THE ELEMENTS OE THE ORBIT OF A SATELLITE. 
859 
c {!( x -’»)+«} 
Therefore we ought to find, if the analysis has been correctly worked, that 
k dt 1 V, k dt'dt 
This test will be only applied in the case where the viscosity is small, because the 
analysis is pretty short; but it may also be applied in the general case. 
When i= 0, we have from (292), after multiplying both sides by 1— rj, 
shf4f ^(1 — v )^ ! +2677 + 24677- \(1 + 4577+ 6 5 lip) 
And when i= 0 and t—0, from (301) 
_ s il 4 f ^| I=1 + 15 , '+ B ^''- x ( 1 + 27, ) +27S 0 
Hence 
dn 
dt 
=IS from < 291 ) 
Thus the above formulas satisfy the condition of the constancy of the moment of 
momentum of the system. 
2 sin 4f T [i lr ](! +\ 1 r ] ) - 18 X 17(1 2 It?)] 
The most important lunar inequality after the Equation of the centre is the Evection. 
The effects of lagging evectional tides may be worked out on the same plan as that 
pursued above for the Equation of the centre. 
I will not give the analysis, but will merely state that, in the case of small 
viscosity of the earth, the equation for the rate of change of elbpticity, inclusive of 
the evectional terms, becomes 
if _ 
Jc dt 
d log V = 1 H 1 sin 4f T 
g 
6 7 5 I 
l 1 
3 5 2\ 
K n) j 
where fl' is the earth’s mean motion in its orbit round the sun. 
From this we see that, even at the present time, the evectional tides will only reduce 
the rate of increase of the ellipticity by g^-th part of the whole. In the integra¬ 
tions to be carried out in Part YI. this term will sink in importance, and therefore it 
will be entirely neglected. 
