444 Mr. W. J. M. Raukine on the Vibrations of 



account for the immense velocity of light, the masses of the 

 atomic nuclei must be supposed to be very small as compared 

 with the mutual forces exerted by them. 



lu stating the third supposition of the hypothesis, the nuclei 

 are said to vibrate independently, or almost independently, of their 

 atmospheres ; for the absolute independence of their vibrations 

 is probably an ideal case, not realized in nature, though ap- 

 proached very nearly in the celestial space, where the atomic 

 atmospheres must be inconceivably rarefied. 



As a pendulum is known to be accompanied in its oscillations 

 by a portion of the air in which it swings, so the nuclei pro- 

 bably in all cases carry along with them in their vibrations a 

 small portion of their atmospheres, which acts as a load, increasing 

 the vibrating mass without increasing in the same proportion 

 the elasticity, and consequently retarding the velocity of trans- 

 mission. The amount of this load must depend on the density 

 of the atomic atmosphere ; and accordingly we find that, gene- 

 rally speaking, the most dense substances are those in which 

 the velocity of light is least. 



Now if we assume, what is extremely probable, that in crystal- 

 lized media the atomic atmospheres are not similarly diffused in 

 all directions round their nuclei, but are more dense in certain 

 directions than in others, we must at once conclude that in such 

 media the velocity of propagation of \ibratory movement depends 

 on the direction of vibration ; for upon that direction depends 

 the load of atmosphere which each nucleus carries along with it. 



4. Having thus shown that the conjecture of Fresnel, which 

 has been confirmed by the experiments of Professor Stokes, is a 

 natural consequence of the hypothesis of molecular vortices, I 

 shall now prove that that hypothesis leads to those mathematical 

 laws of the transmission of light in crystalline media which 

 Fresnel discovered. 



Considering it desirable in this paper to avoid lengthened 

 algebraical analysis, I shall with that view state in the tii'st place 

 certain known geometrical properties of the ellipsoid, to which 

 it will be necessary for me to refer. 



I. If a curved surface be described about a centre, such that the 

 sum of the reciprocals of the squares of any three orthogonal 

 diameters is a constant quantity, that surface, if no diameter is 

 infinite, is an ellipsoid. 



II. Every function of direction romid a centre, whose variation 

 from a given amount varies as the reciprocal of the square of the 

 diameter of an ellipsoid described about that centre, is itself pro- 

 portional to the reciprocal of the square of the diameter of an- 

 other ellipsoid described about the same centre with the first, 

 and having the directions of its axes the same. 



III. It follows from the last proposition, that if there be a 



