1: 
2 
The points where the curve touches the planes z= + C are pro- 
jected in the right lines 
§ 14. Special cases. At the conclusion of § 8 the special cases were 
named which may appear. They are: 
A. For given values of C, and C, we find k=O. The relation 
Va aa, cos p = 0 
allows of various possibilities. 
1. One of the «’s is continually zero. Not one of these forms of 
motion, however, proves to be possible on substitution into (1). 
T JT 
2. cosp=0; p is continually > or 3° The form of motion chan- 
ges periodically between those for which $= C, (¢, = 0) and those 
tor which. § = C, (e, = 0). 
B. For given C, and C, we find k* maximum. Here 8 is constant, so 
the es are also constant; the circumscribed parallelopiped does 
not change. The ?’s increase uniformly with the time; the osculating 
curve changes its form; sin p =O remains however. The osculating 
curve is thus represented by (9); @ inereases uniformly with the time. 
{ zi a a, 2 5 2 
C. C, is equal to zero. Then — =~. The movement of the vertices 
nl 1 js 
of the circumscribed  parallelopiped takes place along a plane 
curve; the plane passes through the Z-axis. When C,==0 and at 
the same time / =O, then the form of the movement approaches 
asymptotically the Z vibration. 
D. C,=C,. An X-vibration continually takes place. 
Approvimated relation n, +n, —n, = 9. 
§ 15. We must imagine g to be of order 4. Now 
—Kh=P 4,929; — HRO 
As first approximation we take for g,, q., and q, the same expres- 
sions as in the case of the pure relation. We find for fas function 
of the «’s and p's 
es oO 
s 
= =p VAAT, COS Qi ee ds 
2 (n, ={-%5) 
