258 Prof. H. F. Dawes on Image 



the plane of the meridian, the focal lines, which are deter- 

 mined by these curvatures, will be at right angles to and 

 parallel to the axis of revolution, and hence at right angles 

 to and parallel to the optic axis of the crystal. Thus in 

 fig. 4, which represents the extraordinary wave from a 



Fig. 4. 



point P, the optic axis of the crystal is parallel to the ^-axis 



and the geometrical axis of the refracting system lies along 



the £-axis. The wave travels with the velocity a along the 



optic axis and with the velocity c at right angles to it, so 



that the section by the zzy-plane is the equatorial circle and 



that by the ^^'-plane the meridional ellipse. The focal line 



corresponding to the former section is parallel to the A'-axis 



and intersects the z-axis at the image-point, as determined 



for a spherical wave of the same curvature travelling with 



the same velocity in an isotropic substance. Similarly, the 



focal line corresponding to the meridional section is parallel 



to the 3/-axis, and its point of intersection with the £-axis is 



the same as if this wave were spheroidal about this line as 



axis of revolution. The position of this point of intersection 



will therefore be determined in accordance with the principles 



which we have been considering in previous sections ; the 



necessary modification of the formulae will consist simply in 



interchanging the indices n l and n 2 , since the velocities a 



and c are now interchanged with reference to the incident 



wave-front. 



