282 Mr Hicks, On the proUem of two [Oct. 27, 



If a . 6 be the mean radii, and the spheres pulsate in the same 

 period T with a difference of phase 6, and with ampHtudes a . yS 



respectively, the mean values of a^ -rr and b^ -,^ are both 



= — -nw a^^^^yS cos 0, 



a, /S being supposed so small that we may neglect quantities com- 

 parable to their cubes. 



Hence i^, = i^, = - -^ . ^^^ cos 6", 



and the spheres attract one another when their pulsations are on 

 the whole concordant, and repel when not so. 



As an example, if the spheres be equal, their radii 6 in., distance 

 of centres 2 ft., the amplitude of pulsation -^ in., the time of 

 pulsation be -^ sec, and the fluid water, the force is about the 

 weight of '42 oz. 



6. The property possessed by two pulsating spheres in a fluid 



acting on one another with a force whose principal part varies 



inversely as the square of the distance, belongs also to all pulsating 



bodies. This follows at once from a remark made by Stokes in his 



paper " On some cases of Fluid Motion," where he states that 



whenever there is a chancre of volume of a body in a fluid, the 



. A 



velocity potential contains a term of the form — . It at once 



suggests itself to apply this principle to the explanation of gravi- 

 tation. All we have to suppose is that atoms pulsate with a 

 constant period, and that none have phases differing by more than 

 90", or that if such once existed, they have been eliminated. The 

 properties of a system consisting of a mixture of atoms pulsating 

 with every possible difference of phase would be interesting to 

 investigate : one curious property follows at once, that though of 

 three atoms two might attract the third, they would not neces- 

 sarily attract each other. If the theory offered is the true one 

 for the explanation of gravitation, it would be possible to have 

 celestial systems, the parts of which in each would obey the law 

 of gravitation, but which would not influence each other, or would 

 repel each other. 



It has been pointed out, that though Thomson's theory of the 

 vortex atom explains more properties of the atom than any other 

 theory, yet it seems not to lend itself to any reasonable explana- 

 tion of gravitation. In consequence Sir W. Thomson himself 

 resuscitated Le Sage's theory of ultramundane corpuscles; but 



