M. Lorenz on the Theory of Light. $11 



the plane of the wave, and the result in regard also to the direc- 

 tion of the vibrations is now in perfect accordance with the 

 common theory. Thus whether we assume p = or p = 2, the 

 plane which passes through the excursion and the perpendicular 

 to the plane of the wave coincides, as in the ordinary theory, with 

 the plane passing through the perpendicular to the plane of the 

 wave and the corresponding ray. 



We only require to go a step further, that is, to take the higher 

 powers of a p into consideration as well as the lower ones, in 

 order to arrive at the theory of chromatic dispersion. As already 

 pointed out, the coefficients a in the equations (B) admit of being 

 developed according to powers of I, m, n, so that only even num- 

 bers of them occur as factors ; hence they can also be developed 



according to powers of — 5 by introducing the values given above 



for I, m, n. Herein lies the law of chromatic dispersion of light 

 so far as it is known to us. There would be no difficulty in car- 

 rying out the calculation in its most general form ; but, as it 

 seems to me, there would be no practical interest in doing so. 

 If the body is not crystalline, that is, if no one direction is dif- 

 ferent from the rest, the velocity s will be given by 



& 2 



~2~ —#1,1 — #2, 2 = a 3, 3} 

 S 



where a x x admits of being developed according to even powers 



4 ' 



According to this theory, chromatic dispersion appears as a 

 property of material bodies, dependent on their periodic hetero- 

 geneity, whereas, on Cauchy's theory, the absence of chromatic 

 dispersion in a vacuum can only be explained by new hypotheses. 

 It has already been shown by M. F. Eisenlohr (PoggendorfPs 

 Annalen, vol. cix.) that, even when we retain the common con- 

 ception of the nature of luminous vibrations and of the aether, 

 the phenomena of chromatic dispersion lead to the assumption 

 of periodical changes in the density of the sether in material 

 bodies. It also results from the present investigation, that double 

 refraction can likewise be deduced from this assumption, which 

 is in fact the most general that we can make. 



PresneFs supposition, that the explanation of double refraction 

 lies in an unequal elasticity in different directions, may perhaps 

 appear to receive confirmation from the fact that uncrystalline 

 bodies become doubly refracting by pressure. It must, however, 

 be likewise observed that the dimensions of the body are altered 

 by pressure, and that consequently the periodic constants, and 



P2 



