( 747 ) 
Va 
—— cos (n,t + 2n,8,), 
n 
1 
i) 
ra 
Va, 
oo = cos (n,t + 2n,p,), 
2 
la 
a EEN En 
Qs — n, is COS (7, = n,)t Le 2 (7, a. (OE 
The «a's must necessarily be positive quantities and in general do 
not become zero during the motion. We now write — R= p'4,4.4: 
as a function of the a’s, p's, and 4, and we then omit the terms, 
containing ¢ explicitly. Then we find: 
— R= p"Va,a,a, cos p, 
where 
a p 
Ann, (n, Bn). 
g=2 m8, + 2,8, — (n, zr 12) 25}. 
The system of equations, determining the variability of the a@’s 
and 9’s, runs: 
P 
NL 
a) P Va,a,a, 
20 re OPA ET BE 
ad, = 2n,p Vata, sin p, BR COS Pp, 
2 a, 
" a 
3 Ees = ) Va act 
eo) NU ae eet pd Dante Spree € 
a, = 2n,p V a,a,a, sin gp, D= 5 ——cosg, ) + + + (2) 
a a, 
4 Eee | ; go Va aa, 
u, = — Aln, tn)p Wae,esnp, 8, = ———— cosg, 
An integral of this system is: 
Va aa, COLP CONSLANE. 5“) vent Waneer vaat (ek 
Furthermore we notice that: 
eek tt, 
n, n, Nn, +n, 
a, + a, + a, == 
Therefore : 
at at a at sh GE at 
OA OF, A tS (0,0h }) 
es OM ie tT, nm, nN, +n, 
di hg AF Osje CORBI po ip als ds, ed ont, (0) 
Here C, and C, are constants; C, is positive and C, > C,. We 
suppose C’, to be positive too, which does not imply a restriction; 
for if C, were negative, we should have but to exchange the coor- 
dinates g, and q,. 
