The following investigation was commenced some years ago, at a time when the discussion as to the atomic weight of Radium raised the question as to the dependence on their atomic weights of the wave-lengths of corresponding spectral lines of different elements of the same group. The arguments were necessarily vague and unconvincing in the absence of any exact knowledge as to the connection of wave-length with atomic weight, even supposing such connection existed. Our knowledge of series spectra is chiefly—one might say almost wholly—due to the sets of very exact measurements of Kayser and Runge, and of Runge and Paschen, supplemented by extensions to longer and shorter wave-lengths by Bergmann, Konen and Hagenbach, Lehmann, Ram age, and Saunders. These have been only quite recently added to by Paschen and by the remarkable extension of the Sodium Principal series up to 48 terms by Wood. A most valuable feature of Kayser’s work was the publication of possible errors of observation. This has rendered it possible to test with certainty whether any relation suggesting itself is true within limits of observational error or not. In fact, without this, the investigation, of which the present communication forms a first part, could not have been carried out. So far as the author knows, Saunders is the only other observer who has accompanied his observations with estimates of this kind. Others have given probable errors—practically estimates of the exactness with which they can repeat readings of that feature of a line which they take to be the centre—an estimate of little value for the present purpose. In deducing data from a set of lines it is thus possible to express their errors in terms of the original errors in the observations, and limits to the latter give limiting variations to the former. We therefore know with certainty what latitude in inferences is permissible, and are often enabled to say that such inference is not justifiable.
R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS