420 Mr. O'BRIEN, ON THE PROPAGATION OF LUMINOUS WAVES 



If the theory of transverse vibrations be true, R cannot = - — , for 



then B is < 0. Hence, even waiving the objection of neutral equilibrium, 

 a repulsive molecular force varying as (dist.)~* is inadmissable. As to 

 an attractive molecular force varying as (dist.) -2 , it is clearly out of the 

 question, for particles held together by such a force could not possibly 

 vibrate. It appears to me that these considerations are decisive against 

 the Newtonian Law, unless we abandon the theory of transversal 

 vibrations. 



$ 27. Having thus arrived at the necessary equations, I now pro- 

 ceed to make use of them for the purpose of explaining the dispersion 

 of light in passing through a prism. 



§ 28. To shew that, in consequence of the action of the material 

 upon the ethereal particles, different colours must be propagated with 

 different velocities in transparent bodies, supposing the particles to vibrate 

 according to the cycloidal law. 



Let us take the case of plane waves of transversal vibrations ; the 

 equations to be used in this case are the equations (G). 



Suppose the particles to vibrate according to the cycloidal law ; and 

 accordingly put for a the well-known form, a sin—— (vt — u), and similar 



A 



values for /3 and 7, and we find by substitution in the above equations, 



4tt 2 v 2 4tt 2 w m, „ 



— — — - — 2 -ti C \ 



X m X m 



and therefore v* = mB + -~r X 2 ; 



47T 



which shews that the velocity of propagation in general depends on 

 the length of the wave. In vacuum however C = 0, and therefore 

 the velocity of propagation does not depend on the length of the wave. 

 Hence the direct action of the particles of matter must produce an 

 alteration in the velocity of light depending on the length of the 

 wave, unless we admit the supposition that C is zero, which, as I have 

 shewn, is most improbable. I need not shew that the consequence of 



