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[Jan. 21 , 
vibrating ring to be cut at one of the nodes and the two ends 
straightened out, it will be seen that there are really two vibra- 
tions or stationary waves as they sometimes are called, in the ring, 
and the harmonics are the fractional parts of one wave. Suppose 
each of these waves to be divided into 3 parts, that is to be ac- 
companied by the second harmonic. Then the circumference of 
the ring would have twelve nodes ; an arrange ment that would 
permit three other rings to be hinged at angles of 120 degrees apart, 
and if these were swung upwards until they touched each other 
they would form a stable combination, but the angle made be- 
tween the base and the side of this pyramidal structure would de- 
pend upon the relative diameters of the ring composing the base 
and sides. The smaller the latter the greater the inclination. 
With similar structures there could grow up another hexagonal 
system, having a differently distributed field from the other but 
still symmetrical and therefore capable of growing a symmetrical 
shape. 
So far we have got an explanation of both attraction and selec- 
tive attraction. 
When a ring is vibrating only in its fundamental rate it would 
seem as if it would be quadrivalent. As a matter of fact, all of 
our experience with chemical reactions is a long way from absolute 
zero, and there must therefore be few or no fundamentals pres- 
ent — the energy must appear in the harmonics. This multiplies 
the nodes which will be multiples of two or three or five. Again 
given an atom having a strong field like carbon, it must strongly 
tend to neutralize the difference in pressure between the nodes 
and loops of a weaker atom, say, hydrogen. 
If at a given temperature two different kinds of atoms have no 
common ratios in their vibrations, their nodes will be unsymmet- 
rical with reference to each other, and their fields will more or less 
neutralize each other, rendering cohesion more or less precarious 
or altogether impossible as in the case of oxygen and fluorine. 
Now this vibratory motion of the atoms has certain limits of am- 
plitude. Suppose two atoms of different sorts to be combined into 
a molecule as IIC1. Let their temperature be increased higher and 
higher ; as the amplitude increases their impacts become more 
and more violent and as a consequence their stability becomes less 
until they are broken apart by the vigorous bumping. Of course 
heir fields will in reality be stronger but not necessarily propor- 
