The Molecular Tactics of a CrystalKelvin, William Thomson, Baron
Science
The Molecular Tactics of a Crystal
Kelvin, William Thomson, Baron
Crystallography, Mathematical
Considering now the three fours of parallel edges of the
parallelepiped, let the straight lines of one set of four be altered to
equal and similar parallel curves in the manner which I have described;
and proceed by the same rule for the other two sets of four edges. We
thus have three fours of parallel curved edges instead of the three
fours of parallel straight edges of our primitive parallelepiped with
corners (each a point of intersection of three edges) unchanged.
Take now the quadrilateral of four curves substituted for the four
straight edges of one face of the parallelepiped. We may call this
quadrilateral a curvilineal parallelogram, because it is a circuit
composed of two pairs of equal parallel curves. Draw now a curved
surface (an infinitely thin sheet of perfectly extensible india-rubber
if you please to think of it so) bordered by the four edges of our
curvilineal parallelogram, and so shaped as not to cut any of the
substance of any molecule of the assemblage. Do the same thing with
an exactly similar and parallel sheet relatively to the opposite face
of the parallelepiped; and again the same for each of the two other
pairs of parallel faces. We thus have a curved-faced parallelepiped
enclosing the whole of one molecule and no part of any other; and by
similar procedure we find a similar boundary for every other molecule
of the assemblage. Each wall of each of these cells is common to two
neighbouring molecules, and there is no vacant space anywhere between
them or at corners. Fig. 7 illustrates this kind of partitioning by
showing a plane section parallel to one pair of plane faces of the
primitive parallelepiped, for an ideal case. The plane diagram is in
fact a realization of the two-dimensional problem of partitioning the
pine pattern of a Persian carpet by parallelograms about as nearly
rectilinear as we can make them. In the diagram faint straight lines
are drawn to show the primitive parallelogrammatic partitioning.
It will be seen that of all the crossings (marked with dots in the
diagram) every one is similarly situated to every other in respect to
the homogeneously repeated pattern figures: _A_, _B_, _C_, _D_ are four
of them at the corners of one cell.
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