252 KINETIC THEORIES OF GRAVITATION. 



" Making the only hypothesis which is consistent with the theoretical 

 principles advor'ated in this work, namely, that the ultimate atoms of 

 the glass are kept asunder by the repulsive action of ietherial 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 uudu-a- 

 tions of the aether for which the values of A 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 ?ether by the vibrations 

 and motions of atoms. Although the periods of the tetherial 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 We 



have Siitherto 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 A would be much larger for the composite waves than for 

 the components." t 



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

 of Attractive an<l Repulsive Forces," says in regard to the discussion of 

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

 ceeded in overcoming the mathematical difBculty of eflectinga second 

 apf»roximation 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 vaiions 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 Hi and 

 Hz^ (rei)resenting 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 licat, molecular attraction, and gravity^ 

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

 l)lete." And he admits that for any purpose of quantitative determina- 



* Opere cltat., iip. 4.56, 459. t Ojjtre cital., pp. 463, 489. 



