( 687 ) 
In the unperturbed motion we have 
et Te en 
and the constants a; must be such, that 
n, = 4p N= EP he 
The integral of areas is 
® — I, + IH, + H‚ = const. 
By means of this integral we can eliminate /7,, and diminish the 
number of degrees of freedom by one. For this purpose we introduce 
Ga TT, GE 
Oni Ee Ip dg Tg 
The equations then preserve the canonic form. *) 
In forming the equations w; =O we need only those terms of A, 
whose integral over a complete period does not vanish, i.e. those in 
whose arguments the mean anomalies do either not occur, or occur 
only in the combinations 
! 
t=1,—21, f=l,— 21, 
of which the mean motions are zero. The constant term will not 
be required in what follows. Of the others, we only require the 
terms of the lowest degree in the excentricities. Thus, introducing 
the further notations 
| 
5 
Bn dg De 
Rs HS. Gs 
| 
8 
we find that A can be replaced by 
__ mm, 
\ 
{ — Ag, cos (l + 2m) + Be, cos (l + w)} + 
mn, 
d, 
“ft { — Ae, cos (! + 2w') + Be, cos(l! + w')} . . . (3) 
as 
where 
A=a' (4 A@) + A,@) 
2 
B (3 Al) + A0) — ==) 
Waa 
The symbols AY? have the usual meaning (LeVERRIER, Annales de 
Paris, tome J], p. 260, 262), and must be computed for the value 
h The integral of areas still exists, if the compression of the planet is taken 
into account, provided only the motion takes place in the plane of the equator. 
Also those terms of the perturbing function which are here used, remain the 
same. The conclusions reached below, thus can be applied unaltered to the case 
of a compressed planet. 
