OUTLINES OF NATURAL PHILOSOPHY. 



draws tne Moon from the Earth, in the direc- 

 tion of the line passing through the centres of the 

 Sun and Earth. 



This force at the conjunction, exceeding that part of 

 the disturbing force which draws the Moon to the 

 Earth, tends to diminish the Moon's gravity to the 

 Earth. At the opposition B it does the same, by 

 becoming negative ; for the Earth is then drawn 

 more than the Moon, and the difference is nearly 

 the same as at the conjunction. 



t>. If MN be taken equal to HK, and NO made per- 

 pendicular to the radius vector, the force MN is 

 resolved into two, one directed from M to O, les- 

 sening the gravity of the Moon to the Earth, and 

 the other directed from O to N, parallel to the 

 tangent to the Moon's orbit at M, and therefore 

 accelerating the Moon from C to A, retarding her 

 from A to D, and so alternately in the other two 

 quadrants. 



At the quadratures C and D, the force HK vanishes, 

 and the only remaining force is directed to the 

 centre of the Earth, so that the areas are there 

 proportional to the times. 



c. The analytical values of these forces are next to be 

 found. Draw CED the line of the quadratures, 

 put SE = <z, EM the radius vector of the Moon's 

 orbit = r, the angle CEM^r, and the mass of the 

 w. The force that retains the Earth in its 



orbit 



