Cause of the Structure of Spectra. 269 



these. If its fundamental frequency is 27r/f2, tlien it contains 

 standing waves of frequencies (p + r/s)2ir/D l . 



Consider an electron travelling round the atom in a nearly- 

 circular path, with the centre of the path near that of the 

 atom, and with the occurrence of periodical collisions between 

 the electron and the atom. Then if the frequency of these 

 encounters is so adjusted that the electron always meets the 

 atom at the middle of a standing wave or internode, it will 

 take up a maximum of energy there ; and if the frequency is 

 a multiple of that of the standing wave there will be resonance, 

 with a maximum absorption of energy by the electron. Let 

 27r(l + /Lt) be an angular interval between two encounters, 

 then an electron can equally well take up energy at each 

 encounter if it meets the atom at angular intervals 2ir(2 + ii) 



2ir(m^-fjb) or generally 27r(p + r/s), where r and s are 



integers and p is any integer. 



The following curves represent three orbits of electron 

 round atom, first where /x = and the electron makes one 



complete revolution between two encounters, second where 

 fi = '2o and it makes one and a quarter revolution, and third 

 where it makes two revolutions. If the electron associated 

 with the atom of an element has a fixed velocity, and if the 

 nearly circular paths have all the same radius, the radius- 

 vector of the electron has a constant angular velocity a>, and 

 the periods between successive collisions of atom and electron 

 will be (p + r/s)27r/co. For resonance these must be a 

 multiple of (/>+ rj^'lirjil the corresponding period for the 

 standing wave in the atom, or of a sulmiultiple of it ; there- 

 fore 27t/g) the characteristic period for an electron must be a 

 multiple of a submultiple of 2irj£l the fundamental mechanical 

 period of the atom. But for different atoms the latter are 

 harmonically related, and we may conclude that probably the 

 period of the harmonic common to the elements is the same 

 as that of the electron. As the positive and negative electrons 

 have possibly different dynamical relations to the atom and 

 different orbits, the values of fx giving resonance for a positive 

 electron may be different from those for a negative. Thus 

 we can write (m +// a )27r/oj and (m -f //, 2 )27r/a) as simple types 



