Simpler Methods in Crystallography. 425 



adapt the standard axis to the monoclinic form, a somewhat 

 complicated method has to be adopted. Call the centre of 

 the cross o, the front-and-back axis of reference A, A^, 

 the right-and-left axis B, b^, and the vertical axis of reference 

 c, c\ On a separate paper draw a line oc. From c, with the 

 radius oc, describe a quadrant of a circle, and with a scale 

 of chords, a protractor, or by other means, set off on this an 

 angle equivalent to jS; drop a perpendicular from this point 

 to oc, and sign the intersection d. Set off od upon the 

 standard, above and below o. On the former paper draw a 

 right angle with sides equal to OA, calling the vertical line 

 OB and that at right angles to it OA. From o, with a radius 

 OA, describe a quadrant of a circle, and on this, from b set 

 off the angle p. From the point so determined drop a per- 

 pendicular to OA, and sign the point e. Transfer the distance 

 oe to the standard on OA. From e draw a line parallel to 

 oc, and from d draw another line parallel to OA. The point 

 of intersection of the two lines so drawn is the true direc- 

 tion and the standard length for the position of the inclined 

 axis projected at the angle /?• All that is now required is 

 to adapt this line, taken as unity, to its parametral length 

 proper to the species, and, of course, to adapt the vertical 

 axis of reference, also taken as unity, to its own proper para- 

 metral length, as in the case of the other axis. 



In adapting the standard axial cross to Akorthic species, 

 the three rectangular axes of reference themselves remain 

 unaltered, as in the case of those of the Monosymmetric 

 System. There are now three inclinations to deal with, p 

 measured, in this case, from the vertical axis of reference in 

 the front. The method of doing this has just been described. 

 Next the axis h has a double inclination, nearer to, or farther 

 from, the front horizontal axis of reference, and nearer to, or 

 farther from, the vertical axis of reference. The former angle 

 is denoted by 7, and the latter by a. The angle 7 is always 

 dealt with first, and the clinographic projection and length 

 of the axis in question is obtained in exactly the same way 

 as that just described. Putting this into language more 

 easily understood by many people, set off on the front 

 horizontal axis of reference OA, or<f = oAXcos 7; and on the 

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