shall always be positive or what is equivalent to the same thing, every velocity V should be smaller than _c_. _c_ shall therefore be the upper limit for all substantial velocities and herein lies a deep significance for the quantity _c_. At the first impression, the axiom seems to be rather unsatisfactory. It is to be remembered that only a modified mechanics will occur, in which the square root of this differential combination takes the place of time, so that cases in which the velocity is greater than _c_ will play no part, something like imaginary coordinates in geometry. The _impulse_ and real cause of inducement _for the assumption of the group-transformation G_{c}_ is the fact that the differential equation for the propagation of light in vacant space possesses the group-transformation G_{_c_}. On the other hand, the idea of rigid bodies has any sense only in a system mechanics with the group G_{infinity}. Now if we have an optics with G_{_c_}, and on the other hand if there are rigid bodies, it is easy to see that a _t_-direction can be defined by the two hyperboloidal shells common to the groups G_{∞}, and G_{_c_}, which has got the further consequence, that by means of suitable rigid instruments in the laboratory, we can perceive a change in natural phenomena, in case of different orientations, with regard to the direction of progressive motion of the earth. But all efforts directed towards this object, and even the celebrated interference-experiment of Michelson have given negative results. In order to supply an explanation for this result, H. A. Lorentz formed a hypothesis which practically amounts to an invariance of optics for the group G_{_c_}. According to Lorentz every substance shall suffer a contraction 1:(√(1 - v²/_c²_)) in length, in the direction of its motion _l_/_l′_ = 1/√(1 - _v²_/_c²_) _l′_ = _l_(1 - _v²_/_c²_). This hypothesis sounds rather phantastical. For the contraction is not to be thought of as a consequence of the resistance of ether, but purely as a gift from the skies, as a sort of condition always accompanying a state of motion.