(1543 
an ellipse, as it counts as a double line of intersection and as the whole 
intersection with the wave-surface is of the 4‘ degree), which by 
its radii vectores through O indicates the possible rays of light. 
The tangent plane just mentioned touches the electric and the 
magnetic ellipses in the XZ-plane in the points A and B, and is 
parallel to the Y-axis; the rays g, and g, are the radii vectores of 
these points of contact, so that it is directly to be seen from the 
wave-surface that they belong to the cone of rays. Let now the ray 
be given by a point C of the ellipse of contact, then we find D as 
the intersection of the wave-front with the plane through g,, and the 
ray, so that CB indicates the direction of D; in the same way CA 
indicates the direction of DS. D and B being also conjugate diameters 
of the section of the wave-front with the electric and the magnetic 
ellipsoid, it follows directly, that the curve of contact must be similar 
to these elliptic sections with the same direction of axes. This 
might be seen, even if we did not yet know that the curve of 
contact is an ellipse. Further AB is a diameter of the ellipse of 
contact. (Internal conic refraction). 
17. Let now the ray-plane be a section of similitude of the two 
reciprocal ellipsoids, then it passes through the middle reciprocal 
principal direction, so that the ray lies in the X Z-plane. Indeed, 
the ray of light is now the radius vector of one of the conic 
points of the wave-surface, and these points are only to be found 
in the X Z-plane. The wave-front is now indeterminate, being a 
tangent plane to the wave-surface in the conic point. (It is a 
quadratic conic point; else the line which connects it with a 
second conic point would have more than four points in common 
with the wave-surface). In a similar way as in the preceding case 
we can now show that the planes S, and S, which are electrically 
and magnetically conjugate to the ray, belong to the possible wave- 
fronts. This is also directly seen from the wave-surface, as the planes 
Se en S, are both parallel to the Y-axis, and, if transferred to the 
conic point, touch respectively the electric and the magnetic ellipse in 
the X Z-plane and so also the tangent vone in the conic point. 
By their intersection with the wave-front these planes S, and Sn 
indicate directly the directions of D and %. If, the wave-front 
coincides with S, D falls in the X Z-plane and touches the electric 
ellipse; 3 is then parallel to the Y-axis. Similarly with what we 
have found, when the wave-front is determinate but the ray in- 
A 
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