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

Book III. 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 les, and permits the orbit to be again contracted. The Moon moves lower in the dilated, and fater in the contracted orbit; and the annual equation, by which this inequality is regulated, vanihes in the apogee and perigee of the Sun. In the mean ditance of the Sun from the Earth it aries to about 11'. 50". In other ditances 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 paSS undefineding from its aphelion to its perihelion. and ubducted while the Earth is in the oppoite emicircle. Taking for the radiuof the orbis magnus, 1000, and $16 7⁄8$ for the Earth eccentricity, this equation when of the greatet magnitude, by the theory of gravity comes out 11'. 49". But the eccentricity of the Earth eems to omething greater, and with the eccentricity this equation will be augmented in the ame proportion. Suppoe the eccentrity $16 11⁄12$, and the greatet equation will be 11'. 51".

Further. I found that the apogee and nodes of the Moon move fater 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 ditance from the Sun. And hence arie annual equations thoe 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 ditance from the Sun, and the greatet equation of the centre, which this inequality generates, is 1°. 56'. 20". correponding 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 ditance, this inequality would have generated the greatet equation 2°. 54'. 30"