42 Mr. J. S. Ames on Relations betiveen 



several overlapping identical series ; and in each series the 

 intervals from one ray to the next (measured in wave- 

 numbers) form approximately an arithmetical progression." 

 As Deslandres remarks, for most bands it is immaterial which 



we use, X, - , or r-* ; but - seems to apply most generally. In 



A A, A 



a later paper Deslandres says that the bands themselves form 

 groups, and that the same law governs the distribution of bands 

 as governs the lines in any one band. Thus for any ray, 



i = Am 2 + Bm + C, m = 0, 1, . . . 



A 



C = Dn 2 + Ew + F, n = 0, 1, . . . 



\ = Am 2 + Bm + Dn 2 + E?2 + F. 

 A 



Deslandres gives reasons for believing the general formula 

 is of the form : — 



I =f(n*,p>)m* + Bn 2 + <l>{p*). 

 A 



This he compares with that of a vibrating rectangular prism, 

 which likewise is a function of three positive parameters. 

 These laws of Deslandres apply fairly well to all banded spec- 

 tra ; - but they are only approximations. I had made measure- 

 ments of many of the bands of carbon and cyanogen to test 

 their accuracy, but have been anticipated in their publication 

 by Kayser and Runge*. They find, as I had done, that these 

 laws fail in some cases. They study with particular care the 

 most regular of the cyanogen bands, the one at wave-length 

 3883*5, and find that the empirical formula 



- = a + fo cw sin (dn 2 ), 

 A 



where a, b, c, d are constants and n — 0, 1, 2,... applies 

 reasonably well. But in testing this formula they make no 

 correction for atmospheric refraction, which would, I think, 

 make some difference. They come to the conclusion that no 

 exact formula, which is reasonably simple, can be found by 

 trial. If one is ever to be known it must be deduced 

 theoretically. 



Some New Relations. 

 The two elements between whose spectra there is the most 

 striking resemblance are, as is well known, zinc and cadmium. 



* Abhd. Berlin Akad. 1889; Wied. Ann. xxxviii. (1889). 



