28 THE THEORY OF ROLLING CURVES. 



(Cardioid whose equation is r = 2a (1+ cos 0). 



5 - 1 r 1 



[Curve whose equation is 0=sin~ I - + log-^= 



f Conchoid, r = a (sec I ). 

 Ex. 6. I -, r 



(.Curve, = A./ 1 u +sec" 1 - 



V r* a 



f Spiral of Archimedes, r = a0. 



Ex- 7- r r 



[Curve, = - + log-. 



ft ct 



f Hyperbolic spiral, r = ^- 



Ex. 8. j ff 



(Curve, r = - . 



9+1 



fEllipse whose equation is r = a - n . 



Ex. 9. \ 2 + cos0 



{Involute of circle, = 7-^1 sec" 1 - 



V a 



i 



Fifth. Examples of curves rolling on themselves. 



Ex. 1. When the curve which rolls on itself is a circle, equation 



r = a cos 0, 

 the traced curve is a cardioid, equation r = a(l + cos#). 



Ex. 2. When it is the curve whose equation is 



the equation of the traced curve is 



B xn+l 



(ft \n+i 

 008 -TT) 

 n+l/ 



Ex. 3. When it is the involute of the circle, the traced curve is the spiral 

 of Archimedes. 



