Mr. L. Fletcher's CrystaUographic Notes. 279 



for attention is not directed to the difference in the explana- 

 tions, and, further, it is unlikely that Nanmann had been able, 

 so soon after the publication of Haidinger's work, to under- 

 take a special and minute study of this particular law. 



"We feel that the above reasoning shows clearly enough that 

 Xaumann's statement is a simple misinterpretation of that of 

 Haidinger, and that this can only have resulted from the fact 

 that Naumann referred to the secondary, and not to the ori- 

 ginal, explanation given by the author of the law. 



As Naumann's ' Crystallography ' became the recognized 

 and universal text-book on the subject, this statement, though 

 a mistaken one, has been extensively circulated, and appears 

 probably in every text-book of the present day, though, as 

 might have been expected, the explanation of 1822 is repeated 

 in Haidinger's own manual of 1845. 



In 1868* Sadebeck published the results of his study of 

 specimens of copper pyrites (belonging chiefly to the Berlin 

 collection), and in the explanation of the twins assumed the 

 correctness of Naumann's statement of the law. In a second 

 paper, published in the following yearf, he gives an explana- 

 tion of his position, so very brief and so clearly illustrative of 

 the present difficulties that a translation is given here: — 



" In my memoir on copper pyrites I have wrongly stated the 

 law of twinning; for I have supposed the twin-plane to be also 

 the composition-plane. According to this, one pair of tetra- 

 hedron-faces should meet in a salient angle of 1° 24', and the 

 opposite pair in a reentrant angle of the same magnitude. 

 After I had published the memoir, Haidinger informed me 

 by letter that this was not the explanation he himself had 

 given, as may be seen from his statement in the 'Edinburgh 

 Journal of Science/ which runs thus: — 'Composition takes 

 place perpendicular to the terminal edges of P.' In conse- 

 quence of this friendly private communication from so famed 

 a Nestor of the science, I subjected the crystals again to a 

 careful study. The result was that I found it impossible to 

 say whether the tetrahedron-faces actually coincided, or formed 

 an angle of 1° 24/. This led me to retain my old view, since 

 that law seemed to me a simpler one which regarded a plane 

 of the form {101} as at once twin-plane and composition- 

 plane. But if I now apply the general law for tetrahedral 

 twins to this case, it follows that, as faces of the positive 

 tetrahedron of the one individual are adjacent to faces of the 



* "Ueber die Krystallformen des Kupferkieses/' Zeit. d. deutsch. geolog. 

 GeseUsch. p. 605, vol. xx. 1868. 



t " Allgemeines Gesetz fuv tetraedrische Zwillingsbiidung," Zeit. d. 

 deutsch, yeohg. Gesellsch. p. 642, vol. xxi. 1869. 



