Cause of the Structure of Spectra. 265 



common harmonic ; and the effect of the discontinuity after 

 union would be to emphasize this harmonic at the expense 

 of the fundamental of period p x +p 2 . That a compound 

 molecule should have a period which is the sum of the 

 periods of its atoms, implies that two different atoms in com- 

 bination are attached to one another in a decidedly intimate 

 way. It is to be noticed that the rule does not apply to 

 molecules containing more than two atoms. The periods for 

 the two halogen atoms in compounds like CaF 2 , Brl 2 are not 

 double those for the single halogen atoms. The important 

 points brought out are the intimate mechanical contact of the 

 atoms in chemical combination, and the change of their 

 periods of vibration to harmonics of the periods for the 

 elementary state. On account of the harmonic relationships 

 between the periods of the atoms of different elements and 

 between those of the same atom in the elementary and com- 

 bined states, it seems likely that there is a mode of motion 

 common to all the atoms. 



There remains to calculate the order of magnitude of the 

 mechanical period of vibration of some atom such as that 

 of Li. This has already been done in an indirect manner in 

 "A Kinetic Theory of Solids " (Phil. Mag. [5] xxxii. p. 542), 

 for the period of external vibration of the Li molecule at the 

 melting-point of the metal is there estimated at about 

 16 x 10 — 15 seeond, representing a frequency 6 X 10' 3 , while 

 the luminous part of the spectrum gives frequencies ranging 

 from about 4x 10 14 to 8 x 10 u per second. To calculate the 

 period for Li by (16) directly we use the relations 



2lN£m/Jcmp:=4-6, 



bTml= -044, 



to find N, which, with the known data for Li, comes out 

 7 x 10 10 in c.G.s. units, with p = *59 this gives 35 x 10 4 for 

 the velocity ^N/p. Taking Kelvin's estimate of about 10 25 

 ordinary molecules to the c. c, we have 5 x 10~ 9 for the order 

 of the linear dimensions of the Li atom, and then the required 

 frequency 35 x 10 4 -^l()- s is of the order 3"5 x 10 13 . That this 

 eomes so near the known periods in the luminous spectra I 

 take to be strong confirmation of our principle that the 

 mechanical vibrations of the atoms are an important part of 

 the cause of their luminous vibrations. 



The substance of this section can be summarized popularly, 

 if somewhat loosely, in the statement that the light emitted 

 by atoms is simply their sound electrically transformed. 



As we have just proved that the elastic vibrations of the 



