MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 537 



on the ellipse whose equation is 



a' V 

 the pole will trace the axis b. 



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



J 



on the hyperbola whose equation is 



^! _ £: _ , 



the pole will trace the axis b. 



Ex. 9. If we roU the htuus, whose equation is 



on the hyperbola whose equation is 



X y ^ (V 



the pole wUl trace the asymptote. 



Ex. 10. The cardioid whose equation is 



r = a (1 + cos S) 



rolled on the cycloid whose equation is 



y = a versin - f 

 a 



''' VTV 



traces the base of the cycloid. 



Ex. 11. The curve whose equation is 



. - i r „ 2 a , 

 6 = versin - + 2./ 1 



rolled on the cycloid traces the tangent at the vertex. 



Ex. 12. The straight line whose equation is 



r = a sec 6 

 rolled on a catenary whose parameter is a, traces a line whose distance from the 

 vertex is a. 



Ex. 13. The part of the polar catenary whose equation is 



^J 



r 



rolled on the catenary traces the tangent at the vertex. 



Ex. 14. The other part of the polar catenai-y whose equation is 



roUed on the catenary traces a line whose distance from the vertex is equal to 2 a. 



