Table of contents

Distinguishing between a supercooled dew and frost below 0 °C in dew/frost-point measurements is an important and challenging problem that has not yet been completely solved. This study presents a new method for the recognition of a supercooled dew in a dew/frost-point sensor. A quartz crystal microbalance (QCM) sensor was used as a dew/frost-point sensor to detect a dew and a supercooled dew as well as frost. The slip phenomenon occurring at an interface between the water droplet and the surface of the quartz crystal resonator of the QCM sensor gives a simple and accurate way of distinguishing between a supercooled dew and frost below 0 °C. This method can give a highly accurate measurement of the dew or the frost point without misreading in the dew-point sensor at temperatures below 0 °C.

We present improved results for the ac longitudinal resistance at the high-potential side of a quantum Hall device. Previous measurements indicated a different frequency- and current-dependence at either side of a device. This asymmetry is now attributed to a loading effect which has been overlooked. When the measuring bridge is modified to eliminate this effect, the ac longitudinal resistances at the high- and the low-potential side show a very similar and consistent behaviour.

The gravitational redshift is one of the main biases in the comparison of primary frequency standards; even if it is not a limit for the present accuracy of the microwave frequency standards such as Cs beam or fountain clocks, it could be a challenge for the forthcoming generation of atomic optical clocks. In this article we report the evaluation of the gravitational redshift with respect to the Geoid reference at Istituto Nazionale di Ricerca Metrologica (INRIM) laboratories, with an accuracy of 1 × 10⁻¹⁷ in terms of relative frequency. The evaluation is based on GPS/levelling measurements and on the use of both a local and a global model for the Earth Geoid; the main limitation to the accuracy is given by the Geoid reference potential itself.

Secondary mass standards are usually made of stainless steel. One of the main problems in mass metrology is the stability of such stainless steel standards. Consequently, new materials have been investigated for the realization of mass standards, and this has led to the selection of nickel-based superalloys. The stability of materials is strongly dependent on surface reactivity; accelerated oxidation tests were performed, either in dry or wet air, and after a kinetic study, microstructural analysis of the oxide films was performed by scanning electron microscopy. The structure of the oxide films was also characterized by grazing x-ray diffraction and finally by x-ray photoelectron spectrometry (XPS) analysis. XPS associated with sputtering by argon ions allowed us to differentiate the nature of the oxides from the outer surface to a given depth in the film.

In mass metrology, the standards currently used are calibrated by a chain of comparisons, performed using mass comparators, that extends ultimately from the international prototype (which is the definition of the unit of mass) to the standards in routine use. The differences measured in the course of these comparisons become smaller and smaller as the standards approach the definitions of their units, precisely because of how accurately they have been adjusted.

One source of uncertainty in the determination of the difference of mass between the mass compared and the reference mass is the sensitivity error of the comparator used. Unfortunately, in the market there are no mass standards small enough (of the order of a few hundreds of micrograms) for a valid evaluation of this source of uncertainty. The users of these comparators therefore have no choice but to rely on the characteristics claimed by the makers of the comparators, or else to determine this sensitivity error at higher values (at least 1 mg) and interpolate from this result to smaller differences of mass.

For this reason, the LNE decided to produce and calibrate micro-mass standards having nominal values between 100 µg and 900 µg. These standards were developed, then tested in multiple comparisons on an A5 type automatic comparator. They have since been qualified and calibrated in a weighing design, repeatedly and over an extended period of time, to establish their stability with respect to oxidation and the harmlessness of the handling and storage procedure associated with their use. Finally, the micro-standards so qualified were used to characterize the sensitivity errors of two of the LNE's mass comparators, including the one used to tie France's Platinum reference standard (Pt 35) to stainless steel and superalloy standards.

The absolute frequencies of the hyperfine components of the R(26) 62-0 transition in molecular iodine at 501.7 nm are measured for the first time with an optical clockwork based on a femtosecond laser frequency comb generator. The set-up is composed of an Ar⁺ laser locked to a hyperfine component of the R(26) 62-0 transition detected in a continuously pumped low-pressure cell (0.33 Pa). The detected resonances show a linewidth of 45 kHz (half-width at half-maximum). The uncertainty of the frequency measurement is estimated to be 250 Hz.

This paper deals with the evaluation of the uncertainty in the equilibrium value of the eutectic temperature of the eutectic systems Fe–C and Co–C in their pure state. The first step towards this is deriving the equilibrium value of the liquidus temperature of the actual impure system and its associated uncertainty, the second estimating the uncertainty in the correction for the effect of impurities. The derivation of liquidus temperature and its uncertainty from the observed melting behaviour forms the core of this study. It involves the extrapolation of the measured melting plateaus, obtained at finite growth rates of the preceding freezes, towards the plateau related to zero growth rate, i.e. to the state of structural thermodynamic equilibrium. The uncertainty in the correction for the effect of impurities will be evaluated by means of 'the sum of individual estimates' and 'the overall maximum estimate', earlier shown to be applicable to eutectic systems.

