322 Mr. G. H. Darwin. [Jan. 20, 



class, all cases which, show a difference in the configuration of the 

 boundaries on the two sides of the plate. All the distributions in the 

 experiments with different temperatures, strengths of solution and of 

 current, belong to the first class ; also those distributions obtained in 

 the non-homogeneous fields, and with ebonite screens. 



On analysing a non-homogeneous field of larger dimensions, parallel 

 distributions were obtained all along a line running between the 

 electrodes, as well as along a central line at right angles to this. But 

 for some distance from the electrodes at the ends, the plates showed 

 non-parallel distributions. 



The paper concludes by drawing attention to the simplicity of the 

 method, and the permanent form of the self-recorded results, and 

 indicates the direction in which it is desirable to extend the research. 



III. " On the Tidal Friction of a Planet attended by several 

 Satellites, and on the Evolution of the Solar System." By 

 G. H. Darwin, F.R.S. Received December 27, 1880. 



(Abstract.) 



The first part of the paper contains the investigation of the changes 

 produced by tidal friction in a system consisting of a planet with any 

 number of satellites revolving round it in circular orbits. The planet's 

 equator and the satellites' orbits are all supposed to be in one plane. 

 The planet is formed of homogeneous viscous fluid, but a large part of 

 the results, due to the particular sort of tidal friction which arises in this 

 special case, would be equally true under a more general hypothesis as 

 to the nature of the planet. The mutual perturbations of the satellites 

 are neglected, so that only the rotation of the planet and the distances 

 of the satellites have to be considered. 



It is then proved that if E be the whole energy, both kinetic and 

 potential, of the system, and if £ be a function of the distance of any 

 one of the satellites from the planet (which function, when the mass of 

 the satellite is small compared with that of the planet, is the J power 

 of the distance), the equation expressive of the rate of change of £ is 



<% = _ A b J? 

 dt eg 



where t is the time, A a certain constant, and b expresses partial 

 differentiation . 



A similar equation applies to each satellite, and the whole of the 

 equations form a system of simultaneous differential equations, which 



