Professionals working with weighing instruments often pay little attention to the weights used for verification, and are likely even less familiar with the kilogram prototype. Introducing knowledge about the kilogram prototype is therefore highly relevant for those in the field.
The International Prototype of the Kilogram is a cylinder made of a platinum-iridium alloy (90% platinum, 10% iridium) with a diameter of 39 mm and a height of 39 mm; its density is approximately 21.5 g/cm³. Since its mass was first defined as the international standard for the kilogram by the General Conference on Weights and Measures in 1889, the prototype has been preserved at the International Bureau of Weights and Measures (BIPM) in Sèvres, near Paris.
Mass differs fundamentally from other base quantities. Unlike the current definitions of the meter (length) and the second (time), which are linked to natural constants, mass is defined by a specific physical object. Consequently, its magnitude (or size) can only be determined through the "force" it experiences. In a sense, the definition of "force" is an abstract physical concept, unlike length (meters) and time (seconds), which correspond to concrete sensory perceptions. Even today, the magnitude of "mass" is linked to a fundamental physical quantity via electrical methods—a link that bears no direct relationship, in terms of physical concepts, to the definitions of inertial mass and gravitational mass commonly used in mechanics. It lacks the inherent physical connection found in definitions where quantum mechanical transitions characterize frequency (time) and wavelength (length). Thus, the so-called "natural standard" for mass merely resolves the uncertainty and unpredictability regarding magnitude fluctuations associated with previous artifact-based standards.
China's national kilogram prototype was acquired from the United Kingdom in 1965 (at a time when China had not yet joined the International Organization of Legal Metrology).
China's national kilogram prototype bears the serial number No. 60. Mass: M (No. 60) = 1 kg + 0.27 mg ± 0.08 mg
Volume: V (0°C) = 46.3867 cm³
Expansion coefficient: α = (25.863 + 0.00562t) × 10⁻⁶/°C
Volume: V (20°C) = 46.4108 cm³
This prototype was officially approved as a national mass standard in 1986. National prototypes from various countries are linked to the BIPM's International Prototype of the Kilogram via prototype balances and are sent to the BIPM for comparison in accordance with BIPM requirements. The first international comparison (conducted from 1899 to 1901) took nearly two years to complete. It involved comparing 18 national prototypes, four unassigned prototypes, two working prototypes of the BIPM, and two earlier BIPM working prototypes—C (a cylinder) and S (a truncated sphere)—against the International Prototype of the Kilogram (Prototype No. 1).
The comparisons revealed that the mass changes of unused prototypes remained within the permissible microgram range, whereas the BIPM's working prototype No. 31 lost 20 μg of mass due to frequent use.
A second international comparison took place between 1948 and 1953, involving 33 prototypes; a third international comparison was conducted between 1987 and 1993, involving 39 prototypes. China's national kilogram prototype No. 64 participated in this comparison; the results for prototype No. 64 are as follows:
M(No. 64) = 1 kg + 0.251 mg ± 0.0023 mg

II.
A weight serves as a vehicle for representing the magnitude of "mass," but it cannot itself function as an instrument for measuring the mass of an object. Measuring the mass of an object involves comparing the object to a weight (the mass carrier); specifically, under the influence of gravity, a comparison device is used to verify the equality of the forces and moments acting on the objects being compared. Such a comparison device is known as a "weighing instrument" (or balance).
The result obtained from a weighing instrument is treated as an approximation of the mass and is referred to as the "weighed value."
When an object is situated within a medium (such as air or another fluid), in addition to the force of gravity, it is subject to the medium's buoyant force in accordance with Archimedes' principle.
When the densities of the object being weighed and the weight differ, the equilibrium equation for the balance of 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 weight and the object being weighed;
g1 and g2 — gravitational acceleration at the locations of the weight and the object being weighed;
l1 and l2 — moment arms of the forces acting on the objects;
Vm and Vp — volumes of the weight and the object being weighed;
mm and mp — "true" masses of the weight and the object being weighed. Under normal circumstances, it can be assumed that g1 = g2 and l1 = l2. If both objects are weighed in air with a density of ρ0 (where ρ0 = ρ1 = ρ2), the relationship is:
mp = mm + ρ0(Vp - Vm)
When weighing objects, the scale of measurement can range from grams to tons; therefore, a variety of weights with corresponding mass values and accuracy classes are required to transfer mass values—essentially using weights to calibrate the weighing instruments.
Modern weights are predominantly made of stainless steel, creating a significant difference in density compared to the objects being weighed. This means that objects of the same weight can differ greatly in volume. As is well known, the effect of air buoyancy need not be considered only when the volume of the object being weighed is equal to the volume of the weight.
