450 SCIENCE PROGRESS 



thesis gave a term of the above type, its magnitude was too small 

 to account for the observed facts of absorption. The term 

 mn* r is a force of elastic type, tending to draw the electron back 

 to its mean position. The electron, if isolated, and under the 

 action of this force, would emit radiation of frequency n , which 

 may accordingly be called the " natural free period " of the 

 electron. 



The root of the present theory is contained in the fact that 

 the electron, when in the presence of other electrons, will emit 

 radiation of a frequency differing from n . It has been shown by 

 Larmor (vide ALther and Matter) that a system of electrons 

 will emit no radiation if, and only if, a certain condition holds, 

 viz. that 



Se'f = o or P = o 



If then a gas is in such a condition that it is emitting radiation, 

 P must be different from zero, and it must be concluded that it 

 is electrically polarised. The gas on the whole will not neces- 

 sarily exhibit any signs of polarisation, because the polarisation 

 will change rapidly from point to point in both magnitude and 

 direction, but in the neighbourhood of each point it must be 

 assumed that there exists a polarisation P definite as regards 

 magnitude and direction, so that the equation of motion of an 

 electron in it is given by 



mr + mn'r = 47raeP 



The frictional term has been dropped from this equation because 

 it only becomes important when the electron is acted upon by a 

 periodic force whose period is nearly equal to its own natural 

 free period. That this is permissible is also evidenced by the 

 fact that light from a flame or arc may be made to interfere with 

 a path difference of millions of wave lengths, showing that the 

 electrons maintain their vibrations undamped through an 

 enormous number of periods. 



Consider, therefore, the ideal case of a system consisting 

 simply of N similar electrons per unit of volume. Then P = Ner, 

 and may be eliminated from the equation of motion giving 



mr + (mil* - 47rNae 2 )r = o 



and so radiation is emitted of a frequency n given by the equation 



n 2 = n - 47rNae ! /m 

 or, since the second term is found to be small, n is given by 



n = n - 2jrNae 2 /mn 



