IDOG.] on Electric Disclumic and Sppctrosropy. 199 



neighbouring atoms, comes to an atom will be proportional to the 

 rate at which energy is being communicated to the gas, i.e. to F x i, 

 where F is the electric force and i the current density ; and thus for 

 a constant electric force w^ould be proportional to the current density. 

 The atom will radiate away some of its internal energy; if the rate of 

 this radiation is proportional to the amount of energy E possessed by 

 the atom, say equal to y8 E, then if q is the rate at which energy is 

 being communicated to the atom, we have 



d E 



dt-^-^"" 

 so, if E vanishes with /, 



E=J(1 -e-^) 



Thus q/p is the limit to the energy acquired by the atom, and this is 

 proportional to </, while q is proportional to F * ; so that the atom will 

 acquire the critical amount of energy, or not, according as F/ is 

 greater or less than a certain value. 



Application of these Results to Spectroscopy. — We have seen that 

 the passage from the dark to the luminous discharge occurs with great 

 abruptness, an increase of the potential difference by y^oth of a volt 

 being sufficient under certain circumstances to convert a discharge in 

 which no luminosity at all could be detected to one where it was 

 quite bright. This suggests that the luminosity sets in when the 

 internal energy of the atom — or rather of that part of it which gives 

 rise to the particular kind of light present in the luminous discharge — 

 attains a perfectly definite value. This way of regarding the origin 

 of the luminosity affords a very simple explanation of the variation 

 of the spectrum with the kind of discharge, and of the effect of 

 introducing capacity or self-induction into the circuit containing the 

 discharge tube. Let us consider the rise in energy of a vibrating 

 system inside the atom. Let E be the energy at the time t ; a the rate 

 at which it is absorbing the work done in the discharge tube. The 

 energy may be supplied to it from the Rontgen radiation in the tube, 

 or from the corpuscles which come into collision with the atom : a will 

 be proportional to the rate at which the electric field producing the 

 discharge is doing work in the neighbourhood of the atom we are 

 considering. It will thus be proportional to the product of the electric 

 force and the flux of corpuscles in this neighbourhood. Let us suppose 

 that the system radiates energy at a rate proportional to E, say equal 

 to /? E ; then we have 



dt 



a 



if E = when t = 0. 



or E = - (1 



