112 Mr. R. T. Forstcr w« Mt' 



new molecules attached, this external row lost its polarities, then 

 dodecahedral laces will appear. In like manner, if only the 

 extreme corner molecule lost its polarities, then all would be 

 covered but that one, and the plane formed would beloug to the 

 octahedron. In fact, we have the molecules becoming consecu- 

 tively attached in one direction, and the polarities of those mole- 

 cules to which they are to be attached being consecutively 

 removed in exactly an opposite direction ; of course, then, after 

 a certain number of m.olecules have become attached, no more 

 molecules will be attached on that layer, and a new layer will 

 be commenced in exactly the same manner, and exactly the same 

 result will ensue, the same number being dropped as in the last 

 layer, and the consequence being that a plane will be formed 

 being a tangent plane to those molecules to which no others 

 have become attached. It might appear at first sight that this 

 is not true, since the number of molecules in each face are as 

 the squares of the number of molecules along an edge ; but we 

 are to remember that all those molecules equidistant from the 

 centre have new molecules attached to them at the same time ; 

 therefore the time which elapses while the whole face is being 

 covered is only that which elapses while a single row is being 

 covered. 



There is one description of crystals which have been left 

 nearly altogether unnoticed by all writers on this subject, namely 

 hemihedral forms. The only person who mentioned them at all 

 was Wollaston, and he contented himself with proposing a theory 

 for the formation of the tetrahedron, leaving quite unexplained 

 the union of the cube with the tetrahedron (although his own 

 thoughts were elicited by the octahedral cleavage of cubical fluor 

 spar). His theory of the formation of the tetrahedron I have 

 already shown to be faulty. I will now endeavour to show 

 under what circumstances hemihedral forms without parallel 

 faces will be produced. The theory I am about to put forward 

 is not sufficient to explain the formation of crystals with parallel 

 faces ; but this does not invalidate it, inasmuch as, from the 

 well-known fact that forms of these two denominations are never 

 found united, we can safely infer that there is something essen- 

 tially different in their nature ; indeed we might say, that if any 

 theory was capable of accounting for both, the fact of its doing 

 so would be an argument for its rejection. If the molecules be 

 spheres, each having twelve poles, or centres of attractive force, 

 on its surface, and these poles were arranged as shown in fig. 7, 

 the form which such molecules would assume is the tetrahedron. 

 (The intersection of the great circles in the figure show the 

 position of the poles ; each great circle is divided into six equal 

 parts bythe others,and they cut each other at angles of 70°31'44".) 



I 



