hy Means of Grajphical Methods. 



consider the relation in terms of tangents rather than cotan- 

 gents. The tangent principle, though simple, is so exceed- 

 ingly important that it is thought best to introduce an 

 example indicating a graphical method of solution. The illus- 

 tration, figure 12, is chosen from barite, the forms shown being 

 those of the macrodome zone, with <?=001, and a =100. It is 

 assumed that the angles have been measured as follows : 

 cA?=21° 56i'; c/\d=^^° 51^^ and cA'i^=58° 10^^ The 

 poles are easily located on the graduated circle, and the slopes 

 of the several faces plotted by drawing lines from x to points 

 on the periphery equal to twice the value of the angles, meas- 

 ured from —X. It is then evident that if u is taken as the 

 unit dome 101, the intercepts of d and I on the vertical axis 

 are respectively -J- and J, and their symbols therefore lU2 

 and Jul:. If the length of the a axis of barite were 

 known (<:i^=0'815), the slopes of 2/, d and I would naturally 

 be plotted from the unit length of a^ when the slope of ti 



13 



14 



would determine the length of the vertical axis (<? = 1*311:). 

 For plotting and measuring the lengths of axes, the radius of 

 the divided circle may be taken as iinity^ and measurements of 

 axial lengths made by means of scale ]^o. 1: of the sheets on 

 which the divided circles are printed. 



Another procedure applicable to all cases where the axial 

 inclinations are 90° is illustrated by figures 13, 14 and 15. In 

 figure 13 three axes meeting at 90° at (9, and their intersec- 

 tions with a pyramid abc, are shown in clinographic projection. 

 The line Ox^ at right angles both to the vertical axis and the 

 edge (ib^ is an important factor to consider, and may be desig- 

 nated as the hase-line of the triangle cOx. Another important 

 factor to be considered is the slope of the pyramid, or its in- 

 clination, along the line xc, with the base-line Ox. From 

 figure 14, which represents a section along the plane cOx of 

 figure 13, it may be seen that the slope of a pyramid, or the 

 angle made by the line ex with the hase line Ox^ is the same as 

 the interfacial angle of base on pyramid, 46° 6' in the figure. 

 Knowing the hase-line Ox and the slope of any pyramid, there- 



