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on the electric ellipse. © falls now along a principal direction and 
® touches the electric eliipse, as follows from the construction. Both 
constructions for © and ® fail only when the ray is both electrically 
and magnetically conjugate to the wave-front, and falls therefore along a 
principal direction; the wave-front passes then through the two other 
principal directions. By now paying attention to the adjacent points 
of the wave surface, specially to points lying in the planes of coordinates, 
we find that D touches the electric ellipse and B the magnetic 
ellipse in the planes cf coordinates. 
15. To every wave-front belong two rays; if I and II are the 
directions of the possible electric and magnetic induction in the 
wave-front, the two rays of light are: the line of intersection of the 
planes through I and ge and through II and g» and the line of 
intersection of the planes through I and g, and through II and ge. 
The question might be raised: When do the two rays of light 
fall in the same direction? Evidently when the ray of light is 
doubly conjugate both to I and to IL and accordingly isa principal 
direction. We find also that this is the only case in which the two 
wave-fronts betonging to one direction of the ray coincide. The 
wave-front passes then through the two other principal directions, 
16. Let us now examine the case of the wave-front being a section 
of similitude of the electric and the magnetic ellipsoid. The two 
lines ge and g, which resp. are electrically and magnetically 
conjugate to the wave-front, now lie both in the plane through two 
principal directions, viz. the X-axis and the Z-axis, the wave-front 
passing through the middle principal direction, the Y-axis; and they 
do not coincide. The ray being the line of intersection of the plane 
through B and ge and the plane through D and gy, while 3 and D are 
indeterminate, we get a cone of rays passing through ge and gm; 
for, if D falls in the X Z-plane and ® along the Y-axis, g, becomes 
the ray, and if B falls in the X Z-plane and D along the Y-axis, 
gm becomes the ray. Moreover it is easily seen that these are 
the only rays falling in the XZ-plane and that therefore the 
cone is quadratic. If inversely the ray is given in this case, D and 
% may be found by means of one of the two given constructions. 
But whatever the course of the ray may be, we have always the same 
value of s, so that we have to deal with but one tangentplane to 
the wave-surface. This must touch along a curve (which is of course 
