Simpler Methods in Crystallography. 333 



this line should be perpendicular to ab at m. Next, from ac 

 on the working map, take off the distance ad or cd, and set it 

 out with its symbol d (101) on ac. In like manner set ofp&e 

 or ce on he, and sign the point e (Oil). Draw lines from m 

 through d and e : also from h through d and a through e : pro- 

 duce them indefinitely. The point where these letters cross 

 mc should be that of their common intersection. It marks 

 the point of contact of the plane of projection with the 

 sphere of projection, and also the pole of o (111), or that 

 pyramid whose face touches each of the three axes at their 

 normal length. 



26. It may be remarked here that the points a, h, c, d, e, m, o, 

 whose positions are thus determined, are the seven cardinal 

 poles or primary points, marking the poles of the unit forms 

 in all these projections and in all systems. As that is so, it 

 is desirable to employ for them a uniform set of symbols, 

 which has not yet been consistently done by any writer, but 

 will be done so here. 



27. In determining the position of the poles to the 

 secondary faces on a gnomonogram, it is quite possible to 

 work by a system of intersecting lines drawn from various 

 points whose position can be laid down in succession on the 

 drawing itself. As the principle upon which this method of 

 working is one of great importance in practical Crystallo- 

 graphy, it may be referred to in some detail, even though 

 the position of any pole may be more easily determined by 

 methods to be presently described. The principle referred 

 to depends upon the fact, already stated here more than 

 once, that the various poles in Crystallography lie in zones 

 whose axes bear a very definite geometrical relationship to 

 each other, and this relationship is of a proportional nature 

 rather than of one connected with the kind of angular 

 measurement of the kind employed for other purposes. If 

 we can determine the position of a few of these cardinal 

 points, lines drawn from them through certain other positions 

 will at once determine the positions of sets of poles belonging 

 to other zones, and the process may be continued from point 

 to point until each pole on the projection is connected with 

 every other pole with which it lies in zone. 



