CRYSTALLOGRAPHY. 



449 



Theory, the axis and the prismatic faces. This is the case with 

 W "Y" W ' certain crystals in which the prism is very short, and 

 resembles an hexagonal plate. 



From the preceding account, we see upon what all 

 the different metamorphoses depend, under which the 

 primitive form of crystals presents itself in the second- 

 ary forms, whether simple or compound. Sometimes 

 decrements take place at once upon all the edges, as 

 when the rhomboidal dodecahedron is formed from the 

 cube ; or upon all the angles, as when the regular oc- 

 tahedron is formed from the cube. Sometimes they take 

 place only on certain edges or certain angles. Some- 

 times they are uniform, so that only one law exists of 

 decrements by one, two, three, &c. ranges, which acts 

 upon different edges or angles. Sometimes the law va- 

 ries from one edge to another, or from one angle to an- 

 other ; and this happens chiefly when the nucleus has 

 not a symmetrical form, as when it is a parallelopiped, 

 whose faces differ in the respective inclinations of their 

 faces, or in the measure of their angles. In certain 

 cases, the decrements on the edges concur with those 

 on the angles to produce the same crystalline form. It 

 happens likewise, sometimes, that the same edge, or the 

 same angle, undergoes different laws of decrement, 

 which succeed each other. And, finally, there are a 

 great many cases where the secondary crystal preserves 

 faces parallel to those of the primitive form, and which 

 combine with the faces produced by decrement to mo- 

 dify the figure of the crystal. 



If in the midst of such a diversity of laws, some- 

 times acting solitary, and sometimes in combination, 

 upon the same primitive form, the number of ranges 

 subtracted were likewise very variable ; if, for exam- 

 ple, there were decrements by 20, 30, 40, or a greater 

 number of ranges of molecules, as is very possible in 

 conception ; the multitude of forms which might ex- 

 ist in each mineral species would be sufficient to con- 

 found the imagination ; and the study of crystallogra- 

 phy would present an immense labyrinth, from which, 

 even when assisted by the theory, it would be difficult 

 to extricate one's self. But the force which produces 

 the subtractions appears to have a very limited action. 

 Generally these subtractions take place only by one or 

 two rows of molecules. None have hitherto been ob- 

 served beyond six rows. But such is the fecundity 

 united with this simplicity, that, supposing we confine 

 ourselves to decrements by one, two, three, and four 

 rows, and exclude those that are mixed or intermediate, 

 we find that the rhomboid is susceptible of 8,388,604 

 varieties of crystallization. Doubtless many of these 

 varieties do not occur in nature. But there is reason 

 to expect, that discoveries in this field of enquiry will 

 be made in great numbers for a long time to come. 

 Accordingly, many new varieties of crystals have been 

 described since Hauy published his Treatise on the sub- 

 ject ; indeed they occur in such abundance, that we 

 can hardly examine a group of crystals without ob- 

 serving varieties that have not yet been described. We 

 are greatly within bounds when we say, that, from tlie 

 observations already made, it would be possible to at 



ast double the number of crystals described by Hauy; 

 nor have we reason to believe that the field is in the 

 least degree exhausted. Indeed the number of persons 

 who have turned their attention to crystallography, is 

 much too small to be consistent with a careful survey 

 of the crystals already collected, and deposited in dif- 

 ferent cabinets. 



To have a still more correct idea of the power of 



VOL. VII. PART II. 



crystallization, we must join to that facility which it has Tlieoi y. 

 of producing so many different forms in setting out """ "V"""' 

 from the same form, that of the power wfrich it has of 

 arriving at the same form by different structures. The 

 rhomboidal dodecahedron, for example, which we have 

 seen formed by a combination of cubic molecules, exists 

 likewise in the garnet composed of tetrahedral mole- 

 cules, with isosceles triangular faces. It occurs also in 

 fluate of lime, where it is composed of regular tetra- 

 hedrons. It is even possible for similar molecules, sub- 

 jected to different laws, to present the same result. Thus 

 the regular six-sided prism, which in calcareous spar 

 exists usually in consequence of a decrement on the in- 

 ferior angle, is produced sometimes in consequence of 

 a decrement upon the edges adjacent to that angle. 

 Even the primitive form may be produced by a law of 

 decrement. In those species, particularly where the 

 primitive form has a certain symmetry, as when it is a 

 rhomboid, analogies and properties present themselves 

 on all sides. It seems as if geometry could not touch 

 a single term of the immense series of possibles, without 

 leaving the mark of some interesting truth. 



The preceding details, we presume, are sufficient to 

 give a general and pretty accurate notion of the forma- 

 tion of those secondary crystals, whose molecules are 

 parallelopipeds. But we have observed above, that 

 there are many species in which the molecules are te- 

 trahedrons or triangular prisms. It will be requisite 

 to make a few observations on the method of proceed- 

 ing in such cases. 



Of Secondary Forms, when the Molecules differ from 

 Parallelopipeds. 



It is a character common to all the primitive forms, of seconc!- 

 to be divisible by fractures parallel to their different ary forms. 

 faces. In the parallelopiped, when it is not joined by 

 some other in a different direction, such a division 

 leads us obviously to the form of a molecule, similar to 

 that of the primitive crystal. In the regular six-sided 

 prism, it gives us for a molecule a triangular equilate- 

 ral prism. In the octahedron, it appears to produce 

 molecules of two different forms, some by tetrahedrons 

 and octahedrons ; the same thing happens with respect 

 to the tetrahedron. Various ideas have been suggest- 

 ed by philosophers to get over the difficulty in this 

 case. Dr Wollaston has got rid of it by supposing the 

 molecules to be spherical, and to produce the tetrahe- 

 drons and octahedrons, by combining in fours and sixes. 

 Hauy conceives that the tetrahedron is the integrant 

 molecule, and that the octahedrons are nothing else 

 than empty spaces between the molecules, produced by 

 these molecules uniting by their angles. The subject 

 does not admit of decision ; but as it is of no conse- 

 quence to the theory of crystallography what opinion 

 we adopt, there is no occasion to enter upon the discus- 

 sion of the subject here. The rhomboidal dodecahe- 

 dron, when divided in this manner, gives tetrahedrons 

 of isosceles triangular faces, equal and similar to each 

 other. 



With respect to the dodecahedron with isosceles tri- 

 angular faces, we cannot extract its integrant molecules 

 without dividing it in directions different from those 

 which are parallel to the faces. The cutting plains 

 must pass through the axis, and through the edges con- 

 tiguous to angles of the summit. The molecules ob- 

 tained are irregular tetrahedrons. The other primi- 

 tive forms sometimes admit of division in directions 

 3l 



