BALANCE. A machine for weighing substances. The process of weighing may be performed in various ways, and accordingly there are several kinds of balances ; as the common balance or scales, the bent lever balance, the spring balance, the steel-yard, the hydrostatic' balance, &c. The term is also applied to any apparatus employed for comparing the intensities of very small forces; as the electric balance, the balance of tor sion, &e. We shall here confine our re marks to the philosophical balance, the instrument used when great accuracy is necessary ; for instance in assaying, and in the more delicate investigations of physics and chemistry.
Neglecting the mere circumstance of construction, and the particular methods of suspension, the balance may be repre sented thus: A and B are the points from which the scales are suspended at the extremities of the beam, C the point of support, G the centre of gravity of the beam, D the point in which the straight line C G in tersects the straight line Joining A and B. The properties required in a good bal ance are seasibiliey and stability. The balance must be sensible; that is to say, when it is properly poised a very small addition of weight to either scale should disturb the equilibrium, and cause the beam to turn ; and it must be stable, that is to say, when the equilibrium has been disturbed it should return, and oscillate about the position of rest. These two properties are in some degree op posed to each other; in order to attain them both, as far as possible, it is neces sary to attend to certain mechanical prin ciples, as well as to the physical circum stances of construction. Lot us suppose W = the weight of the beam.
L = the load, i. e. the weight of the scales and whatever is in them when the beam is poised.
P = the preponderating weight, or that which causes the beam to turn. Suppose now the beam to be poised, or that the scales being loaded the posi tion of the line A B is perfectly hori zontal. The sensibility will evidently be measured by the angular space through which the beam turns when a small weight P is added to either scale ,• but the force which acts in turning the beam is proportional to P X D B, that is, pro portional to the weight multiplied into the length of the lever at the extremity of which it acts; therefore for a given weight P, the sensibility of the balance, all other circumstances being equal, is proportional to the length of the beam.
Let us next consider the force which tends to restore the beam when the equi librium is disturbed. This is made up of two parts ;_the first of which is pro portional to 'W X C G, that is to say, proportional to the weight of the beam (which may be regarded as concentrated at the centre of gravity) multiplied into the length of the lever on which it acts ; and the second proportional to L X C D, that is, to the load also multiplied into its length of lever. The whole restoring force is therefore proportional to W X C G L X C D. Now this force is pre cisely that which the preponderating weight P has to overcome in turning the scale ; consequently any circumstance which tends to increase it, increases the stability and diminishes the sensibility of the balance ; and any thing which tends to diminish, it, diminishes the stability and increases the sensibility. By bend ing the arms of the balance, or altering the points of suspension of the scales, the points G and 1) may acquire different positions relatively to C. Supposing to be above C in the vertical line joining those points ; the term WXCG would become negative, and the restoring force proportional to L X CD—W X0 G. In this case, if the load L, or the distance C D, were diminished till L X C D be came less than W X C the balance would be useless ; because if moved ever so little from the position of rest, it would have no tendency whatever to return. The best construction is to make C D = 0, that is, to place the three points of action A, C, B, in the same straight line, and to construct the beam so that G, the centre of gravity, shall fall a little below the line A B. the sensibility is then in dependent of the load, and is simply in the inverse portion of WXCG; so that by diminishing the weight of the beam. or the distance C G, it may be increased to any required degree. It is supposed that the two arms are precisely of the same length, or that C is placed exactly in the middle between A and B and also that they are perfectly inflexible.