222 The A^nerican Naturalist. [April, 
reduced by cleavage to the same solid figure, this cleavage solid 
has the form of the ultimate particles into which any crystal 
may, in, imagination, be separated by repeated subdivision, 
and that this is, therefore, the form of the structural unit, al- 
though not necessarily that of the chemical molecule. Hence 
a crystal is to be regarded as constructed of polyhedral parti- 
cles, having the form of the cleavage fragment, placed beside 
one another in parallel positions. A crystal of salt, for exam- 
ple, which naturally cleaves parallel to the faces of the cube, is 
constructed of cubic particles. 
Upon the relative dimensions of the structural unit depends 
the form assumed by the crystals of a given substance. 
This theory not only accounts for the existence of cleavage, 
but further defines the faces which may occur upon crystals of 
a substance having a given cleavage figure ; for, if once it is 
assumed that a crystal-face is formed by a series of the parti- 
cles whose centres lie in a plane, it follows that all such planes 
obey the well-known law which governs the relative positions 
of crystal- faces. 
A natural advance was made from the theory of Haiiy, with- 
out detracting from its generality, by supposing each polyhe- 
dral particle in Hauy's system to be condensed into a point at 
Its centre of mass, so that the positions of the molecules, and 
therefore of the crystalline planes, remain the same as before ; 
but the space occupied by a crystal is now filled, not by a con- 
tmuous structure resembling brickwork, but by a system of 
separate points. 
In such a system of points, if the straight line joining any 
pair be produced indefinately in both directions, it will carry 
particles of the system at equal intervals along its entire length ; 
in other words, all the structural molecules of a crystal must lie 
at equal distances from each other along straight lines. The 
mterval between particles along one straight line will, in gen- 
eral, be different from those along another, but the molecular 
mtervals along parallel straight lines will always be the same. 
Bravais,- following in the steps of Delafosse and Franken- 
' " Etudes cristallographiques." i (Paris, 1866.) 
