LUMINIFEROUS MEDIUM, AND THE MECHANICAL VALUE OF SUNLIGHT. 59 



actual and potential, of the disturbance within that space at any time is ^ p &. 

 The mechanical energy of circularly polarized light at every instant 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 par- 

 ticle, double the preceding expression gives the mechanical value of the whole dis- 

 turbance in a unit of volume in the present case. Hence it is clear, that forany ellipti- 

 cally polarized light the mechanical value of the disturbance in a unit of volume will 

 be between \gv 2 and gv 2 , if v still denote the greatest velocity of the vibrating par- 

 ticles. 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 ac- 

 quired 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 considerable 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. Recurring, however, to the definite expression for the mechani- 

 cal 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 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 actual and potential energy, of the disturbance in a certain 

 space traversed by it ; and from all we know of the mechanical theory of undu- 

 lations, it seems certain that this velocity must be a very small fraction of the 

 velocity of propagation in the most intense light or radiant heat which is pro- 

 pagated according to known laws. Denoting this velocity for the case of sun- 

 light at the earth's distance from the sun by v, and calling W the mass in pounds 



