104 DISSERTATION SECOND. [ M *f u. 



This was a new proof of the reality of the principle of 

 gravitation, which, however, was rendered less conclusive by 

 the consideration, that the exact quantity of the motion of the 

 apsides observed, did not come out from the diminution of 

 the moon's gravity as above assigned. There was a sort of 

 cloud, therefore, which hung over this point of the lunar the- 

 ory, to dissipate which, required higher improvements in the 

 calculus than it was given to the inventor himself to accom- 

 plish. It was not so with respect to another motion to which 

 the plane of the lunar orbit is subject, a phenomenon which 

 had been long known in consequence of its influence on the 

 eclipses of the sun and moon. This was the retrogradation 

 of the line of nodes, amounting to 3' 10'' every day. New- 

 ton showed that the second of the forces into which the solar 

 action is moved being exerted, not in the plane of the moon's 

 orbit, but in that of the ecliptic, inclined to the former at an 

 angle somewhat greater than five degrees, its effect must be 

 to draw down the moon to the plane of the ecliptic sooner 

 than it would otherwise arrive at it; in consequence of 

 which, the intersection of the two planes would approach, ul- 

 it were, toward the moon, or move in a direction opposite to 

 hat of the moon's motion, or become retrograde. From 

 the quantity of the solar force, and the inclination of the 

 moon's orbit, Newton determined the mean quantity of 

 this retrogradation, as well as the irregularities to which 

 It is subject, and found both to agree very accurately with 

 observation. 



Another of the lunar inequalities, — that discovered by 

 Tycho, and called by him the Variation, which consists in 

 the alternate acceleration and retardation of the moon in 

 each quarter of her revolution, was accurately determined 

 from theory, such as it is found by observation ; and the 

 same is true as to the annual equation, which had been long 

 confounded with the equation of time. With regard to the 



