534 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES, 



therefore suppressing the suffix, 





us) 



dr\ ^ _ _ ^ 

 a 



d 6 

 d n 





. • . 6 = COS"" 



2a 

 r = 



1 — cos 6 



the polar equation of the parabola whose parameter is 4 a. 



The last case which we shall here consider, affords the means of constructing 

 two wheels whose centres are fixed, and which shall roll on each other, so that 

 the angle described by the first shall be a given function of the angle described 

 by the second. 



Let «., = ?> «i then /•, + r, = a, and -^ = ~ 



d (p ^j) r, 



d 6^ ~ a — r^ 



Let us take as an example, the pair of wheels which will represent the angu- 

 lar motion of a comet in a parabola. 



df 1 r 



Here ^2 = t^" 



"1 



2 ■ rf^j cos^Ji 



2 



2 + cos «j 



4 

 therefore the first wheel is an ellipse, whose major axis is equal to -^ of the dis- 

 tance between the centres of the wheels, and in which the distance between the 

 foci is half the major axis. 



Now, since «, = 2 tan-' 6^ and r^ — a — r.. 



a 2 (2 - «*) 



«* = 2 - — ^~ 



2_r -2 



a 

 which is the equation to the wheel which revolves with constant angular velocity. 



