M. Lorenz on the Thewy of Light, 83 ; 



at the point considered. We will now assume that the law of 

 these vibrations is expressed, for isotropic homogeneous media, 

 by the following partial differential equations : — 



r A ^-l^ AV-!££ *&£& (1) 



[a *~ a* dt*> A v ~ to* dt 2i *~ co* dt 2 ' ' r } 



d 2 d 2 d 2 

 where A 2 denotes -%- 2 + j-% + -r^, co denotes a constant, and t 



the time. 



Hence in such a medium, supposing it to be unlimited, th 

 amplitude of vibration may be expressed by terms of the form 



«cos (kt — lx—my—nz + d), 

 or 



Light accordingly consists of periodic undulations which pro- 

 pagate themselves in the direction of the perpendicular to the 

 plane lx + my + nz=0, with the constant velocity 



k 



&)= — -. — — » 



W 2 + m 2 + n 2 



2. In homogeneous isotropic media the direction of vibration 

 is perpendicular to the ray; or, more generally (including, that 

 is, the case in which the medium is limited), the three compo- 

 nents are connected by the differential equation 



f + p + f =0 (2) 



ax ay dz 



3. The plane drawn through the direction of vibration and 

 through the direction of the ray is perpendicular to the plane of 

 polarization of the ray. This assumption can scarcely affect the 

 results in relation to the propagation of light in heterogeneous 

 media, in so far as they come within the scope of our considera- 

 tion, since, as already mentioned, it is possible to conceive this 

 as deduced without any assumptions as to the position of the 

 direction of vibration relatively to the plane of polarization. I 

 consider it, nevertheless, as in any case proved by my experi- 

 ments on the diffraction of light (Poggendorff's Annalen, vol. cxi. 

 p. 315) ; for, as I shall show in the sequel, the assumptions that 

 are there made can be deduced from the equations (1) and (2) 

 alone. 



These three hypotheses, then, in conjunction with Fresnel's 

 formulae for the refraction and reflexion of light at the limiting 

 surface of two isotropic transparent media, form the foundation 

 of the present theory of light. There can, in fact, no longer be 



G 2 



