422 On the Dispersion of Light in Refracting Media. 



the length A, parallel to N 0, towards the position of equili- 

 brium, and carry with them the corporeal particles in paths 

 the equivalent length of which will be A'. If for the position 

 of equilibrium all the elasticity is transformed into vis viva, 



A 2 A /2 



this resolves itself as before into m~$ +S??i / 7 p J « 



If, on the other hand, in pure aether the same initial dis- 

 placement is produced in order to attain the same elasticity, 

 we have, in order that we may replace the interfering external 

 force by a wave-motion of the same amplitude A and the same 

 deviation, to bring the above parallelogram, by twisting its 

 sides, into the form of a rectangle, and also to shorten its 

 length V to Z, while I must be made —V cos A. The maximum 

 vis viva corresponding to this displacement is 



A A 9 e A 9 



The same end, however, is attained by displacing the aether 

 particles A , while retaining the same extent I', and forming 

 a rectangle out of A and V instead of A and I. It is pre- 



e e 



cisely ^ A 2 = ^ A^. Accordingly we get the coordinated rela- 

 tions : — 



(26) 



m A2iV m A/2_ e A2 2 i _ im'A" 



^A+2^A — ^A; n — 1— —^ ; 



^AJcos'A + S^A^AJ; ^_cos 2 A=^ 



The first two have the same form as those of isotropic media ; 



but they do not contain, like the dispersion-formula (22), the 



v 

 velocity-ration^ — and the corresponding internal wave- 



sin. e / ?'\ 

 length V (measured on the ray), but the sine-ratio n=— — I =- ) 



and the wave-length I associated with it (measured on the nor- 

 mal), and lastly, not the full amplitude of the aether particles 

 A perpendicular to the ray, but its value reduced to the height 

 of descent A perpendicular to the normal. 



This law of the actual vires vivw forms therefore the com- 

 plement to the expression of the virtual vires vivo? in equa- 

 tion (18). 



[To be continued.] 



