ON STATICS. 12,5 



scales, being freely suspended from fixed points in the beam, act on them al- 

 ways in the direction of gravity ; and the effect is the same as if the whole 

 weight were concentrated in those points. The beam supports the scales, and 

 is itself supported, by means of line edges of hard steel, working on steel, agate, 

 or garnet, in order that the motion may be free, and the distances of the 

 points precisely defined. The best beams are made of two hollow cones of 

 brass, united at their bases ; they are lifted off their supports when the ba- 

 lance is not used, in order to avoid accidental injuries; the scales also are 

 supported, so as not to hang from the beam, until they have received their 

 weights. According to the position of the fulcrum, with respect to the points 

 of suspension of the scales, the equilibrium of the balance may be either stable, 

 neutral, or tottering; or if the beam be too flexible, it may pass from one 

 of these states to the other by the effect of the weights. The stable equili- 

 brium is the most usual and the best, because it gives us an opportunity of 

 determining the degree of inequality of the weights, by the position in which 

 the centre of gravity rests, or by the middle point of the vibrations of the 

 beam, which are sometimes measured by an index, pointing to a graduated 

 arc. If, however, the fulcrum be too much elevated above the centre of 

 gravity, the equilibrium may be too stable, and may retjuire too great an in- 

 equality, in order to produce a sensible preponderance. If, on the contrary, 

 by the elevation of the points of suspension of the scales, the equilibrium be 

 rendered tottering, the lower scale will not rise, even if it be somewhat less 

 loaded than the upper; and sieelyards of this construction have scmietimes 

 been employed, in order to impose on the purchaser by the appearance of an 

 ample weight. It is necessary, where great accuracy is desired, to bring the" 

 equilibrium very near the state of neutrality, and to make the vibrations of 

 the beam slow and extensive, whether the scales have weights in them or 

 not: for this purpose a small weight is sometimes inclosed within the beam, 

 which is raised or depressed at pleasure, by a screw, so as to bring the 

 centre of gravity of the whole moveable apparatus, as near to the fulcrum as 

 may be required for the occasion. IVfr. llamsden's balance, made for the 

 Royal Society, is capable of weighing ten pounds, and turns with one ten 

 millionth part of the weight. (Plate VIII. Fig. 107 . • IO9.) 



The arms of a balance have sometimes been made imequal for fraudulent 

 purposes, the weight being placed nearer to the fulcrum than the substance 



