MECHANICS. 75 



great stability, that is, when disturbed, it should 

 quickly return to a state of rest. 



That the first requisite may be obtained, the beam 

 must have equal arms ; and that this equality may be 

 more easily ascertained, the beam should be straight, 

 or the point on which the beam turns, and the points 

 to which the weights are attached, should be in the 

 same straight line. The centre of suspension must 

 also be higher than the centre of gravity. Were 

 these centres to coincide, the beam, when the weights 

 were equal, would rest in any position, and the addi- 

 tion of the smallest weight would overset the balance, 

 and place the beam in a vertical situation, from 

 which it would have no tendency to return. The 

 sensibility, in this case, would be the greatest pos- 

 sible ; but the other two requisites, of level and sta- 

 bility, would be entirely lost. The case would be 

 even worse, if the centre of gravity were higher than 

 the centre of suspension, as the balance, when deran- 

 ged, would make a revolution of no less than a semi- 

 circle. When the centre of suspension is higher 

 than the centre of gravity, if the weights be equal, 

 the beam will be horizontal ; if they be unequal, it 

 will take an oblique position, and will raise the centre 

 of gravity of the whole, making the momentum on 

 the side of the lighter weight, by that means, equal 

 to the momentum on the side of the heavier, so that 

 an equilibrium again takes place. 



The second requisite, is the sensibility of the balance, 

 or the small ness of the weight by which a given 

 angle of inclination is produced. If a be the 

 length of the arm of the balance, and b the distance 



between 



