Fig. 26.
Note 97, [p. 31]. In the diagonal, &c. Were the line A S, fig. 26, 100,000 times longer than A B, Jupiter’s true place would be in the direction A Sʹ, the diagonal of the figure A B Sʹ S, which is, of course, out of proportion.
Note 98, [p. 31]. Aberration of light. The celestial bodies are so distant that the rays of light coming from them may be reckoned parallel. Therefore, let S A, Sʹ B, fig. 26, be two rays of light coming from the sun, or a planet, to the earth moving in its orbit in the direction A B. If a telescope be held in the direction A S, the ray S A, instead of going down the tube, will impinge on its side, and be lost in consequence of the telescope being carried with the earth in the direction A B. But, if the tube be held in the position A E, so that A B is to A S as the velocity of the earth to the velocity of light, the ray will pass through Sʹ E A. The star appears to be in the direction A Sʹ, when it really is in the direction A S; hence the angle S A Sʹ is the angle of aberration.
Note 99, [p. 32]. Density proportional to elasticity. The more a fluid, such as atmospheric air, is reduced in dimensions by pressure, the more it resists the pressure.
Note 100, [p. 32]. Oscillations of pendulum retarded. If a clock be carried from the pole to the equator, its rate will be gradually diminished, that is, it will go slower and slower: because the centrifugal force, which increases from the pole to the equator, diminishes the force of gravity.
Note 101, [p. 34]. Disturbing action. The disturbing force acts here in the very same manner as in [note 63]; only that the disturbing body d, fig. 14, is the sun, S the earth, and p the moon.
Note 102, pp. [35], [36], [86]. Perigee. A Greek word, signifying round the earth. The perigee of the lunar orbit is the point P, fig. 6, where the moon is nearest to the earth. It corresponds to the perihelion of a planet. Sometimes the word is used to denote the point where the sun is nearest to the earth.
Note 103, [p. 35]. Evection. The evection is produced by the action of the radial force in the direction S p, fig. 14, which sometimes increases and sometimes diminishes the earth’s attraction to the moon. It produces a corresponding temporary change in the excentricity, which varies with the position of the major axis of the lunar orbit in respect of the line S d, joining the centres of the earth and sun.
Note 104, [p. 35]. Variation. The lunar perturbation called the variation is the alternate acceleration and retardation of the moon in longitude, from the action of the tangential force. She is accelerated in going from quadratures in Q and D, fig. 14, to the points C and O, called syzygies, and is retarded in going from the syzygies C and O to Q and D again.