1905.] on the Strurtare of the Atom. 55 



electricity is incompressible, i.e. that its density is constant ; if we 

 had assumed that the volume of the positive electrification is the 

 same whatever may be the quantity of electricity, we should have 

 found that, although there would still have been changes from one 

 element to another, the general trend would have been in the opposite 

 direction, i.e. the simple atoms containing only one corpuscle would 

 gradually condense into more and more complex atoms. 



Chemical Comhination. Action of the Atoms on each other. — We 

 have hitherto confined our attention to the consideration of the 

 stability of the arrangements of the corpuscles in the atom. We shall 

 now proceed to discuss the question of the action of one atom on 

 another, and the possibility of the existence of stable configurations 

 of several atoms, in fact the problem of chemical combination. 



As far as I know, the only cases in which the conditions for equi- 

 librium or stable steady motion of several bodies acting upon each 

 other have been investigated, is that suggested by the solar system ; 

 the case in which a number of bodies — suns, planets, satellites — attract 

 each other with forces inversely proportional to the square of the 

 distance between them. The complete solution of this problem, or 

 anything approaching a complete solution, has proved to be beyond 

 the powers of our mathematical analysis ; but enough has been done 

 to show that with this law of force, stable arrangements of the 

 mutually attracting bodies only occur under stringent conditions. 

 Thus, to take a very simple case, that of three bodies, it has been 

 shown that, when the bodies are equal, there is no arrangement in 

 which the steady motion is stable ; if, however, the masses are very 

 unequal, then it is possible for such an arrangement to exist. Another 

 very interesting case is one investigated by Maxwell in connection 

 with the theory of Saturn's rings. It is that of a large planet sur- 

 rounded by a ring of satellites, each satellite following its neighbour 

 at equal intervals round one circular orbit. Maxwell showed that 

 this system was only stable under certain conditions, the most im- 

 portant being that the mass of the planet must be much greater than 

 that of the satellite. The proportion between the mass of the smallest 

 planet able to retain the ring in steady motion and the mass of one 

 of the satellites increases very rapidly as the number of the satellites 

 increases : if P is the mass of the planet, S that of a satellite, n the 

 number of satellites, Maxwell showed P must be greater than • 43 n^ S. 

 The consequences of this are interesting from the analogy shown in 

 the case of chemical combination. Thus, suppose the mass of a satel- 

 lite were y^-,j part of that of the planet, then the result shows that 

 the planet could retain 1, 2, 3, 4, 5, 6 satellites, but not more than 6. 

 With 6 satellites the planet is, to use a chemical term, saturated with 

 satellites, and the behaviour of the system is equivalent to that of the 

 atom of a sexavalent element, which can unite with 6 but with not 

 more than 6 atoms of hydrogen. 



The existence of a limit to the number of systems in a ring, which 

 a central system can hold in stable equilibrium, is not peculiar to any 



