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the determination of the mass of bodies by means of balances. A high degree of accuracy in weighing is achieved by taking into consideration all possible errors of the balances, the weights, and the weighing method used, as well as errors caused by external conditions, such as the influence of aerostatic, electric, and magnetic forces and variations in air temperature and humidity. (The limits of permissible error for balances of various types and for weights are given in the articles BALANCE and WEIGHTS.)

When a high degree of accuracy is not required and when the effects of aerostatic and other forces are not considered, the direct weighing method is usually used: the mass of a body is taken as equal to the algebraic sum of the mass of the weights that balance the body and of the readings on the balance. In this case, weighing on an equal-arm balance includes errors because of the inequality of the balance beam. Greater accuracy in direct weighing is achieved on a one-arm balance, which eliminates this error, since the body to be weighed and the balancing weights are on the same side of the balance beam. To completely eliminate error caused by inequalities of the balance beam when weighing on equal-arm balances, so-called accurate weighing methods are used.

The displacement method (Borda method) consists of the following steps: after balancing the body with a counter-weight (metal scraps, shot, and so on) placed on the opposite arm of the balance beam, the body is removed from the balance and replaced by weights such that the balance achieves the original equilibrium position. The mass of the body is determined by the mass of the weights needed to balance the scales and according to the reading on the balance corresponding to the part of the mass not balanced by the weights.

In the method of D. I. Mendeleev, one of the balance cups is filled with weights that correspond to the weight limit of the balance; a counterweight to balance the first weights is placed in the other cup. The body to be weighed is placed in the cup with the first weights, which are removed to the point at which the balance returns to its initial position of equilibrium. The mass of the body is determined by the amount of mass removed and by the reading on the scale.

The double weighing method (Gauss’ method) consists of a repeated direct weighing after transposing the body and the weights from one cup of the balance to the other. The mass of the body M = 1/2(M1+M2), where M1 and M2 are the results of two direct weighings. All three methods are equally accu-rate. The choice of a method depends on the construction of the balance and the weighing conditions. On balances of any type, weighing can be accomplished only with limited accuracy, since balances and weights always have a certain error.

Figure 1. Accuracy characteristics of mass measurements depending on size and the method of measurement: (1) comparison of the State Standard of Mass (the kilogram), (2) metrological research, (3) high-accuracy analytic research, (4) high-accuracy industrial weighing, weighings of precious metals, (5) commercial and economic measurements. The shaded area represents measurements made on automatic screen scales and other industrial scales and batchers.

Thus, on a balance with 0.1 percent error, it is impossible to weigh a body with less error. For particularly accurate weighing, accurate weighing methods are used, as well as calculating the error of the weights. To simplify evaluation of the error caused by aerostatic forces arising from the inequality of volumes of the measured body and the weights (Archimedes’ law), the specific density of the material is taken to be 8.0 x 103 kg/m3 (regardless of the material from which they are made) for all weights except standard weights. The accuracy of weighing in various branches of science, technology, and the national economy is shown in the form of a graph in Figure 1.


Rudo, N. M. Laboratornye vesy i tochnoe vzveshivanie. Moscow, 1963.
Smirnova, N. A. Edinitsy izmerenii massy i vesa v Mezhdunarodnoi sisteme edinits. Moscow, 1966.


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