Simpler Methods in Crystallograjphy. 329 



sideration consists of points and of straight lines connecting 

 those points with others. 



19. It is advisable now to copy the lines on to paper, and 

 then to repeat the experiment with crystal sets belonging to 

 several different systems (avoiding the monosymmetric and 

 anorthic for the present). Much is learnt by the process, 

 and a good solid foundation is laid for the work that is to 

 follow. When this has been done, it will be clear that the 

 gnomonogram represents an eighth of the surface of the 

 sphere in the Cubic, Tetragonal, and Orthorhombic systems, 

 and a twelfth in the case of the Ehombohedral. There is no 

 practical disadvantage in this which is not quite counter- 

 balanced by many advantageous features which this mode of 

 projection presents. Also it is w^ell to notice that in the 

 case of the gnomonogram, it is the poles and zones on the 

 convex surface of the sphere which are projected, and that 

 on the side next the observer's eye. 



20. As soon as the worker feels that the principle of 

 construction has been made quite clear by the method of 

 procedure described, this rough and inexact mode of work 

 may be exchanged for geometrical methods, by which almost 

 any required degree of precision may be attained. 



21. At this stage the wooden ball marked with all the 

 leading poles and their zones, may well be kept constantly 

 before the eye. Its utility at the present stage is increased 

 if rather large pins are fixed in the position of the principal 

 axes {a, h, c). If we turn the ball about so as to view it in a 

 variety of directions, it will be quite clear that each point 

 on its surface is equidistant from o, the centre. Bearing 

 this in mind, let us lay down a circle to represent the 

 boundaries of the sphere, choosing some radius easily divided 

 into decimal parts to at least three places. A decimal scale 

 for this purpose can easily be constructed on a large sheet of 

 good drawing-paper by the following method : — Fix a metre 

 scale some distance to the right hand of the drawing-board 

 upon which the paper is fixed, and parallel to one of its edges, 

 also a fine steel needle at about a decimetre to the left, and at 

 a point parallel with the extremity of the scale. Then with a 

 good steel straight-edge moving against the needle on the one 



