306 



Mr. W. M. Hicks. 



[June 21, 



vanish. If the pulsations of two atoms have natural periods, different 

 or not, bat modified by the action of each other, then there will be a 

 residuary effect also inversely as the square of the distance, but 

 whether attractive or repulsive remains to be seen. It is possible that 

 gravitation may be due to such a residuary action. The force 

 depends on the time of pulsation and the amplitude. For a hollow 

 vortex without core the time for the same atoms depends on the 

 square root of the logarithm of the ratio of the radius of the section 

 to the radius of the aperture, and would therefore vary slowly with 

 alterations of energy. This, therefore, is an objection to the theory 

 that gravitation depends directly on the actual pulsation rather than 

 on the residuary effect mentioned above. The amplitude would 

 naturally vary with the energy, and this would make the attraction 

 between two masses alter with the temperature. On this point no 

 experiments have been made, and the only apparent argument against 

 it that I can think of are Kepler's laws for the motion of the planets. 

 If this theory were true the squares of the periodic times would not 

 vary simply as the cubes of the mean distances, but also as a quantity 

 depending on the mean temperature of each planet. But this is no 

 decisive argument against it, as those distances are not themselves 

 accurately known ; are, in fact, determined by this law from the 

 earth's distance from the sun, determined by other methods. 



The vortex-atom theory has its most interesting connexious with 

 the explanation of the spectral lines of the elements. These lines, so 

 far as they depend on the vibrations of single atoms, might arise from 

 several different kinds of vibrations of the form of the ring. Thus, 

 the hollow ring can have — 



(1.) Deformations of the circular axis: — these must, as has been 

 shown by Sir W. Thomson,* be such that the axis at any time is 

 deformed into a helix wound on the surface of a tore, or the ring is 

 tivisted. This mode of vibration for a solid core of the same density 

 as the surrounding fluid has been investigated by Mr. J. J. Thomson 

 in the memoir referred to above. 



(2.) Waves running round the surface of the ring, so that any cross- 

 section is crimped into small elevations and depressions, and the ring 

 itself is fluted. 



(3.) Vibrations of the aperture. This is really a case of (2). 



(4.) Pulsations of the hollow, whereby the volume of the hollow is 

 periodically altered. 



(5.) Swellings of the ring, travelling in one direction or the other 

 round the ring, so that the ring seems to be beaded. 



Cases (2) and (4), when the ring is moving steadily, are discussed 

 in this paper. 



It would be venturesome to draw conclusions in the present state 

 * " Vortex Statics," " Proc. Roy. Soc. Edin.," ix. 



