42 



-6". L. Penfield— Crystal Drawing. 



at times are only with difficulty, if at all, comprehended from 

 a clinographic projection alone. Figures 2 and 4 have been 

 introduced merely as helps in the development of the clino- 

 graphic projection. It is also worthy of note that in the major- 

 ity of cases a plan and its accompanying clinographic projection 

 may be drawn more readily than a single figure in clinographic 

 projection alone. 



No originality is claimed for the idea of making use of a 

 plan in connection with a clinographic projection. The prin- 

 ciples are those commonly made use of in mechanical drawing, 

 though generally in dealing with that subject orthographic 

 projection alone is employed. In Kokscharow's Atlas accom- 

 panying his " Miner alogie Russlands" it will be found that a 

 plan accompanies almost every figure drawn in clinographic 

 projection, while Miller in his " Treatise on Mineralogy " 

 employs orthographic projection almost exclusively. Lastly, 

 students of crystallography may use an orthographic and its 



accompanying clinographic projec- 

 tion much as a carpenter or builder 

 uses a plan and its accompanying ele- 

 vation. The one supplements the 

 other. 



Projection of the Axes of the Hex- 

 agonal System. — For projecting the 

 hexagonal axes exactly the same prin- 

 ciples may be made use of as were 

 employed in the construction of the 

 isometric axes. Figure 6 is an ortho- 

 graphic projection, a plan, of a hex- 

 agonal prism in two positions, one of 

 them, a x , a 3 , etc., after a revolution 

 of 18° 26' from what may be called 

 normal position. In figure T the ex- 

 tremities of the horizontal axes of 

 figure 6 have been projected down 

 upon the horizontal construction line 



\ 



..11.1 i 



Figs. 6, 7 and 8. — Develop- 

 ment of the axes of the hex- 

 agonal system, in orthographic 

 and clinographic projection. 



hk, and a^ a 2 and — a Q which are 



forward of the line XY in figure 6 

 are located below the line hk in the 

 clinographic projection, the distances 

 from hk being one-sixth of a x x, 



a^y and — a z z of figure 6. Figure 8 is a scheme for getting 



the distances which the extremities of the axes are dropped. 



The vertical axis in figure 7 has been given the same length as 



the axes of the plan. 



