DR. PLUCKER ON A NEW GEOMETRY OE SPACE. 
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tute a cone of the second order. The cone remains the same if the given point moves 
along a right line, passing through O, 21. Peculiar cases, 22-24. A hyperbola enve- 
loped by the doubly refracted rays within any given plane. Its determination, 25. 
Peculiar cases. Geometrical interpretations, 26-28. The complex generated in three 
different ways by a variable linear congruency, 29. Peculiar case of a complex, the 
crystal being cut along a circular section of E. All doubly refracted rays meet that 
diameter of E the conjugate plane of which is the circular section, 30. Peculiar case 
in which the surface of the crystal is a principal section, 31. Case of uniaxal crystals, 
32, 33. The ellipsoid E replaced by a new ellipsoid, the radii vectores of which indicate 
the reciprocal values of optical elasticity, 34. 
Additional Note. 
Coordinates of a right line, 1-10. Complexes. Congruencies. Surfaces generated 
by a moving right line. Developable surfaces and curves of double curvature, 11-22. 
A new system of coordinates, 23, 24. Geometry of forces, 25. 
