Cause of the Structure of Spectra. 263 



periods of vibration of the metallic atoms at the melting- 

 points was (ibid. p. 319) m^/piTh; so that internal period of 

 atom given by (17) differs from period of translatory vibration 

 at melting-point by the factor m^, disregarding a constant. 

 For all the elements this has a range from 1*0 to 1'6, and 

 for any natural family from about 1*2 to 1*6. Allowing for 

 the empirical and other uncertainties in our train of reasoning, 

 which must have introduced this discrepant m^, we take it as 

 fairly proved that the singular harmonic relations of the 

 periods of vibration of the metallic atoms at the melting-points 

 arise from the existence of the same harmonic relations amongst 

 the internal mechanical vibrations of the atoms. This is the 

 main proposition of this section. 



As to the relations between the periods of different families, 

 the table on p. 541 of a " Kinetic Theory of Solids " (Phil. 

 Mag. [5] xxxii.) makes it appear that the period of each 

 member of the Be family is nearly one-half of that for the 

 corresponding metal of the Li family, and therefore it looks 

 .•as though the periods of all the elements are harmonically 

 related to a single fundamental period or a small group of 

 periods. If this is so, then if we remember that each metallic 

 atom besides its fundamental vibration lias all its harmonics, 

 we see that it is possible for all the elementary atoms to have 

 some lowest common period and a series of common higher 

 harmonics. I take it that it is the possession of this common 

 period, and of the same electrical atomic apparatus, that 

 causes the wonderful similarity in the limited range of the 

 strongest parts of all spectra, commented upon in the intro- 

 duction to this paper. 



In the present connexion considerable importance attaches 

 to a second very strange relation that appeared in "A New 

 Periodic Property of the Elements/' namely, that the period 

 of vibration of a compound molecule, such as NaCl or SrBr 2 , 

 at its melting-point, can be got by adding a period charac- 

 teristic of the Na atom to a period for the CI atom, or a 

 period for Sr to a period for Br 2 . In acoustics we know of 

 summation-tones wherein the frequencies of two vibrating 

 sources are added together ; but the case of a vibrating mole- 

 ,cule whose period is the sum of the periods of its parts seemed 

 also very puzzling at the time when that paper was published. 

 And, moreover, the relative periods of the metallic atoms of 

 the Li family in compounds are nearly the same as for the 

 .atoms of the uncombined metals, while the periods of F, ( 1. 

 Br, and I in compounds with the Li family of metals are as 

 1, 2, 3, 1. But when that paper was written it was not pos- 



T2 



