56 Professor J. J. Thomson [March 10, 



special law of force. We have already seen examples of it inside the 

 atom, where the central force on the satellites is supposed to be pro- 

 portional to the distance. We have just seen that it holds in the 

 planetiiry system, where the central force varies inversely as the square 

 of the distance. I have found that this limit exists for all the laws 

 of force I have tried, although of course the numl)er of satellites which 

 can be held in equilibrium depends on, among other things, the 

 law of force. 



The law of the inverse square is not favourable to the formation 

 of stable systems, even when, as in the astronomical problem, the 

 forces between the various bodies are all attractive ; it is quite incon- 

 sistent with stability when, as in the case of the chemical atoms, some 

 of these bodies carry charges of the same sign, and so repel each other. 

 Thus, suppose we have the central body charged with positive elec- 

 tricity, while the satellites are all negatively electrified, so that the 

 central body attracts the satellites, while the satellites repel each 

 other. With forces varying inversely as the square of the distances 

 between them, it is easy to show that with more than one satellite 

 stability is impossible. 



The mathematical investigation of the case where the satellites 

 repel each other shows that, in order to ensure stability, the central 

 attraction must, in the neighbourhood of the satellite, increase when 

 the distance of the satellite from the planet increases. Inside the 

 atom we have supposed that the central attraction was proportional 

 to the distance from the centre, so that in this region the central 

 force increases rapidly with the distance at all points. It is not neces- 

 sary for equilibrium that the increase should be as rapid as this, nor 

 indeed that the force should everywhere increase with the distance ; all 

 that is necessary is that in the neigh])ourhood of the satellite the 

 force should increase and not decrease as the distance increases. 



It might appear at the outset as though atoms of the kind we 

 have been considering, made up of positive electricity and corpuscles, 

 could never form stable arrangements, for there is a theorem known 

 as Earnshaw's theorem, to the effect that a system of bodies attract- 

 ing or repelling each other with forces varying inversely as the 

 square of the distance between them, cannot be in stable equilibrium. 

 This result does not prevent the existence of stable arrangement of 

 atoms in the molecule, for Earnshaw's theorem only applies to the 

 case when the bodies are at rest ; it does not preclude the existence 

 of a state of steady motion, in which there is no relative motion of 

 the atoms. Again, in the case of our atoms there are other forces 

 besides the electrostatic attractions and repulsions, for if the corpuscles 

 are in rotation inside the atom, they will produce magnetic forces, so 

 that outside the atom there will be a magnetic, as well as an electric 

 field. The magnetic field will greatly promote the stability of the 

 atoms if these are charged, for it will, if strong, practically prevent 

 motion at right angles to the direction of the magnetic force, so that 

 the arrangement of atoms will be stable provided the electrostatic 



