LUMINIFEROUS MEDIUM, AND THE MECHANICAL VALUE OF SUNLIGHT. 59 
actual and potential, of the disturbance within that space at any time is } 9 7°. 
The mechanical energy of circularly polarized light at every instant is (as has been 
pointed out tome 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 ina unit of volume in the present case. Hence it isclear, that forany ellipti- 
cally polarized light the mechanical value of the disturbance in a unit of volume will 
be between 402? and ¢v”, 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 2, and calling W the mass in pounds 
