9 J: Prof. W. Voigt on the Behaviour of Pleochroitic 



itself &) ] ~g) 2 approximately — is constant over ellipses having 

 the points 0, and 0,' for foci. This difference vanishes along 

 the straight line C 1 Ci / , and increases as the ellipse opens out. 

 (The mean square of the velocity, ^(o^ + or, 2 ), on the other 

 hand, is constant along straight lines perpendicular to the 

 direction A[ A 2 .) 



(b) The parameters k x and k 2 , which determine the absorp- 

 tion of the two waves (corresponding to the same direction Z), 

 are constant along hyperbolas having their foci at C x and 

 C/. They have the same value k along the straight lines 

 obtained by producing C^ d' both ways, and along any 

 hyperbola have values which differ from /.- by equal amounts 

 of opposite sign, the maximum difference occurring along the 

 f-axis. 



(c) The vibration-ellipses of the two waves (corresponding 

 to the same direction Z) have constant ratios of axes along 

 circles whose centres lie on the straight lines obtained by 

 producing C : C/ both ways, and whose radii are such that 

 all the circles cut the circle described on C x C/ as diameter 

 orthogonally. The ellipses degenerate into circles at the 

 points C 1 and C/ 7 and become straight lines in the f-axis. 

 The direction of vibration is of opposite sense on the two 

 sides of the f-axis, but is everywhere the same for the two 

 waves. 



(d) The principal axes of the vibration-ellipses of the two 

 waves are crossed; their position is constant along equilateral 

 hyperbolas whose vertices lie on the lemniscate having Ci 0/ 

 for axis, and which pass through the points C 1 and C/. The 

 coordinate-axes £ and rj are special cases of these hyperbolas. 

 In order to determine the positions of the axes of the ellipses 

 corresponding to these hyperbolas, it is most convenient to 

 use the well-known theoretical result according to which 

 in the case of weak absorption the vibrations, within a 

 certain distance from the optic axes, differ only imperceptibly 

 from those taking place in transparent crystals, and are 

 therefore nearly rectilinear along directions determined by 

 the famous construction due to Fresnel. According to this 

 construction we have to draw planes through the axes Z 

 and A l5 and Z and A 2 , and to bisect the angle I between 

 them; the ordinary wave is then polarized in a direction 

 parallel, and the extraordinary one in a direction normal, to 

 this bisecting plane. 



In fig. 3 are shown the curves corresponding to propo- 

 sitions (c) and (d) ; in addition to this the double-headed 

 arrows arranged round the circumference of a circle indicate 

 the directions of polarization of the ordinary waves when the 



