346 Proceedings of the Royal Physical Society. 



They give most excellent results in all cases where they 

 happen to fit. The arcs of circles on the maps I have made 

 for Heddle's " Mineralogy of Scotland " were mostly drawn 

 by means of the set of railway curves belonging to the 

 Edinburgh Museum of Science and Art. 



51. The principle upon which yet another device is 

 employed may be best understood by drawing the ends of 

 a flexible rod towards each other against two fulcra. If 

 the rod is exactly uniform in structure and in dimensions 

 throughout its entire length, and is flexed by equal force at 

 each end, the curve into which it is thus bent will be an 

 arc of a circle, by which means a curve of the required form 

 can easily be drawn on the map. Many instruments have 

 been constructed upon this principle. In practice, a slender 

 and flexible steel straight-edge, uniform in width and thick- 

 ness, and equal in length to about four radii of the primitive, 

 is the best for the purpose, and the fulcra employed may be 

 two small brass studs fixed on a strip of metal at a distance 

 equal to three radii of the primitive. It is important to bear 

 in mind that a thrust from any single point letween the 

 fulcra will give a curve which is not an arc of a circle. 

 Some well-known books on Crystallography have seriously 

 misled their readers in this connection. 



52. After the description already given of the mode of 

 finding the positions of poles which cut all three axes — a 

 case for which the general symbol (Jikl) is employed in 

 Crystallography — there is no need to repeat the direction 

 here. What applies to the more -easily- constructed 

 gnomonogram applies equally to the cases specially under 

 consideration here, only that arcs of circles have to be 

 drawn instead of straight lines. 



53. We may now pass on to consider the mode of con- 

 structing stereograms of Monosymmetric crystals, a process 

 which requires more care and labour than any constructions 

 yet noticed, and up to which, in fact, much of the foregoing 

 description is really meant to lead. 



54. We may first advantageously consider the principles 

 which underlie the construction in the case under considera- 



