ISOMORPHISM. 139 



The angles of crystals are, therefore, affected in their values 

 within small limits by causes of an accidental character, and 

 absolute identity in crystalline form may require the concur- 

 rence of circumstances which are not found together in the 

 ordinary modes of producing many crystals, which are still 

 truly isomorphous. 



2. It appears that the same body may assume in different 

 circumstances,, two forms which are totally dissimilar and have 

 no relation to each other. Thus sulphur on crystallizing from 

 solution in the bisulphuret of carbon or in oil of turpentine,, 

 at a temperature under 100, forms octohedrons with rhombic 

 bases, but when melted by itself and allowed to cool 

 slowly, it assumes the form of an oblique rhombic prism 

 on solidifying at 232. These are incompatible crystalline 

 forms, as they cannot be derived from one common form. 

 Carbon occurs in the diamond in regular octohedrons, and in 

 graphite or plumbago in six-sided plates, forms which are like- 

 wise incompatible. Sulphur and charcoal have each, therefore, 

 two crystalline forms, and are said to be dimorphous, (from 

 cig, twice, and juop^/, shape). Carbonate of lime is another 

 familiar instance of dimorphism, forming two mineral species, 

 calc-spar and arragonite, which are identical in composi- 

 tion, but differ entirely in crystalline form. G. Rose has 

 lately shewn that the first or second of these forms may 

 be given to the granular carbonate of lime formed artificially, 

 according as it is precipitated at the temperature of the air, 

 or near the boiling point of water. Of its two forms, carbonate 

 of lime most frequently affects that of calc-spar; but carbonate 

 of lead which assumes the same two forms, and is therefore 

 doubly isomorphous with carbonate of lime, chiefly affects that 

 of arragonite, and is very rarely found in the other form. Had 

 these carbonates, therefore, been each known only in its com- 

 mon form, their isomorphism would not have been suspected, 

 an important observation, as the want of isomorphism between 

 certain other bodies may be caused by their being really dimor- 

 phous, although the two forms have not yet been perceived. 

 There is no physical impossibility in a body's assuming three 

 different forms, or being /ri-morphous as well as dimorphous, 

 but no case of trimorphism has been hitherto observed. 



3. The observation of the isomorphism of bodies is of the 

 greatest value as an indication that they possess a similar con- 



