175 



As is known, this theorj of Gibbs and Curie's plays a very im- 

 portant part in the crystallograpliical literature. Frequent crystallo- 

 graphical applications have been made of it'); it has been now and 

 then extended by the introduction of "side energies" and "angular 

 point energies" by the side of "surface energies" k^, /f, . . ., and by 

 making the former have a share in the determination of the equilibrium 

 figure '') ; of late years criticism has not been wanting either, which 

 now and then even comes to a full rejection of Gibes and Curie's view.') 



On the other hand it seems that except Sohnke's indications *), 

 which concur with Bravais' views, no attempts have been made as 

 yet to interpret the energetic theory of Gibbs and Curie in a viole- 

 cular scheme. Such an attempt would be the more desirable as there 

 is in this region a whole series of dark or paradoxical points to be 

 analysed. 



In view of the great difficulties which are to be overcome here, 

 I should like to confine myself to a single of these points, and 

 demonstrate how this can entirely be elucidated by the aid of an 

 extreme simplified molecular scheme. It is seen the more clearly 

 on this occaeion how much there remains to be done to elucidate 

 other points. 



^ 2. Does the capillarity constant of a crystal plane depend con- 

 tinuously or discontinuously on its orientation ? The problem of the 

 vicinal planes. 



The polyhedrical shape of the crystals and the law of the small 

 rational indices easily gives rise to the sup\>os\{\on oi & discontinuous 

 dependence ; accordingly it seems to have been made, at least impli- 

 citly by most cryslallographers, as soon as they made use of Gibbs 

 and Curie's theory. Explicitly it is found expressed in two often 



') Chiefly to be able to draw some conclusions ou the structure from the 

 crystal form see: I-'eodorow, Z. f. Kryst. Vol. 34 — 53, compare also the appli- 

 cation to twin formations H. Hilton. The energy of twin crystals. Mineraiog. 

 Magazine 15 (1909) p. 245. 



2) Brillouin. Ann. Ghim. Phys [7] 6 (1895) p. 540; Vernadsky. Bull, de la 

 Soc. Imp. de Naturalisles de Moscou 1902 p. 495; P. Pawlow. Zschr. f. Kryst. 

 40 (1905) 189; 42 (1906) 120; Zschr. I', phys. Ch. 72 (1910) p. 385. 



') A. Berthüud. Journ. de Ghim. phys. 10 (1912) p. 624 ; G. Friedel. Journ. 

 de chim. phys. 11 (1913) p. 478. — Of. also J. J. P. Valeton. Thesis for the 

 doctorate, loc. cit. 



*) F. SoHNKE. Ueber Spallungsflachen und natiirliche Krystallfl. Z. f. Kryst. 13 

 (1888) p. 214. 



