218 ETHER AND GRAVITATIONAL MATTER. 



acquired b}- a particle, when the disturbance consists in the superpo- 

 sition of different series of plane polarized waves; and we ma}^ con- 

 clude, for every kind of radiation of light or heat except a series of 

 homogeneous circularh^ 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 h}' 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 can not 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, can not exceed in any great ratio the true mechan- 

 ical value of the disturbance. 



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

 mechanical value of the disturbance in the case of homogeneous cir- 

 cularly polarized light, the only case in which the velocities of all 

 particles are constant and the same, we ma}^ define the mean velocity 

 of vibration in an}^ case as such a velocity that the product of its square 

 into the mass of the vibrating particles is equal to the whole mechan- 

 ical value, in kinetic and potential energy, of the disturbance in a certain 

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

 of undulations, it seems certain that this velocity must be a very small 

 fraction of the velocity of propagation in the most intense light or radi- 

 ant heat which is propagated according to known laws. Denoting this 

 velocity for the case of sunlight at the earth's distance from the sun b}^ 

 V, and calling W the mass in grams of any volume of the luminiferous 

 ether, we have the mechanical value of the disturbance in the same space, 

 in terms of terrestrial gravitation units, 



W 2 



where g is the number 981, measuring in (C.G.S.) absolute units of 

 force, the force of gravit}^ on a gram. Now, from Pouillet's obser- 

 vation, we found in the last footnote on section 1 above, — ^ 



for the mechanical value, in centimeter-grams, of a cubic centimeter 

 of sunlight in the neighborhood of the sun; and therefore the mass, in 

 grams, of a cul)ic centimeter of the ether, must be given bj^ the equa- 

 tion, 



^,, 981X1235X46000 



w- ^ 



