We may expect important physical properties to be expressible in terms of such integrals, in particular where
is an invariant form for the equations of transformation of [52.2], and when the conditions, which the quantity represented by the integral satisfies, are also invariant in their expression in different time-systems.
The formulae of this subarticle hold of each type of kinematics.
52.4 The hyperbolic type of kinematics has issued in the formulae of the Larmor-Lorentz-Einstein theory of electromagnetic relativity, namely, the theory by which with a certain amount of interpretation the electromagnetic equations are invariant for these transformations.
The physical meaning of
is also well known; namely, any velocity which in any time-system is of magnitude
is of the same magnitude in every other time-system. No assumption of the existence of a velocity with this property or of the electromagnetic invariance has entered into the deduction of the kinematic equations of the hyperbolic type. A velocity greater than