ETHEE AND GRAVITATIONAL MATTER. 217 



equilibrium b}^ A; and the wave leng-th by A. Then, if V denote the 

 velocity of propagation of light or radiant heat, we have 



— = 27t — ; 

 V X 



and therefore if A be a small fraction of A, r must also be a small 

 fraction {^tt times as great) of V. The same relation holds for cir- 

 cularly polarized light, since in the time during which a particle 

 revolves once round in a circle of radius A the wave has been propa- 

 gated over a space equal to A. Now, the whole mechanical value of 

 homogeneous plane polarized light in an intinitely small space con 

 taining only particles sensibly in the same phase of vibration, which 

 consists entirel}" of potential energy at the instants when the particles 

 are at rest at the extremities of their excursions, partly of potential 

 and partly of kinetic energy when they are moving to or from their 

 positions of equilibrium, and whollv of kinetic energy when they are 

 passing through these positions, is of constant amount, and must 

 therefore be at ever}^ instant ecjual to half the mass multiplied by the 

 square of the velocity which the particles have in the last-mentioned 

 case. But the velocity of any particle passing through its position 

 of equilibrium is the greatest velocity of vibration. This we have 

 denoted by v, and, therefore, if p denote the quantity of vibrating 

 matter contained in a certain space, a space of unit volume, for in- 

 stance, the whole mechanical value of all the energy, both kinetic and 

 potential, of the disturbance within that space at any time is ^Pff. 

 The mechanical energy of circularly polarized light 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 preceding expression gives the mechanical value of the whole 

 disturbance in a unit of volume in the present case. 



Sec. 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^, if v still denote the greatest velocity of the 

 vibrating particles. The mechanical value of the disturbance kept 

 up l)y a number of coexisting series of waves of diti'erent 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. Exactl}'^ 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 



