PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 59 



If RYDBEKG'S opinion, that the true formula should be of the form f(m+n), is 

 correct, then D would be of the form 



D = m+p. + +.... 

 m+p. 



This, however, would be included in the previous formula with sufficient exactness 

 except possibly for m = 1 or 2. Any term added to m + p. will, of course, by giving 

 an additional arbitrary constant, produce a formula capable of reproducing spectral 

 series with greater accuracy. The criteria justifying the form of a new term should 

 be a very considerable increase of accuracy over a wide range (and particularly for 

 m =1), and that it should bring to light further relationships. RITZ,* from certain 

 theoretical ideas, has taken D = m + /j. + ft/m 2 or m + /A + /3/(m+'5) 2 , and with a large 

 number of series has obtained very close agreement. It was not until I had made 

 some progress with this work that I became acquainted with his paper. I believe 

 this to have been fortunate, for had I known his work, and the great increase of 

 accuracy obtained by his forms, I should probably not have attempted to essay any 

 further improvement. As it was I had proceeded so far as to feel certain that I was 

 on correct lines, and had already obtained even more accurate results than his, 

 besides some of the relationships presented below. The first important result was 

 that it was rarely necessary to go beyond the a/m term in fact, not at all for the 

 alkali metals that if a, ft were both included, and, of course, an additional line used 

 for calculation, ft always came out a small fraction of a, and that with a alone the 

 agreement was much better than with ft alone (RiTz). Evidence of this is given 

 below. 



As will be seen later, there are indications that a form D = m+ju,+a/(m+a) may 

 be the true form, at least for certain series. These indications will be mentioned in 

 due course, but as the metals of Group II. are not discussed in the present communi- 

 cation, the case may be further illustrated from a special series in Mg, which will at 

 the same time serve to show that too much stress must not be laid in favour of a 

 particular formula on the mere fact that it reproduces the observed lines, unless the 

 observations are very exact, or comprise the first members and a considerable number 

 of the others. The series in question was first discovered by RYDBERG! in K.R.'s 

 observations, and consists of six observed lines contained between 5528 and 3987, 

 which he called a " new kind of series " of the Mg spectrum. Neither his own nor 

 K.R.'s formula reproduce the lines, and he suggested a combination of the two, viz., 



As will be seen, this involves four constants and requires four lines to find the 

 constants. The formula reproduces the two last lines within error of observation. 



* 'Ann. d. Phys.,' 12, p. 264. 

 t ' Ann. d. Phys.,' 50, p. 625, 



I 2 



