346 
PROFESSOR DONKIN ON THE 
p, p^, c are defined by the equations 
p=m\/(jtja{l—e^), cos I. 
/, are the angles between the principal plane and the planes of the two orbits, and 
are given functions of the elements a, a^, e, e^, I, by virtue of the equations 
— pa sin i=-pp sin ii=pPi sin I, 
from which we have also 
(T cos cos I, ff cos cos I 
^for the values of tan U tan^? see art. 91.^. 
0 )^ is tiie angular velocity of the principal plane about the line of nodes ; 
Ml the angular velocity of the principal plane about a line in itself perpendicular to 
’ the line of nodes ; 
the angular velocity of the line of nodes estimated in the direction of the prin- 
cipal plane. 
Differential Equations of the Problem. 
93. The nine intrinsic elements, as we may perhaps appropriately call them, namely, 
a, a^, e, e,, s, I, 
are determined as functions of t by the following system of nine simultaneous differ- 
ential equations of the first order ; 
, na Vl—e^[d£l . /- 
, nfl, dl—e^ fdn, , , / 
mfta ,= (1 -y 1 
r n odn , wav'! — —dH 
7nm=- — 2na^—-\ 
da 
my. f cos I dfl 1 dfl^ 
sinl[ p ^^‘Pi (11 
! „ .,d£i, , n,a,s/\—e^ , # d£l, 
[cosl dVl^ 1 d^ 
sin jOy d\ p d\ 
dfl 
my. J 
cos I 
de 
sin 
P 
’• dfl/ 
miy., 
/cos 
dCi 
sin I 
1 Pi 
Pi « 
, , 1 
'^p dl J 
