166 ox FARADAY'S LINES OF FORCE. 



together, since the rate of decrease of pressure along any line will be the sum 

 of the combined rates, the velocity in the new system resolved in the same 

 direction will be the sum of the resolved parta in the two original systems. 

 The velocity in the new system will therefore be the resultant of the velocities 

 at corresponding points in the two former systems. 



It follows from this, by (9), that the quantity of fluid which crosses any 

 fixed surface is, in the new system, the sum of the corresponding quantities in 

 the old ones, and that the sources of the two original systems are simply 

 combined to form the third. 



It is evident that in the system in which the pressure is the difference 

 of pressure in the two given systems the distribution of sources will be got 

 by changing the sign of all the sources in the second system and adding them 

 to those in the first. 



(16) If the pressure at every point of a closed surface be the same and 

 equal to p, and if there be no sources or sinks within the surface, then there 

 will be no motion of the fluid within the surface, and the pressure within it 

 will be uniform and equal to p. 



For if there be motion of the fluid within the surface there will be tubes 

 of fluid motion, and these tubes must either return into themselves or be 

 terminated either within the surface or at its boundary. Now since the fluid 

 always flows from places of greater pressure to places of less pressure, it 

 cannot flow in a re-entering curve; since there are no sources or sinks within 

 the surface, the tubes cannot begin or end except on the surface ; and since 

 the pressure at all points of the surface is the same, there can be no motion 

 in tubes having both extremities on the surface. Hence there is no motion 

 within the surface, and therefore no difference of pressure which would cause 

 motion, and since the pressure at the bounding surface is p, the pressure at 

 any point within it is also p. 



(17) If the pressure at every point of a given closed surface be known, 

 and the distribution of sources within the surface be also known, then only 

 one distribution of pressures can exist within the surface. 



For if two different distributions of pressures satisfying these conditions 

 could be found, a third distribution could be formed in which the pressure at 

 any point should be the difference of the pressures in the two former distri- 

 butions. In this case, since the pressures at the surface and the sources within 