An experimental assembly has been constructed to measure the specific heat capacity of macroscopic graphite samples at room temperature. The same batch of graphite constitutes the core of a graphite calorimeter, which is currently being realized to measure the absorbed dose due to ionizing radiation. Two different experimental procedures have been applied. In the first method the specific heat capacity of graphite was measured directly, where its value is corrected for the influence of impurities. The second method, to our knowledge not previously applied to macroscopic samples, is based on a series of differential measurements where no correction for added impurities is needed. By its nature, the second method reduces systematic effects. The specific heat capacity of a particular graphite sample is determined to be 706.9 J K⁻¹ kg⁻¹ with a combined relative standard uncertainty of 9 parts in 10⁴ at 295.15 K. The specific heat capacity of cyanoacrylate has also been determined.

The shift of the melting curves of Zn samples was measured as a function of impurity concentration by explicit doping with some of the impurities that are usually present in high purity Zn samples. The following shifts were obtained in mK/ppm wt (mass fraction in parts per million) for Fe, Pb, Cd, In, Cu, Ag and Au, respectively: −0.51, −0.27, −0.33, −0.39, +0.23, +0.26 and +0.078.

The requirement to aggregate measurement data, in the case where each measured value corresponds to nominally the same quantity, is important throughout metrology. Correlation associated with measured values is shown to arise in a number of measurement problems, with examples taken from the areas of interlaboratory comparisons, including key comparisons, the calibration of measuring systems and instruments, wireless sensor networks and prediction on the basis of different models. Consideration is given to the effect that correlation has on the determination of an aggregated estimate of the measured quantity, and on testing the consistency of measurement data. Approaches to quantifying the correlation associated with measured values are presented, and a formulation is given of the problem of determining the largest consistent subset of data having associated correlation. Results for three measurement problems are given, concerned with an interlaboratory comparison of noise in a coaxial line, the calibration of a thermometer and the analysis of data arising from a wireless sensor network.

This paper is concerned with bringing together the topics of uncertainty evaluation using a Monte Carlo method, distributed computing for data parallel applications and pseudo-random number generation. A study of a measurement system to estimate the absolute thermodynamic temperatures of two high-temperature blackbodies by measuring the ratios of their spectral radiances is used to illustrate the application of these topics. The uncertainties associated with the estimates of the temperatures are evaluated and used to inform the experimental realization of the system. The difficulties associated with determining model sensitivity coefficients, and demonstrating whether a linearization of the model is adequate, are avoided by using a Monte Carlo method as an approach to uncertainty evaluation. A distributed computing system is used to undertake the Monte Carlo calculation because the computational effort required to evaluate the measurement model can be significant. In order to ensure that the results provided by a Monte Carlo method implemented on a distributed computing system are reliable, consideration is given to the approach to generating pseudo-random numbers, which constitutes a key component of the Monte Carlo procedure.

The identification of the measurand in a comparison of standards may seem a simple matter. This choice can, however, be complicated by (extremely) varied interpretations, as this paper seeks to show. Cases affected by possible ambiguities are presented, involving the intrinsic nature of the standard, the way the standard is implemented or the way the comparison is conducted. Ambiguities can lead to controversial scientific and formal decisions. The paper reviews and discusses a broad variety of aspects of measurand identification that have arisen in CIPM key comparisons, mainly in thermal metrology.

The Welch–Satterthwaite (W–S) formula described in the Guide to the Expression of Uncertainty in Measurement enables an effective number of degrees of freedom to be associated with the standard uncertainty of a measurement estimate. This facilitates the calculation of an expanded uncertainty interval for the value of the measurand. However, the W–S formula is only applicable when the components of measurement error with finite degrees of freedom are uncorrelated. This paper considers the generalization of the formula to accommodate correlated components with finite degrees of freedom. We show that the number of degrees of freedom to be associated with any estimate derived from repeated observation of several quantities is n − 1, where n is the number of sets of observations, and we then give two equations by which the number of effective degrees may be calculated.

A procedure is proposed to calculate the uncertainty of the energy content associated with real-time flow measurements of natural gas. The procedure was applied to a measuring scheme consisting of an arrangement of orifice plate meters installed in parallel, coupled to an on-line gas chromatograph and a real-time data processing flow computer. Two distinct sources of natural gas with appreciable fluctuations in chemical properties were considered. The analysis suggests that the uncertainty depends mainly on these fluctuations, on the flow regime and on systematic errors. The work also suggests that the chemical analysis-sampling rate plays an important role in the overall uncertainty budget.

