104 ON FARADAY'S LINES OF FORCE. 



medium through which the fluid is supposed to flow. This resistance depends on 

 the nature of the medium, and will in general depend on the direction in which 

 the fluid moves, as well as on its velocity. For the present we may restrict 

 ourselves to the case of a uniform medium, whose resistance is the same in all 

 directions. The law which we assume is as follows. 



Any portion of the fluid moving through tJie resisting medium is directly 

 opposed by a retarding force proportional to its velocity. 



If the velocity be represented by v, then the resistance will be a force equal 

 to kv acting on unit of volume of the fluid in a direction contrary to that of 

 motion. In order, therefore, that the velocity may be kept up, there must be a 

 greater pressure behind any portion of the fluid than there is in front of it, so 

 that the difference of pressures may neutralise the effect of the resistance. Con- 

 ceive a cubical unit of fluid (which we may make as small as we please, by (5)), 

 and let it move in a direction perpendicular to two of its faces. Then the resist- 

 ance will be kv, and therefore the difference of pressures on the first and second 

 faces is kv, so that the pressure diminishes in the direction of motion at the rate 

 of kv for every unit of length measured along the line of motion ; so that if we 

 measure a length equal to h units, the difference of pressure at its extremities 

 will be kvh. 



(11) Since the pressure is supposed to vary continuously in the fluid, all 

 the points at which the pressure is equal to a given pressure p will lie on a 

 certain surface which we may call the surface (p) of equal pressure. If a series 

 of these surfaces be constructed in the fluid corresponding to the pressures 0, 1, 

 2, 3 &c., then the number of the surface will indicate the pressure belonging to 

 it, and the surface may be referred to as the surface 0, 1, 2 or 3. The unit of 

 pressure is that pressure which is produced by unit of force acting on unit of 

 surface. In order therefore to diminish the unit of pressure as in (5) we must 

 diminish the unit of force in the same proportion. 



(12) It is easy to see that these surfaces of equal pressure must be perpen- 

 dicular to the lines of fluid motion ; for if the fluid were to move in any other 

 direction, there would be a resistance to its motion which could not be balanced 

 by any difleTence of pressures. (We must remember that the fluid here con- 

 sidered has no inertia or mass, and that its properties are those only which are 

 formally assigned to it, so that the resistances and pressures are the only things 



