ox FARADAY'S LINES OF FORCE. 167 



it are the same in both distributions, the pressure at the surface in the third 

 distribution would be zero, and all the sources within the surface would 

 vanish, by (15). 



Then by (16) the pressure at every point in the third distribution must 

 be zero ; but this is the difference of the pressures in the two former cases, 

 and therefore these cases are the same, and there is only one distribution of 

 pressure possible. 



(18) Let us next determine the pressure at any point of an infinite body 

 of fluid in the centre of which a unit source is placed, the pressure at an 

 infinite distance from the source being supposed to be zero. 



The fluid will flow out from the centre symmetrically, and since unity of 

 volume flows out of every spherical surface surrounding the point in unit of 

 time, the velocity at a distance r from the source will be 



1 



v = 



47JT 3 ' 



Tc 



The rate of decrease of pressure is therefore kv or 3, and since the 



pressure = when r is infinite, the actual pressure at any point will be 



ft 



The pressure is therefore inversely proportional to the distance from the 

 source. 



It is evident that the pressure due to a unit sink will be negative and 



equal to - . 



47JT 



If we have a source formed by the coalition of S unit sources, then the 



resulting pressure will be p = - - , so that the pressure at a given distance 

 varies as the resistance and number of sources conjointly. 



(19) If a number of sources and sinks coexist in the fluid, then in order 

 to determine the resultant pressure we have only to add the pressures which 

 each source or sink produces. For by (15) this will be a solution of the 

 problem, and by (17) it will be the only one. By this method we can 

 determine the pressures due to any distribution of sources, as by the method 



