2I S .] 



CONDITIONS OF EQUILIBRIUM. 

 p=* 



I2 9 



L[ 



IJ! 



H l 



H' 



The central axis being defined (Art. 204), as that line for 

 which the vector of the resulting couple is parallel to the direc- 

 tion of the resultant, the point <9'(f, ??, ) will lie on the central 

 axis if the direction cosines of H' are proportional to those of 

 J?, viz., to 



<* = -> = -> =- 



j~) j~) I r) 



J\ J\. I\. 



Hence the equations of the central axis are 



B ~ C 



or 



A 



B 



C 



215. To show the application of the conditions of equilibrium, let us 

 consider the simple machine called the wheel and axle. It consists of a 

 horizontal shaft (Fig. 71) resting with its ends on the supports or bear- 

 ings A, B, and is intended to raise a weight W, suspended vertically by 

 means of a rope wound around the shaft. The driving force F is applied 





W 



Fig. 71. 



on the circumference of the "wheel,"/.*, in a vertical plane at right 

 angles to the axis of the shaft. It is required to find the relation 

 between F and W for equilibrium, and the pressures on the bearings 



PART II 9 



