40 



8. L. Pen field — Crystal Drawing. 



construct the angle 18° 26', draw a perpendicular at any point 

 on the horizontal line, as at o figure 1, make op equal one- 

 third Oo, and join and p. The next step in the construc- 

 tion is a change from orthographic to clinographic projection. 

 In order to give figures the appearance of solidity it is sup- 

 posed that the eye or point of vision is raised, so that one looks 



down at an angle upon a crystal 

 which is figured ; thus, in the 

 case under consideration, figure 

 3, the top face of the cube conies 

 into view. The position of the 

 crystal, however, is not changed, 

 and the plane upon which the 

 projection is made remains ver- 

 tical. From figure 1 it may be 

 seen that the positive ends of the 

 axes a x and a t are forward of the 

 line JTY, the distances a x x and 

 d v y being as 3:1. In figure 2 

 it must be imagined, and by the 

 aid of a model it may easily be 

 seen, that the extremities of these 

 same axes are to the front of an 

 imaginary vertical plane (the 

 projection of XY above) pass- 

 ing through the center of the crys- 

 tal, the distance being the sam% 

 as a x x and a 9 y of the plan. In 

 figure 4 the distance ax is drawn 

 of the same length as a 1 x of the 

 plan, and the amount to which 

 it is supposed that the eye is 

 raised, indicated by the arrow, 

 is such tha't a, instead of being 

 projected horizontally to x, is 

 projected at an inclination of 

 9° 28' from the horizontal to w, 

 the distance xiv being one-sixth 

 of ax ; hence the angle 9° 28' 

 is such that its tangent is -J-. 

 Looking down upon a solid a t an angle, and still making the 

 projection on a vertical plane, may be designated as clinographic 

 projection / accordingly, to plot the axes of a cube in clino- 

 graphic projection in conformity with figures 1, 2 and 4, draw 

 the horizontal construction line 7ifc, figure 3, and cross it by 

 four perpendiculars in vertical alignment with the points 

 a v — a l and a^ — a 2 of figures 1 and 2. Then determine the 



Figs. 1-4. — Development of the 

 axes of the isometric system in 

 orthographic and clinographic pro- 

 jection. 



