87 



il plinioiiK na and physical states in the broadest sense of th- 

 ird. Also in these questions we shall in most cases not go into 



limit*' (It-tails of such phenomena, but content ourselves with indi- 

 tlu- general way of deduction and only occasionally shall we 



ive some special illustrations of what is said, by considering some 



triking phenomena more in particular. 

 In this connection we must remember in the first place, that 



>r us those cases are of special interest, in which the axis, or the 



ces of symmetry, have a period which is infinitely small, n in the 



27T 



cpression : = - being infinitely great. We have called axes of 



rv 



lis kind, axes of isotropy ; and there are many physical phenomena 



which they play a preponderant 

 >le. The possible symmetries in 

 stems which possess such axes of 

 )tropy, are easily deduced if the 

 >rresponding groups of symmetry 

 considered as the limiting cases 

 which the endospherial-groups, 

 le dihedron-groups D n , and the 

 relic groups C n , both of the first 

 id of the second order, are approa- 

 ling, when the number n gra- 

 lually increases. 



On closer examination all endo- 

 )herical groups appear to approach 



icn to two definite groups, which will be called spherical groups, 

 id to which we shall attribute the symbols K%> and K^ 

 spectively. 



ie crystal forms, but the so-called ,, solution-bodies" are investigated. In general 

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

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

 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. Phenomemes des Corps cristallises, Lugano, 1865; 

 V. Spring, Zeits. f. phys. Chemie, 2. 13. (1888) ; G. Cesard, 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. 88.656. (1904); 

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

 sen, S2e Vers. Deuts. Naturf. und Aerzte, Konigsberg, (1910); W. Burkhardt, 

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



Fig. 91. 



