( 152 ) 
of the electric and the magnetic ellipsoid with that plane). The wave- 
surface having a finite number of conic points (16), it cannot 
degenerate into 2 other surfaces if bj >, > bz. The two sheets 
cohere in the 4 real conie points. 
If ba =b3, the wave-surface degenerates into two ellipsoids 
g2 2 2 2 
ee al te a Ne bee GE nm? w? 
and 
LN Ed en Ci 
En ape ee Ss Nin’ we 
the first of which is similar to the electric, the second to the mag- 
netic ellipsoid, and which I therefore call the electric and the mag- 
netic part of the wave-surface. The two ellipsoids intersect the X-axis 
in the same point and touch each other in that point. The electric 
part of the wave-surface lies inside or outside the magnetic part, 
according to whether bj > bg or bj < ba. 
If bj = bg = bs, the two ellipsoids coincide. 
14 Let us return to the case bj > bg >b;. We have seen that 
the ray of light is electrically conjugate to Ò and magnetically to ®. 
The ray of light is therefore the line of intersection of two planes; the 
first of these is electrically conjugate to 2, and passes through 3 and 
the line ge which is electrically conjugate to the wave-front; the 
second is magnetically conjugate to B, and passes through D and 
the line gm, which is magnetically conjugate to the wave-front. 
If a point of the wave-surface is given, so that the wave- 
front and the ray is known, we find D and 9 by letting planes pass 
through the ray and resp. through gm and ge, and making these 
planes intersect with the wave-front. We may also use the planes 
Se and S, which are electrically and magnetically conjugate to the ray 
and which intersect the wave-front resp. along Dand DS. If the ray is 
electrically conjugate to the wave-front, the first construction fails 
for B and the second for D, so that we can still apply one of the 
two constructions in order to find 8 and D. (If the ray is magne- 
tically conjugate to the wave-front, the reverse takes place). ®D is 
then doubly conjugate to D and to the ray and must therefore be 
a principal direction. The ray will consequently he in a plane through 
two principal directions, and so also the point of the wave-surface ; 
since ray and wave-front are electrically conjugate, this point will lie 
