Workers in the weighing industry often pay little attention to the weights used to calibrate weighing instruments, and may be even less familiar with the kilogram prototype. Introducing knowledge about the kilogram prototype here is of great significance to weighing professionals.

The international kilogram prototype is a cylinder of platinum-iridium alloy, 39 mm in diameter and 39 mm in height, containing 90% platinum and 10% iridium, with a density of approximately 21.5 g/cm³. Since it was first defined as the mass of the international kilogram prototype by the General Conference on Weights and Measures in 1889, it has been kept at the International Bureau of Weights and Measures (BIPM) in Sèvres, Paris.

Mass differs fundamentally from other fundamental quantities. Unlike the current definitions of the meter (a unit of length) and the second (a unit of time), it cannot be traced back to a natural constant but is defined by a specific physical object. Therefore, its value (i.e., its magnitude) can only be determined by the value of the "force" acting upon it. In a sense, the definition of "force" is an abstract physical concept, unlike length (meters) and time (seconds), which are concrete sensations to our senses. Even now, the value of "mass" is linked to a fundamental quantity of matter through electrical methods. This fundamental quantity, however, has no direct physical relationship with the definitions of inertial mass and gravitational mass (gravitational mass) used in mechanics. It doesn't have a physical connection like the definitions of frequency (time) and wavelength (length) in quantum mechanics. Therefore, the so-called "natural standard" of mass only addresses the uncertainty and unknowability of changes in the value of past physical standards.

China's national prototype kilogram was introduced from Britain in 1965 (at which time China had not yet joined the International Organization of Legal Metrology).

China's national prototype kilogram is numbered No. 60. Mass: M (No. 60) = 1kg + 0.27/mg ± 0.08mg
Volume: V (0℃) = 46.3867cm³

Coefficient of Expansion: α = (25.863 + 0.00562t) × 6/℃
Volume: V (20℃) = 46.4108cm³

This prototype was officially approved as a national mass standard in 1986. National prototypes from various countries are correlated with the BIPM's international kilogram prototype using a prototype balance and, according to BIPM's requirements, sent to BIPM for comparison. The first international comparison (from 1899 to 1901) took nearly two years to complete. Eighteen national prototypes, four unassigned prototypes, two working prototypes from the International Bureau of Weights and Measures (IBGB), and two earlier working prototypes from the IBGB, C and S (C being a cylinder and S a truncated sphere), were compared with the International Kilogram Certification Standard Prototype No. 1.

The comparison showed that the mass changes of the unused prototypes were within the permissible microgram range, while the IBGB working prototype No. 31, due to frequent use, had a mass reduction of 20 μg.

The second international comparison was conducted between 1935 and 1948, involving 33 prototypes; the third international comparison was conducted between 1987 and 1993, involving 39 prototypes. China's No. 64 national kilogram prototype participated in this comparison. The comparison results of China's No. 64 prototype are as follows: M(No. 64) = 1kg + 0.251mg ± 0.0023mg. II. Weights are a carrier representing the magnitude of "mass," but they cannot themselves be used as instruments to determine the mass of an object. Measuring the mass of an object is achieved by comparing the object being measured with the weights that act as a mass carrier. That is, under the influence of gravity, a comparison device is used to verify the mass of the object being compared. Introduction to the National Kilogram Prototype (Weights) □ Zhou Zulian, National Institute of Metrology, China Document Identifier: B Article Number: 1003-1870 (2023) 05-0047-03 1. The forces and torques acting on the compared objects are equal, therefore this comparison device is called a "weighing instrument" (or balance). The result measured by the weighing instrument is used as an approximation of the mass, called the measurement value. When an object is in a medium (such as air or other media), in addition to gravity, it is also subject to the buoyancy of the medium according to Archimedes' principle.

When the density of the object being measured is different from that of the weights, the equilibrium equation for the comparison forces in the presence of a medium is:
mm·g1
·l1
-ρ1
·Vm·g1
·l1=mp
·g2
·l2
-ρ2
·Vp
·g2
·l2
Where: ρ1 and ρ2—densities of the weights and the object being weighed;
g1 and g2—acceleration due to gravity at the location of the weights and the object being weighed;
l1 and l2—torques of the forces acting on the object;
Vm and Vp—volumes of the weights and the object being weighed;
mm and mp—the "true" masses of the weights and the object being weighed. Under normal circumstances, we can assume g1 = g2, l1 = l2, and both substances are weighed in air (ρ0 = ρ1 = ρ2). Therefore: mp = mm + ρ0(Vp - Vm).

When measuring the mass of an object using a weighing instrument, the unit of measurement can be increased from the "gram" level to the "ton" level. Therefore, various weights of corresponding weights and accuracy levels are needed to transmit the mass value; that is, weights are used to calibrate the weighing instrument.

Currently, the weights used for weighing are mostly made of stainless steel, which has a significant difference in density from the object being weighed. This means that objects of the same weight can have vastly different volumes. As is well known,

the effect of air buoyancy is only unnecessary to consider when the volume of the object being weighed is equal to the volume of the weight.

