No. 3.] ATOMS AND MOLECULES. 579 
and oxygen and aluminium in the ruby. Furthermore, an ele- 
ment having but a small mass like hydrogen could produce a field 
of slight strength compared to that of an element moving with 
the same velocity, yet having decidedly a greater mass, so that 
when it combined with any other element, it would be because 
of the greater energy of the other’s field; that is to say, oxygen 
holds on to hydrogen rather than hydrogen to oxygen, and one 
would expect that hydrogen could be replaced by some other 
element in a compound more readily than any other element. 
Hence, whatever might be the relative rates of vibration when 
compared with other elements, one might infer it could be asso- 
ciated with them. One might explain its weak affinities by its 
small mass and consequent small vibrating energy. With larger 
masses, however, the case would be different. If one made five 
vibrations while the other made but one, they would be in the 
same phase but one-fifth of the time, and in more or less interfer- 
ence the other four-fifths ; and unless there was a considerable 
disparity in their masses, there would apparently be but slight 
cohesion. If one made four while the other made one, they 
would be in similar phases three-fourths of the time, and could 
thus form a more stable alliance. 
As has already been said, atoms vibrate in harmonic series, 
and this must frequently modify the position of the nodes when 
adhesions can occur. Now the harmonic series is 2, 3, 4, and 
so on, times the fundamental rate. If one will imagine such a 
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 three parts, — 
that is, to be accompanied by the second harmonic; then the cir- 
cumference of the ring would have twelve nodes, —an arrange- 
ment that would permit three other rings to be hinged at angles of 
120° apart ; and if these were swung upwards until they touched 
each other, they would form a stable combination, but the angle 
made between the base and the side of this pyramidal structure 
would depend upon the relative diameters of the ring composing 
the base and sides. The smaller the latter, the greater the 
inclination. With similar structure there could grow up an- 
other hexagonal system, having a differently distributed field 
