Not only does this deduction, being
made in the logical form,
If A is B, X is Y;
but X is Y;
therefore A is B,
not follow at all, but it is absolutely not true. The body under the
circumstances might describe an hyperbola as welt as an ellipse, as
Professor Mitchell himself subsequently remarks.
The author's explanation of the manner in which the attraction of the
sun changes the position of the moon's orbit is entirely at fault. He
supposes the line of nodes of the moon's orbit perpendicular to the
line joining the centres of the earth and sun, and the moon to start
from her ascending node toward the sun, and says that in this case
the effect of the sun's attraction will be to diminish the
inclination of the moon's orbit during the first half of the
revolution, and thus cause the node to retrograde; and to increase it
during the second half, and thus cause the nodes to retrograde. But
the real effect of the sun's attraction, in the case supposed, would
be to diminish the inclination during the first quarter of its
revolution, to increase it during the second, to diminish it again
during the third, and increase it again during the fourth, as shown
by Newton a century and a half ago.
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