( RYSTALLOGRAPIH 



view and the relative positions of objects on the table is at once 



seen. A clino^raphical projection of an octahedron is represented 

 in 1 in. l { ., in which the projection of the plane of the lateral axes 

 - aa'a is the result of ^ 



an elevation of the eye 

 .) 2S'. Referring to 

 Ki;. 50, cc' is the trace 

 of the plane of projec- 

 tion; it will be seen 

 that every point on 

 the horizontal plane in ^ '"'" 



a 



ae 



c 



FIG. 50. 



front of the plane cc' a 



will appear below o, and 

 every point behind cc' 

 will appear above o ; 

 the distance above or 

 below o at which any 

 point will appear de- 

 pends upon the angle 



of elevation of the eye and the distance from o of the point in 

 question. Take any point a, Fig. 50, the line of vision aa' is 9 28' 

 from the horizontal, and a will appear on the plane of projection at 

 a'. In the triangle aoa', where oa = 1, oa' = the tangent of oaa' = 

 tangent 9 28' = oa ; the point ai will appear at a/, ^ of aio 

 ^ above o ; the point e will 



appear at e', ^ oe below o, 

 etc. When the angle of 

 elevation is 9 28', the 

 distance of any point from 

 the plane of projection, 

 measured below o if the 

 point is in front and 

 measured above o if the 

 point is behind the plane 

 of projection, will deter- 

 mine the projection of 

 the point in question. 



Construction of the 

 axial crosses. Unless to 



-a: 



FIG. 51. The Axial Cross of the Isometric 



System. 



illustrate some peculiar conditions the angles 18 26' and 9 e 

 have proven the most satisfactory and are in general use. 



28' 



