THE THEOEY OP ROLLING CURVES. 25 



Ex. 7. If we roll the curve whose equation is 



fa n 

 r = a cos I T 6 



\b 



on the ellipse whose equation is 



the pole will trace the axis b. 



Ex. 8. If we roll the curve whose equation is 



on the hyperbola whose equation is 



the pole will trace the axis b. 



Ex. 9. If we roll the lituus, whose equation is 



rf = 36' 

 on the hyperbola whose equation is 



the pole will trace the asymptote. 



Ex. 10. The cardioid whose equation is 



r = a (1 +cos 6), 

 rolled on the cycloid whose equation is 



y = a versin -1 - + Jzax x 1 , 

 a 



traces the base of the cycloid. 



Ex. 11. The curve whose equation is 



6 = versin" 1 - + 2 /-I, 

 a \j r 



rolled on the cycloid, traces the tangent at the vertex. 

 VOL, I. 



