determination of these values. The desire to test this hypothesis was one of the chief motives for some of the most careful determinations of atomic weights which have ever been made. These determinations resulted in proving that the divergences of the atomic weights from whole numbers were greater than could be accounted for on the basis of experimental errors. This precluded the possibility that the atom of hydrogen was the common ultimate unit, but did not dispose of the possibility that a half, or quarter, or some other fraction, of the hydrogen atom might play that rôle.
In 1901 Strutt[1] applied the mathematical methods of the theory of probabilities to the most accurately determined atomic weights, and calculated that the chance that they should fall as close to whole numbers as they do was only one in one thousand. The inference from this is that it is not a matter of chance, but that there is a regularity in the atomic weights which we do not understand; a regularity which points to the probability that our elements are complex substances, constructed according to some system, from some simpler substance.
All the facts comprised in that great generalization, the periodic law, which states that the properties of the elements, both chemical and physical, are functions of their atomic weights, and most of them are periodic functions, point unmistakably to the same conclusion.
The evidence from spectroscopic analysis is so abundant that it is not easy to compress it into a few general statements.
In the first place, the spectrum of each of our elements consists of numerous lines, a fact not exactly compatible with the notion of extreme simplicity of the particles emitting the light.
In the second place, one and the same element, contrary to common belief, frequently has two or three distinctly different spectra, the particular spectrum which appears depending upon the pressure and the temperature at which the element is while emitting the light. In fact the extraordinary spectroscopic results obtained when highly rarefied gases enclosed in tubes (variously called Plücker, Hittorf, Geissler or Crookes tubes) were made luminous by the passage of high potential electricity, induced Crookes to suggest in 1887 a theory that the elements were all built up by gradual condensation with falling temperature from a fundamental substance to which he gave the name protyl.[2]
In the third place, the lines in the spectrum of one element may be separated out into several series. Each line corresponds, as is well known, to light of a definite wave length. The wave lengths of the lines comprised in one series are related to each other in such a way that a general formula may be derived for them. This means that, given some of the lines, the wave lengths, and thus the positions, of
