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



the nature of that vibration will depend upon the law of force which 

 acts upon the material particles, and causes them to rush together; 

 that this law should be always such as to produce cycloidal vibrations 

 we have not the least reason to suppose ; on the contrary, I conceive it 

 very probable that these vibrations will follow different laws in different 

 kinds of combustion. 



Hence we must not assume a priori that light is always propagated 

 with a constant velocity in transparent bodies ; for I have proved that if 

 the velocity be constant, the particles must necessarily vibrate according 

 to the cycloidal law. What the velocity of propagation is, must de- 

 pend on the law of vibration; I hope hereafter to investigate the con- 

 nexion between them. At present I shall only explain generally the 

 effect of a variable velocity of propagation on the refraction of light 

 at a plane surface, and shew that it must cause a dispersion of homo- 

 geneous light in passing through a prism. 



§ 35. To determine the law of refraction at a plane surface, without 

 assuming that the velocity qf propagation is constant. 



Let A be an origin of light, MBB a plane refracting surface 

 bounding two different media, 

 ABC the course of an elementary 

 disturbance originating at A ; 

 i. e. a spherical wave is supposed 

 to spread from A, an element of 

 which takes the course AB, pro- 

 duces a disturbance at B which 

 spreads in a spherical wave from 

 B into the lower medium, an 

 element of which takes the course 

 BC. Let ABC be the neigh- 

 bouring course of a similar ele- 

 mentary disturbance which comes 

 from A to C. Take AE = AB, BD — BC, then a disturbance takes 

 the same time to travel from A to B, and from A to E, and ultimately 



