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PRINCIPLE OF RELATIVITY

*impulse-vector*, and *m-times* the acceleration-vector at P as the *force-vector of motion*, at P. According to these definitions, the following law tells us how the motion of a point-mass takes place under any moving force-vector^{[1]}:

*The force-vector of motion is equal to the moving force-vector. *

This enunciation comprises four equations for the components in the four directions, of which the fourth can be deduced from the first three, because both of the above-mentioned vectors are perpendicular to the velocity-vector. From the definition of T, we see that the fourth simply expresses the "Energy-law." Accordingly *c²-times the component of the impulse-vector in the direction of the t-axis* is to be defined as *the kinetic-energy* of the point-mass. The expression for this is

*i.e.*, if we deduct from this the additive constant *mc*², we obtain the expression ½mv² of Newtonian-mechanics up to magnitudes of *the order of* . Hence it appears that *the energy* depends *upon the system of reference*. But since the *t*-axis can be laid in the direction of any time-like axis, therefore the energy-law comprises, for any possible system of reference, the whole system of equations of motion. This fact retains its significance even in the limiting: ease c = ∞, for the axiomatic construction of Newtonian mechanics, as has already been pointed out by T. R. Schütz.^{[2]}