ON THE STRUCTURE OF CRYSTALS. 303 



hexagonal prism, contains two sets of prisms differently orientated. This 

 case will be alluded to again (see p. 327). 



The Sjmce-lattice. 



We next come upon investigations based on Haiiy's conclusions de- 

 rived from cleavage, but widely differing in essential character from them, 

 in which this property is found to take quite a subordinate place, and 

 is treated merely as evidence of internal symmetry, the question of the shape 

 of the ultimate units having sunk into insignificance. We find, indeed, 

 that while Haiiy's discovery of the law of rational indices proved to be 

 an epoch-making one, his suggestions as to the nature of the ultimate 

 particles, based on cleavage, came very soon to be treated as merely 

 diagrammatic, and as expressing more than is justified by the experimental 

 facts. 



Without following Haiiy in his speculations and arguments, or striking 

 out any new path of deduction for themselves, Weiss • and Mohs ^ by 

 their well known method placed in a far clearer light the ascertained 

 facts, not only those respecting outward form, but also the optical facts 

 relating to double refraction. By this time the occurrence of many new 

 varieties of symmetry had been recognised both on morphological and on 

 physical evidence ; in particular the existence of the monosymmetric 

 system had been established, and attempts were being made to classify the 

 varieties of crystal forms according to their symmetry. 



To this period belongs the remarkable work of Hessel,^ an investigation 

 which, though published in 1830, remained overlooked until the year 

 1891, when it was unearthed by Sohncke.'' 



Hessel considered the general question of the possible symmetry of 

 solid plane-faced figures, and then, by imposing the limitation that these 

 figures should obey Haiiy's law of rational indices, deduced the result 

 that only thirty-two types of symmetry are possible for crystals. This 

 achievement is all the more surprising since, at the time when Hessel 

 wrote, comparatively few of these thirty-two types had been discovered 

 in nature. The same important result was independently rediscovered by 

 Gadolin (1867), to whose methods reference will presently be made.'' 



In the previous year (186G) Viktor von Lang, in his treatise on 

 crystallography,'' had very clearly laid down the principles of crystal 



' 'De indagando foiraarum crystallinarum cliaractoro geometrico principal! 

 dissertatio.' LipsiiB, 1809. ' Uebersichtliche Darstellung der verschiedenen natiir- 

 lichen Abtheilungen der Krystallisationssysteme ' (^Ahhandl. d.Berl.Ak.d.Wissen- 

 schaft, Phys. Klasse, 1S14-15, pp. 289-336). 



- ' Tiie cliaracters of the classes, orders, genera, and species ; or, the character- 

 istics of the Natural History System of Mineralogy,' Edinburgh, 1820. Treatise on 

 Mineralogy ; or the Natural History of the Mineral Kingdom (translated from the 

 German), Edinburgh, 1825. 



., 3 Article ' Krystall' in Gehler's PliysUtal. Worfcrbuch, 1830, v. 1023-1340. Also 

 ' Krystallometrie oder Krystallonomie und Krystallographie.' Leipzig, 1831, and 

 reprinted in 2 vols, in Ostwaid's Klass. d. exaJit. \Viss., 1897, Nos. 88 and 89. 



* 'Die Entdeckung des Eintheihingsprincips der Krystalledurch J.F. C. Hessel,' 

 Zeits.filr Kryst. J/i?t., 1890, xviii. 486. Gomp Groth's translation of Gadolin's work 

 on the same subject, Ostwaid's Klass. d. exalden TFms., No. 75, p. 8G. 



* See below, p. 309. 



^ Lelirhuoh der ErystallograpJde, Wien, 1866. Thirty years later he shows that 

 theSe classes may be obtained on the principles established in this work. Sitzung^l>. 

 Ak. Wien, 1896, cv., II a, p. 362, and Ann. Phys. Chem., 1896, Iviii.pp. 716-7^i. 



