Simpler Methods in Crystallography. 343 



methods to be adopted in drawing arcs of circles, it may be 

 well to refer to the Tables at the end of this paper, which are 

 taken in part from GrifiBin's " Crystallography." These give 

 the relative length of the lines which correspond to all the 

 indices, except some of those of very rare occurrence. The 

 Table is a valuable one, and will be found to save a large 

 amount of labour. 



46. Another device to serve the same purpose, and which 

 I have used extensively, is on the same principle as the 

 decimal scale already described. Instead of using the 

 division on a metre scale, the proportional lengths corre- 

 sponding to those given in the Table are set off from the 

 metre scale, and are drawn convergent to a point some 

 distance to the left of the drawing-paper used for the scale. 

 The advantage of having such a scale is that one has only 

 to measure off the distance to be divided up by sliding a set- 

 square against a straight-edge placed parallel to the base 

 until the unit length is intercepted, and then the length 

 required for the fractional part can be measured off, and set 

 out upon the working copy direct. It may be remarked 

 that, owing to the large amount of geometrical work in- 

 volved in a very complex map, it is hardly possible for even 

 the most skilful draughtsman to complete a single copy of 

 the map without its appearance having suffered from, various 

 causes. Much of this may be avoided by a judicious use of 

 these scales, and in most cases it is well to work out the 

 lines on a separate map from that which is intended for the 

 final copy. 



47. Now, let us take those cases in which it is required 

 to lay down the position of a pole which cuts all three axes. 

 First we may take 111, i.e., that face which cuts a, h, and c, 

 each at unit length. To determine this, an arc of a circle has 

 to be drawn. To do this, any one of various plans may be 

 adopted. In most cases the arc may be described simply by 

 finding the centre of the circle which will pass through the 

 three points in question by the method commonly used, and 

 then describing the curve with a pair of compasses, with 

 a lengthening bar attached, if need be, or with the beam 



VOL. XIV. z 



