258 BULLETIN OP THE UNIVERSITY OF WISCONSIN. 



(b) Theoretical. — The great importance of the phenomenon 

 of anomalous dispersion in the theory of light is, perhaps, best 

 seen when the various theories framed for the explanation of 

 dispersion are examined. Kundt's discovery of the evident de- 

 pendence of dispersion upon absorption rendered necessary a 

 thorough revision of the older theories regarding this phenome- 

 non. 



The fundamental assumption of the wave theory of light is 

 the existence of a medium, called the ether, which pervades all 

 space and in which luminiferous vibrations are propagated as if 

 in an elastic solid. Upon this basis the velocity of transmis- 

 sion* of a light wave is given by the expression, 



V = cl / § (3). 



i 



where E is the elasticity of the medium; D, its density; V, 

 wave velocity ; and C, a constant. 



To account for the difference in the velocitv of the transmis- 

 sion of light in transparent media and in free space by this equa- 

 tion, three suppositions may be made. 



(a). E may be constant and D variable, .\ V = -g- (4). 



(b). E may be variable and D constant, .*. V = C 2 V~E, (5). 



(c). Both E and D may vary, .-. V = C V g (6). 



The first assumption was made by Fresnel 1 while the theories 

 of Neumann 2 and llcCullagh 3 depend upon the second. Both 

 assumptions lead to identical results, except, that the plane of 

 vibration must be considered perpendicular to the plane of in- 

 cidence in the first case and parallel to it in the second. The 

 third case, if treated by methods similar to those employed by 

 Fresnel, Neumann, or McCullagh, leads to results not agreeing 

 with known facts. These theories would be sufficient to explain 



I Fresnel, Ann. de Chim. et de Phys. XLVI., p. 2IJ5. Oeuvres complete, I., p. 767, 

 3 Neumann, " Vorlesungen ilber Tkeoretische Optik," edited by Dr. E. Dorn, Leipzig, 

 1885. 

 3 McCullagh, Trans. Roy. Soc. Irish Acad. Vol. XXL 



