In doing this, however, he has fallen into errors so numerous, and
occasionally so grave, that they are difficult to be accounted for,
except on the supposition that some portions of the work were written
in great haste. Passing over a few mere oversights, such as a
statement from which it would follow that a transit of Venus occurred
every eight years, mistakes of dates, etc., we cite the following.
On page 114, speaking of Kepler's third law, the author says, "And
even those extraordinary objects, the revolving double stars, are
subject to the same controlling law." Since Kepler's third law
expresses a relationship between the motions of three bodies, two of
which revolve around a third much larger than either, it is a logical
impossibility that a system of only two bodies should conform to this
law.
On page 182, it is stated, that Newton's proving, that, if a body
revolved in an elliptical orbit with the sun as a focus, the force of
gravitation toward the sun would always be in the inverse ratio of
the square of its distance, "was equivalent to proving, that, if a
body in space, free to move, received a single impulse, and at the
same moment was attracted to a fixed centre by a force which
diminished as the square of the distance at which it operated
increased, such a body, thus deflected from its rectilinear path,
would describe an ellipse," etc.
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