232 BALALAIKA BALANCE JBalaklava. is supposed to be the site of the celebrated tem- ple of Diana Taurica, of which in the legend Iphigenia was priestess. BALALAIKA, a musical instrument with two or three strings, played with the fingers like the guitar, very popular in Russia for accompa- niments, and found in almost all the cottages of the peasantry. Russian ballads have been collected, under the title of this national instru- ment, in French (1837) and in German (1863). BALANCE, an instrument intended to measure different amounts or masses of matter by the determination of their weight, using as stand- ards of comparison certain fixed units, as the gramme, the pound, the ton, &c. The instru- ment is founded on the law that gravitation acts in a direct ratio to the mass, and on the mechanical principle that when a solid body is suspended on one point, the centre of gravity will place itself always perpendicularly under that point. If therefore a beam, alt, fig. 1, is supported in the middle at c, and movable around this point, its centre of gravity, , will place itself under the point c ; and if disturbed from that position, this centre will oscillate like a pendulum, and the beam will finally come to rest only with the centre of gravity in the per- pendicular passing through the point of sup- port. It is evident that when the distances from atoc and from 6 to c are equal, the two sides of the beam equal, and the whole made of homogeneous material, the horizontal posi- tion will be arrived at, and also when at a and 6 equal weights pp are suspended ; the gravity of such scales and weights must be considered con- centrated in the points of suspension a and J, and their common centre of gravity will be either in, under, or above the point of support, according as the line ab uniting them passes through, under, or above the support c. But suppose we place an additional weight r in one of the scales, then the common centre of gravity of the weights in the scales will be shifted toward the side of that additional weight. Suppose it to be in d, then the centre of gravity of the whole balance will be in the line ds, uniting the centre of gravity d of the FIG. l. Common Balance. weights with that of the balance ; if then it is somewhere at TO, it is evident that the balance can no longer maintain the horizontal position, but will only come to rest when m is under c, or the line cm has attained a perpendicular posi- tion. It is evident that the angle which the beam in this case makes with a horizontal line is equal to the angle sem. If the centre of grav- ity is in the point of support, the balance is indifferent ; that is, it will, when charged with equal weights, remain at rest in any position. And if the centre of gravity is above the point of support, we have a case of so-called unstable equilibrium ; the balance will with equal ease tip over to the right or left, and the beam can never be brought into the horizontal position. In either case the balance is useless, and it follows
