as an ellipse, in case B on the XZ-plane as a hyperbola on the X)- 
and the }’Z-plane as an ellipse. 
The osculating curve described in a definite parallelopiped can 
be given in the equations 
= Acos(n,t + a), 
y = Beos (n,t + b), 
sis (2 Se a 
where « and / represent the momentary values resp. of 27,(?,;—B,) 
and of 2n,(8,—8;). 
In the extreme parallelopiped curves are described for which 
sin p = 9, so for which 
Pia ae, 
where / is an integer. 
For this case we have, if we suppose / to be even, 
1 Ah 
==) cos! — =e poss! 
RELATIONS BETWEEN 4 OF THE FREQUENCIES OF VIBRATION 
FOR WHICH S= 4. 
$ 22. There are two of these relations to be discussed, namely: 
(A) nn, +n, +2, — 1, =O; : 
(B) n, +n, NN, =O 
After the preceding it will be clear that we have to take. 
„=d 
ieee ee ee 
UZ n-" or + 1, (is Jor Vs: qa)s 
=| 
r—4 , r=4 s=4 : ed 
ft pepe os = 2 3: 2 > Pp 
4 = dr + 3 re (Per Gr le 25 rsQr ds)s 
r= ill 
where 
Prs= 4 rq," + 4 Orsqa® + Heres + 4 FreQs” + Ors, Ia + rela Aat 
+ Orsa Aa + rss Aa + Borsa Aa + Sess Aer 
“We can again point out which terms in the different equations 
of motion are to be regarded as disturbing, and we can reduce 
them according to the method indicated in $ 17. 
The result of the reduction is that the disturbing terms of the 
second kind in the equations for q,, G2, Ys, andg, are the derivatives 
resp. tO 91, Qas Ys» and qg, of: 
