278 Mr. L. Fletcher's CrystaHographk Notes. 



This interpretation can never have been intended by Haidinger. 

 At the beginning of the series he had remarked that, for the 

 precise definition of a twin-growth, two planes must be given: — 

 first, the twin-plane, or plane of rotation, to indicate the 

 relative directions of corresponding faces of the two individuals ; 

 and, secondly, the composition-plane, or plane of junction, to 

 indicate their relative positions. Haidinger' s initial sentence, 

 "regular composition takes place parallel to a plane of {1 1}, 

 or perpendicular to the terminal edges of {1 1 1}," may there- 

 fore refer either to the plane of twinning or to that of com- 

 position, and to this extent is indefinite. But seeing that 

 no plane of {101} is perpendicular to a terminal edge of 

 {1 1 1}, the above sentence must indicate two distinct cases 

 if the reference be to a composition-plane, while if the refer- 

 ence be to a twin-plane, only a single case is indicated ; for, 

 as will be shown later, a rotation through two right angles 

 in a plane of the octahedron {101} is crystallographically 

 identical in its results with a rotation through two right 

 angles perpendicular to (or round) a terminal edge of the octa- 

 hedron {1 1 1}. That Haidinger only recognizes a single case 

 is evident from the italics in the next line of the above quotation. 

 As a matter of fact, the figure of the twinned octahedron, 

 repeated from his first paper, shows the plane of composition 

 as perpendicular to the twin plane, though this is only evident 

 after careful inspection. His final reference to the original 

 memoir without calling attention to any deviation therefrom, 

 shows that he was still in accord with the explanation there 

 given. 



From this we conclude that either a careful study of this 

 later paper of Haidinger on the regular composition of crys- 

 tallised bodies, or a simple reference to his original memoir 

 on the crystallisations of copper pyrites, would have made 

 clear the fact that Haidinger regarded the composition-plane 

 as perpendicular to the twin-plane (101), though we grant 

 that at first glance his second paper might suggest that the 

 composition-plane is, in some cases at least, parallel to the 

 plane of twinning (101). 



In 1830, Naumann's well-known work* did in fact state 

 the law differently from Haidinger, and assumed the plane of 

 composition to he parallel to that of rotation. In his preface 

 Naumann makes special mention of the help he had derived 

 from Haidinger's series of papers on regular composition, and 

 in his description of these particular growths adopts some of 

 the figures there given. It seems cpiite impossible for this 

 deviation from Haidinger to have been introduced wittingly; 

 * Lehrbuch tier reinen und angewimdten KrystaUographie, 1830. 



