According to the analogy of the hyperboloid of two sheets, this consists of two sheets separated by _t_ = 0. Let us consider the sheet, in the region of _t_ > 0, and let us now conceive the transformation of _x_, _y_, _z_, _t_ in the new system of variables; (_x’_, _y’_, _z’_, _t’_) by means of which the form of the expression will remain unaltered. Clearly the rotation of space round the null-point belongs to this group of transformations. Now we can have a full idea of the transformations which we picture to ourselves from a particular transformation in which (_y_, _z_) remain unaltered. Let us draw the cross section of the upper sheets with the plane of the _x_- and _t_-axes, _i.e._, the upper half of the hyperbola _c²__t²_ - x² = 1, with its asymptotes (_vide_ fig. 1). Then let us draw the radius rector OA′, the tangent A′ B′ at A′, and let us complete the parallelogram OA′ B′ C′; also produce B′ C′ to meet the x-axis at D′. Let us now take Ox′, OA′ as new axes with the unit measuring rods OC′ = 1, OA′ = (1/c) ; then the hyperbola is again expressed in the form _c²__t′²_ - x′² = 1, t′ > 0 and the transition from (_x_, _y_, _z_, _t_) to (_x′_ _y′_ _z′_ _t_) is one of the transitions in question. Let us add to this characteristic transformation any possible displacement of the space and time null-points; then we get a group of transformation depending only on _c_, which we may denote by G_{_c_}. Now let us increase _c_ to infinity. Thus (1/c) becomes zero and it appears from the figure that the hyperbola is gradually shrunk into the _x_-axis, the asymptotic angle becomes a straight one, and every special transformation in the limit changes in such a manner that the _t_-axis can have any possible direction upwards, and _x′_ more and more approximates to _x_. Remembering this point it is clear that the full group belonging to Newtonian Mechanics is simply the group G_{_c_}, with the value of _c_ = ∞. In this state of affairs, and since G_{_c_} is mathematically more intelligible than G_{∞}, a mathematician may, by a free play of imagination, hit upon the thought that natural phenomena possess an invariance not only for the group G_{∞}, but in fact also for a group G_{_c_}, where _c_ is finite, but yet exceedingly large compared to the usual measuring units. Such a preconception would be an extraordinary triumph for pure mathematics. At the same time I shall remark for which value of _c_, this invariance can be conclusively held to be true. _For c, we shall substitute the velocity of light c in free space._ In order to avoid speaking either of space or of vacuum, we may take this quantity as the ratio between the electrostatic and electro-magnetic units of electricity. We can form an idea of the invariant character of the expression for natural laws for the group-transformation G_{_c_} in the following manner.