344 On the Construction and 



tion, the effect to put the system in motion will be equal to 

 the difference of the moments. 



In the case of an equilibrium the moments will be equal, 

 and no motion will ensue. 



When the angle £ is equal to 180°, the above formula will 

 become 



A.a. cosin Inclin. 



B./3. cosin Inclin. 

 and if the moments are equal in one position, they will also 

 be equal in all, because the differences of the moments will be 

 the same in all positions. 



If the angle £ is greater than 180°, that is when a line 

 joining the two points of suspension would pass below the 

 centre of motion ; if the moments are equal in one position, 

 and the system is displaced by an extraneous force which in- 

 creases the angle of inclination of the arm A with the verti- 

 cal, then the moment of the force A will be decreased, and the 

 moment of B increased, therefore the system when again at 

 liberty will regain the position of equilibrium. 



If the angle £ is less than 180°, an increase of the inclination 

 will increase the moment of A, and decrease that of B, and 

 therefore when the system is again at liberty, the action of 

 the forces will continue the displacement, which will not be 

 regained until the system is overturned. 



In the foregoing the beam of the balance has been con- 

 sidered for the sake of simplicity as being devoid of weight, 

 but to take this into account, a third force may be considered 

 as acting upon the centre of gravity of the mass. 



If D = the weight of the beam. 



8 = its distance from the centre of motion. 



Then if £ is greater than 180° and D is below the centre of 

 motion — then in the case of an equilibrium, A. a. (| e + 

 Inclin)= B. j3. Sin {\ £— Inclin.) + 



H- D. 8. Sin Inclin. 



