﻿7 he Theory of Spectral Series. 661 



If .r, //, z are the coordinates of the centre of mass of the 

 n electrons we have 



nw = %#, ny=%y, nz = %~. 



The radiation is therefore determined by the acceleration of 

 the centre of mass of the electrons in the atom. This can 

 be easily found, for each electron is attracted to the origin 

 by a force — fir proportional to its distance (V) from the 

 origin and acted on by forces due to the other electrons. 

 The forces between the electrons will not affect the motion 

 of the centre of mass, so that we have 



with similar equations for y and z. Here M denotes the 

 mass of one electron. Thus the centre of mass has three 

 equal periods of vibration about the origin of period 



'M 



T = 2™/M 

 V fi 



This therefore is the period" of the radiation emitted by the 

 atom, for all other possible periods are practically ineffective. 

 We have also fju — ^irep, where e is the charge on one electron 

 and p the charge per c.c. in the positive sphere. Hence 

 if v =l/\, where X is the wave-length of the light emitted, 

 we get 



-V 



37TC 2 M 



where c denotes the velocity of light. 



It appears therefore that v depends only on p since c, e, 

 and M are constants. To explain the different values of v 

 in the spectra we must therefore suppose that p has different 

 values in the molecules emitting the different lines. 



There are two distinct ways in which p can be supposed 

 to be changed. First we may suppose that when a number 

 of atoms combine to form a molecule they produce a positive 

 sphere of different density, so that if m denotes the number 

 of atoms in a molecule we have a series of values of p corre- 

 sponding to m = l. 2, 3, 4 ... . Secondly, a molecule may 

 lose a number of electrons, say n 9 and we may suppose that 

 the loss of an electron produces a change in p. 



According to this we should expect p and hence v to be a 

 function of the two integers m and ». 



When two atoms combine there is as a rule a diminution 



