538 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 
Ex. 15. The tractory of the circle whose diameter is a, rolled on the tractory 
of the straight line whose constant tangent is a, produces the straight line. 
Ex. 16. The hyperbolic spiral whose equation is 
(== 
2/8 
rolled on the logarithmic curve whose equation is 
x 
y =alog a 
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 | 
EN rama ig ( x? x 
y=5,V% a” + 5 log Np acre 
traces the axis of y. 
Ex. 18. The curve whose equation is 
nia, es: Gg 
s=(S41) 2241 
rolled on the witch, whose equation is 
¥y = 2 a SSS 1 
traces the asymptote. 
Ex. 19. The curve whose equation is 
7 = a tan @ 
rolled on the curve whose equation is 
r= $oe(S—2) 
traces the axis of y. 
Ex. 20. The curve whose equation is 
2r 
ya. 
rolled on the curve whose equation is 
6 
a? 
=i Or 7 = ata 8 
Va? — x 

y= 
traces the axis of y. 
Ex. 21. The curve whose equation is 
r = a (sec 6 — tan @) 
rolled on the curve whose equation is 
2 
y=alog (5 4 1) 
traces the axis of y. 

