1881.] On Harmonic Ratios in the Spectra of Gases, 337 



IV. " On Harmonic Ratios in the Spectra of Gases." By Arthur 

 Schuster, Ph.D., F.R.S. Received January 10, 1881. 



It would be a matter of the greatest importance if we could dis- 

 cover an empirical law connecting together *the different periods of 

 vibration in which we know one and the same molecule to be capable 

 of swinging. According to the most simple supposition the vibrations 

 might be harmonical overtones of one fundamental note. Various 

 attempts have been made to prove that such indeed is the case, and 

 that the wave-lengths of different spectral lines bear to each other the 

 ratio of two comparatively small integer numbers. M. Lecoq de 

 Boisbaudran and Professor Johnstone Stoney, especially, have dis- 

 cussed this question ; the wave-lengths used by the former do not 

 possess the accuracy necessary for a final settlement of the point, but 

 Professor Stoney has, in the case of hydrogen, shown that three out of 

 the four lines in the visible part of the spectrum have wave-lengths r 

 which, to a high degree of accuracy, are in the ratios of 20 : 27 : 32. 



I have occupied myself at various times during the last ten years 

 with this question, and have naturally accumulated a large quantity 

 of material. About three years ago, however, I came to the con- 

 clusion that only a systematic investigation could lead to a decisive 

 result. In any spectrum containing a large number of lines, it is 

 clear that, owing to accidental coincidences, we shall always be able to 

 find ratios which agree very closely with the ratios of small integer 

 numbers. We can, however, by means of the theory of probability, 

 calculate the number of such coincidences which we might expect to 

 find on the supposition that no real law exists, and that all the lines 

 are distributed at random throughout the whole range of the visible 

 spectrum. If, on calculating out all fractions which can be formed in 

 a spectrum by any pair of lines, the number of ratios, agreeing within 

 certain limits with ratios of integer numbers, greatly exceeds the most 

 probable number, we should have reason to suppose that the lines are 

 not distributed at random, but that the law suggested by Messrs, 

 Lecoq de Boisbaudran and Stoney is a true one. 



I have been engaged during the last three years in discussing some 

 of the spectra in the manner indicated, and I now wish to lay the 

 results of the investigation before the Royal Society. I took the 

 spectra of the following elements ; the numbers in brackets indicate 

 the number of lines for each body : — 



Magnesium (7) 



Sodium (10) 



Copper (15) 



Barium (26) 



Iron (149) 



