420 Prof. Lorenz on the Theory of Light. 



* p = we easily find 



ai ,,=l-S^V, a»=l-X e fb*, a,, s =l-2^V- 



If a body is, for instance, stratified in one direction only, and 

 we take the perpendicular to the layers as the axis of cc, we have 

 a p =l, and b p = c p =Q. Consequently the velocities b and c 

 become equal to each other when a, or the velocity of propaga- 

 tion of the components in the direction of the perpendicular, has 

 reached its greatest value. Such a substance therefore behaves 

 like a doubly refracting, uniaxal, negative crystal, whose axes are 

 perpendicular to the layers of the body. This result agrees 

 with the experiments of M. Schultze (Verh. derrheinl. Geseltsch. 

 1861). 



If we call the velocity of light in vacuo 0, the refractive 



index corresponding to the velocity a is — , and a mean refractive 

 index will be expressed by 



This mean refraction coefficient is independent of the position of 

 the axes chosen, even if the small magnitudes a p are not quite 

 neglected ; for we find 



6 2 £2 



whence we have 



_°Vi l S a.,. 4 2 °S 2 "/\ 



a value which is independent of the choice of the axes. 



In the last equation k is put = — , where X denotes the wave- 



length, in order that it may at once be evident that the mean 



refraction coefficient, or its square, assumes the form a + b — 2 , 



where b is always a positive quantity. The smaller therefore the 

 wave-length is, so much the more refrangible does the light 

 become — a law which has universally proved true ; still, the above 

 approximate formula might possibly not be sufficient for absorb- 

 ent media, and in this way exceptions to the rule might arise. 



The form which we have given to the function co has been 

 the most simple and convenient for the foregoing calculations ; 

 but if we wish in addition to form any conclusions respecting 

 the internal constitution of bodies, it becomes necessary to de- 



