the Lines of various Spectra. 41 



wave-lengths of the elements is so great, though, that they 

 have been unable to test it sufficiently. In a more recent 

 paper* they give a formula for one of the cyanogen bands ; 

 but this is not, I judge, their general formula, nor even a 

 special case of it. 



The various bands found in the spectra of carbon and its 

 compounds, and of many other substances also, seem at sight 

 to be especially suitable for mathematical investigation ; and 

 many of them have been studied most carefully. 



The first to hit upon an approximate law was Prof. A. S. 

 Herschelf of Newcastle-on-Tyne. On seeing Piazzi Smyth's 

 map of the green band of CO, which was plotted in wave- 

 numbers or frequencies, he at once noticed that the differences 

 of the lines were in arithmetical progression. This was in 

 November 1883. He announced his intention of studying 

 other bands ; but I can find no record of his having done so. 

 Prof. Rowland, independently, detected a similar law as soon 

 as he began his work on the solar spectrum, which was in 

 1885. He investigated the A, B, and a bands first, and after- 

 wards all the carbon bands. He found that the law was not 

 so exact as the accuracy of his measurements demanded, and 

 so never published his work. 



Later on, M. H. Deslandres, working in Oornu's laboratory, 

 came upon the same approximate law. CornuJ had noted 

 that the reciprocals of the wave-lengths of the homologous 

 lines in the three bands A, B, and a were nearly in arithmeti- 

 cal progression ; and in his monograph on these telluric bands 

 (Paris 1886) he says that the law of distribution of the doub- 

 lets is sensibly the same in all three. This law, stated 

 analytically, is 



AX_ AX' _ AX" 



XXX 



where AX, AV, AX" are the distances from the homologous 

 lines to the "isolated" ones; and X, X', X" are the averages 

 of the rays whose intervals are AX, AX', A". This law is 

 only the roughest approximation. Cornu does not seem to 

 have thought of testing the fines of each group separately. 

 But in 1886 Deslandres § published his investigation of the 

 nitrogen bands ; and stated that for all of them, and in fact 

 for all bands so far examined, the following law is true :— 

 " In general, the rays composing a band can be divided into 



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



t Trans. Roy. Soc. Edinb. xxxii. [3] (1884). 



\ Comptes Rendus, xcviii. (1884). 



§ Comptes Rendus, ciii. (1886) ; also vol. civ. (1887), and vol. cvi. (1888). 



