174 ON FARADAY'S LIMES OF FORCE. 



the pressure is therefore S'p'. The whole work done by the fluid may there- 

 fore be expressed by 



or more concisely, considering sinks as negative sources, 



(31) Let S represent the rate of production of a source in any medium, 

 and let p be the pressure at any given point due to that source. Then if we 

 superpose on this another equal source, every pressure will be doubled, and 

 thus by successive superposition we find that a source nS would produce a 

 pressure np, or more generally the pressure at any point due to a given 

 source varies as the rate of production of the source. This may be expressed 

 by the equation 



where R is a coefficient depending on the nature of the medium and on the 

 positions of the source and the given point. In a uniform medium whose 

 resistance is measured by k, 



&? /?_A 

 P ~vr' ~47rr' 



R may be called the coefficient of resistance of the medium between the source 

 and the given point. By combining any number of sources we have generally 



(32) In a uniform medium the pressure due to a source S 



A^ 

 P ~47r r' 



At another source S" at a distance r we shall have 



k 



if p' be the pressure at S due to &. If therefore there be two systems of 

 sources 2(<S') and S(6"), and if the pressures due to the first be p and to the 

 second p', then 



For every term &p has a term Sp' equal to it. 



