Plates 8, 9.] 1. In the preceding Part II we have shown that Neumann bands are lamellae, parallel to the {112} planes, which are in twin orientation with respect to the matrix. It remains to show how the nature of the movement, from which a band results, can be determined. For this purpose we have to find a means of measuring the extent and the direction of the movement of the matrix on one side, with respect to that on the other, when a band of measurable width is formed. Since all the bands

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... e not formed simultaneously, it must happen that the tracks of some will pass, through the matrix, across the tracks of others formed earlier. The displacement of the parts of an earlier track, with respect to one another, produced during the formation of a later band, can then be used to determine the movement from which the later band results. 2. There is one type of crossing, of one band by another, to which this method does not apply. It is convenient to begin with the consideration of this type, since it throws light upon the others. The {112} planes of the cubic system can be grouped in four sets of three. The three planes of each set intersect along a trigonal axis and each plane is inclined at 120° to the other two ; it is convenient to describe them as " associated " planes. The four sets can be visualised by the aid of fig. 6 .* They are, respectively, the planes 1, 5 and 9 ; 2, 8, 12 ; 3, 6, 11 ; 4, 7, 10. Each plane of the first set is, in fig. 6 , perpendicular to the plane of the paper as is the trigonal axis through P in which they intersect. The trigonal axes associated with the other sets are parallel to UX, VQ and WT, respectively. 3. Fig. 19 is intended to represent the problem which arises when a band * parallel to one of a set of associated planes is produced in a matrix already crossed by a band parallel to another plane of the same set.