in Singly and Doubly Refracting Media. 415 



velocity-surface of the normal (corresponding to the " first 

 ellipsoid "), as the primary, has been derived. Making use 

 of this latter, the velocity-surface of the rays, the " wave- 

 surface " (corresponding to the second or Pliicker's ellipsoid), 

 is then obtained as the envelope of the same. The wave- 

 surface thus appears only as secondary or derived from the 

 former, while in nature it is quite the reverse : here the wave- 

 surface only has a physical meaning, and the normal surface 

 is associated with it solely as an (of course valuable) auxiliary 

 surface. 



The incorrectness referred to can only be avoided by ad- 

 mitting also the vibrations of the corporeal particles. 



Let the medium whose doubly-refracting properties are in 

 question have resulted from an isotropic one, with molecular 

 distance 'r equal on all sides, through being exposed in 

 three perpendicular directions to the pressure- or pull-forces 

 P*> TPy> P*> and thereby attained linear extensions exactly pro- 

 portional (as we will assume) to these pressures, which then 

 have for their consequence the coordinate-distances % = x Q (\ + 

 ap,)=x (l + *), y=y (l + ap y )=y (l+/3), z=z (l + ap z ) = 

 z (l +7). The variable molecular distance r for any direction 

 whatever, which forms with the axes of pressure the angles 

 a, b, c, is calculated therefrom (as I will further on show) by 

 means of the equation 



1 cos 2 a cos 2 6 cos 2 c 



+ ..2/1 ■ OX 2 + 



r 2 ~ ^ 2 (1 + «) 2 T r \l + py T r a *(l + yf 



If now an aether-point of the medium is permanently shaken 

 by any external force, this motion is propagated to all the 

 # surrounding aethereal and corporeal particles ; and after the 

 lapse of, say, the unit of time, it has proceeded as far as a 

 surface called tear' i^o^rjv the wave-surface. Along each radius 

 vector of this surface (a " ray ") the aethereal and corporeal 

 particles are therefore in associated motion. The condi- 

 tions, however, of this association are, in my opinion, the 

 following : — 



a. The vibrations of the aethereal and corporeal particles 

 necessarily take place in the plane given by the ray and the 

 wave-normal, which therefore at the same time appears as a 

 certain plane of symmetry of the medium. 



b. The vibrations of the aether particles (which latter, on 

 account of their minuteness, we conceive as at least approxi- 

 mately continuous) lie, by virtue of the incompressibility of 

 the particles, within the tangential wave-plane. 



c. On the contrary, the force which results from the resist- 

 ance of the more discretely situated corporeal particles stands 



