Now that we have a method of determining the arrangement and distances apart of the atoms in a crystal, the next step will be to examine the intensity and type of forces which are brought into play to keep the atoms in equilibrium and relatively fixed in their places. It is to be expected that the atoms are able to move to and fro about their position of equilibrium, and this is indicated by the effect of lowering the temperature of the crystal; for the intensity of the diffraction spectra increases as the amplitude of motion of the atom diminishes. The sharpness of the diffraction spectra suggests that the atoms are not only arranged at definite distances from one another but that each atom is orientated in a definite position with regard to its neighbor.
While varieties of crystals are known of all degrees of hardness, the work of Lehmann has brought to light the unexpected existence of crystalline arrangement in some liquids. These liquid crystals are best shown in certain complex organic substances at a temperature slightly above their melting point, and they are only observable in the liquid by the patterns and colors developed when polarized light passes through them. These crystals are mobile like a drop of oil in a solution and can be squeezed into a variety of patterns. Such results would indicate that the molecules of the liquid have a tendency to arrange themselves in ordered patterns, although it is difficult to understand how the freedom of relative motion that is supposed to characterize a liquid can contemporaneously exist with an ordered arrangement of some of the constituent molecules.
We will now direct our attention to another type of phenomenon which ultimately promises to throw much light on the detailed structure of the atom. When the light from an incandescent vapor or gas is passed through a prism or reflected from a grating, it is resolved and gives a characteristic spectrum consisting of a number of bright lines. By suitable methods, the wave-length of these radiations can be determined with great accuracy. Each of these lines represents a definite and characteristic mode of vibration of the atom, and from the exceeding complexity of the spectra of many of the heavy elements, we are forced to conclude that an atom can vibrate in a great variety of ways. When the meaning of the dark lines in the solar spectrum was correctly interpreted, we were enabled at one stride to extend our methods of observation to the sun and the furthest fixed stars. It was soon recognized that atoms of the same element always vibrated the same way under all conditions. It was found, for example, that hydrogen atoms in the earth vibrated in exactly the same way as the same atoms in a distant star. The important bearing of this result on the structure of atoms was pointed out by Clerk Maxwell in his well-known address on "Atoms