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.

In Chapter XV. we find the greatest number of errors. Take, for
example, the following computation of the diminution of gravity at
the surface of the sun in consequence of the centrifugal force,--part
of the data being, that a pound at the earth's surface will weigh
twenty-eight pounds at the sun's surface, and that the centrifugal
force at the earth's equator is 1/289 of gravity.

"Now, if the sun rotated in the same time as the earth, and their
diameters were equal, the centrifugal force on the equators of the
two orbs would be equal. But the sun's radius is about 111 times that
of the earth, and if the period of rotation were the same, the
centrifugal force at the sun's equator would be greater than that at
the earth's in the ratio of (111)^2 to 1, or, more exactly, in the
ratio of 12,342.27 to 1. But the sun rotates on its axis much slower
than the earth, requiring more than 25 days for one revolution. This
will reduce the above in the ratio of 1 to (25)^2, or 1 to 625; so
that we shall have the earth's equatorial centrifugal force (1/289) x
12,342.27 / 625 = 12,342.27/180,605 = 0.07 nearly for the sun's
equatorial centrifugal force. Hence the weight before obtained, 28
pounds, must be reduced seven hundredths of its whole value, and we
thus obtain 28 - 0.196 = 27.804 pounds as the true weight of one
pound transported from the earth's equator to that of the sun."

In this calculation we have