Dolbear.] 
192 
[Jan. Si, 
nodes on the open end to which another similar atom could 
be attached by its four bonds forming a cubical box having 
a high degree of mechanical stability. It will have a symetrical 
but not a uniform field. The corners being the places having 
maximum displacements and the middle of each edge the minimum 
as the nodes are all in such positions, hence other similar ones 
would be moved to assume symmetrical positions when in contact 
and thus a cubical structure or prismatic form would be built up 
by aggregation of similar molecules. This is on the supposition 
that all the atoms combining thus together are equal in size as 
well as uniform in their vibrations, and this cubical form is one in 
which not a few of the elements crystallize, for example, gold, 
iron, copper. 
That there is a real difference in directive action between the 
sides and edges of crystals is apparent upon examination of many 
types of them. For instance, what are called skeleton crystals in 
which the growth takes place only in axial directions is one. An- 
other one is illustrated by salt crystals forming as it often does 
only upon the edges of a crystalline mass producing cavernous 
crystals. 
The same thing is sometimes seen in quartz ; cavernous forma- 
tions on both sides and pyramidal ends. 
Again, in dissolving large crystals not too rapidly, the frame 
work frequently persists longer than the rest. These phenomena 
show that there is a real difference in crystallizing conditions be- 
tween the edges and the faces of crystals and that the cohesion is 
greater at the edges than elsewhere. 
If one would see more clearly how these nodes and loops fit to- 
gether in such structures let him make paper models, drawing a 
set of circles with their peripheries touching at one point as shown 
in fig. 4 ; Make points on each circle to indicate the nodes and 
then bend them up as described. If another one similar to 3 be 
made hinged at 6 it will form the cover to the cube and all the 
nodes will be adjacent. 
So far such vortex atoms have been considered as being all of 
one magnitude or as all having a similar rate of vibration, but the 
different elements have different masses and therefore vibrate with 
different rates ; the greater the mass the slower the rate according 
to the law of energy. When two elementary atoms come into con- 
tact with each other while vibrating at their individual rates, 
