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grant molecules are spheres, each having six poles on its sur- 
face, and it is owing to the different degrees of force possessed 
by these poles that the different cleavages are due.’ In this 
he is clearly in error, for no matter with what cleavage we 
divide a cube, we will eventually separate every pole from 
every other. 
‘‘ J will, in this paper, confine my observations to the first 
system, but it will be readily perceived that they apply (mu- 
tatis mutandis) word for word to the other systems. 
** The cleavages are of three kinds, cubical, octahedral, and 
dodecahedral ; the cubical we have already explained ; the oc- 
tahedral formation will arise if each spherical molecule have 
twelve poles on its surface, whose position is given by the in- 
tersections of four great circles, having the same inclination 
and relative position as the faces of the tetrahedron; the form 
which they will assume will be the same as Wollaston pro- 
pounded. 
*« Tf each layer of molecules be deficient by one row, planes 
will appear on the edges, which planes belong to the cube; 
we have thus got a compound form consisting of the cube and 
tetrahedron, or in other words, we have a cube with half its 
corners replaced by planes. By other decrements at the edges, 
or corners, we can explain all forms of the first system, except 
hemihedral forms with parallel faces, which never combine 
with forms without parallel faces. 
‘*¢ Thirdly, the dodecahedral formation will result if each 
molecule be a sphere with eight poles on its surface, situated 
with respect to each other in the same positions as the angles 
of a cube; as can be very easily demonstrated. 
*«* Any crystal will of course cleave in whatever direction 
the least resistance is met with. Thus in the cubical forma- 
tion the cleavage is cubical because by such division we sepa- 
rate each molecule from one adjacent molecule only, whereas 
if we divided it in any other direction, we would have to sepa- 
rate each molecule from two or three others. In the octahedral 
