Nipher — The Electrical Capacity of Bodies. 117 



If the sphere be collapsed by external pressure the radius 

 being shortened by dr, the work applied to the element dS 

 against the opposing electrical repulsion is 



aHxt a a ^^ ^^ a 

 d W = d p dr = o 1 d<«; 



The work required to shorten the radius from r" to r' will 

 be found by integrating in co over the surface of the sphere 

 and by integrating in r between r" and r'. Hence we have 



r" 4 n 



This shows that the work done on the sphere is equal to the 

 difference between its initial and final energy. 



Q' 1 

 If the initial radius were infinite, the work done is -tt — 



2 r 



The force within the electrified surface is zero, but as the 

 radius of the sphere shortens, the electrical density and there- 

 fore the strength of field at the surface increases. Accord- 

 ing to older views the charge on the surface exerts mutual 

 repulsions, and the work done consists in overcoming this 

 repulsion. This view still gives color to modern statements 

 just as astronomers sometimes speak of the daily motion of 

 the sun. But we may also say that as parts of the medium 

 pass through the electrified surface, they are thrown 

 into a condition of stress. When a point in the medium is 

 at the contracting surface the force is 4 jra where a is the den- 

 sity at the point. As the surface leaves this point, the force 

 at the point remains unchanged. The condition of 

 stress into which the medium is thrown is main- 

 tained constant at a value directly dependent on the 

 value of <r when the surface was at the point. 

 As the surface is pressed in toward the system, it must 

 deform and coincide with the equipotential surfaces of the 



