Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/335

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Book III.
of Natural Philoſophy
299

according to cor. 6. prop. 66. book I. The force of this action is greater in the perigeon Sun, and dilates the Moon's orbit; in the apogeon Sun it is leſs, and permits the orbit to be again contracted. The Moon moves ſlower in the dilated, and faſter in the contracted orbit; and the annual equation, by which this inequality is regulated, vaniſhes in the apogee and perigee of the Sun. In the mean diſtance of the Sun from the Earth it ariſes to about 11'. 50". In other diſtances of the Sun, it is proportional to the equation of the Sun's centre, and is added to the mean motion of the Moon, while the Earth is paſſing from its aphelion to its perihelion. and ſubducted while the Earth is in the oppoſite ſemicircle. Taking for the radiuſof the orbis magnus, 1000, and 16 7/8 for the Earth eccentricity, this equation when of the greateſt magnitude, by the theory of gravity comes out 11'. 49". But the eccentricity of the Earth ſeems to ſomething greater, and with the eccentricity this equation will be augmented in the ſame proportion. Suppoſe the eccentrity 16 11/12, and the greateſt equation will be 11'. 51".

Further. I found that the apogee and nodes of the Moon move faſter in the perihelion of the Earth, where the force of the Sun's action is greater, than in the aphelion thereof, and that in the reciprocal triplicate proportion of the Earth's diſtance from the Sun. And hence ariſe annual equations thoſe motions proportional to the equation of the Sun's centre. Now the motion of the Sun is in the reciprocal duplicate proportion of the Earth's diſtance from the Sun, and the greateſt equation of the centre, which this inequality generates, is 1°. 56'. 20". correſponding to the abovemention'd eccentricity of the the Sun 16 11/12. But if the motion of the Sun had been in the reciprocal triplicate proportion of the diſtance, this inequality would have generated the greateſt equation 2°. 54'. 30"