X. A critical study of spectral series.—Part V. The spectra of the monatomic gases

The present communication has two objects. Its subject matter is an attempt to obtain some knowledge of the series relations in the spectra of the group of the monatomic rare gases Ne to Raem, whilst the methods employed will serve to illustrate the fundamental importance as instruments for further research of the new facts brought to light in the previous communications. The importance of the first object will be generally acknowledged, but it does not yet seem to be realised how definite and exact those new relationships are, even in their as yet undeveloped form, and how powerful an instrument is placed in our hands for the analysis of spectra. It may be well therefore to commence by a briefrésumé of some of these laws as applied in the succeeding pages. Further, as the establishment of the results obtained must by its nature depend on the numerical comparison of a very large number of lines in all five spectra, and as this evidence must be fully set out to enable a specialist judgment to be formed on it, the communication has unfortunately become very lengthy. The mass of detail will perhaps be rather dreary to the general reader not specially interested in this line of study. It is apt also to hide by its amount and complexity the general conclusions arrived at. I propose therefore to give a slight general survey of these conclusions before giving the evidence. As is well known the wave-numbers of series lines depend on four types of sequencesp(m), s(m), d(m), f(m ) , and that in any one series they depend on the differences between one sequent of one type and the successive terms of the sequence of another type. These sequences are all of the form N{ø(m )}2 where N is Rydberg's constant and ø(m ) is of the formm +fraction, the fraction being, as a rule, determinable as a decimal to six significant figures. Our aim is to discover the properties of these functions. The fractional part depends in some way on the orderm , although whether it can be considered a definite function ofm in the ordinary sense is doubtful. This fractional part will be referred to as the mantissa, and in dealing with it, it will be regarded as multiplied by 106 ,i. e ., as if the decimal point were removed.