The "weighing value" mentioned earlier actually refers to the mass of an object as determined by a scale calibrated with weights, without accounting for air buoyancy. Thus, the measured value depends on air density and the volume of the object. In trade, when the relative error (Δm/m) is less than 10⁻³, the weighing value is—for practical purposes—considered the object's mass; consequently, the maximum permissible errors for Class III and Class IV scales are set within this range.
The density of the International Prototype of the Kilogram is approximately 21.5 g/cm³. When transferring its mass value to working weights (reference weights), the precise density or volume of the weights and the precise air density must be known. As a result, the entire measurement process is highly complex.
To simplify mass comparison measurements, legal metrology allows for the specification of weight density and the performance of comparisons under a defined standard air density. This approach minimizes measurement uncertainty and facilitates the process; the mass value determined in this manner is known as the "conventional mass value." Since the adoption of this new verification method in 1975, the standard value of a weight is no longer defined by its actual mass, but rather by the mass of a reference weight (working weight). This reference weight has a density of 8000 kg/m³ and is defined as balancing a prototype weight under conditions where the air density is 1.2 kg/m³ and the temperature is 20°C; this conventional measurement value is designated as the mass value.
Under these regulations, the weight of any object being weighed is considered equivalent to the weight of an object under the conditions of a conventional air density of ρ₀ = 1.2 kg/m³ and a conventional object density of ρₖ = 8000 kg/m³. When the density of the object being weighed and the actual air density differ from these conventional values, the reading on the weighing instrument will not match the nominal value of the calibration weight. The error between the measurement result and the object's "true" value is denoted as Δm, and its relative error with respect to the weight's standard value is expressed as:
Δm/mₖ = (ρL - ρ₀)(1/ρ - 1/ρₖ)
Where: Δm — the mass that must be added for the object to balance the reference weight in air;
mL — the nominal value of the weight (the reading of the calibrated weighing instrument);
ρL — the air density 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 conventional mass values is that any weights with the same nominal value—regardless of their actual density—will experience the same force as the reference weight when placed 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 difference in densities results in different air buoyancy forces; consequently, the readings on the weighing instrument differ, with the discrepancy being Δm. However, by appropriately selecting the density of the weights and the air density at the measurement site (i.e., the values of ρ and ρL), it is always possible to ensure that the relative error of the weight (Δm/mk) does not exceed the specified limit; this method is highly advantageous for the dissemination of mass values using weights.
In legal metrology, there are specific regulations regarding the permissible density of weights: the density must be such that, when air density deviates from the reference value of 1.2 kg/m³, the resulting error is at most 0.25 times (i.e., one-quarter of) the maximum permissible error. Internationally, the limit for air density deviation from the reference value of 1.2 kg/m³ is set at 10%; this figure typically represents the deviation of indoor air density from the mean value of 1.2 kg/m³ (approximately ±10%). Therefore, "as long as the air density remains within the specified range, there is no need to apply air buoyancy corrections, even for weights of the highest accuracy class."
When using weights to calibrate weighing instruments, the absolute value of the weight's permissible error must not exceed one-third of the instrument's permissible error. During the dissemination of mass values, the weight used as the standard should be of at least one accuracy class higher. For example, to verify high-precision F1-class weights, an E2-class weight must be used as the standard.
However, under typical environmental conditions, the influence of environmental factors and user-related factors can result in measurement errors that are two to three times the verification value or scale interval of the weighing instrument.
Mass is one of the three fundamental physical quantities in classical physics—alongside time and length—yet its definition differs from theirs. While time and length are intuitive quantities, mass can only be characterized through "force" or "energy" (kinetic or potential); it is an abstract physical term (or concept). We cannot perceive its magnitude directly through our senses; instead, we must measure it via gravitational and inertial forces. Furthermore, the question of whether gravitational force and inertial force are fundamentally the same phenomenon remains a subject requiring further in-depth exploration. Although electrical methods now allow the value of mass to be equated to an intrinsic material parameter—creating a so-called "natural standard"—the practical effect is merely to preserve the magnitude of the fundamental physical quantity "mass" (originally defined by the International Prototype of the Kilogram) within a material parameter assumed to be constant. While this resolves the difficulty of detecting changes in the value of the original physical mass standard, the material parameter's physical constants cannot replace the definition and concept of mass itself; in contrast, the physical concepts of time and length have been successfully redefined through physical "transitions."
In short, the physical quantity of mass still requires the use of weights to disseminate its value, and the measurement of an object's mass relies on weighing instruments operating on the principles of force and torque equilibrium; the definition of mass remains unchanged by these methods. I believe that a true understanding of the nature of mass can only be achieved through a profound insight into the essence of universal gravitation or gravitational strength.