512 Prof. E. Ketteler on the Dispersion of Light 



tremely close approximation to the proper course of the bend- 

 ing or splitting of the incident wave. 



The two principles hitherto advanced separately, now find 

 their complement and combination in 



III. The principle of the conservation of the vires vivse. — 

 This receives at once, in consequence of the above, first the 

 form 



where the M's are the so-called optical equivalents — that is, 

 the spaces passed through by the waves in equal times. And 

 when the previous values of p are introduced and the vibrations 

 of the corporeal particles (J&, J?) immediately eliminated by 

 means of equation (26), it is simplified into 



M(A| - Ai) = Wj>n»A'.S + M' V" 2 A" 2 D . • (34) 



As regards the ascertaining of the volumes M, M D , let those 

 wave-portions within the medium be considered which are 

 reflected at a dividing surface with finite limits (e.g. of angular 

 form, one side of which is parallel to the X-axis), or enter 

 through it into the second medium. During the time T these 

 wave-portions are displaced along the direction of the ray to 

 distances proportional to the previous wave-length V\ and the 

 parallelepipedal spaces described by them, of the height /, are 

 just those sought. They can next be replaced by their halves 

 — that is, by the so-called Huyghens's prisms, immediately 

 contiguous relatively to the dividing surface, and the volumes 

 of which are evidently as the lengths h of the perpendiculars 

 let fall from the respective points of contact of the wave-sur- 

 faces upon the dividing surfaces. Consequently M : M D — h : li\. 



13. This being presupposed, the question is merely to de- 

 termine the angles IT, Y, which the perpendiculars let fall, 

 each in its vibration-plane, upon the four rays make with the 

 X- and Y-axes, and, further, the angles Wi between the direc- 

 tion of vibration and the Z-axis, as well as the heights h of 

 the Huyghens's prisms. 



For this purpose let the axes OX and OZ be constructed in 

 the plane of the paper as the XZ plane (plane of incidence), 

 and OY perpendicular to them. Let OS be the direction of 

 the ray, and ON that of its normal, which in the plane of XZ 

 is distant the refraction-angle r ( = «o — 180°) from OZ. If, 

 finally, we draw the line OH in the plane SON and perpendi- 



