426 Mr. J. H. Jeans on the 



of stable equilibrium exists. It is not hard to see that positive 

 and negative charges would rush together and annihilate one 

 another until there would be nothing left to distinguish the 

 point at which a body ought to be from a point in empty 

 space. In fact a consideration of the physical " dimensions '*. 

 of the quantities concerned, will show that there could be 

 nothing to determine the linear scale of the atom *. 



§ 10. An escape from this dilemma is for the moment 

 made possible by supposing the stability of an atom to be 

 kinetic rather than statical, but this seems (to the present 

 author at least) to lead to a new and apparently insurmount- 

 able difficulty. There will be an infinite number of steady 

 motions possible, and a different series of vibrations will be 

 possible about each state of steady motion. The periods of 

 the vibrations, then, will not form a spectrum of disconnected 

 lines, but of continuous bands. We cannot suppose the ions 

 in an atom to be oscillating about a state of steady motion 

 which is the same for all atoms, for even if the atoms were 

 once arranged in this special state, they would rapidly depart 

 from it under the influence of collisions. To explain the line- 

 spectrum of an element, it would be necessary to suppose that 

 the vibrations by which it was produced were not vibrations 

 of the ions as rigid bodies, but vibrations internal to the ions, 

 and, moreover, vibrations which do not depend on the con- 

 figuration of ions in the atom. If this is the true account of 

 the origin of the line-spectrum, it is very hard to see why the 

 spectra of different elements are not all the same. Further,, 

 the ratio of the charge of an ion to its mass, which is deduced 

 from the magnitude of the Zeeman effect, on the assumption 

 that the spectral lines arise from bodily vibrations of the 

 negative ions, is in close agreement with the actual value of 

 this ratio ; and this fact supplies a powerful argument against 

 supposing that the lines of the visible spectrum arise from 

 vibrations of units smaller than the negative ion. 



§ 11. A second way of escape from the dilemma of § 9 is 

 opened by supposing that the ions are not strict point charges, 

 but that in some sense they possess size. In this case the law 

 of force will not be that of the inverse square at all distances. 

 The law of the inverse square will require correction at dis- 

 tances comparable with the size of an ion, so that two 

 ions of opposite charge will not necessarily rush together and 

 annihilate one another, and the objection of § 9 falls through. 



For this explanation to hold, it is necessary that two ions 

 should repel one another at very small distances, independently 

 of their sign, and this shows that the force cannot be pro- 

 portional simply to the product of their charges. 

 * Cf. Larmor, ^Ether and Matter, § 122. 



