Eakle.] 



Colemanite from Southern California . 



43 



It' with a radius of h = 1 = c-axis, a circle is described, then 

 this circle would represent in ground plan a sphere of projection. 

 The plane of projection would be tangent to this sphere at the 

 end of the c-axis, 8 would be the pole of the projection, and 8Y 

 the first meridian. Any faee pq would have the point of inter- 

 section of its normal with this plane, located by the angle <t> 

 which it makes with the first meridian 8Y, and the distance from 

 the pole df = tg p. (Figure 1). The face pq is further defined 

 by the two rectangular coordinates % y , whose values deduced 



from the right triangles are 



x — sin 4> tg p 

 y' = cos 4> tg p. 



By means of the measured 

 y angles and p, all forms 

 can be plotted on cross 

 section paper, and the co- 

 ordinates x' y' give graph- 

 ically the symbols for any 

 form in terms of the ./ y / 

 of the unit form pq. In 

 monoclinic crystals the 

 projection of the base-normal lies in front of the pole at a dis- 

 tance e = tg p, and the distances p' and q' are the coordinates 

 for the unit pyramid pq reckoned from the base; therefore for 

 any values of pq, / = pp' + (/ and y' = qq' . 



Determination of /, p-, and P. — An average of twenty read- 

 ings on the basal pinacoid gave p = 20°7, with <j> = 90°; 

 e' = tg p = 0.3663. This value of e / was also obtained from 

 the readings of the clinodomes. For these forms x = e' , and an 

 average of forty-four values of / for the domes 01 and 02 gave 

 ,/ = 0.3663; thus agreeing with the direct measurements. Also 

 ,/ = C ot p. = 6!)° 53' and j8 = 180° — /* = 110° 7'. 



Determination of //,, and </',,. — By means of the two formulae 



* = sin 4> tg p 

 y = cos <t> tg p 



the coordinates x' y' were calculated for all the best faces. For 



