LEVER WITH FKICTIO.V. 



through ' '. 1 7 be the angle between the directions of 

 I <?, and the resultant of P and Q; then 



-1* + (f + iPQeoty. 



lir.vti-.ii of 8 be represented by the dotted line 

 ng an angle with R. Then since /, R t and S are in 

 im, 



11 - 8 con (I), 



F-Sin0 2). 



of equilibrium FpR\ therefore 

 tan*-,*. ..... (3). 



We may now fm<l the relation between Pand Q, by taking 



moments r>m<l the centre of the exterior circle; let r be the 



radius of this circle ; a and b the distances of A and D from 



; a and ft the angles which the directions of P and Q 



make with these distances ; then 



Asina-f /V- 

 or by (S) and (3), 



Pasino 4- 



suppose the friction to act in the opposite direction to 

 that in the figure, we shall obtain 



iKritun will not subsist unless P, Q, a, i, a, /9, 7 are so 

 (4) or (5) can be satisfied without giving to /i 

 a value greater than its limit known by experiment 



The following form may be given to the limiting oqu.v 

 Let be the length of the perpendicular from the centre 



circle on the dotted 1 and S are in equi- 



librium, we have by taking moments 



Jfr- &; 

 therefore 



