538 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 



Ex. 15. The tractory of the circle whose diameter is a, rolled on thetractory 

 of the straight line whose constant tangent is a, produces the straight line. 

 Ex. 16. The hyperbolic spiral whose equation is 



a 



rolled on the logarithmic curve whose equation is 



y = a\og~ 



traces the axis of y or the asymptote. 



Ex. 17. The involute of the circle whose radius is a, rolled on an orthogonal 

 trajectory of the catenary whose equation is 



^ = ia ^^^' + ^°S (^^! - 1 + ^ ) 



traces the axis of y. 



Ex. 18. The curve whose equation is 



. = (^.l)J^l 

 rolled on the witch, whose equation is 



traces the asymptote. 



Ex. 19. The curve whose equation is 



r = a tan S 



rolled on the curve whose equation is 



traces the axis of y. 



Ex. 20. The curve whose equation is 



2r 



rolled on the curve whose equation is 



y = -— r^^^ — or r = a tan 



traces the axis of «/■ 



Ex. 21. The curve whose equation is 



r — a (sec 6 — tan 6) 



roUed on the curve whose equation is 



y = alog(^4 l) 



traces the axis of y. 



