348 SCIENCE PROGRESS 



between corresponding crystal faces on any number of specimens 

 of the same substance however the faces differ in size; (c) the 

 varieties of symmetry indicated by the various kinds of cleavage 

 and by the different relative dispositions of the crystal faces 

 in different substances ; (d) the way in which crystals grow. 



The phenomenon of supersaturation is important in con- 

 nection with the last. Solutions of many substances saturated 

 at a certain temperature can be cooled far below that temperature 

 without depositing crystals; crystallisation is as it were held 

 back owing to the lack of a nucleus around which the structured 

 edifice can be built up. A sufficient number of particles cannot 

 get into position at the same time. If however a single crystal 

 of the substance be introduced into the solution, the appropriate 

 particles can instantly marshal themselves upon the pattern 

 thus introduced among them and crystallisation proceeds. The 

 supercooling of liquids is another phenomenon of the same 

 order. The introduction of a particle of the solid substance into 

 a supercooled liquid provides a nucleus upon which the liquid 

 particles can arrange themselves. All such phenomena point 

 to a definite arrangement of particles in crystalline matter. 



The discovery of liquid crystals has been already mentioned. 

 These substances, of which cholesteryl chloride is an example, 

 give evidence of being arranged structures : while still in the 

 liquid condition, the}'' exhibit optical properties generally asso- 

 ciated only with crystalline solids ; and if drops of such sub- 

 stances be suspended in other liquids they assume not spherical 

 but other geometrical forms. These liquid crystals are im- 

 portant as forming a link between the solid and the liquid states. 



The Growth of the Mathematical Theory of 

 Crystal Structure 



It is not possible in this short account to give more than 

 a general idea of the salient points of the mathematical treat- 

 ment of the subject just referred to. 



The form of the theory of crystal structure, based on 

 Haiiy's great discovery, which obtained general acceptance and 

 held complete sway for many years was that developed by 

 Bravais. He supposed crystals to be composed of identical 

 similarly orientated detached particles and attributed the 

 symmetry observed, partly to the uniform distribution of these 



