22 Prof. W. H. Bragg on the "Elastic Medium " 



of restitution is E#, and the energy of the displacement is 



2 • JiliOCr. 



In this case, then, the energy due to the strain of the matter 

 in the cell is i . E# 2 . d . s. 



But considering the equilibrium of the element, 



(p + 8p)s— ps^'Exd.s ; 



E#d=Sp, 



and x.s=$f. 



Thus the energy = ^ . 8p . Bf. 



The energy, therefore, in a cell bounded by a unit tube and 

 two surfaces drawn so that the pressure on one differs by 

 unity from the pressure on the other, is J. 



Hence in any particular case of strain, if we can count the 

 number of cells into which space is divided by tubes and 

 surfaces drawn as above, we can calculate the total energy of 

 the strain. 



4. Since the sether in a conductor is to be regarded as an 

 incompressible fluid free from strain, it possesses the properties 

 of a perfect weightless fluid, and the pressure is the same at 

 every point of the conductor. If the charge on the conductor 

 be Q, then Q unit tubes start from it. If the pressure at the 

 conductor be V, each of these tubes will cut through V sur- 

 faces before it reaches the region of zero-pressure. Conse- 

 quently the number of cells into which space is divided by 

 the surfaces and tubes of a system of conductors containing 

 charges Q 1? Q 2 , Q 3 , &c, the pressures at them being Y 1? V 2 , V 3 , 

 &c, is 



Q1V. + Q2V2 + ..., 



or 



2QV. 



The energy of the system is therefore -J2QV. 



5. As a particular case, consider the energy of strain of a 

 charge Q on a sphere of radius a, there being no other con- 

 ductors near. 



The pressure at the surface of the sphere is 



The energy is therefore 



2 *47r a 

 The energy in the space between the sphere and a con- 



