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 deflection of light demanded by theory was first confirmed during the solar eclipse of 29th May, 1919. (Cf.  Appendix III.)

**) This follows from a generalisation of the discussion in Section 20

BEHAVIOUR OF CLOCKS AND MEASURING-RODS ON A ROTATING BODY OF REFERENCE

Hitherto I have purposely refrained from speaking about the physical interpretation of space- and time-data in the case of the general theory of relativity.  As a consequence, I am guilty of a certain slovenliness of treatment, which, as we know from the special theory of relativity, is far from being unimportant and pardonable.  It is now high time that we remedy this defect; but I would mention at the outset, that this matter lays no small claims on the patience and on the power of abstraction of the reader.