84 Mr HOLDITCH, ON ROLLING CURVES. 



CD 



Let the small angle BDC*=6; .: z CEA = Q.-~ 



V.U. *J . CE _ CD 



„„„ „ (CD CD\ 



■■• < FCE = d icE-CF)> 



sinC j£ /Ci> CZ>\ 



or, if a and 6 be the major and minor distances of the wheel B, and R a , R b re- 

 present the radii of curvature at B and G, and similar quantities with dashes those 

 of the other wheel, and a - b - I; then 



l-R-R a =(l-R).R a .(~-^j; 

 P.(R bi -R a ) 



and therefore, R = 



l.(R bl -R a ) + R a .R bi 



To prevent clogging at G, therefore R < - R b , 



I 1 



I i I R a Rb 



.-. by equation (6) — — - --<-+- 



*/ + *-) 



ly b i P(R b -R a ) 



i 



< T + 



1 '■(---) 



U, Rj 



Now — = - + 



R„ a f. , JV' 



Mi) 



and 



the curves being considered convex to the centres at the minor apses; 



