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LXII. Intelligence and Miscellaneous Articles. 



ON HARMONIC RATIOS IN SPECTRA. BY J. L. SORET. 



fT^HE idea of seeking harmonic relations between the different lines 

 -*- of the spectrum of one and the same body is doubtless not new, 

 several savants having already occupied themselves with this ques- 

 tion*; but the article which has just been analyzed*}*, as well as 

 Mr. Stoney's previous note, appears to us to present a special in- 

 terest : — 1st, by the extreme precision with which the calculated 

 wave-lengths coincide with those deduced from experimental deter- 

 minations which are capable of inspiring great confidence ; 2ndly, 

 by the high order of the harmonics which are indicated — such that 

 the ratios of the numbers of vibrations are by no means very simple. 

 The complication of these ratios, particularly for chlorochromic acid, 

 as well as the absence of the greater number of the harmonics in the 

 case of hydrogen, is even of a nature to excite doubts of the correct- 

 ness of the hypothesis which is to be controlled. 



Nevertheless the coincidence of the calculated with the observed 

 values is too exact for it to be possible to attribute it to chance : if 

 not due to the existence of harmonics, it must proceed from some 

 other determinate cause. It seems, then, to us that here are motives 

 for urging the study of this interesting subject. By taking into 

 account the ultra-violet lines, of which a great number have already 

 been determined photographically by M. Mascart, we should have a 

 much more extensive field than if we confined ourselves to the 

 visible spectrum, which does not comprise even an entire octave. 



As an example, I will notice some relations at which I arrived 

 with facility in a very superficial and incomplete examination of the 

 question. 



It is known that the spectrum of magnesium presents, among other 

 bright lines, a group of three green lines (coinciding with the solar 

 lines b). M. Mascart J, in studying the ultra-violet portion of this 

 spectrum, has found two other groups of three lines perfectly resem- 

 bling the preceding in their appearance ; and to his record of this fact 

 he adds : — " The reproduction of such a phenomenon can hardly re- 

 sult from chance ; is it not natural to admit that these groups of 

 similar lines are harmonics, depending on the molecular constitution 

 of the luminous gas ? " 



The wave-length of the least-refrangible of the three lines in each 



* Among others, M. Lecocq deBoisbaudran {Comptes Rendusde VAcad. 

 des Sciences, 1869 and 1870) has noticed a great number of approximately 

 simple ratios between the wave-lengths of the various lines belonging to 

 one and the same body, as well as certain relations between the positions 

 of the lines of different bodies 



t Messrs. Johnstone Stoney and Reynolds's article, in the Philosophical 

 Magazine for July 1871, "On the Absorption-spectrum of Chlorochromic 

 Anhydride." 



J Comptes Rendus de VAcad. des Sciences, 1869, vol. lxix, p. 337. 



