Physics. — “Double refraction by regular crystals”. By Prof. H. A. 
LORENTZ. 
(Communicated at the meeting of November 26, 1921). 
1. It is well known that erystals of the regular system are an- 
isotropic as to their elastic properties. Their three constants of elasticity 
are not connected by the same relations as those of isotropic sub- 
stances. Therefore geometrically equal rods cut frem the erystal in 
different directions are bent or twisted to different degrees. 
Substances as rocksalt and fluor-spar on the contrary are single 
refracting to a first approximation. The’ FresNer ellipsoid from which 
in crystal optics all phenomena are derived, is a sphere; this is also 
in accordance with the electromagnetic theory of light on the assump- 
tion that the optical properties are defined by the dielectric constant. 
Crystals witb. three equivalent mutually perpendicular principal 
directions can have but one dielectric constant. 
More detailed considerations however teach that this optic isotropy 
can only exist as long as the distance d of the molecules is very 
small compared with the wavelength 4. When 2 becomes of the 
same order to this distance, we have for each direction of propagation 
two mutually perpendicular directions of vibration, the “principal 
directions” to which belong different velocities of propagation. 
2. In 1877 I was led to the treatment of this problem') by the 
discussion of the explanation of the chromatic dispersion that was 
often excepted in those days. The unequal velocities of rays of 
different wavelength were explained by the assumption that the 
mutual distances of the molecules may not be neglected compared 
with the wavelength, which assumption may f.i. still be found in 
old papers of Kervin. In the cited paper I explained how this 
assumption is in contradiction with the fact, that with a few exceptions, 
the regular crystals are single refracting; when namely the ratio 
d/2 was so great that it could give rise to the dispersion, this should 
necessarily be accompanied by a detectable double refraction. 
1) H. A. Lorentz: Over het verband tusschen de voortplantingssnelheid van het 
licht en de dichtheid en samenstelling der middenstoffen. Verh. der Akad. van 
_ Wetenschappen te Amsterdam, 1878. 
22 
Proceedings Royal Acad. Amsterdam. Vol. XXIV. 
