126 



of crystallographical phenomena, Bravais' supposition of the 

 parallel orientation of all crystal-molecules appears more particularly 

 untenable: the phenomena of twin-formation, and those concerning 

 the homogeneous deformations along so-called "gliding-planes", 

 prove the incorrectness of this hypothesis in a convincing way. 



The more general solution of the problem: to deduce all 

 possible homogeneous and symmetrical arrangements of equal 

 things, independent of their accidental qualities, was solved by 

 Sohncke 1 ) for the cases in which only symmetry-properties of the 

 first order were considered; afterwards the complete solution, inclu- 

 ding also the symmetry-properties of the second order, was given 

 by Von Fedorow 2 ) and by Schoenflies 3 ), while similar stu- 

 dies on the principle of homogeneity were published by Barlow 4 ) 

 and others 5 ). Of course, as soon as tridimensional arrangements 

 be considered which have also symmetry-properties of the second 

 order, the necessity arises of adopting the possibility in such systems 

 of two kinds of "motifs" which are enantiomorphous with respect 

 to each other. For by the operations of the second order characteristic 

 for the tridimensional pattern, each motif is converted into its 

 mirror-image ; and as soon as the motif itself is deprived of all qua- 

 lities, and therefore of all specific symmetry, its mirror-image must 

 be in general non-superposable with itself. 



Therefore, homogeneous systems in space, possessing also symme- 

 try-properties of the second order, must be built up by two enantio- 



1 ) L. Sohncke, Entwickelung einer Theorie der Krystallstruktur, Leipzig. 

 (1879); Wied. Ann. der Physik., 16, 489, (1882); Zeits. f. Kryst., 13, 214, 

 (1888); 14, 417, 426, (1888); Pogg. Ann. d. Phys., 137, 177, (1869). 



2 ) C. E. Von Fedorow, Symmetrie der regelmdssigen Systeme von Figuren 

 (1890); Zeits. f. Kryst., 20, 25, (1892); 24, 209, (1895); 25, 113, (1896); 28, 

 232, 468, (1898); 31, 17, (1900); 36, 209, (1902); 37, 22, (1903); 38, 322, 

 (1904); 40, 529, (1905); 41, 478, (1906). 



3 ) A. Schoenflies, Krystallsysteme und Krystallstruktur, Leipzig, 1891), 

 p. 237; Zeits. f. Kryst., 20, 359, (1892); 54, 545, (1915); 55, 323, (1916). 



4 )' W. Barlow, Nature, 29, 106, 205, (1883); Chem. News, 53, 3, 16, Zeits. f. 

 Kryst., 23, 1, (1896); 25, 86, (1897); 27, 449, (1897); 29, 433, (1899). 



5) L. Wulff, Zeits. f. Kryst., 13, 503, (1888); 14, 552, (1888); E. Blasius, 

 Ber. d. bayr. Akad. d. Wiss. Miinchen, 19, 47, (1889); Zeits. f. Kryst., 19,512, 

 (1892); C. Viola, ibid., 31, 114, (1900); 35, 229, (1902); 41, 521, (1906); 

 A. Nold. ibid., 40, 13, 433, (1905); 41, 529, (1906); 48, 321, (1911); F. Haag, 

 Zeits. f. Kryst., 14, 501, (1888); K. Rohn, ibid., 35, 183, (1902); J. Becken- 

 kamp, Zeits. f. Kryst., 44, 576, (1908); 45, 225, (190); 47, 35, (1910); E. 

 Riecke,. Zeits. f. Kryst., 36, 283, (1902). 



