based upon Electromagnetic Theory. 587 



This may be converted into the mathematically equivalent 

 conception of a tension along the surface by the formula, 



T=p AWH p ' • • • • (73) 



T being the tension and r and r the two radii of curvature 

 of the surface, which merge into a when the surface is 

 spherical. Let it now be supposed that the original sphere 

 is distorted by rotation, say, into the form of an oblate 

 spheroid, while both the volume of the charge and the 

 tension along the surface remain unaltered. The work done 

 against the tension to stretch the surface over a larger area, 

 say A, is, therefore, AT. But this energy must be equated 

 to ???c 2 /4, giving 



AT = A^P = 3AE 2 /167ra 3 £ = mc 2 /4, . . (74) 

 it 



whence. A=]$ira 2 (75) 



The original area of the sphere being four great circles must 

 be stretched according to this 16/15ths of a great circle. If 

 the shape is an oblate spheroid, this assumption deter- 

 mines the eccentricity, and the major and minor axes of the 

 ellipse representing the meridian section. The result is 

 the eccentricity 



e = 0'945, (76) 



and the ratio of the axes is 



a/b = 3-058 (77) 



A rigorous way to approach the problem of completely 

 determining the internal state of motion is obviously to 

 divide the body of charge up into elementary coaxial con- 

 tinuous rings, and after obtaining the effect of one upon the 

 other integrate for a distribution that will keep the surface- 

 pressure constant, but so far the problem has not been solved 

 even for two elementary rings in such close proximity as 

 to include both within the same body. The difficulty is that 

 the method employed for great distances breaks down for 

 distances comparable with the radius of the ring, the series 

 becoming non-convergent. The solution must be reached in 

 another way. 



For the present it will be assumed that, since the electrons 

 in the atom are not to revolve in rings, and since the nucleus 

 is the main body contributing to the mass of the atom, it 



2R 2 



