177 



nearly 60 or 1 20 ; in this case the vertical binary axis of the crystal 

 has the direction of an approximately hexagonal or trigonal axis 

 of the space-lattice, and the rhombic crystal mentioned above is 

 a real pseudo-hexagonal or pseudo-trigonal limit-form. If a monoclinic 

 crystal has an angle /? only slightly different from 90 ,while, moreover, 

 in its axial ratio a : b : c, one or two of the quotients are close to 

 unity, the said monoclinic crystal has a space-lattice which is dis- 

 tinctly pseudo-tetragonal or pseudo-cubic. 



Such pseudosymmetrical crystals will often betray in their external 

 habit a certain approximation to higher symmetrical forms: thus 

 rubidium-nitrate has a strikingly simulative hexagonal aspect '). 

 Or they will have a definite set of gliding-, or of cleavage-planes 

 which are nearly parallel to the faces of a crystal-form with a 

 higher symmetry. 



Pseudosymmetrical crystals are, therefore, those which closely 

 simulate a higher symmetry than they really have ; this higher sym- 

 metrical form is in many respects like an ideal model to which the 

 proper symmetry of the crystal tends, without ever reaching it. 



Now it is one of the most remarkable facts observed in inorganic 

 nature, that such pseudosymmetrical crystals seem to exhibit a strong and 

 undeniable tendency to increase their deceptive appearance yet more 

 by repeated twinning and regular aggregation-). 



The new complexes thus produced are called mimetic forms; 

 the phenomenon itself bears the name of mimicry 3 ). This mimicry 

 is often so perfect, that only a careful study of the optical and physi- 

 cal properties, which in general reveal the true symmetry of the real 

 molecular arrangement of the crystal, can show its true character. 

 As the optical properties are, therefore, evidently often in discordance 



*) F. M. Jaeger, Zeits. f. Kryst., 43, 588, (1907). 



2 ) G. Friedel, (Bull, de la Soc. miner., 29, 14, (1906); Dictionnaire de Wurtz, 

 2ieme Supplem., art: Mdcles\ Cours de Cristallographie i 2ieme Ed., (1918); etc.), is 

 of opinion that the approximation to special values of the parameters, which is 

 often completely accidental, is sometimes the primary cause of the twin -formation 

 of this kind, and not true "pseudosymmetry" as such. Thus, for instance, boleite 

 is not "pseudo-cubic", but tetragonal, with a : c = 1 : 3,996, or about 1 :4. And, 

 according to Friedel, it is this peculiarity, accidental as it may be, that should be 

 the cause of the crystals appearing in an aggregation of several individuals, which 

 apparently imitates the symmetry of a "cubic" individual. 



3 ) G. Tschermak, Lehrbuch der Mineralogie, (1897), p. 91; O. Miigge, Neues 

 Jahrb. f. Miner., Beil. Bd., 14, 245, (1901); 16, 335, (1903); P. Fischer, Disser- 

 tation, Gottingen, (1911); V. Goldschmidt, Zeits f. Kryst., 43, 353, (1907). 



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