54 OUTLINES OF NATURAL PHILOSOPHY. 



254. The Variation is an equation derived from 

 the force at right angles to the radius vector, 

 which, from the quadratures to the syzygies, 

 accelerates the motion of the Moon, and from 

 fhe syzygies to the quadratures retards it. This 

 force was found to be proportional to the sine 

 of twice the Moon's angular distance from the 

 Sun, and the equation itself is nearly propor- 

 tional to the same quantity. 



If the angular distance of the Moon from the Sun 

 = A, the variation, according to MAYER, is = 



+ (S5'.47") sin 2 A 

 + (2") 3 sin A 

 + (H") sin 4 A. 



Beside the above inequalities, first found out by ob- 

 servation, and now explained by the Theory of 

 Gravity, there are several others of smaller amount, 

 which theory alone has discovered ; all that ob- 

 servation could do, being to ascertain that some 

 unknown inequalities existed, which introduced 

 an uncertainty into all the calculations of the 

 Moon's place. The causes of this uncertainty 

 have been discovered by the theory, and their ef- 

 fects calculated, so that the Tables of the Moon 

 have been brought to agree very nearly with 

 observation. 



255. One of the equations which theory has 

 discovered, is remarkable for the great length 



of 



