582 A DYNAMICAL THEORY OF TUB ELECTROMAGNETIC FIELD. 



If we perform the operation V* on this equation, it becomes 



Since the medium is a perfect insulator, e, the free electricity, is immove- 

 able, and therefore -j- is a function of x, y, z, and the value of J is either 



constant or zero, or uniformly increasing or diminishing with the time ; so that 

 no disturbance depending on J can be propagated as a wave. 



(100) The equations of the electromagnetic field, deduced from purely 

 experimental evidence, shew that transversal vibrations only can be propagated. 

 If .we were to go beyond our experimental knowledge and to assign a definite 

 density to a substance which we should call the electric fluid, and select either 

 vitreous or resinous electricity as the representative of that fluid, then we might 

 have normal vibrations propagated with a velocity depending on this density. 

 We have, however, no evidence as to the density of electricity, as we do not 

 even know whether to consider vitreous electricity as a substance or as the 

 absence of a substance. 



Hence electromagnetic science leads to exactly the same conclusions as 

 optical science with respect to the direction of the disturbances which can be 

 propagated through the field ; both affirm the propagation of transverse vibra- 

 tions, and both give the same velocity of propagation. On the other hand, both 

 sciences are at a loss when called on to affirm or deny the existence of normal 

 vibrations. 



Relation between the Index of Refraction and the Electromagnetic Character 



of the substance. 



(101) The velocity of light in a medium, according to the Undulatory 

 Theory, is 



Iv 



i y " 



where i is the index of refraction and V t is the velocity in vacuum. The 

 velocity, according to the Electromagnetic Theory, is 



T 



47T/t' 



where, by equations (49) and (71), = -g , and & = 



