in the direction of motion of an object to the value
is, however, in the new theory the expression of the general fact that the dimensions of a body have only a relative meaning, that is, that their values depend on the state of motion of the observer, which determines the dimensions of the body in question. This holds for the extension of bodies in time as well as in space. From the point of view of the new principle of relativity the negative result of the Michelson-Morley experiment was self-explained. But what was the position with regard to the other fundamental facts of optics and electrodynamics? The result of Fizeau's experiment concerning the velocity of light in flowing water became a direct test of the kinematics arising out of the new formulæ. According to the Lorentz transformation the two velocities,
and
with which, for example, two locomotives approach each other, do not merely become added, so that
would be the relative velocity of each with respect to the other, but rather each engine-driver will find as the velocity with which he passes the other driver, the value