Mr maxwell, ON FARADAY'S LINES OF FORCE. 37 



(21) If the system of pressures and the distribution of sources which produce them 

 be known in a medium whose resistance is measured by k, then in order to produce the 

 same system of pressures in a medium whose resistance is unity, the rate of production 

 at each source must be multiplied by k. For the pressure at any point due to a given 

 source varies as the rate of production and the resistance conjointly; therefore if the pressure 

 be constant, the rate of production must vary inversely as the resistance. 



(22) On the conditions to be fulfilled at a surface which separates two media whose 

 coefficients of resistance are k and k'. 



These are found from the consideration, that the quantity of fluid which flows out 

 of the one medium at any point flows into the other, and that the pressure varies con- 

 tinuously from one medium to the other. The velocity normal to the surface is the same 

 in both media, and therefore the rate of diminution of pressure is proportional to the 

 resistance. The direction of the tubes of motion and the surfaces of equal pressure will 

 be altered after passing through the surface, and the law of this refraction will be, that it 

 takes place in the plane passing through the direction of incidence and the normal to the 

 surface, and that the tangent of the angle of incidence is to the tangent of the angle of 

 refraction as k' is to k. 



(23) Let the space within a given closed surface be filled with a medium different 

 from that exterior to it, and let the pressures at any point of this compound system due 

 to a given distribution of sources within and without the surface be given ; it is required 

 to determine a distribution of sources which would produce the same system of pressures 

 in a medium whose coefficient of resistance is unity. 



Construct the tubes of fluid motion, and wherever a unit tube enters either medium 

 place a unit source, and wherever it leaves it place a unit sink. Then if we make the 

 surface impermeable all will go on as before. 



Let the resistance of the exterior medium be measured by k, and that of the interior 

 by k'. Then if we multiply the rate of production of all the sources in the exterior medium 

 (including those in the surface), by k, and make the coefficient of resistance unity, the 

 pressures will remain as before, and the same will be true of the interior medium if we 

 multiply all the sources in it by k', including those in the surface, and make its resistance 

 unity. 



Since the pressures on both sides of the surface are now equal, we may suppose it 

 permeable if we please. 



We have now the original system of pressures produced in a uniform medium by a 

 combination of three systems of sources. The first of these is the given external system 

 multiplied by k, the second is the given internal system multiplied by k', and the third is the 

 system of sources and sinks on the surface itself. In the original case every source in the 

 external medium had an equal sink in the internal medium on the other side of the surface, 

 but now the source is multiplied by k and the sink by k', so that the result is for every 

 external unit source on the surface, a source = {k - Ic). By means of these three systems of 

 sources the original system of pressures may be produced in a medium for which i = 1. 



