34 CRYSTALLOGRAPHY. 



2e : 2 : 1, 4c : 2 : 1, 5c : 3 : 1, and so on; or, giving it a general form, 

 me i n : 1. 



In the lettering of the planes on figures of dimetric crystals, the firs! 

 number (as in the isometric and all the other systems) is the coefficient 

 of the vertical axis, and the other is the ratio of the other two, and 

 when this ratio is a unit it is omitted. 



The expressions and the lettering for the planes are then as follows : 



Expressions. Lettering. 



For square prisms j£ *J \ \ \ \ ™ QJ . j 



For eight-sided prisms ic : n : 1 i-n 



-c , , -, ( 1. me : i : 1 m-i 



For octahedrons \ mjm . -t . + ^ 



( 2. me : 1 : 1 m 



For double eight-sided pyramids, mc : n : 1 m-n 



The symbols are written without a hyphen on the figures of crystals. 

 On figure 14, the plane i-n is that particular i-n in which n = 2, or i-2. 

 in fig. 21 the planes of the double eight-sided pyramid, m-7i, have 

 m = 1 and ft, = 2 (the expression being 1:2:1), and hence it is lettered 

 1-2. In fig. 8 and in fig. 22 it is the one in which m = 3 and n = 3 

 (the expression being 3:3:1), and hence the lettering 3-3. 



The length of the vertical axis c may be calculated as follows, pro- 

 vided the crystal affords the required angles : 



Suppose, in the form fig. 18, the inclination of on plane 1-i to have 

 been found to be 130°, or of i-i on the same plane, 140° (one follows 

 from the other, since the sum of the two, as has been explained, is 

 necessarih '370). Subtracting 90% we have 40° for the inclination of 

 the plane on the vertical axis c, or 50 D for the same on the lateral axis 

 a, or the basal section. In the right-angled triangle, OBC, the angle 

 OBG equals 40 \ If G be taken as a = 1, then BG will 

 be the length of the vertical axis c ; and its value may be 

 obtained by the equation cot 40° = i?C, or tan 50° = BG. 

 On fig. 18 there is a second octahedral plane, lettered 

 4-?', and it might be asked, Why take one plane rather 

 than the other for this calculation ? The determination 

 on this point is more or less arbitrary. It is usual to 

 assume that plane as the unit plane in one or the other 

 series of octahedrons (fig. 16 or fig. 17) which is of most 

 common occurrence, or that which will give the simple st 

 symbols to the crystalline forms of a species; or that 

 which will make the vertical axis nearest to unity ; or 

 that which corresponds to a cleavage direction. 

 The value of the vertical axis having been thus deter- 

 n ined from 1 t the same may be determined in like manner for %-i in 

 the same figure (fig. 18). The result would be a value just half that of 

 BO. Or if there were a plane 2-i, the value obtained would be twice 

 BG, cr BB in fig. 24 ; the angle OBG + 90° would equal the inclina- 

 tion of O on 2-i. So for other planes in the same vertical zone, as 3-i, 

 4.-i, or any plane m-i. 

 If there were present several planes of the series m-i, and their incli« 



