LECTURE IV. 



THE VARIATION. 



THE Variation is the first inequality we shall consider ; this is the 

 inequality which is independent of eccentricities and mutual inclination in 

 the orbits of the Sun and Moon. 



Let us first take the equations in the first form in which they are 

 given in Lecture IT., namely with t as independent variable: 



-- 



de dt 



/ T . 



r dt \ dt) 



we omit the equation of motion in latitude, and in the expressions for 

 P, T we suppose s = ; moreover it is possible and convenient to discuss 

 separately the terms that involve the Sun's parallax ; let these be omitted 

 and we have 



1 ffir dd it 1m' 3m' ,, 



2drd6 3m' 



and if 



d 2 2 dr d6 



df + rdtdi = 



these are the equations to discuss. 



