On the Intimate Structure of Crystals. 271 



range, before exerting mutual action on each other ; in the solid, on 

 the other hand, they are so closely packed that in many cases the 

 abstraction of heat is accompanied by only a very inconsiderable 

 approach of the atoms to nearer proximity. Thus among metals, 

 that having one of the highest coefficients of expansion is indium ; 

 but this only contracts 0'00004< of its bulk for every degree centi- 

 grade that it is lowered below the ordinary atmospheric temperature ; 

 nor does it continue to contract at this rate, but at a continually 

 diminishing one, as its temperature is progressively reduced. A 

 metal with a very low coefficient of expansion is iridium, which 

 loses only O000006 of its volume for every degree that it falls in 

 temperature. Among non-metallic elements we may point to the 

 remarkable case of the diamond, which, with the small coefficient of 

 O'OOOOOllS, actually ceases to contract at all when cooled below 

 42 C. It may be possible by other means to effect greater reduc- 

 tions in the volume of solids, but so far as the withdrawal of thermal 

 energy is concerned, it evidently accomplishes but very little, at 

 least in the case of solids treated at a temperature considerably 

 below their fusion points. 



The assumptions made in the study of gases are of the fewest and 

 simplest kind, but they include one that is of fundamental import- 

 ance in the investigation of solids, viz., that in some sense an atom 

 is a body occupying space ; it is only by making this admission that 

 deviations from important laws like Boyle's find an explanation. 



The dominion of an atom over a certain region of space endows 

 that space with form ; what that form is we do not know, though we 

 may eventually discover. In the absence of knowledge it is permis- 

 sible to make some kind of assumption, and then to endeavour to 

 discover how far the consequences of that assumption accord with 

 ascertained facts. I propose to make the simplest assumption 

 possible, and to regard the volume of space appropriated by an atom 

 as having the form of a solid of revolution, and very generally of a 

 sphere. Within this space there exists something, the energy of the 

 atom, or a force of repulsion, or both, which preserves it from inva- 

 sion by other atoms' ; outside it there is something, a pressure or force 

 of attraction, which drives the atoms as close together as possible 

 without causing interpenetration. It will probably be found also 

 that these influences, pressures, and thrusts, are directed, or that the 

 atoms are polar. 



Dalton's law of multiple proportions seems to meet with its counter- 

 part in crystallography in Haiiy's law of " the rationality of the 

 indices," and the conception by which Haiiy sought to explain this 

 and other facts relating to the form and structure of crystals 

 presents singular points of resemblance to Dalton's ideas of atoms. 

 Haiiy's views on crystalline structure appear to me to contain the 



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