416 Prof. Lorenz on the Theory of Light. 



contained between the perpendicular to the plane of polariza- 

 tion of the visible light and the axes of coordinates, whereas 

 Neumann's resultants lie in this plane ; thus we have 



The last resultant, moreover, lies in the plane of the wave, whence 

 we have 



lg + mr)' + n?=0. 



From these equations result the following relations between 

 the two sets of components, namely, 



*P = n Vs - m£ s , fa/ = K s - n% s , k?=m% s - ! Vs , 



equations to which we can also give the form 



dt dz dy dt dx dz' dt dy dx' 

 Our limiting equations, which we may write as follows, 



w;::-«. [«:>», B-fO 



Lax dzJ x=0 



where e is an infinitely small quantity, shall now be expressed 

 with the new components. From the last two equations we get 

 at once 



ws-fik ^d [n:::=o. 



By the first equations, we have 



Ldz dyJ x=0 

 accordingly 



[r]::;=o. 



Thus all the components, £', if, f, take the same values at the 

 limiting surface of the two media, which agrees perfectly with 

 Neumann's hypotheses. Lastly, the fourth limiting equation, 

 which with our components we may express by 



[my 8 +nQ x x Z e =0, 



may be arrived at as follows for the new components. 



Let q be the angle which the perpendicular to the plane of 

 the wave makes with the ray of light. Since our resultant, as 

 was shown in the previous memoir, makes the same angle with 



