the Lines of various Spectra. 37 



zinc, and cadmium. But it is hardly safe to draw inferences 

 from spark-spectra ; for, although they are undoubtedly charac- 

 teristic, yet the state of affairs in the spark-discharge is so 

 unnatural, if I may use the term, that similar molecules could 

 not be expected to act alike. The study of the arc-spectra of 

 the elements leads to many modifications and additions, as will 

 be shown later. Prof. Hartley called attention also to a most 

 remarkable relation connecting the lines in the series of 

 triplets in the spectra of magnesium, zinc, and cadmium. He 

 corrected the wave-lengths for atmospheric refraction, and 

 then calculated their reciprocals ; that is, he deduced quantities 

 proportional to the frequencies of the waves. He then found 

 that the differences of these frequencies for each triplet in any 

 one series is a constant quantity. Tins law holds also for 

 series of doublets. I will return to this point when the 

 spectra of cadmium and zinc are discussed. That there are 

 mathematical expressions connecting the many series of rays 

 in the spectra of the elements no one can doubt. Their regu- 

 larity and analogy are evidently not accidental. But there 

 are two ways of arriving at such a mathematical formula : 

 one is to deduce it from theoretical considerations and to test 

 it by experiment ; the other is to give up all preconceived 

 ideas and simply to " guess," as Kepler did. Cornu* advises 

 the latter method. He thinks that relations are to be found, 

 if at all, between the lines which are "reversed." It is 

 true that most of the lines in these series which obviously 

 obey some common law are reversed ; but different observers 

 are continually finding different reversals. The conditions 

 must be specified. While studying, then, the reversed lines 

 of aluminium and thallium, Cornu noticed the resemblance 

 between the series which they formed and the one of hydrogen 

 lines. He thought he could trace a linear relation between 

 them. That is, for all the ultra-violet reversed lines of 

 aluminium (and of thallium) the following formula held : — 



X = a -f b \ 1? 



where Xi is the wave-length of one of the lines in the hydrogen 

 series, beginning with wave-length 4340. That this for- 

 mula is not true will be shown later when the wave-lengths 

 of the aluminium lines are given. 



In the spectra of zinc and cadmium some new points of 

 resemblance were noted by Mr. Bell f quite recently ; but he 

 worked with the spark-spectra, and so was at a disadvantage. 

 For the sake of completeness some notice must be taken of 



* 'Comptes Rendus, c. (1885). 



t Amer. Journ. Sci. [3] xxxi. (1886). 



