176 
Book 1II. 
F. Dccre 
ments on 
eges. 
2. Decre 
ments on 
the angles. 
AFFINITT. 
An example of the first law of decrement, or of de 
crement on the edges, has been given, above in conver 
sion of the cubic nucleus to a rhomboidal dodecahedron. 
In that example the decrement consisted of one row of 
particles, and it took place on all the edges. But these 
decrements may be more rapid; instead of one, they 
may consist of two, three, four, or more rows: and in 
stead of taking place on all the edges, they may be con 
fined to one or two of them, while no decrement at all 
takes place on the others. Each of these different mo 
difications must produce a different secondary crystal. 
Besides this, the laminae may cease to be added before 
they have reached their smallest possible size ; the con 
sequence of which must be a different secondary form. 
Thus, in the example given above, if the superposition 
of laminae had ceased before the pyramids were com 
pleted, the crystal would have consisted of 18 faces, 6 
squares parallel to the faces of the primitive nucleus 
and 12 hexahedrons parallel to the faces of the seconda 
ry dodecahedron. This is the figure of the borat of 
lime-and-magnesia found at Luneburg. 
The second law in which the decrement is on the 
angles, or parallel to the diagonals of the faces of the 
primitive nucleus, will be understood from the follow 
ing example : Let it be proposed to construct around 
the cube ABGF (fig. 22.), considered as a nucleus, a 
secondary solid, in which the laminae of superposition 
shall decrease on all sides by single rows of cubes, but 
in a direction parallel to the diagonals. Let ABCD 
(fig. 23.), the superior base of the nucleus, be divided 
into 81 squares, representing the faces of the small 
cubes of which it is composed. Fig. 24. represents the 
superior surface of the first lamina of superposition