Spectra and Planch's Law. 421 



effect caused by systems in the normal atom having periods 

 of vibration identical with those of the lines absorbed, and 

 that there are in the normal atom vibrators with the same 

 period as some of those in the luminous atom. There are, 

 however, lines in the subordinate series in the emission 

 spectrum which do not appear in the absorption one : thus it 

 would appear that some of the atoms in the luminous gas 

 differ from those in the normal gas inasmuch as the electrons 

 vibrate with different periods in the two cases. The absorp- 

 tion spectrum is, however, sufficiently complicated to prove 

 that it cannot be represented by the vibrations of a few 

 electrons under the influence of their own repulsions and 

 the attraction exerted upon them by a positive charge, if 

 these attractions and repulsions follow the simple law of 

 the inverse square. 



Though it is natural in any investigation of the equilibrium 

 of electrons and positive charges to begin by assuming that 

 the attraction between the positive and negative charges 

 varies inversely as the square of the distance, we must bear 

 in mind that we have no direct evidence from experiment 

 that this law holds at distances comparable with those which 

 separate the electrons and the positive charges in a molecule. 

 The measurement -i and the phenomena which furnish the 

 evidence for the inverse square law relate to distances which 

 are enormous compared with atomic distances. If c l9 c 2 , c 3 

 are of the order of atomic distances, there are no experiments 

 yet made which would distinguish between a force of ljr 2 

 and one of 



fr-*)(i-j)('-;> 



and yet at atomic distances the two forces are quite dis- 

 similar, the second changing from attraction to repulsion 

 and back to attraction again as r passes through the values 

 •Ci, c 2 , c 3 , &c. 



If the positive part of the atom is built up of distinct 

 units the repulsion between them cannot continue down to 

 distances such as those which occur in this part of the atom, 

 otherwise an atom containing several of these units would 

 explode. 



I shall, therefore, consider the consequences of supposing 

 that the field of force round the positive charge, although 

 varying inversely as the square of the distance at large 

 distances from the atom, yet in the atom itself changes 

 backwards and forwards between attraction and repulsion. 

 To fix our ideas let us suppose that the expression for the 



