This conception is feasible, because to us the experience of the existence of a field of force (namely the gravitation field) has shown that it possesses the remarkable property of imparting the same acceleration to all bodies. The mechanical behaviour of the bodies relative to K′ is the same as experience would expect of them with reference to systems which we assume from habit as stationary; thus it explains why from the physical stand-point it can be assumed that the systems K and K′ can both with the same legitimacy be taken as at rest, that is, they will be equivalent as systems of reference for a description of physical phenomena. From these discussions we see, that the working out of the general relativity theory must, at the same time, lead to a theory of gravitation; for we can “create” a gravitational field by a simple variation of the co-ordinate system. Also we see immediately that the principle of the constancy of light-velocity must be modified, for we recognise easily that the path of a ray of light with reference to K′ must be, in general, curved, when light travels with a definite and constant velocity in a straight line with reference to K. § 3. The time-space continuum. Requirements of the general Co-variance for the equations expressing the laws of Nature in general. In the classical mechanics as well as in the special relativity theory, the co-ordinates of time and space have an immediate physical significance; when we say that any arbitrary point has _x₁_ as its X₁ co-ordinate, it signifies that the projection of the point-event on the X₁-axis _ascertained_ by means of a solid rod according to the rules of Euclidean Geometry is reached when a definite measuring rod, the unit rod, can be carried _x₁_ times from the origin of co-ordinates along the X₁ axis. A point having _x₄_ = _t₁_ as the X₄ co-ordinate signifies that a unit clock which is adjusted to be at rest relative to the system of co-ordinates, and coinciding in its spatial position with the point-event and set according to some definite standard has gone over _x₄_ = _t_ periods before the occurrence of the point-event. This conception of time and space is continually present in the mind of the physicist, though often in an unconscious way, as is clearly recognised from the role which this conception has played in physical measurements. This conception must also appear to the reader to be lying at the basis of the second consideration of the last paragraph and imparting a sense to these conceptions. But we wish to show that we are to abandon it and in general to replace it by more general conceptions in order to be able to work out thoroughly the postulate of general relativity,—the case of special relativity appearing as a limiting case when there is no gravitation.