298 EEPORT— 1901. 



advance being suggested or confirmed by the knowledge obtained from the 

 invesrigatiou of the morphological and physical characters of crystals. 

 Since the means at our disposal do not admit of the proof of the existence 

 of similarly repeated parts in ciystals by direct observation, any such 

 proof jnust necessarily be indirect, and, to be conclusive, the properties of 

 homogeneous structures mathematically deducible must be shown to be 

 in complete harmony with those actually observed in crystals. 



Early Views. 



Many of the physical properties of matter may be explained without 

 any idea of structure or grain, and some physicists have so defined homo- 

 geneity ; ^ but such definitions merely ignore and do not preclude the 

 conception of a homogeneous repetition of definite parts. ^ Indeed, 

 the call for such a conception seems imperative. Without structure it 

 would be difficult, for example, to explain the striking polarity displayed 

 by such a mineral as tourmaline. From considerations based upon known 

 facts in physics and chemistry, it has been shown that the dimensions 

 of the atoms, or, perhaps, the distances between their centres, though 

 extremely small, must lie within definite limits.^ 



That by the packing together of similar bodies artificial systems may 

 be obtained whose symmetry of form closely resembles that of certain 

 crystals was perceived nearly two- and-a-half centuries ago by Robert 

 Hooke from a study of the forms presented by alum. Thus he says : 

 ' I think, had I time and opportunity, I would make probable, that all 

 these regular Figures, that are so consj^icuously various and curious . . . 

 arise only from two or three positions or postures of Globular particles, 

 and those the most plain, obvious and necessary conjunctions of such 

 figur'd particles that are possible. . , . And this I have ad oculum demon- 

 strated with a company of bullets and some few other very .simple bodies ; 

 so that there was not any regular Figure, which I have hitherto met 

 withal, of any of those bodies that I have above named, that I could not 

 with the composition of bullets or globules and one or two other bodies, 

 imitate, even almost by shaking them together.' ■* 



Just after Hooke had put forward his idea, evidence of the regularity 

 of crystal structure was supplied by the observation of Nicolaus Steno,^ 



' Cf. the definitions given by Biot in ' Mcmoire sur la Polarisation lamellaire,' 

 Mem,. Acad. Sci., 1842, xviii. p. 633, and by Thomson and Tait in Natural Philo- 

 soj/hy, § 675. 



- The following definition of a crystal, based exclusiyely on physical behaviour, 

 was first enunciated by Groth : ' A crystal is a homogeneous solid body whose elasti- 

 city differs in different directions within it' {Ber. d. Berliner Ah, 1875, p. 549). As 

 Schonflies remarks, it is now generally admitted that the constancy of the crystal 

 substance is revealed by its physical properties rather than by its external form, the 

 latter being indeed more or less fortuitous and dependent on the conditions of growth 

 (see Schonflies Krystallsr/iteme und Krystallstru ctvr, p. 5). 



' Lord Kelvin (Sir W. Thomson), Nature, 1870, vol. i. pp. 551-553, reprinted 

 Appendix F, ' Natural Philosophy,' by Thomson and Tait. It is interesting to note 

 that certain of Jordan's groups of movements, in which some of the minimum dis- 

 tances separating similarly repeated ultimate parts are infinitesimally small as 

 compared with the others, are incompatible with the symmetry of actual crystal 

 forms, i.e., forms obeying the law of rational indices (see below, p. 312). 



■* MicrograpMa, London, 1665, p. 85. 



5 Be solido intra solidnmnaturaliter contento dissertationis prodromus, Florentiffi, 

 1669 (English translation, London, 1671). 



