Let a source of fluid be a point from which an incompressible fluid is emitted in all directions.
Stokes's theorem becomes an obvious truism if applied to an incompressible fluid.
But this excess of their contraction is resisted by the almost incompressible inner layers so that the outer layers are prevented from contracting as much as they naturally would if unopposed, and they are thereby virtually stretched.
In the limiting case in which the medium is regarded as absolutely incompressible S vanishes; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new function of the co-ordinates.
A liquid is a fluid which is incompressible or practically so, i.e.
When an electric current flows round a circuit, there is no accumulation of electricity anywhere in the circuit, hence the current strength is everywhere the same, and we may picture the current as analogous to the flow of an incompressible fluid.
To every proposition in electrostatics there is thus a corresponding one in the hydrokinetic theory of incompressible liquids.
But when the rate of change of aethereal strain - that is, of (f,g,h) specified as Maxwell's electric displacement in free aether - is added to it, an analytically convenient vector (u,v,w) is obtained which possesses the characteristic property of being circuital like the flow of an incompressible fluid, and has therefore been made fundamental in the theory by Maxwell under the name of the total electric current.