Secular Acceleration of the Moon's Mean Motion. 



325 



It is well known that the sun's attraction diminishes the moon's 

 gravity toward the earth, and thus increases its periodic time j 

 and if it can be shown that the effect is greater than it would be 

 if the earth revolved in a circle at the same mean distance from 

 the sun, it is manifest that so long as the present change in the 



grow less and less. 



Let S (fig. 1) represent 

 the sun, E the earth, AEB 

 a portion of the earth's orbit, 

 and BCAD the moon's orbit 

 regarded as a circle. 



As gravitation varies in- 

 versely as the square of the 

 distance, when the moon is 

 at D it is drawn away from 

 the earth by the difference 

 m the attractive forces of 

 the sun on the earth and 

 moon, and when it is at C, 

 the earth is drawn away 

 from it by the same cause. 

 In both cases the tendency 

 ts to diminish the moon's 

 gravity toward the earth. 

 But when the moon is at 

 A or B, its distance from 

 the sun is the same as that 

 °f the earth, and conse- 

 quently the sun's attraction 

 °u them is equal, but not 

 be ing in the same direction 

 11 tends to draw them near- 

 er together, and thus to in- 

 crease the moon's gravity 

 toward the earth. 

 The 



periodic 



Fig. l. 





moon 



being 



thus 



drawn toward the earth in some parts of its orbit, and from it in 

 ot hers, it might seem rather difficult to determine whether on the 

 ^hole it was drawn toward or from the earth. If we reflect 



v °l- xlvii, No. 2.— July-Sept. 1844. 42 



