MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 539 
4th. Examples of pairs of rolling curves which have their poles at a fixed 
distance = a 



The straight line whose equation is @= sec — 
x, 1. Sawa I 
The polar catenary whose equation is = J = 4 
Bix. 2. Two equal ellipses or hyperbolas centred at the foci. 
Ex. 3. Two equal logarithmic spirals. 
Circle whose equation is r= 2a cos 0. 
Ex. 4. . ears 
Curve whose equation is aR 2° — 1 + versin 
t 
Cardioid whose equation is r= 2a(1 + cos 4.) 
Ex. 5 yan 
is Curve whose equation is j= fine oe log Z 
og a—r?+ta 
Conchoid, r = a (sec 6 — 1.) 
Ex, 6. 2 
Curve, a a se “ at seo} 
Spiral of Archimedes, r=aé 
Ex. ve Curve, = a ae log — 
a a 
Hyperbolic spiral, r= = 
Ex. 8. 
Curve, SAI 
Ellipse whose equation is, Ap armenay, 
Ex. 9. l 
Curve, r=@ (1 = ») 
| Involute of circle, j= Rs is SWsee = 
Ex. 10. et 1 ——— 
Curve, a mE (F1 1/5027) 
a~ a a a a 
5th. Examples of curves rolling on themselves. 
Ex. 1. When the curve which rolls on itself is a circle, equation 
r= acosé 
the traced curve is a cardioid, equation 7 = a (1 + cos 8). 
Ex. 2. When it is the curve whose equation is 
f) n 
a aa( cos =) 
i 
the equation of the traced curve is 
4 . +1 
n +1 
VOL. XVI. PART V. 6 z 

72 fom Pea) a( cos 
