82 M. Lorenz on the Theory of Light. 



the calculation so far that it shall also give the laws of the motion 

 of light in heterogeneous media, since this motion must arise as 

 the resultant effect of the rays that are transmitted and those 

 that are reflected to infinity. I have in fact worked out the cal- 

 culation for the comparatively simple case in which the medium is 

 made up of very thin parallel layers; and the result shows that such 

 a medium not only disperses light, but doubly refracts it, like an 

 optically uniaxial crystal whose optic axis is perpendicular to the 

 layers. Nevertheless, although the possibility of solving the 

 problem in a more general form, and without any further phy- 

 sical assumptions, is already apparent, an imperfection is inhe- 

 rent in the method itself which led me on to insurmountable 

 difficulties as soon as I attempted the case of a medium com- 

 posed of two systems of parallel layers making an angle with 

 each other. It then becomes necessary to have recourse to the 

 more perfect mathematical methods, and to express the laws of 

 the motion in heterogeneous media by means of partial differ- 

 ential equations, and to deduce thence, by subsequent integra- 

 tion, the path of the rays of light. 



It is then also further needful to define our hypotheses with 

 greater precision, and especially to introduce the conception of 

 the plane of vibration instead of that of the plane of polarization. 

 The motion must be determined in relation to magnitude and 

 direction by the amplitude and direction of the vibrations ; but 

 although these expressions are borrowed from our common mode 

 of considering the vibrations of elastic bodies, it is not intended 

 to attach to them here any such absolute meaning; thus, for 

 instance, the vibrations may be conceived of as rotatory, in which 

 case the l ' direction of vibration M would be the direction of " the 

 axes of rotation," and the " amplitude of vibration " would be 

 the angular distance of the molecules from their position of 

 equilibrium. 



I must at once insist upon this double point of view, because the 

 following calculation renders no further determination of these 

 primary physical hypotheses necessary ; and inasmuch as I shall 

 hot have another opportunity of returning in this memoir to this 

 physical side of the theory of light, I may be allowed to point 

 out at once that, so far from this latter mode of conceiving the 

 vibrations being a mere mathematical speculation, the results of 

 the present investigation appear to indicate it as probably the 

 true foundation for the physical theory of light. 



Retaining, then, the latitude of interpretation that has been 

 indicated, the following are our assumptions :■ — 



1. The " amplitude of vibration " and the "direction of vibra- 

 tion " give us three components f , 97, f in the direction of the 

 three rectangular axes of coordinates for determining the motion 



