Simpler Methods in Crystallography. 345 



48. In the very common case in which the centres of the 

 arcs required are at too great a distance to be drawn with 

 compasses, even when eked out by the lengthening bar, 

 some other device must be employed. This is usually diffi- 

 cult to do, and the difficulty is increased by the fact that all 

 the curved lines in the stereogram must be arcs of great 

 circles, so that a merely smooth curve connecting any three 

 points is not necessarily all that is required. In practice, it 

 is often sufficient for us to determine accurately the position 

 of a sufficient number of points which lie exactly within the 

 required arc, and then to connect these points by a curve 

 drawn in by hand — the only really essential feature being 

 that the points shall be correctly laid down in an arc of a 

 great circle. 



49. One simple device which answers well in those cases 

 in which the height or rise of the arc is not very small, is to 

 draw, on a separate piece of cardboard, a line equal in length 

 to about two diameters of the primitive. Mark the centre, 

 set off the length of the radius on each side for the " span " 

 of the arc, and then erect a perpendicular above the middle 

 point, which shall be equal in length to the height of the arc 

 required to be drawn. From the "rise" thus determined, 

 draw a line to one extremity of the " span," and another line 

 parallel to and above the other extremity of the " span." 

 With a sharp knife, against a steel straight-edge, make a 

 clean cut along the two lines thus drawn. If, now, two 

 slender needles are fixed in the diametral points in the 

 primitive through which the required curve has to pass, and 

 the cardboard triangle be moved in its own plane in contact 

 with these needle-points, the apex of the triangle will pass 

 through the arc of the great circle required, and any desired 

 number of points in that arc can be laid down. In practice 

 this answers very well if no attempt be made to draw the 

 curve directly by the aid of this instrument. If the triangle 

 be varnished, it may be used many times for arcs of the 

 same " span " and " rise." 



50. Another device is to employ a set of the cardboard 

 curves cut to various radii, which are used by engineers for 

 laying down railway curves upon their working plans. 



