On the Drawing of Figures of Crystals. 37 
intersection of these lines, is one extremity of the macrodiagonal ; 
and the line E’E, in which ME= ME’, is the macrodiagonal. AA’ 
DD’, EE’ are the axes in a diclinate form in which the axes are 
equal. From the observations on the preceding systems of crys- 
tallization, the method to be employed in giving the axes their rel- 
ative values in a particular diclinate form, is sufficiently obvious. 
The construction of the oblique rectangular prism is analogous to that 
of the cube. ; 
12. Triclnate system.—The vertical sections through the hori- 
zontal axes, in the triclinate system, are obliquely inclined; also the 
inclination of the axis a to each axis 6 and ¢, is oblique. In the adap- 
tation of the monometric axes to the triclinate forms, it is therefore 
necessary, in the first place, to give the requisite obliquity to the 
mutual inclination of the vertical sections, and afterwards, to adapt 
the horizontal axes, ‘as in the diclinate system. The inclination of 
these sections we may designate A, and as heretofore, the angle be- 
tween a and 6,7, and aandc,f. BB’ is the analogue of the brachy- 
diagonal and CC’ of the macrodiagonal. An oblique inclination 
may be given the vertical sections, by varying the position of either 
of these sections. Permitting the brachydiagonal section ABA’ B’ 
to remain unaltered, we may vary the other section as follows: 
Lay off on MB, Mb’=MB x cos 
A, and on the axis C’C, (to the right 
or left of M, according as the acute 
angle A is to the right or left) Mc= 
MC xsin A; completing the paral- 
lelogram JMb/ De, and drawing the di- 
agonal MD, extending the same to 
D’ soas to make MD’/=MD, we 
obtain the line DD’; the vertical 
section passing through this line is 
the correct macrodiagonal section. 
The inclination of a to the new ma- 
crodiagonal DD’, is still a right angle; as also the inclination of a 
to 6, their oblique inclinations may be given them by means of the 
same formulas employed in the diclinate system, except that the 
axis D’D is to be substituted for C’C. The vertical axis 4A’ and 
the horizontal axes EE’ (brachydiagonal) and FF’ (macrodiagonal) 
thus obtained, are the axes ina triclinate form in which a=b=c=1. 
Different values may be given these axes according to the method 
heretofore illustrated. 
