considerations only for the case, which is never strictly realised, in which the
electrical masses are quite at rest relatively to each other, and to the co-ordinate
system. Should we be justified in saying that for this reason electrostatics is
overthrown by the field-equations of Maxwell in electrodynamics ? Not in the
least. Electrostatics is contained in electrodynamics as a limiting case ; the laws
of the latter lead directly to those of the former for the case in which the fields
are invariable with regard to time. No fairer destiny could be allotted to any
physical theory, than that it should of itself point out the way to the introduction
of a more comprehensive theory, in which it lives on as a limiting case.
In the example of the transmission of light just dealt with, we have seen that the
general theory of relativity enables us to derive theoretically the influence of a
gravitational field on the course of natural processes, the Iaws of which are
already known when a gravitational field is absent. But the most attractive
problem, to the solution of which the general theory of relativity supplies the
key, concerns the investigation of the laws satisfied by the gravitational field
itself. Let us consider this for a moment.
We are acquainted with space-time domains which behave (approximately) in a "
Galileian " fashion under suitable choice of reference-body, i.e. domains in
which gravitational fields are absent. If we now refer such a domain to a
reference-body K1 possessing any kind of motion, then relative to K1 there
exists a gravitational field which is variable with respect to space and time.[3]**
The character of this field will of course depend on the motion chosen for K1.
According to the general theory of relativity, the general law of the gravitational
field must be satisfied for all gravitational fields obtainable in this way. Even
though by no means all gravitationial fields can be produced in this way, yet we
may entertain the hope that the general law of gravitation will be derivable from
such gravitational fields of a special kind. This hope has been realised in the
most beautiful manner. But between the clear vision of this goal and its actual
realisation it was necessary to surmount a serious difficulty, and as this lies deep
at the root of things, I dare not withhold it from the reader. We require to extend
our ideas of the space-time continuum still farther.
Notes
*) By means of the star photographs of two expeditions equipped by a Joint
Committee of the Royal and Royal Astronomical Societies, the existence of the