38 Mr. J. S. Ames on Relations between 



the recent attempt by Prof. Anton Griinwald * of Prague to 

 deduce a mathematical theory of spectra and spectral relations. 

 A synopsis of his theory and the objections to it have been 

 given by myself f, and later by Kayser J. In his last paper 

 Prof. Griinwald claims to find coincidences between lines in 

 the spectra of antimony, tellurium, and copper, and then to 

 deduce the proof of a new element. In fact, there is not a 

 single coincidence between these three spectra. It is evident 

 from his writings that Prof. Griinwald has never had the 

 benefit of using and working with a spectroscope. 



Harmonic and Combinational Lines. 



There has been an attempt to solve the question of the 

 origin of lines in spectra, which is quite different from the 

 theories and relations already discussed. Since the motion 

 imparted to the aether and known to us as light is a periodic 

 one, it seems but natural to apply Fourier's series and to see 

 if the presence of the various harmonics of the fundamental 

 can be found. The first to find such simple relations was 

 M. Lecoq de Boisbaudran § . He thought that line for line 

 the two visible bands of nitrogen were related to each other 

 in the ratio 3 : 4. Later and more accurate measurements 

 have shown this relation to be inaccurate. Soon after Prof. 

 G. Johnstone Stoney || pointed out some harmonic relations in 

 the spectrum of hydrogen. At the same time he studied the 

 absorption spectrum of Cr0 2 Cl a with a view to testing his 

 theory ; but the result was not satisfactory. At the best all 

 the harmonics are never present ; all the lines are not ac- 

 counted for ; and several fundamentals have often to be 

 supposed. The ultra-violet lines of magnesium and cadmium 

 were examined by SoretU in the search for harmonic ratios ; 

 but his coincidences are very rough. 



Liveing and Dewar** also engaged in the quest for these 

 harmonic relations in the spectra of lithium, sodium, and 

 potassium, but with indifferent success. A few such relations 

 can be found in every spectrum ; but is this number greater 

 than that which a chance-distribution would give? This 

 question occurred to Schuster, while he was working on the 

 spectrum of iron. He proposed the following problem : — 



* Astr. Nach. p. 2797 (1887) ; Wien. Sitzb. 1887, 1888, 1889. 

 t Amer. Ohem. Journ. xi. (1889) ; ' Nature/ xl. (1889). 

 % Chem. Ztg. xiii. pp. 1655 and 1687 (1889). 

 § Cdmptes Rendus, lxix. (1869). 

 || Phil. Mag. [4] xlii. (1871) ; 'Nature/ xxi. (1830). 

 ^f Bibliot. Univ. Archives des Set. Phys. et Nat. Sept. 1871 ; Phil. Mag. 

 [4] xlii. (1871). 

 ** Proc. Roy. Soc. xxix. (1879) ; xxx. (1880). 



