S6 Mr maxwell, on FARADAY'S LINES OF FORCE. 



difference of the pressures in the two former distributions. In this case, since the pressures 

 at the surface and the sources within 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 (l6) 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 



The rate of decrease of pressure is therefore kv or — -, and since the pressure = 



when r is infinite, the actual pressure at any point will he p = . 



47rr 



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 



k 



47rr 



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



kS 



pressure will be » = , so that the pressure at a given distance varies as the resistance 



47rr 



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 of (14) we can determine the distribution of sources to which a given distribution 

 of pressures is due. 



(20) We have next to shew that if we conceive any imaginary surface as fixed in 

 space and intersecting the lines of motion of the fluid, we may substitute for the fluid 

 on one side of this surface a distribution of sources upon the surface itself without altering 

 in any way the motion of the fluid on the other side of the surface. 



For if we describe the system of unit tubes which defines the motion of the fluid, 

 and wherever a tube enters through the surface place a unit source, and wherever a tube 

 goes out through the surface place a unit sink, and at the same time render the surface 

 impermeable to the fluid, the motion of the fluid in the tubes will go on as before. 



