Balance, Steelyard, &c. 163 



259. The steelyard also is a lever of the first kind ; but the Fi<r J43j 

 fulcrum or axis of this instrument divides the distance between 



the points of application of the weights into unequal parts ; and 

 instead of different weights placed at the same distance, a con- 

 stant weight or poize is placed at different distances to effect an 

 equilibrium with the article to be weighed ; and the weight of 

 this article will be to that of the poize inversely as their distances 

 from the axis. When these distances are equal, the weight of 

 the poize is equal to that of the article weighed. At double this 

 distance, the poize indicates a weight double its own, and at half 

 this distance the weight indicated is half that of the poize, and 

 so on. The longer arm of the steelyard, therefore, being grad- 

 uated upon this principle, it becomes a convenient and sufficient- 

 ly accurate instrument for weighing all gross substances. 



The same rule is to be observed with respect to the position 

 of the axis of motion in the construction of the steelyard, as in 

 that of the balance ; that is, the axis must be in a line with the 

 points of suspension, and a little above the centre of gravity, so 

 that the arms when unloaded, or when equal moments are in- 

 dicated, shall preserve a horizontal position. 



260. In the bent-lever balance represented in figure 144, instead Fig.l4jft 

 of a moveable weight resting upon a horizontal beam, the natural 

 weight of an inclined arm is made use of, and is drawn out to 

 different distances from a vertical position according to the weight 

 attached to the other arm. By applying different known weights 



to the arm A, and graduating the arc CD according to the posi- 

 tions of the arm B, we shall have an instrument very analogous 

 to the steelyard ; for the weight B may be considered as shifted 

 to different distances along the horizontal line FD, since it would 

 have precisely the same effect here as in its actual position. 

 Consequently, if the direction of the weight attached to the arm 

 A preserved always the same horizontal distance from the axis 

 of motion (which it might be made to do, by suspending it from 

 a single cord applied to the arc of a circle having the axis for its 

 centre,) the arc CD might be graduated by dividing the radius 

 DF into equal parts in the manner of the steelyard, and then 

 transferring these divisions with the numbers denoting the weights 

 to the arc CD, by means of vertical lines. 



