340 Proceedings of the Royal Physical Society. 



simple. There exists, therefore, need for a projection which 

 does not possess these defects, and the only really satisfactory 

 one that answers to the requirements is the Stereoscopic 

 Projection, or what Lewis has named the Stereogram. 



42. The principle of construction is not difficult to 

 understand. In the Gnomonogram, lines are supposed to 

 be drawn from the centre of the sphere perpendicular to 

 the faces of the crystal to be delineated, and the lines are 

 supposed to pass outward from the surface of the sphere of 

 projection until they touch a plane in contact with the 

 sphere. In the Stereogram, lines are projected on to the 

 surface of a sphere, as before, and the positions so marked 

 are supposed to be viewed from a point at the opposite 

 surface of the sphere. Lines drawn from the surface of the 

 sphere to the point of sight pass through a diametral plane, 

 which is perpendicular to the line joining the line of sight 

 and the centre of the sphere. This plane is the plane of 

 PROJECTION in the present case, and it is inside the sphere, 

 instead of outside, as it is in the projection last considered. 

 By this method all zones are projected into either straight 

 lines or else into arcs of circles — not into ellipses or into 

 any other conic sections, as seems often to be supposed, and 

 is really the case in both the Orthographic and the Globular 

 projections. 



43. The first step in the process is to draw a circle of such a 

 radius as admits of easy division into decimal parts to not less 

 than three places, and then to draw diameters at right angles 

 to each other, which are prolonged to any convenient length 

 beyond the primitive. The centre is to be signed o, and if 

 the crystal is to be viewed from above, o will coincide with 

 z, and with the axis c if the crystal to be mapped belongs 

 to any but the Monosymmetric and the Anorthic Systems. 

 Let us assume that it is required to map an Orthorhombic 

 crystal, as before. In that case, the front and back axis, 

 on which a is to be, will be on some part of the diametral 

 line in that position, and which, assumed to be of indefinite 

 length, is signed x. The right and left, on which h will 

 be determined presently, is to be signed Y. As we are now 

 viewing the far side of the sphere of projection, the quadrants 



