424 Proceedings of the Royal Physical Society » 



mark these extremities respectively a, a^. If these instruc- 

 tions are followed with proper care, as good an axial cross 

 may be constructed thus as by the method described by 

 Dana. It will be observed that in this, as in all other 

 crystallographic measurements, the proportional method is 

 followed — h always being understood to be unity. 



The axial cross thus drawn is adapted to the Cubic, the 

 Tetragonal, and the Orthorhombic Systems, without any 

 change of inclination of the lines, 



Dana's method of adapting the standard axial cross to the 

 Ehombohedral System is simplicity itself. It is described 

 on p. 549, op, cit. Briefly stated, the method is this : — 

 Extend oa, oa^ to 1*732 (= ^3 its own length) and mark the 

 extremities A, A^ as before. Join a&, hk^, a¥, and ¥a, so as 

 to form a rhomb. Bisect each side of the rhomb, and connect 

 the points at the back and those at the front, and draw lines 

 through the points where they cut the rhomb through the 

 centre. Cancel from the original the line aoa^ and the 

 angles of the rhomb adjacent, and there is left the clino- 

 graphic projection of a regular hexagon, with its one 

 vertical and three horizontal axes of reference. All that is 

 needed to adapt this to any particular species is to vary the 

 length of the vertical axis to suit. The vertical axis is 

 denoted by i, the right-and-left axis as k, — h. The axis to 

 the right in front is —I (and -{-l behind), and that to the left 

 in front is h, while its back half is —h. The axes thus 

 read, starting from the left and going counter-clockwise: 

 -k, -\-h, -I, -{-k, -h, +/. 



To adapt the standard axial cross to the Monosymmetric 

 System, the front-and-back axis has to be altered in both 

 direction and length, and the vertical axis, regarded simply 

 as an axis of reference, is altered in length only — all three 

 of these elements varying with the species. The right-and- 

 left axis h remains constant in both direction and length, 

 which latter is always unity; h therefore coincides with the 

 right-and-left axis of reference under all circumstances. 

 The front-and-back crystallographic axis is inclined to the 

 vertical axis of reference at an angle denoted by /3. It is 

 measured behind and above. To project this angle, and thus 



