Chap. XLI.] THE BALANCE. 497 



fulcrum. The weight R in the scales, and P, are counter- 

 poised by moving the position of the arm in F, the 

 distances of R and P from 

 F being inversely as their 

 weights. Previous gradua- 

 tion enables one to say 

 what positions correspond 

 to various weights in the 

 scale pan. 



The ordinary balance Fi s- 208.-Dauisli Balance, 

 consists of two scales 



hanging from the ends of a horizontal bar, which 

 is suspended by a fine edge. The point of sus- 

 pension is so arranged that the scales are equi- 

 poised. This balance should exemplify two equal 

 and parallel forces acting on a rigid bar suspended 

 by its middle. The accuracy and sensibility of the 

 instrument depend on the diminution of friction at 

 the point of suspension of the bar and the points of 

 suspension of the scales from its ends. This is 

 effected by making these points of very hard material 

 (steel or agate), in the form of knife edges. S'riisi- 

 bility also depends on the length and lightness of the 

 beam, and on the centre of gravity of the beam being 

 in the same vertical line as the axis of suspension, 

 and very little below it. 



Pulleys also exemplify the elementary dynamical 

 principles that have been referred to. 



The SINGLE PULLEY (Fig. 209) does not effect any 

 advantage in the way of diminishing the power to be 

 employed. Suppose c to be a fixed pulley acted on 

 by two parallel forces represented by the weights X 

 and Y. The moment of x is its amount multiplied by 

 the distance from its point of application to the axis 

 on which the pulley turns (i.e. AC), and the moment of Y 

 is its amount into its distance. Now the distance is 

 in each case the same. It is, therefore, evident that 

 G G 7 



