1 889.] Theories of Crystal Structure. 223 
heim, investigated the possible ways in which a system of 
points may be arranged in space so as to lie at equal distances 
along straight lines — in other words, so as to constitute what 
may be called a solid network {assemblage, Raumgitter). 
The geometrical nature of a network may be best realized 
as follows: Take any pair (o Ci) of points in space, draw a 
straight line through them, and place points at equal distances 
along its entire length (c.,, C3, . . •) ; such a line may be called 
a thread of points {rangee). Parallel to this line, and at any 
distance from it, place a second thread of points (Ai a^, identi- 
cal with the first in all respects ; in the plane containing these 
two threads place a series of similar jequidistant parallel threads 
(A.a^, &c.) in such positions that the points in successive threads 
lie at equal intervals upon straight lines whose direction (o A,) 
is determined by the points upon the first two threads. Such a 
system of points lying in one plane may be called a r^ueb 
{re'seau). Now, parallel to this plane, and at any distance from 
it, place a second web (b^ b,), identical with the first. Finally, 
parallel with these, place a series of similar equidistant webs in 
such positions that the points in successive planes lie at equal 
mtervals i:pon straight lines whose direction (o Bi) is deter- 
mined by the points in the first two webs. 
In this way a network of points is constructed, in which the 
line joining any two points is a thread, and the plane through 
any three points is a web. 
The space inclosed by six adjacent planes of the system, 
having no other points of the network between them is a par- 
allelopiped (o A, Bi Ci), from which the whole system may be 
constructed by repetition, and which may be taken to repre- 
sent the structural element {molecule soustractive) of Haiiy. 
The complete investigation of all possible solid networks led 
Bravais to the conclusion that these, if classified by the char- 
acter of their symmetry, fall into groups, which correspond 
exactly to the systems into which crystals are grouped in 
accordance with their symmetry. 
It follows that two (not, however, independent) features of 
crystals are fully accounted for by a parallelopipedal arrange- 
