422 Sir J. J. Thomson on tlie Origin of 



sin cu 



force contains the factor where u = l/?\ and r is the 



cu 



distance from the centre. When r is great compared with c T 



sin cujcu is unity, so that this factor does not affect the force 



at great distances. Inside the atom, if atomic dimensions 



are comparable with c, there will be a series of positions of 



equilibrium determined by cu~nir or r=c/nw w 7 here n is an 



integer. Thus even if there is only one positive charge and 



one electron there may be a single infinite series of atoms 



with the electron at distances from the centre represented 



by r = — ; the times of vibrations of the electrons about 



these positions would be different, so that a collection of 

 such atoms could give rise to an infinite number of lines 

 both in the absorption and emission spectra. Each line- 

 would arise from a different kind of atom ; the brightness of 

 the line would depend, along with other things, on the 

 number of atoms of the kind giving out the particular line. 

 The theory of dispersion enables us, if we know the con- 

 nexion between the refractive index and the wave-length,. 

 to calculate the number of systems which vibrate in any 

 particular period. Bevan applied this method to find the 

 number of atoms in sodium vapour wdiich could vibrate 

 in unison with the different lines in the principal series of 

 this metal. He found that the number of atoms which can 

 give out or absorb the D line is about one twelfth of the 

 total number of atoms, while only about one in 1000 can 

 give out the pair 3303, and about one in 5500 the pair 2852. 



Thus the number of atoms corresponding to a line in the 

 principal series diminishes very rapidly as the number which 

 represents the position of the line in the series increases, 

 and though different kinds of atoms may exist, the great 

 majority of them are of one kind. 



It is remarkable that only about 9 per cent, of the Sodium 

 atoms are of the type giving lines in the visible part of the 

 principal series. This suggests that perhaps the strongest 

 line in the series may be a line in the infra red. An atom of 

 one kind may, by physical or chemical processes^ be trans- 

 formed to one of another kind. Thus, if an atom with the 

 electron at P were ionized, it would be positively electrified 

 and would attract an electron from outside ; this electron 

 might, however, settle at another point of equilibrium Q, 

 giving rise to a different type of atom. 



It would seem that these different types of atoms would 

 differ in other respects than the period of vibration of the 



