2 Mr. W. Barlow on Crystal Symmetry. 



different individuals possessing some lower type of sym- 

 metry, which are found interlocked or intercalated, are so 

 related that their arrangement more or less closely resembles 

 that proper to a single crystal of a higher type. 



The tendency to persist in regarding external form as the 

 one proper index to the symmetry is meanwhile evidenced by 

 the common use of the term optical anomalies to designate 

 some of the discrepancies alluded to ; the use of this term 

 seeming to imply that the classification of crystals has to be 

 determined by the external form, and that any incongruity of 

 the internal structure with the result is to be regarded as 

 exceptional. If, however, it is asked whether it has ever 

 been the practice to admit that the symmetry of the arrange- 

 ment of individual crystals in a group, and not the symmetry 

 of each individual considered alone, is to be taken into 

 account in a systematic classification of crystals, the reply is 

 in the negative — the grouping of crystal individuals has 

 always been treated separately, and no notice has ostensibly 

 been taken of it for the purposes of classification ; it is only 

 in cases where ignorance of the nature of the internal struc- 

 ture has led to a group of differently-orientated crystal 

 individuals being for a time regarded as a single individual, 

 that the form of the group instead of the form of the individual 

 has been made the basis of the classification ; e.g. crystals of 

 leucite, formerly regarded as belonging to the regular system, 

 are now known to be rhombic twins. 



Having regard to the facts just alluded to, it is somewhat 

 remarkable that the important work of deducing the existence 

 of 32 classes of crystal symmetry from first principles lias 

 been based on crystal form and not on internal structure. 

 Thus Gadolin, in his classical work on the subject, defines 

 likeness of two directions in a crystal as depending on the 

 similarity of their disposition with respect to the faces of the 

 crystal*. And Hessel, the original discoverer of the 32 

 classes f, treats crystal symmetry purely as a matter of simi- 

 larity of position with respect to one another of lines and 

 planes which obey Haiiy's law of rational indices J. 



Clearly it is a valid objection to this reference of the 



* Gadolin, " Meraoire sur la deduction d'un seul principe de tous les 

 systemes cristallographiques avec leurs subdivisions," Acta Soc. Scient. 

 Fennica, ix. 1867; and separate, Helsingfors, 1871. Translated "by 

 Groth, Ostwald's Klassiker d. exakt. Wiss. No. 75, 1896. 



t See L. Sohncke : "Die Entdeckung des Eintheilungsprincips der 

 Krystalle durch J. F. C. Hessel," Zeitschrift filr Kryst. xviii. p. 486. 



\ Hessel's " Krystallometrie," in Ostwald's Klassiker der exakten 

 Wissenschaften, Nr". 88 & 89. 



