in Singly and Doubly Refracting Media. 337 



For the variable a we find 



or 



£.-' 



3. In order to proceed from the moving forces to the vires 



vivce, let us imagine the particles of the medium brought out 



of their position of equilibrium into a relative position which 



would correspond as extreme to any internal wave-length I for 



any instant, and kept in this position by a suitable force. The 



tension thus produced is the same as if no ponderable particles 



were present. If the medium is then left to itself, the aether 



particles press back to the position of equilibrium, carry with 



them the corporeal particles, and the previous tension-force is 



converted into vis viva, which distributes itself to both kinds 



of molecules. Both pass the position of equilibrium with an 



energy which may be denoted respectively by ??iC 2 and m'C' 2 , 



A 2 A /#2 

 or by m ^, ml -^ . And since in the aether of space with 



identical displacement (i. e. identical A and /) an equal ten- 

 sion-force is developed, which now generates the maximum 



A 2 

 vis viva mC ; l=nijj^, we have 



°A 2 ,A /2 A 2 

 m ^ + m -™- = m^, 



-L 1 ± Q 



e 

 which relation, on account of l = vT = coT and r 2 = — , changes 



^ + m / -^ ¥ = ^A 2 , .... (5a) 



into A 2 / A' _ e 



rm ~i~ "^ np2 — 7 



or even, if instead of the maximal the variable oscillation-velo- 

 cities or excursions be at the same time introduced, into 



/ /2 



n 2 -l=—^ (5 b) 



The so-called refracting force is therefore equal to the ratio in 

 which a given vis viva is distributed to corporeal and aethereal 

 particles. 



This presupposed, we have to examine whether, and under 

 what conditions, our dispersion-equations are compatible with 

 the theorem here deduced. To this end we multiply the two 

 differential equations respectively with p, p f , and add. We 

 thus get 



Phil Mag. S. 5. Vol. 2. No. 12. Nov. 1876. Z 



