MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 
on the ellipse whose equation is 
the pole will trace the axis 0. 
Ex. 8. If we roll the curve whose equation is 
aé _aé 
b a 
r= a eex 
2 
on the hyperbola whose equation is 
the pole will trace the axis 0. 
Ex. 9. If we roll the lituus, whose equation is 
a’ 
li nie 
Srey, 
on the hyperbola whose equation is 
Ly=a@ 
the pole will trace the asymptote. 
Ex. 10. The cardioid whose equation is 
r= a(l + cos @) 
rolled on the cycloid whose equation is 
y = aversin "= + V2ax— x 
traces the base of the cycloid. 
Ex. 11. The curve whose equation is 
zh Moray 2a 
§ = versin flag 2 | A 
rolled on the cycloid traces the tangent at the vertex. 
Ex. 12. The straight line whose equation is 
r=asec é 
537 
rolled on a catenary whose parameter is @, traces a line whose distance from the 
vertex iS a. 
Ex. 13. The part of the polar catenary whose equation is 
je eg 2 
; 
rolled on the catenary traces the tangent at the vertex. 
Ex. 14. The other part of the polar catenary whose equation is 
4 Eee 
a 
rolled on the catenary traces a line whose distance from the vertex is equal to 
2a. 
