"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) × 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 three errors, the effect of one of which would be to increase the true answer 111 times, of another 28 times, and of a third to diminish it 10 times; so that the final result is more than 300 times too great. If this result were correct, Leverrier would have no need of looking for intermercurial planets to account for the motion of the perihelion of Mercury; he would find a sufficient cause in the ellipticity of the sun. Considered from a scientific point of view, some of the gravest errors into which the author has fallen are the suppositions, that the perihelia and nodes of the planetary orbits move uniformly, and that they can ever become exactly circular. At the end of about twenty-four thousand years the eccentricity of the earth's orbit will be smaller than at any other time during the next two hundred thousand, at least; but it will begin to increase again long before the orbit becomes circular. Astronomers have long known that the eccentricity of Mercury's orbit will never be much greater or much less than it is now; and moreover, instead of diminishing, as stated by Professor Mitchell, it is increasing, and has been increasing for the last hundred thousand years. Finally, the chapter closes with an attempt to state the principle known to mathematicians as "the law of the conservation of areas," which statement is entirely unlike the correct one in nearly every particular.