252 KINETIC THEORIES OF GRAVITATION. 



" Making the only hypothesis which is consistent with the theoretical 

 principles advocated in this work, namely, that the ultimate atoms of 

 the glass are kept asunder by the repulsive action of cetherial undula- 

 tions which have their origin at individual atoms, it may be presumed 

 that this atomic repulsion is attributable to undulations incomparably 



smaller than those which cause the sensation of light The only 



additional hypothesis that will now be made is that there are undu'a- 

 tions of the ajther for which the values of I are very much inferior in 

 magnitude to those of the undulations which produce the phenomena of 

 light. The origin of this class of undulations may, as well as that of 

 all others, be ascribed to disturbances of the rather by the vibrations 

 and motions of atoms. Although the periods of the retherial vibrations 

 may, under particular circumstances, be determined by the periods of 

 the vibrations of the atoms, this is not necessarily the case. . . . "* 



" However small may be the condensation propagated from a single 

 atom, the resulting condensation from an aggregation of atoms con- 

 tained in a spherical space will be of sensible magnitude at distances 

 from the center of the space very large compared to its radius, provided 

 the space be not less than a certain finite magnitude, and the atoms 



contained in it be not fewer than a certain finite number Wo 



have hitherto had under consideration the waves of atomic repulsion 

 and the waves of molecular attraction, and it was argued that the lat- 

 ter might result from compositions of the former, and that in that case 

 the values of X would be much larger for the composite waves than for 

 the components."! 



In 1872, the author again writing " Ou the Hydrodynamical Theory 

 of Attractive ami Repulsive Forces," says, in regard to the discussion of 

 the first and second orders of small quantities, " Having in fact suc- 

 eeeded in overcoming the mathematical difficulty of effecting a second 

 approximation by this means, [starting from the first approximation,] 

 1 have ascertained that the solution contains terms of indefinite increase, 

 whence it must be concluded that the logic of the process is somewhere 

 at fault Both in this Magazine and. in my work on the Mathe- 

 matical Principles of Physics, I have in various ways attempted to solve 

 to the second approximation the problem of the motion of a small 

 sphere acted upon by the vibrations of an elastic fluid. But I must 

 confess that owing to the difficulty of including the effect of the spon- 

 taneous vibrations, my efforts have been only partially successful." He 

 remarks that as his equations involved two unknown constants H x and 

 H 2 , (representing the amounts of wave condensation on the nearer and 

 on the further hemispheres of the atom,) "on this account the theo- 

 ries which attribute the forces of Jicat, molecular attraction, and gravity, 

 to action on the atoms by pressure of the aether in vibration, are incom- 

 plete." And he admits that for any purpose of quantitative determina- 



* Opere citat., pp. 456, 451). t Opcrc dial,, pp. 46)3, 489. 



