472 oS. W. Gibbs—Double Refraction and Circular 
where U represents the common value of U; and U;. The 
polarization is therefore circular. The converse is also evident 
from equations (29), viz: that a ray can ey circularly polarized 
e direction of its wave-normal is such that 
U,=U,. Such a direction, which i detonated by a pieulee 
section of the ellipsoid vo presse - an optic axis of a crys- 
tal which conforms to Fresnel’s law of double refraction, may 
be called an optic axis, although its s physia properties are not 
the same as in the mor inary case. we write Vp an 
V,, respectively, for the wave- welcahes of the right-handed and 
left-handed rays, we have 
2 ; 2.772 Pp 
=U*+ +e Pelt ove 5 (33) 
whence - v. 
r+ 
i“ ee +y)= a ee 
and 
ViVi (34) 
L 
‘The phenomenon best observed with respect to an optic axis 
is the rotation of the plane of linearly polarized light. If we 
denote by @ the amount of this rotation per unit of the distance 
traversed by the wave- we regarding it as Hosa when it 
appears s clock-wise to the observer, who looks in the direction 
opposite to that of the propagation of the ieee we have 
a 
6=—( — — > 
Ave va) es 
By the preceding equation, this reduces to 
°= EVE (36) 
Our pa arate pon ledge of circularly or Bom tiered Sarah: media is 
cinbiee'y such as are optically either isotropic or uniaxia ral theory 
of such se embracing the case of two optic axes, has Soueye: fer discussed 
by Professor von Lang. eorie der Circeularpolarization, Sitz.-Ber. Wiener Akad. 
vol. Ixxy, p. 719.) The general results of the present paper, although derived 
pore physical hypotheses pr an entirely different ner are quite similar to those 
of the memoir cited. They would become identical, the writer believes, by the 
substitution of a constant for ” ori in the equations of this paper. [See es- 
pecially equations Ge (20), (2 8) 
That a complete discussion of the subject on any theory must include the case 
of biaxial media having the property of circular or elliptical polarization, is evi- 
dent i i m i 
