TRANSACTIONS OF SECTION A. 59 



Eether from a spherical conductor, the conductor being far from 

 all other conductors. The strain is obviously symmetrical. 



Let Q = amount of charge, a the radius of the conductor. 

 Then, all round the conductor the medium is pushed back a 



distance , ., ; and at a distance r from the centre of the 

 47ra" 



sphere the displacement is j^ . 



Suppose that, when a unit volume of the medium is dis- 

 placed a distance x, the force called into play is E.r. 



Draw a cone of very 

 small angle from o, the 

 centre of the sphere. Let 

 it intercept on the surface 

 of radius r an area s, and 

 on that of radius r-\-h- an 

 area s'. The angle of the 

 cone being exceedingly small, 

 s may be considered equal to .s'. The volume included by the 

 cone and the two surfaces = s8r. 



Hence the force of restitution due to the displacement of 



this amount of matter through a distance 7 — 5- 



= E.s8r.-9_, 

 47rr- 

 E being the elastic constant. 



If, now, ]) be the pressure at a distance r from 0, and 

 p + hp the pressure at a distance r + Zr, we have at once 



. E8r .Q.s 



- % . s = — . , 



^ 47rr- 



_ ^ _ E Q 



dr 4:Trf^ 



Or « = _— + constant. 



^ 47rr 



The constant must = 0, since 2^ must vanish at co. 



" ^^ 47rr" 

 3. If we consider the case of a " charge " imparted to a 

 conductor of any shape whatever, it will not be ordinarily pos- 

 sible by this method to determine the actual state of any 

 part of the dielectric ; neither is it possible by the other 

 method. But, just as in the ordinary case lines of force and 

 equipotential surfaces may be drawn, so here we may learn a 

 great deal by drawing lines of displacement and surfaces of 

 equal pressure. 



