89 



this book deals with general aspects of the subject only, rather 

 than with its applications to a special science 1 ). 



7. We, therefore, prefer to draw attention now to some other 

 subjects relating not only to the symmetry of crystalline matter, but 

 to that of physical phenomena and physical states in the broadest 

 sense of the word. Also in these questions we shall in most cases 

 not go into minute details of such phenomena, but content ourselves 

 with indicating the general way of deduction and only occasionally 

 shall we give some special illustra- 

 tions of what is said, by considering 

 some striking phenomena more in 

 detail. l ) 



In this connection we must re- 

 member in the first place, that for 

 us those cases are of special interest, 

 in which the axis or the axes of 

 symmetry, have a period which is 

 infinitely small, n in the expression : 



& = _ _ being infinitely great. We 



have called axes of this kind, axes 

 of isotropy ; and there are many phy- 

 sical phenomena in which they play a preponderant role. The 

 possible symmetries in systems which possess such axes of isotropy 

 are easily deduced, if the corresponding groups of symmetry be 



Fig 93 



*) It may be remarked that the same views hold in the case where not 

 the crystalforms, but the so-called "solution-bodies" are investigated. In general 

 these approximately polyhedral objects, limited by curved planes, and obtained 

 by the slow action of a solvent on a sphere cut from a homogeneous crystal, 

 are the polar-iorms of the crystal-forms. Therefore, they possess also the same 

 symmetry as these have. The solution- phenomena mentioned were first studied 

 by Lavizzari, and more in detail, with success by Goldschmidt and others. 

 Cf. also: L. Lavizzari, Nouv. Phenom ernes des Corps cristallises, Lugano, 1865; 

 V. Spring, Zeits. f. phys. Chemie, 2, 13, (1888) ; G. Cesaro, Ann. de Chim. et Phys. 

 17, 37, (1889); V. Goldschmidt and F. Wright, Neues Jahrb. f. Miner. (1903); 

 Beil. Bd. 18, 235, (1904); 26, 151, (1908); Zeits. f. Kryst. 38, 656, (1904); 

 50, 459, (1912); O. Miigge, Festschr. H. Rosenbusch, (1906). p. 96; A. John- 

 sen, 820 Vers. Deuts. Naturf. und Aerzte, Konigsberg, (1910); W. Burkhardt, 

 Inaug, Diss., Leipzig. (1911); W. Schnorr, Zeits. f. Kryst. 54, 289, (1914); etc. 



*) Cf. also: G. Kirchhoff, "Vorlesungen iiber mathematische Physik" Mechanik, 

 page 389, 390. (1876), where the principle of symmetry is used in the study of 

 the phenomena of elasticity of solid bodies; ibidem, p. 240 243; 378; etc. 



