1G6 Mr GlazehrooTc, On some equations connected with [Nov. 28, 



Thus the first of our equations of condition becomes in the 

 case of a wave passing from one crystal to another 



/j,S cos sin 2 p + f* 1 S 1 cos X sin 2 ^ + fi 2 S 2 cos 2 sin 2 ^, 

 = fju'S' cos 0' sin 2 9' + fj,"S" cos 0" sin 2 <£", 



while for the fourth we have 



fis sin 2 </> (sin cos <£ + tan y, sin fa 



— /Lt^j sin 2 ^ {sin 6 X cos (^ + tan y^ sin ^ } 



- fi 2 S 2 sin 2 p 2 (sin 2 cos 2 + tan %2 sin p 2 } 



= fi'S' sin 2 p' {sin 0' cos $' + tan % sin 0' } 



+/i,''$' / sin 2 p''{sin#''cosp'' + tan % sin <£"], 



%, v etc. being the angles between the rays and wave normals in 

 the respective waves. The other equations can be written down 

 in a similar manner. 



They may moreover be simplified by remembering that in all 

 known transparent dielectrics //, differs but little from unity, we 

 may therefore put very approximately 



fi = fi t = fi s = fi - fi", 



but even then the equations are very complicated to solve. 



Let us return to our four original equations (24 — 27), S, S t , S' 

 are here electrical displacements. If we require the amplitude of 

 the light vibration we must remember that the total energy corre- 

 sponding to a displacement S is 47t/aF 2 # 2 . Now the amplitude of 

 the light vibration varies as the square root of the energy, thus if 

 a, a , a be the amplitudes required remembering that /a is the 

 same for the two media 



*'.* x \<r'=VS\ V x 8 t \ V'S' = S sin <f> : Sf, sin fa: S' sine/)'. 



The formulae given above agree with those found by J. J. Thom- 

 son, Phil. Mag. April, 1880, if we put % = in the fourth equation 

 so that the second medium also is isotropic. 



As has been said already they agree also with the results of 

 Lorentz and Fitzgerald. It will be useful to give as Lorentz has 

 done the relations between 0, 0' and i when only one wave tra- 

 verses the crystal. 



"We easily find by eliminating the ratios S/S i and S/S' from the 



equations (24 — 27), 



. ., . • ,,. sin 2 fa tan % . 



tan = tan cos (<f> — 9 ) -j ^7—. — / , , ,,, (-0;, 



vr r cos sin (<p + <p ) 



