136 



PARTICULAR CASES OF EQUILIBRIUM. 



loci of the points where the tangent is vertical is evidently the 

 asymptote found in the preceding problem (144), and the equation 

 of which is 



tan 2 o>=2. 



153. Equations (14) and (15) of (146) give for the values of the 

 force on the axis, and on the transversal, at A and B (Fig. 40), 



and therefore 



S Q A T 



Fig. 40. 



From equation (17) we have for a point P at the same distance in 

 any direction whatever w, 



Y= - = -GT 



= 3 sin w cos CD. 



J 



Through the point O as centre, draw a circle of radius R, passing 

 through the point P, and consider at this point the perpendicular 

 component F w , and the tangential component F^ of the force ; we 

 have 



(ao) 



= X cos o> + Y sin o> = 2 cos w, 

 R 3 



T 



. = - X sin o> + Y cos o> = sin w. 



' 



