Illustrate the Propagation of Ligld in Biaxals, 325 



Section of Surface by Plane y = 2. 



Inner section a point, the origin. 

 Outer, 



x. y. 



0-00 3-46 



1-09 3-00 



1-50 2-60 



1-53 2-58 



1-96 2-00 



2-44 1-00 



2-60 0-00 



Tbe projection of the curve appears to go through the 

 singular points, but does not actually do so. It cuts the 

 circle in the point «=1"50, z = 2'60 and not in the singular 

 point. 



The line OMis an optic axis, the angle MOX=tan- l! 845 = 



40° 10' ; the angle ZOM, the semi-angle between the optic 



axes, = 4l>° 50' as we saw before from the ellipsoid of elasticity. 



The line OP is an axis of single-ray velocity, the angle 



XOP=tan- 1 l-69 = 59° 20'. 



The circle N'M' is the circle of contact, its diameter is 1*97. 

 The co-ordinates of the point M are 



0=2-29, 

 sr=l-94, 

 y = 0-00. 



The lines N E P', N C P' are normal to the ellipse and circle 

 respectively, while T E P' and T C P' are the tangents. The 

 equations to the lines N E P', N C P' with reference to P' as 



orimn are 



_a A 2 -c 2 

 '- c V a 2 — b* 



Z= - \/ -5 77,# 



and 



- £ A 8 -c a 



'"aV a 2 -6 2 



b* x 



respectively. The tangent of the angle which N C P' makes 

 with the negative direction of axis of x is thus "423, and the 

 angle is 22° 50'. The angle which N C P' makes with the 

 same direction has been found above to be 59° 20'. The 

 angle N,P'N C is thus 36° 30' and the angle T E P'T c is 143° 30'. 



Fig. gives the ellipse and circle in principal section by 

 the ZOY plane. The radius of the circle is 4. The foci of 

 the ellipse are indicated by crosses ; the ellipse has half the 

 linear dimensions of the section of the ellipsoid of elasticity 

 by the ZOY plane. 



Phil. Mag. S. 5. Vol. 44. No. 269. Oct. 1897. 2 A 



