In 1888 Kayser and Runge began a remark able study of the arc spectra of many of the more important elements and showed that most of these elements contain one or more series of lines capable of representation by the fol lowing formula: A + + 4 in which A, B and C are constants for each series, and on denotes the natural numbers be ginning with 3. Each different chemical element has its own different characteristic values for these three constants. This fact is the founda tion of spectrum analysis.
Rydberg has shown that the following ex pression is equally effective in representing the facts: (m-1-10' where A, B and# are constants for each series, while 71. and m have their previous meanings. Thus in the case of Mg, Zn and Cd there are six such series, in each case equivalent to two series of triplets. It is to be hoped that this great advance will be followed some day by a dynamical explanation of the vibrating atom, which will include these two formula as rigidly derived inferences.
In the way of general trea tise, consult Kayser, (Handbuch der Spectro scopie) (Leipzig 1900), as incomparably the most complete and scholarly work in existence.
Here may be found references to the literature of every part of the subject. For a complete theory of the plane grating consult Rowland, (Physical Papers) A most elegant and simple theory of the concave grating is given by Runge in Kayser, (Handbuch der Spectroscopie.' On the general theory of the spectroscope consult a series of papers by Wadsworth in the