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XXIX. On the Atomic Weight of Radium, and on Relation- 
ships between the Atomic Weights of the Elements and their 
Spectra. By W. Marsaatt Warts *. 
[ the Philosophical Magazine for December 1903, Prof. 
Runge criticises adversely some attempts of mine to 
connect the spectra of certain elements with their atomic 
weights, and in particular an attempt to determine the 
atomic weight of radium from spectroscopic data. 
Prof. Runge objects that the lines which I have sought to 
connect together are not homologous, explaining that in 
order to be homologous the lines must have similar character- 
istic features, and in particular must behave in the same 
way in the magnetic field. He gives an example of really 
homologous lines, 4226 of calcium, 4607 of strontium, and 
5536 of barium ; and remarks that “it is to homologous lines 
like these that we must look in order to show the connexion 
between the spectra and the atomic weights.” Now, the 
oscillation-frequencies of these lines (in air) are respectively 
23657°94, 21703°65, and 18064°59, and from these data we 
may construct the formula 
atomic weight = VW (24178°72—O.F.) x 3:08772 
(where O.F. is written for oscillation-frequency for the sake 
of brevity). This formula gives the atomic weights of 
calcium, strontium, and barium as 40°1, 87°42, and 137°4 
respectively ; that is to say, it enables us to calculate the 
atomic weight of strontium from those of calcium and barium 
with reasonable accuracy, obtaining 87°4 instead of 87-6. 
These very lines, therefore, form one instance of the truth of 
my first proposition, “that in some cases, the differences in 
oscillation-frequeney are proportional to the differences 
between the squares of the atomic weights.” 
As only a few of the brightest lines have been examined 
in the magnetic field, this criterion can only be employed in 
a few cases. I have supposed lines in the spectra of allied 
elements to be homologous whose oscillation-frequencies can 
be calculated from the same value of m in the formule of 
Kayser and Runge. In the simpler (arc) spectra of the 
metals of the alkalies, practically all the lines are accounted 
for either in the principal series or in one of the two 
subordinate series which these formule represent. The lines 
of potassium, rubidium, and cesium, quoted below trom my 
paper in the Phil. Mag. of Feb. 1903, for example, are lines 
* Communicated by the Author. 
