( - fh de : 
im (C,--C,)v’, — — — = (C,— CH, — — — =(C,- Gr, 
Ny Me WW Ns nN. n 
where C,, U, Cy, represent positive constants. 
If we put: 
a, = (n,+n,+7,) Sh’, 
we find 
a 
‚=n, (C,—$) i’, a, =n, (C,—S) h?, a, = n, (C,—$) MH. 
The integral /? = constant takes the form: 
VCE) (CS) (C,—8) cos p = pd* + 98 tr 
Case B. 
a a, ie fe a, nee, at, 
=H — = Ch, + = Ch, — — =Car 
i, nnn, nN, n,+N,—Nn, Men a Prey —n, 
a, a, 3 ene) 2 oh en byt ha En 
ae (CC + == (Ch Gt; + 2 (C, TC) 
n, Ny n, ns ns 3 
where C1, C,, and C, are positive constants. 
If we put: 
a, = (n,+n,—n,) Sh’, 
we find 
a, = n, (C,—S)h’, a, =n, (C,—S$)h?, a, = n, (C,+$)h’. 
The integral R = constant takes the form: 
V5 (C,—8) (C,—8) (C, +8) cos wp = po + gS +r. 
It is clear that the problem is again reduced to quadratures and 
that the coordinates with the help of elliptie functions can be 
expressed in the time. 
§ 25. The radius vector ¢ varies periodically between two limits, 
vhs in case A between zero and the smaller of the three quantities 
C., C,, and C,, in case B between zero and the smaller of C, and C,. 
The curves representing the relation between < and pp have here 
again the same form as for the case of the relation n, = 31, 
Thus as general forms of motion we have those where p takes 
all values and those where p moves backward and forward between 
two opposite values; the first we have by preference for great values 
of the residue of relation. 
Furthermore there is again a special case where the amplitudes 
are constant, and sip remains 0; and another special case where 
such a form of movement is asymptotically approached. 
