40 SEC. 2. GEOMETRY. 



flat, and the Hues, planes, and surfaces are represented by coloured strings, 

 which assume their positions when the planes are at right angles. 



1. Illustrating the relation between the projections, traces, directions, and 



lengths of straight lines. 



2. Illustrating the relation between the traces of planes, their inclinations, 



and intersections. 



3. Illustrating the relation between the projections of a line and the traces 



of a plane ; also the normal to a plane. 



4. Illustrating the relation between the projections of lines and the angles 



between them. 



5. Illustrating the relation between the traces of a cone and the traces of 



its tangent plane, and hence the method of drawing a plane having a 

 given inclination. 



6. Model, capable of opening out flat, so as to show how the horizontal and 



vertical planes may be represented on a drawing^ 



166. Stereoscopic Figures, for demonstration and use in 

 the study of stereometry and spherical irigonometry. Edited 

 by Julius Schlotke. L. Friederichsen and Co., Hamburg. 



166a. Stereograms of the Lines of Curvature of 

 Surfaces. Drawn by the exhibitor. Prof. J. Clerk Maxwell. 



Lines of curvature of the cy elide of Dupiu (4). 

 Curves on a sphere (4) : 



a Two systems of orthogonal circles. 



/J Concyclic spherical ellipses. (This represents a spherical har- 

 monic of the second degree.) 

 7 Confocal spherical ellipses. 

 5 The projections of a spherical ellipse on the three principal 



planes. 

 Quadric surfaces (4) : 



Elliptic paraboloid, hyperbolic paraboloid, ellipsoid, and the surface 



of centres of ellipsoid. 

 FresnePs wave surface (3): 



The lines are in the direction of the vibrations of the two polarized 



rays. 



Steiner's surface (2). 

 Twisted cubics (2) : 



tx a sin 26 (vertical). 

 Curves y = b sin 30 (horizontal). 



[ z = c cos 50 (perpendicular to paper). 



f x a sin 29. 

 \ y b sii 



Curve < y = b sin 30. 

 [2 = c sin 70. 

 Icosahedrou in octahedron. 

 22 in all. 



166b. Heal Image Stereoscope for showing the above. 



Prof. "Clerk Maxwell. 



The observer places his eyes about two feet from the large lens, and sees 

 the united real images of the figures at or near the surface of the lens. 



