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.
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.
These equations were found by d'Alembert from two principles - that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published in 1752, in his Essai sur la resistance des fluides, was brought to perfection in his Opuscules mathematiques, and was adopted by Leonhard Euler.
A liquid is a fluid which is incompressible or practically so, i.e.
Then dp/dz=kdp/dz = P, = Poe ik, p - po= kpo(ez Ik -1); (16) and if the liquid was incompressible, the depth at pressure p would be (p - po) 1po, so that the lowering of the surface due to compression is ke h I k -k -z= 1z 2 /k, when k is large.
Stokes's theorem becomes an obvious truism if applied to an incompressible fluid.
Let a source of fluid be a point from which an incompressible fluid is emitted in all directions.
Thomson (Lord Kelvin) to form a theory of vortex atoms in a homogeneous, incompressible and frictionless liquid."
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.
Being is the Full i pes, plenum); not-Being is the Void (nEvov, vacuum), the infinite space in which moved the infinite number of atoms into which the single:Being of the Eleatics was broken up. These atoms are eternal and invisible; absolutely small, so small that their size cannot be diminished (hence the name IITOµos, "indivisible"); absolutely full and incompressible, they are without pores and entirely fill the space they occupy; homogeneous, differing only in figure (as A from N), arrangement (as AN from NA), position (as N is Z on its side), magnitude (and consequently in weight, although some authorities dispute this).
Water is comparatively very heavy, inelastic and incompressible; air, on the other hand, is comparatively very light, elastic and compressible.
In 1762 and 1764 he published experiments in refutation of the decision of the Florentine Academy, at that time generally accepted, that water is incompressible; and in 1768 he described the preparation, by calcining oyster-shell with sulphur, of the phosphorescent material known as Canton's phosphorus.
To every proposition in electrostatics there is thus a corresponding one in the hydrokinetic theory of incompressible liquids.