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



V * 



between the greatest and least values of - , and therefore the whole 

 amount of the variation of the velocity of light within the prism. 



£ 39. I am not aware whether any experiments have been made 

 which would enable us to determine (p, — (j> 2 . Any analysis of the 

 spectrum by second prism is inconclusive on this point, as I shall endeavour 

 to prove hereafter. I suppose that delicate experiments on the inter- 

 ference of a very small portion of the light composing a very pure spec- 

 trum, would enable us to determine whether 0, — <p 2 has any sensible 

 magnitude or not. 



The remarkable appearances exhibited when the spectrum is viewed 

 through coloured glasses, seem to indicate pretty clearly that homo- 

 geneous light suffers dispersion in passing through a prism. 



If experiment shews that 0, — <p 2 is insensible, then we have positive 

 proof that the law of vibration is cycloidal, which is a most important 

 result if true, especially if we bear in mind what has been just proved, 

 namely, that otherwise v must be variable. But if experiment shews 

 that (p, - <f> 2 has any magnitude, then we have to take into account the 

 variation of v in all cases of refraction ; and the fact, that the law of 

 vibration is not cycloidal. 



£ 40. It remains now to prove, that the results thus obtained on 

 the hypothesis of symmetrical arrangement are equally true when the 

 arrangement is unsymmetrical, in consequence of the position of equi- 

 librium of the etherial particles being altered by the action of the 

 material particles ; supposing that several etherial surround each material 

 particle. 



It is evident that the equation expanded in § (8), now becomes a 

 linear equation with variable coefficients, in the form 



— = P— + Q~ B— S— - Ca 



dt dx dy " " dx dx 2 



where P, Q ... R ... S ... C, are functions of x, y, %, is evidently the 

 same for all particles similarly situated with respect to the particles of 