The weighing instrument value mentioned above actually refers to the mass value of the object weighed by the instrument after calibration with weights, without considering air buoyancy.

Therefore, the measured value of an object depends on the air density and the volume of the object being weighed. In trade, when the allowable tolerance Δm/m < 10⁻³, for practical purposes, we consider the weighing value to be the mass of the object. Therefore, in trade, the maximum permissible error of Class III and IV scales should be specified within this error range.

The density of the international prototype kilogram is approximately 21.5 g/cm³. When transferring its mass value to working weights (i.e., reference weights), one must know the accurate density or volume of the weights, as well as the accurate air density. Therefore, the entire measurement process is a very complex task.

To simplify the measurement work of mass comparison, in legal metrology, if we specify the density of the weights and perform mass comparisons under a specified standard air density, the uncertainty in the mass comparison measurement work can be very small and easy to operate. The mass value determined in this way is called a fixed weighing value.

Since the establishment of this new verification method in 1975, the standard value of a weight is no longer its own mass, but rather the mass of a reference weight (working weight). The reference weight has a density of 8000 kg/m³, and under conditions where the density of air is 1.2 kg/m³ and the temperature is 20°C, it remains in equilibrium with the original weight. This conventionally agreed-upon measurement value is the mass value.

This convention assumes that the weight of all objects being weighed is equal to the weight of the object under the agreed-upon conditions of air density ρ0 = 1.2 kg/m³ and the agreed-upon density of the object being weighed ρk = 8000 kg/m³. When the density of the object being weighed and the density of air do not equal the agreed-upon values, the reading of the weighing instrument will be inconsistent with the nominal value of the calibration weight. The error between the measurement result and the "true" value of the object is Δm. Its relative error with the standard value of the weight is: Δm/mk = (ρL - ρ0)(1/ρ - 1/ρk) Where: Δm—The mass required to balance the object with the reference weight in air; mL—The nominal value of the weight (the reading of the calibrated weighing instrument); ρL—The density of air at the time of measurement; ρ—The density of the object; ρk = 8000 kg/m³—The conventional density of the reference weight; ρ0 = 1.2 kg/m³—The conventional air density.

The advantage of using a conventional mass value is that all weights with the same nominal value, regardless of their density, will experience the same force as other reference weights in air with a density of 1.2 kg/m³. However, when the air density at the measurement site deviates from 1.2 kg/m³, the buoyancy forces exerted by the air are different due to the difference in density, resulting in different weighing values with a difference of Δm.

However, if the density of the weights and the air density at the measurement site (i.e., ρ and ρL values) are appropriately selected, the relative error of the weights Δm/mk can always be kept within the specified value. This method is very advantageous for using weights to transfer mass values.

In legal metrology work, the permissible density of weights is specified as follows: the density of the weights must ensure that when the air density deviates from 1.2 kg/m³, the resulting error is at most 0.25 times the maximum permissible value (i.e., 1/4 of the error). Internationally, the limit for air density deviating from the specified value of 1.2 kg/m³ is limited to within 10%, which is usually the deviation of indoor air density from the average value of 1.2 kg/m³, approximately ±10%. Therefore, "as long as the air density remains within the aforementioned specified range, even for the highest precision weights, there is no need to consider correcting for air buoyancy."

When calibrating a weighing instrument using weights, the absolute value of the weight's tolerance must not exceed 1/3 of the instrument's tolerance. In value transfer, the standard weight should be at least one accuracy class higher. For example, to verify a high-precision F1 weight, at least an E2 weight should be used as the standard.

However, under normal environmental conditions, due to the influence of environmental factors and user factors, the error in the measurement result can be 2 to 3 times the instrument's calibration value or scale division.

Mass, as one of the definitions of the three fundamental physical quantities in classical physics—time, length, and mass—is different from the definitions of time and length. Time and length are very intuitive quantities, while mass can only be characterized by "force" or "energy—kinetic or potential energy," and is an abstract physical term (or concept). We cannot directly perceive its value with our senses; we can only measure it through gravity and inertial forces. Furthermore, whether gravity and inertial forces are essentially the same thing in terms of physical reality remains to be explored in depth.

Although we have now used electrical methods to equate the value of mass to a parameter of matter itself—that is, to create a so-called "natural standard"—its actual function is merely to store the fundamental physical quantity of "mass" in a material parameter that is artificially considered "constant" using the "mass" value of the international prototype kilogram. The result is that it only solves the difficulty of judging changes in the original "physical standard" value of mass,

but it cannot replace the definition and concept of "mass" with the physical constant of this material parameter. Time and length, on the other hand, can be replaced by physical "jumps" to replace the original physical concepts of time and length.

In short, the physical quantity of mass still needs to be transmitted through weights, and the mass of an object is measured using weighing instruments based on the principle of force and torque balance. The definition of mass remains unchanged. I believe that only through a deep understanding of the nature of universal gravitation or the strength of gravity can we gain insight into the nature of mass.