in Singly and Doubly Refracting Media. 419 



wave appears to be connected ivith the cooperation of the iden- 

 tical corporeal particles, whether the medium be isotropic, or by 

 external forces transferred into the anisotropic state*. The 

 inference from such external forces to molecular forces is 

 sufficiently obvious. 



If, moreover, the medium is a compound, so that the sum- 

 mation-symbol of equation (18) comes into use, we may 

 provisionally content ourselves with the special case that 8 is 

 the same for all its optico-chemical elementary constituents, 

 and therefore cos 8 can be placed before the symbol of sum- 

 mation. 



9. Assuming this, r and 8 can be calculated in the following 

 manner : — Given the distance R of any particle of the un- 

 modified medium from the origin of coordinates ; let the line 

 which joins the two (perpendicular to the above-noticed row 

 of molecules) make with the axes the angles a , b , c Q . We 

 have then 



cos a = j® , cos b Q = ^ , cos c°= ^-. 



±i £t ±t 



In consequence of the modification the same row of mole- 

 cules arrives at the somewhat different position a, b, c, and the 

 distance R becomes R. Correspondingly there are then 



cos a= p, cos 6= ^, cosc= ^-. For 8, R, and R the rela- 

 tions now hold good : — 



cos 8 = cos a cos a + cos b Q cos b + cos c cos c ; 



Now according as, by means of the axial distances of § 7, 

 we reduce either the angle of the new direction to that of the 

 old, or the angle of the old to that of the new, noticing the 

 proportionality of R, R to r, r QJ we get the following expres- 

 sions : — 



r cos8 = r (l + a) cos\ + r Q (l + /3)cos\ + r 6 (l + 7)cos 2 c ,~| 

 r* = rl(l + «) 2 cos 2 a + rl(l + /3) 2 cos 2 5 + r?(l + 7 ) 2 cos 2 c ;J (20) 



* To the above consideration the theory of aberration (Ketteler, Astron. 

 Aberrationslehre, p. 177) presents the following analogy :— Let a ray AB, 

 incident upon an isotropic or anisotropic medium at rest, produce in its 

 interior the refracted ray BC ; and let the three points A, B, C be imagined 

 as fixed once for all by three dioptrics inseparably connected with the 

 structure of the medium — or, better still, B, C by an infinitely thin ideal 

 tube led through the ponderable particles. The refracted light will pass 

 through the tube without striking against its sides, even when the medium 

 is moved in space with any velocity of translation whatever. And yet, 

 in consequence of the motion, the angle of incidence, angle of refraction, 

 and ratio of refraction change. 



2E 2 



