44 Mr. J. F. Daniell on Crystallization. 



his calculations is answered by imagining the primitive form 

 in all instances the parallelopipedons (or six-sided figures), 

 which would result from the addition of the vacant spaces to 

 the molecules. 



To such imaginary forms he gives the name of substractive 

 molecules, and he observes that ' the theory would not fail of 

 attaining its principal object, if it were to stop at the parallelo- 

 pipedons which the mechanical division of crystals first affords ; 

 and the species of anatomy which these parallelopipedons 

 undergo, when we attempt to ascend to the true form of the 

 integrant molecule, is an ulterior step, without which observa- 

 tion, rather than theory, would leave something to be desired. 

 The parallelopipedon here represents the unity to which all the 

 results of the theory may be referred ; and it matters little 

 whether or not, beyond this unity, there may be fractions 

 formed of its subdivisions*.' 



With regard to the crystals which derive their origin from 

 the octohedron or tetrahedron, he remarks, * We may consider 

 the decrements which give rise to these forms as taking place 

 by one or more rows of small rhombohedrons, with angles of 

 120 and 60. Whether the solid parts of these rhombohedrons 

 be octohedrons, which leave between each other vacuities of 

 the form of tetrahedrons, or whether the contrary be the case, 

 is perfectly indifferent to the theory, which considers here 

 nothing but the rhomboidal spaces, abstracted from the small 

 bodies which occupy those spaces^.' 



Now, the spheroidical hypothesis shows how these abstract 

 geometrical spaces may be filled up more completely, and with 

 a greater regard to the known laws of attraction, than by the 

 method which suggested itself to the mind of the immortal 

 author of the * Treatise on Mineralogy,' the primary object of 

 whose system is not affected by the change. The calculations 

 founded upon his imaginary substractive particles will still 

 furnish the key to the different series of secondary forms ; and 

 we establish, rather than upset, them by showing that they 

 may be referred to a system of attractions which, when tested 

 by the antagonist powers of heat, chemical affinity, and me- 

 chanical force, is found consistent with the observed pheno- 

 mena in every particular. 



* Hiiliy, Trait6 de JVUjieralogie, tome I, p. 97. f Ibid., p, 473. 



