Mr HOLDITCH, ON ROLLING CURVES. 65 



Now / r^- (See Professor Peacock's Examples) 



'J a + /3 COS <p s r ' 



= . . tan ' y - — 



Va* - F Va* - & 



- -4=. tan- fV?. tan <) , 



and tan ? from the equation 

 2 



« + 6 a - i , . , , fa— r 



r — — r — = — - — . cos is round to be = V r> 



2 2 r r — b 



n i i (« + *)* 



g*, + *- 5 n , 



9 = t== .tan" 1 V-- V* - r + a£rf> - A/3 sin + C 



V«6 « r — b 



**.+*. k±^' 



2 



tan 



- \/?- VPI 



V«J a r - b 



- h y/(a -r).(r - b) + k.(a + b). tan" 1 \J t t^L + Q 



2k, + k 



r-b 



{a + by 



or 6 = ' „ 2 .tan- s/\. sj r -^± 

 y/ab b a — r 



- k.\f(a- r).(r - b) - k . (a + *).tan-\A h - , (1), 



a — r 



where 6 is measured from the smaller apse, is the equation to a class 

 of curves, which for the present may be called self-rolling curves. 



If *, = Vab, and k = 0, = 2. tan- V? . \/ r -^ ; 



b a — r 



Vol. VII. Part I. I 



