Fig. 34.
Note 139, [p. 61]. The true longitude of Uranus was in advance of the tables previous to 1795, and continued to advance till 1822, after which it diminished rapidly till 1830-1, when the observed and calculated longitudes agreed, but then the planet fell behind the calculated place so rapidly that it was clear the tables could no longer represent its motion.
Note 140, [p. 65]. An axis that, &c. Fig. 20 represents the earth revolving in its orbit about the sun in S, the axis of rotation P p being everywhere parallel to itself.
Note 141, [p. 65]. Angular velocities that are sensibly uniform. The earth and planets revolve about their axis with an equable motion, which is never either faster or slower. For example, the length of the day is never more nor less than twenty-four hours.
Note 142, [p. 68]. If fig. 1 be the moon, her polar diameter N S is the shortest; and of those in the plane of the equator, Q E q, that which points to the earth is greater than all the others.
Note 143, [p. 73]. Inversely proportional, &c. That is, the total amount of solar radiation becomes less as the minor axis C Cʹ, fig. 20, of the earth’s orbit becomes greater.
Note 144, [p. 75]. Fig. 35 represents the position of the apparent orbit of the sun as it is at present, the earth being in E. The sun is nearer to the earth in moving through ♎ P ♈ than in moving through ♈ A ♎, but its motion through ♎ P ♈ is more rapid than its motion through ♈ A ♎; and, as the swiftness of the motion and the quantity of heat received vary in the same proportion, a compensation takes place.
Fig. 35.
Note 145, [p. 76]. In an ellipsoid of revolution, fig. 1, the polar diameter N S, and every diameter in the equator q E Q e, are permanent axes of rotation, but the rotation would be unstable about any other. Were the earth to begin to rotate about C a, the angular distance from a to the equator at q would no longer be ninety degrees, which would be immediately detected by the change it would occasion in the latitudes.