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This expression approaches infinity as the velocity v approaches

the velocity of light c. The velocity must therefore always

remain less than c, however great may be the energies used to

produce the acceleration. If we develop the expression for the

kinetic energy in the form of a series, we obtain

image022

When

image023

is small compared with unity, the third of these terms is always

small in comparison with the second, which last is alone

considered in classical mechanics. The first term mc2 does not

contain the velocity, and requires no consideration if we are

only dealing with the question as to how the energy of a

point-mass; depends on the velocity. We shall speak of its

essential significance later.