TI3E BALANCE. 119 



describe the arc ss^ and be raised vertically through b s, 

 while the weight describes the arc uu^ and descends 

 through the space u c. The work done by the descend- 

 ing weight must be equal to that required for raising 

 the centre of gravity of the beam, that is, the weight % 

 multiplied by the space u e, must be equal to the weight 

 of the beam multiplied by bs. If A and B (fig. 87) 

 be two beams of equal weight, but A has its centre of 

 gravity nearer to the point of suspension than B, then 

 if the centre of gravity of each beam is to be raised 

 through an equal space bs, A must assume a more 

 inclined position than B, and uu^uc, will be greater for 

 A than for B. But as the weights of A and B are equal 

 and their centres of gravity rise through equal dis- 

 tances, the work done in deflecting them is the sam, 

 and therefore the work done by the descent of the 

 additional weight u must also be the same in both cases ; 

 but in the first case it moves through a greater distance 

 than it does in the second, and hence (as represented 

 by the different lengths of the arrows in the two 

 figures), the additional weight required to deflect the 

 beam A must be smaller than that required to produce 

 an equal deflection of the beam B. 



Supposing, therefore, the lengths and weights of two 

 beams to be equal, it follows that a smaller, excess of 

 weight at one end produces a greater deflection when 

 the point of support a is nearjbhe centre of gravity s, 

 than a larger excess does when the point of support is 

 at a greater distance above the centre of gravity. 

 Hence, the second condition to be fulfilled by a good 

 Balance is that the centre of gravity be as near as possible 

 to the point of suspension. Both points must, however, 



