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Classical mechanics required to be modified before it could come

into line with the demands of the special theory of relativity.

For the main part, however, this modification affects only the

laws for rapid motions, in which the velocities of matter v are

not very small as compared with the velocity of light. We have

experience of such rapid motions only in the case of electrons

and ions; for other motions the variations from the laws of

classical mechanics are too small to make themselves evident in

practice. We shall not consider the motion of stars until we come

to speak of the general theory of relativity. In accordance with

the theory of relativity the kinetic energy of a material point

of mass m is no longer given by the well-known expression

image020

but by the expression

image021