An elementary treatise on crystallography - Softcover

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1848 Excerpt: ...of their axes. The formula or the primitive form is (a: b: c). The other octahedrons which occur with the same substance will then be expressed by the following formulas:--( a: b:mc) ( a: mb: c ) (ma: b:c ) (ma: nb: c ) m and n being very simple rational numbers. The three first formula? may be considered as particular cases of the fourth. The number of octahedrons of the fourth system which can occur with one and the same substance is still greater than was the case in the second system of crystals. But, in reality, this number is very limited, and other octahedrons than those expressed by the following formula? are rarely met with:--(a: b: c) (a:b: c) (a. b: 2c). (a: b: %c) (a: b: 3c) together with the limiting forms, obtained by supposing m and n equal to zero or to infinity in the general formula?. In making m or n equal to zero, the octahedron is reduced to a single face, perpendicular to one of the axes of the crystal. We thus obtain:--1st. A face perpendicular to the principal axis, by making c = 0; the notation for this face ought then to be (ma: nb: oc), it is, however, generally expressed by the formula ( cca: cob: c) which supposes it derived from the octahedrons (ma: nb: c) having the axis C, but in which the secondary axes are supposed to have become endless. 2nd. A face at right angles to the first secondary axis, obtained by supposing a = 0; the notation for this face ought then to be (Oa: mb: nc); it has received the formula (a: ccb: ccc); i. e. it is supposed der rived from the octahedrons (a: mb: nc) in which the secondary axis a exists, but in which the axes b and c have become endless. 3rd. A face at right angles to the second secondary axis, obtained by making 6=0; this will then be denoted by (ma: 06: nc); but the formula usually assig...