the axes, with which the tbui- asymptotes passing- tlu'Ouj>;h O have 

 now coincided in pairs. (A) touches in 4 points at {€<. 



The only forms of motion whicli tlie dynamical problem allows 

 of are an X- vibration, and a }^-vibration. 



quadrilateral domains of motion with vertices on (C) '). 



s = -—7. I /■ = q' -^ — ^- ., ) . On the axes 4 [)airs of cusps 



have coincided. (L) deviates only a little from the shape indi- 

 cated in Fig. 11. 



occur. (The "stirrups" lying within the domains of motion contribute 

 indeed to the envelope). 



s=0jr=3 — -<7 J. Fig. 13. Degeneration in 8 asymptotes. 



Two domains of motion each bounded by a square. 



We now get to the negative values of .v. No iigures have been 

 drawn for them as they are of exactly the same nature as those 

 for the positive values of 0^ ; we have only to revolve the figures 

 45°. Consequently : 



^ <«<0. -\- ^>.>-^^ .Fig.l2,havmg 



(?-2) 

 revolved 45°. 



/ ^,(,-l)(l-~9j 



27 \ ^ ((7—2)' 



{q-2.f \ {q-2) 



. Here we have to take into 



consideration that tlie distancre of the special points to is another 

 one than for 



(1-2^) 



').n\^ 



1) One domain of motion is bounded by two opposite brandies a. as ftxr as 

 they are lying inside (C), and the branches b which pass through the points of 

 intersection of the just mentioned branches a with (C). 



2) This Fig. and Fig. 18 we also find in a treatise of F. Klein: "Uber den 

 Verlauf der ABEL'schen Integrale bei den Curven vierlen Grades". (Math. Ann. 

 10. Bd, 1876). 



