Page:The New International Encyclopædia 1st ed. v. 02.djvu/473

correct, being too great if the standard or known weights are placed in the short pan, and vice versa. Then, as it is necessary that the beam should move freely, there must be a proper mounting or suspension where friction is reduced to a minimum, and as the force of gravity acts vertically, both known and unknown weights must be carried in suitably suspended pans.

Fig. 3. — ANALYTICAL BALANCE.

The balance is an instrument whose use is susceptible of great accuracy, and this is attained in the balances used by physicists and chemists in their measurements of precision. While the theoretical considerations involved are of course applicable to all forms of balances, they become of greater significance in discussing these finer instruments where extreme accuracy is desired. In such a balance the beam is of metal and carries at its middle point, transverse to its length, a steel or agate knife-edge which rests on surfaces of similar material. The line of contact between the knife-edge and the plane is the axis around which the beam revolves; and when the beam is at rest a vertical line through the centre of gravity would include this knife-edge. Connected with the beam, as shown in the illustration, Fig. 3, is a fine pointer, which passes over a graduated scale at the base of the supporting pillar, while at or near its extremities are placed, at equal distances from the central knife-edge, knife-edges upon whose sharp edges, turned upward, are placed the bearing surfaces of the metallic pieces from which the pans are suspended. In order that a minimum of wear should come upon these sharp edges, mechanism is provided to support the beam and pans whenever there is no actual weighing, and the devices to accomplish this vary in different forms of balances. The beam is graduated into 10 equal divisions, which in turn are similarly subdivided, and a hook on a movable rod is provided, by means of which a fine loop or rider of wire can be placed and removed at any desired point on the beam. Such is a general description of a balance, though there are, of course, numerous mechanical modifications and refinements to insure facility of operation and accuracy of measurement. The underlying principles will perhaps better be understood by referring to the diagram, Fig. 4. Let ACB represent the beam of a balance, and let the points where the knife-edges intersect a vertical plane through the beam be located on the line ACB, though this condition in practice is not always realized, and the knife-edges at the end of the beam may be either higher or lower than the centre knife-edge. The point of support is at C, consequently the centre of gravity is situated at C on a vertical line passing through this knife-edge. The location of the centre of gravity of the beam is an important consideration. If it were above the point of support the beam would be in unstable equilibrium, and would seek a more stable position, and in so doing would overturn. If the centre of gravity coincided with the axis of revolution, the beam would rest in any position indifferently, while the stability increases with the distance of the centre of gravity below the point of support. With an increase in the stability of the beam, the less the sensitiveness of the balance and the quicker the time in which it will cease from oscillating and take up a position of rest. The sensitiveness also depends on the length of the arms, increasing with the length, and the ease, or lack of friction resulting from skillful construction, with which the beam oscillates. The more sensitive, the balance the larger the period of oscillation of the beam, though it is necessary to consider the time necessary in making a weighing, and not adjust an ordinary balance to too high a degree of sensitiveness. An ordinary fine balance, as used by the physicist or chemist, is constructed and adjusted to have a period of vibration of between ten and fifteen seconds.

Fig. 4.

Assuming that the arms are equal in length and that equal loads are carried in each pan, or in other words that the beam is in equilibrium, the forces denoted by the dotted lines p and p', acting vertically, are of course equal. If now a small excess of weight be added to the right-hand pan, there will be an increased force on the right-hand arm, which may be represented by p", and the beam will be deflected by an amount which for small additions of weight is proportional to the excess, and is of course indicated by the pointer and scale.

In using a fine balance, precautions must be observed in its care and manipulation. The balance, which is inclosed in a glass case and kept free from dust, is first leveled in order that the supporting pillar should be vertical. If the pointer of the balance is not at the middle point, or zero (many physicists prefer to renumber the scale so that the numbers run consecutively from the left to the right, instead of the usual arrangement where the divisions are numbered to right and left from the centre-mark), i.e. the zero