424 Me. O'BRIEN, ON THE PROPAGATION OF LUMINOUS WAVES 



Hence it appears, that the mere motion of the particles of matter cannot 

 produce any dispersion of light. 



£ 31. On account of the smallness of m compared with m t , it is 

 evident that the second term of the expression for A* in equation (3) is 

 small compared with the first. This confirms what was said in Art. 14., 

 that the motion of the material particles cannot produce much effect 

 on the motion of the etherial particles. 



§ 32. I now proceed to shew that there is another cause capable of 

 producing dispersion, which is in no way dependent on the supposition 

 that white light consists of undulations of different lengths. 



$ 33. To shew that the velocity of propagation is uniform only when 

 the particles of ether vibrate according to the cycloidal law. 



It is evident that if we suppose a to remain invariable, we have 



da , , da , 



-y-dt + -y-du = 0, 

 dt du 



and the value of -j? obtained from this equation is the velocity of pro- 

 pagation: let us suppose it constant and denote it by v, then we have 



da da , d'a d 2 a d f da\ d 2 a 



■ J 



dt ~ du' dP ~ du dt du \ du) ' du 



hence the equations (G) become 



(v>-mB)^+m,C=0, 



and two similar equations for /3 and 7. 



It is clear that if we combine this equation with the equation 



dt 1 ~ V du 2 ' 

 the most general value which a admits of is 



a = COS & (vt — U — e) + d COS k{vt + U - e'), 



when a, h, e, e' are arbitrary constants, and 



/f2 _ m , c 

 " v*-mB' 



