greatest velocity of the vibra- 

 ting particles. The mechanical value of the disturbance kept 

 up by a number of 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 separate 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 

 disturbance 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 circu- 

 larly-polarized waves, that the mechanical value of the disturbance 

 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 com- 

 plex radiation as that of sunlight and heat we cannot tell, be- 

 cause we do not know how much the velocity of a particle may 

 mount up, perhaps even to a considerable value in comparison 

 with the velocity of propagation, at some instant by the super- 

 position 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. Recur- 

 ring, however, to the definite expression for the mechanical value 

 of the disturbance in the case of homogeneous 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 vibra- 

 tion 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 



