It had
long been remarked that the angular velocity of each planet increases
constantly in proportion as the body approaches its centre of motion;
but the relation between the distance and the velocity remained wholly
unknown. Kepler discovered it by comparing the maximum and minimum of
these quantities, by which their relation became more sensible. He
found that the angular velocities of Mars at its nearest and farthest
distances from the sun were in inverse proportion to the squares of the
corresponding distances. This law, deduced, was the immediate path to
the law of orbital ellipticity. For, on attempting to apply his
newly-discovered law to Mars, on the old assumption that its orbit was
a circle, he soon found that the results from the combination of the
two principles were such as could not be reconciled with the places of
Mars observed by Tycho. In this dilemma, finding he must give up one or
the other of these principles, he first proposed to sacrifice his own
theory to the authority of the old system,--a memorable example of
resolute candor. But, after indefatigably subjecting it to crucial
experiment, he found that it was the old hypothesis, and not the new
one, that had to be sacrificed.
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