58 OUTLINES OF NATURAL PHILOSOPHY, 



260. From the same cause arises a variation 

 in the inclination of the Moon's orbit to the 

 ecliptic, confined within very narrow limits. A 

 construction for determining the inclination for 

 any given time, is given ibid. prop. 35., and is , 

 found to agree with observation. 



What respects the motion of the nodes is thus com- 

 pletely explained ; and it is here that the indirect 

 method of determining the Moon's inequalities has 

 been most successful. It has not been equally so 

 in ascertaining the motion of the apsides. 



To conceive, in general, the cause which renders the 

 apsides of the Moon's orbit more than 180 degrees 

 distant from one another, we must begin with sup- 

 posing the Moon at the lower apsis ; then, if that 

 planet were acted on only by the force of gravity, 

 the radius vector, after it had described 180, 

 would arrive at the upper apsis, or would be in- 

 tersected by the orbit at right angles. 



But as the mean disturbing force, in the direction of 

 the radius vector, may be considered as a quanti- 

 ty constantly taken from the Moon's gravity, the 

 portion of her path described in any instant will 

 fall between the tangent and the arch of the ellip- 

 tic orbit which would have been described if the 

 Moon had been acted on by gravity alone. The 

 actual path of the Moon, therefore, will be less 

 bent than the elliptic orbit would have been in the 



same 



