128 C. J. MERFIELD. 



c will be common to both. Secondly we may adopt a value 

 of p the radius of curvature of the cubic parabola at the 

 point of contact c. 



Thus 



Vc 



B 2 =(l +A.) - cos<£ 3 



in which h/R 2 corresponds to <£ and may be found from the 

 tables and 



t/c = Rj ( 1-cos <£) + a 4 



= R r Versin <f> + a 

 we also have 



7? _ 3 yc pr 



2 sin 2 </> cos <£ 

 probably more useful than (3) as we avoid the calculation 

 of h/R 2 . 



Having determined R 2 we may readily find 



x = 2 R 2 sin <f> cos 2 <f> 5a 



x = R 2 sin <f> 



h = y c —R 2 versin <f> 



TK= (R 2 -R 1 ) sin <f> 



2 12 sin </» cos 5 </>. 

 or with the value #/i? 2 the several quantities may be found 

 from the table given in Vol. xxxiv, page 285. 



Let us now take the second case when we adopt a radius 

 of curvature p, equals B 2 at the point of contact c. 



From the theory explained in previous papers we may 

 readily deduce the following equation 



Cos 3^_ ( 1+-|^L-) cos * + 3 ( f 1 p + — } = 6. 



\ A K 2 ' A K 2 



In this and previous formulae the quantity "a" represents 

 the distance between the parallel tangents, see Fig. When 

 in equation (6), R 2 equals Bi and "a" equals "h," it 

 reduces to the form given in (2). 



