Thus equations (i) of [49.7] give
These are the formulae for the ordinary Newtonian relativity.
These formulae are well in accordance with common sense and are in fact the formulae naturally suggested by ordinary experience. To some extent the hyperbolic formulae lead to unexpected results, though, if
be a velocity not less than that of light, the divergences from the deliverances of common sense take place in respect to phenomena which are not manifest in ordinary experience. But when by refined methods of observation the divergences between the two types of kinematics should be apparent to the senses, experiment has, so far, pronounced in favour of the hyperbolic type. Accordingly it is this type which we consider in the sequel.
52.9 There is however one objection to the hyperbolic type, as compared to the parabolic type, which is worth considering. In the hyperbolic kinematics there is an absolute velocity
with special properties in nature. The difficulty which is thus occasioned is rather an offence to philosophic instincts than a logical puzzle. But certainly our familiar experience, in some way which it is difficult to formulate in words, leads us to shun the introduction of such absolute physical quantities. This particular difficulty is largely diminished by noting that the existence of