950 

 having revolved 45°. 



s = q .[r — -{l—q) . ). Fig. 10, Ilea ving revolved 45°. The distance 



1 

 4 

 of the cusps to has changed however. 



•^ < 'Z • ( ^' > 7 (1—?) )• Fig- 9, having revolved 45°. 

 Let us now suppose that q ü- positive and < 1. 



«<^-(''>j(l— ?)) • Fig. 14. {L) has no dynamical meaning for 



the same reasons as in Fig. 9. 



s — q(r^-{l-q)]. Fig. 15. The dynamical problem allows of 



two simple vibrations only. 



q' f (1—5) 1 \ 



^Y3^<'<'?-K(T3^<''<4^^-'?))- Fig. 16. Two domains 



of motion. ^) 



?' ( (l-'7) ^ 



'"^ (1-2^)^ V'^^' (l— 25)* J- ^^^ ^"^P^ ^^ ^^^® preceding Fig. 



have coincided in pairs now. 



'i^<'< {l^2qr {^<'< ^"^ {l^~2% ) • ^^'^- ^^' ^"'"^"^ ^''^^'^'^ *^^^ 

 cusps have disappeared. 



.^ = q\ (;' = 0). Fig. 17. (L) has 4 points of contact with (C). 

 In the dynamical problem we are concerned witii an asymptotical 

 approach to the A^- or )^-vibration. This case should be considered 

 as the transition between two domains of motion and a single domain 

 of motion. 



9' 



<'^<q'\ Jq-^^ <^<^)- Fig. 18. The 



"stirrups" contribute to the "envelope". '^) 



1) Of the closed branch of (L) 4 parts lie inside (C). Each of the domains of 

 motion is bounded by 2 opposite parts and by the infinite branches that pass 

 through their final points. 



~) The inner branch serves partly as exterior, partly as interior envelope. The 

 parts which, seen from the centre, are hollow, touch internally, the rest externally. 



