Mk HOLDITCH, ON ROLLING CURVES. 85 



1 1 * J A 



~r ~ p~ = « + r » and 



"■a ■**», a "/ 



/ 11 1 



M" 6 ' --C-8 



It may be shewn in the same way, in order that the wheels may not clog at 

 the point B before the driving point at A comes into action, that 



1 1 



»(»■♦*$)■ "• ' "(H)' 



and as a, b, a /t b, must be positive quantities, both these conditions will be ful- 

 filled, if 



I 1 



(*. + *i) 



*V l ' 



I* I 



or, *+*._•__, ( 7 ), 



which may be called the clearing equation; if the value oi'k t from this be sub- 

 stituted in the equation 



we have finally 



2 A, k.(a + bf r 2 



-7==+ V ,—T -k.(u + b)--, 



Vo6 • n 



for determining the radii of a friction wheel of 2 n teeth ; and by giving different 

 values to n, sets of friction wheels will be found which will not clog theoretically 

 just before or after the change of the driving teeth : and such wheels will not clog at 

 other points, unless the depth of the teeth be very great in proportion to the radii 

 of the wheels, or the curves used for the construction of the teeth be of complicated 

 forms. 



