The Mathematical auxiliaries developed under ‘B’ at once enables us to
generalise, according to the generalised theory of relativity, the
physical laws of matter (Hydrodynamics, Maxwell’s Electro-dynamics) as
they lie already formulated according to the special-relativity-theory.
The generalised Relativity Principle leads us to no further limitation
of possibilities; but it enables us to know exactly the influence of
gravitation on all processes without the introduction of any new
hypothesis.
It is owing to this, that as regards the physical nature of matter (in a
narrow sense) no definite necessary assumptions are to be introduced.
The question may lie open whether the theories of the electro-magnetic
field and the gravitational-field together, will form a sufficient basis
for the theory of matter. The general relativity postulate can teach us
no new principle. But by building up the theory it must be shown whether
electro-magnetism and gravitation together can achieve what the former
alone did not succeed in doing.
§19. Euler’s equations for frictionless adiabatic liquid.
Let _p_ and ρ, be two scalars, of which the first denotes the pressure
and the last the density of the fluid; between them there is a relation.
Let the contravariant symmetrical tensor