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 _K′_ possessing any kind of motion, then relative to _K′_ there exists a gravitational field which is variable with respect to space and time.[17] The character of this field will of course depend on the motion chosen for _K′._ 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. [17] This follows from a generalisation of the discussion in Section XX. XXIII. 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.