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



there is no alteration produced in the velocity of light when the 

 force exerted by the particles of matter varies as (distance) - -' : and my 

 explanation of dispersion falls to the ground if the law of molecular 

 force be (the distance) -2 . 



I think therefore, that I am fully justified in saying, that M. Lame 

 has not anticipated me in the explanation I have given of dispersion ; 

 indeed, a cursory reading of the two papers is quite sufficient to shew 

 that there is no resemblance between them in principle or detail*. 



ANALYTICAL INVESTIGATION. 



$ 4. I suppose that the etherial medium consists of a set of 

 discrete particles, that one particle exerts upon another a force which 

 acts in the line joining the particles, and is some function of the 

 distance between them ; and I suppose, that in transparent bodies 

 the particles of matter and the etherial particles act upon each other 

 in a similar manner. 



§ 5. To form the equations of motion of the etherial medium as it 

 exists in transparent bodies. 



Let x, y, %, ) be the co-ordinates of any two par- \ 



x', y, %,\ tides of ether, P and P', I when in a state 



the co-ordinates of any particle P \ \ of equilibrium, 

 of the transparent body, J 



x + a, y + /3, as + 7, j the co-ordinates of the same particles 

 x + a, y + /3', % + 7,1 respectively at any time t during 

 x , + ",» V, + Z 3 /' */ + 7/»' tne motion. 



*/. y,> *,.} 



r the distance between P and P',1 when in a state of equi- 

 / ... do do. ... P and P„\ librium. 



r + p,\ the distances between the same particles respectively 

 r + p'J at the time t. 



* M. Lame has also attempted to account for the formation of the dark lines in the 

 spectrum, but he assigns a cause very different from that which I have shewn may produce 

 these remarkable interruptions. 



