Cause of the Structure of Spectra. 261 



Our second supplementary principle can be seen from a 

 study of the values of ix in the Sharp series of the Li family, 

 if we take *597 for Li to be '6, which is 3/5, and '66 for Na 

 to be '667, which is 2/3 ; we then have for the Li family the 

 symmetrical system of values 3/5, 2/3, 4/5, 2/3, 3/5, where 

 we have to do with multiples of 1/3 and 1/5, the first two of 

 the odd harmonic fractions. The difference of these is *133. 

 Now if we take the successive differences in the values of jj, 

 in the Principal series for the Li family, we get *135, *133, 

 •067, 0'0, two of which are equal to the characteristic 

 difference in the Sharp series, and the third is half of that 

 difference. Again, we have evidence of purely numerical 

 relationships in the values of spectral parameters of different 

 elements, pointing to kinematical and not dynamical con- 

 siderations as ruling the relations amongst spectra. We shall 

 consider this matter again at the end of Section 8. 



The data for other families are not completely enough 

 analysed yet to give sure ground for further comparison. 

 For example, the Al diffuse series seems to be better repre- 

 sented if, instead of unit increments in m + jju, we give incre- 

 ments nearly equal to 1, but with a small periodically varying 

 difference. Again the large variation of B for Sr and Ba 

 from the nearly equal values for the other diverse elements 

 may be the result of an imperfect understanding of the series 

 for these elements. Evidently in B we have a great funda- 

 mental constant of nature which may be made to appear to 

 vary by the association of some small variable parameter 

 with it. 



6. Periods of Mechanical Vibration of the Atoms. 



In "A New Periodic Property of the Elements " (Phil. Mag. 

 [5] xxx.), and in a "Kinetic Theory of Solids^ (ibid, xxxii.), 

 I showed that at their melting-points the atoms of the metals 

 have periods of vibration which bear simple harmonic rela- 

 tions to one another ; for example, for the Li family of 

 metals they are 1, 2, 3, 1'5, and 6. I had often puzzled 

 over the meaning of this striking periodicity, but without 

 result, until in investigating " The Spontaneous Change of 

 Oxygen into Ozone and a Remarkable Type of Dissociation" 

 (Phil. Mag. [5] xliii.), and "The Molecular Constitution of 

 Water " (ibid. Nov. 1900), I found instances of molecular re- 

 sonance which suggested that the above periodicity must be 

 another result of molecular resonance. As the temperature 

 of a metal is raised the interspaces between the molecules 

 grow, and each molecule is less completely hemmed in by its 

 neighbours. In moving about within its own domain each 



Phil. Mag. S. 6. Vol. 2. No. 9. Sept. 1901. T 



