Mr holditch, on rolling curves. 79 



for EF = EO - FO = - l - + \/n 2 k? + - A = b„, 



2 4 



and EG = EO+ OG= l - + \/n*k* + - = a„. 



C) 



Examples : if k* ■= -, and n = 1, 3, 4 &c, the figures (17), (18), (19), 

 will roll together, or in pairs, and are also self-rolling curves. 



The point of contrary flexure, when there is one, is always nearer 

 to the centre than the mean distance: for if p be the perpendicular 

 on the tangent from the centre, 



rdd _ k t _ p 



~fo ~ V(a-r).(r-b) ~ V^?' "* * dp = °' 



r = 



» 2 - 1 2ab 



n° 



— — r ; also since (a - bf is positive, 



2ab a + b 

 <, 



a + b '2 



» s — 1 

 and — -j — is an improper fraction ; 



a + b 



'• r < — 7T~ 

 2 



Since r — b, which must be positive, 



= -5-7 jt . (n*l — 2a), 



» . (o + b) v J ' 



there is no point of contrary flexure, unless n*l - 2a is positive. 







The outline of the lobes may be traced without the use of 

 logarithms by observing, since the equation in this case is 



2ab 



r =■ 



a + b + (a - b).cosn9' 