Recent proposals to redefine four of the base units of the International System (SI) have stimulated some debate as to how the SI might best be developed to meet changes in requirements. In this paper we consider whether the proposals are a timely and proportionate response to those changes in requirements that can be identified today. We conclude that, whilst the proposed changes to the definitions of the mole and kelvin appear to have some advantages, the case for changes in the definitions of the ampere and the kilogram is less well made at the present stage of development of the key experiments involved.

The problem is addressed of determining numerical approximations to the area under a curve specified by arbitrarily spaced data. A formulation of this problem is given in which the data are used to model the curve as a piecewise polynomial, each piece having the same degree. That piecewise function is integrated to provide an approximation to the area. A corresponding compound quadrature rule is derived. Different degrees of polynomial give rise to different orders of quadrature rule. The widely used trapezoidal rule is a special case, as is the Gill–Miller rule. The remainder of the paper is concerned with evaluating the measurement uncertainties associated with the approximations to the area obtained by the use of these rules in the case where the data ordinates correspond to measured values having stated associated uncertainties. The case in which there is correlation associated with the measured values, frequently arising when the measured values are obtained using the same measuring instrument, is also treated. A statistical test is used to select a suitable polynomial degree.

Two methods are presented by which a straight line is to be fitted to a cloud of points in Cartesian coordinates. It is assumed that data are available in the form of a series of measurements in each coordinate, together with an assessment of their covariance matrices. In the first (probabilistic) method, the joint probability density function (PDF) for the two parameters of the straight line is considered. An explicit expression for this PDF is derived; it allows one to compute numerically the expectations, the variances and the covariance between the two parameters of the straight line. The second method is that of least-squares; it renders a non-linear system of equations for the point estimates of the parameters, as well as an approximation to their covariance matrix. In contrast to least-squares, the probabilistic method allows for the exact calculation of the probability that the true values of the parameters lie within specified intervals.

The comparison of two methods of measurement or instruments is addressed from a statistical point of view. Several techniques for assessing the degree of conformity between two methods/instruments measuring the same quantity are discussed and compared. Their application in the framework of angle measurements is presented.

Taiwan has more than 300 Global Positioning System (GPS) tracking stations maintained by the Ministry of the Interior (MOI), Academia Sinica, the Central Weather Bureau and the Central Geological Survey. In the future, GPS tracking stations may replace the GPS control points after being given a legal status. Hence, the data quality of the tracking stations is an increasingly significant factor. This study considers the feasibility of establishing a system for monitoring GPS receivers. This investigation employs many data-quality indices and examines the relationship of these indices and the positioning precision. The frequency stability of the GPS receiver is the most important index; the cycle slip is the second index and the multipath is the third index. An auto-analytical system for analysing GPS data quality and monitoring the MOI's tracking stations can quickly find and resolve problems, or changes in station environment, to maintain high data quality for the tracking stations.

The atomic-scale unit, entity (ent), is defined as the number-specific amount of substance, n/N, the amount of substance of a single entity. This unit is an invariant physical quantity (the reciprocal of the Avogadro constant) that serves as the basis for redefining the SI base unit for amount of substance in a direct and easily understood manner. It is argued here that the kilomole should be the base unit in order to avoid factors of 10⁻³ or 10³ appearing in relationships involving both mass and amount of substance expressed in base units. Since, in a compatible formulation, the amount-specific number of entities, N/n (= N_A), is equal to M_u/Da, exactly, where M_u = kg kmol⁻¹ = g mol⁻¹ = Da ent⁻¹, exactly, then N_A = (kg/Da) kmol⁻¹ = (g/Da) mol⁻¹ = 1 ent⁻¹, exactly. The kilomole can thus be defined very simply as: , exactly, where , the exact kilomole-to-entity amount ratio, is identical to the kilogram-to-dalton mass ratio: . The Avogadro constant, , does not appear explicitly in the defining equation, its reciprocal having been replaced by one entity. Like the dalton, the entity would be categorized as a unit in use with SI.

An accurate determination of the dose produced by brachytherapy seeds emitting low-energy photons is an important component of the radiotherapeutic process. As yet, the output of these seeds has usually been specified in terms of the air kerma rate. The desired quantity in radiation therapy is, however, the absorbed dose to water inside a water phantom, for which primary standards are not available.

For this reason, developments are under way in the Physikalisch- Technische Bundesanstalt to establish a primary standard to determine the absorbed dose to water within a phantom. As a fundamental step towards this aim, a method will be introduced in this publication to determine the water kerma inside a graphite phantom housing an extrapolation chamber. Experimental results will be presented and compared with water kerma values obtained from air kerma measurements in free air and applying a conversion factor to water kerma for the conditions of the experiment. First estimates indicate that the relative uncertainty is of the order of 1% (k = 1).

The most widely used procedure for finding the value of a quantity from data obtained from interlaboratory comparisons involves calculating the inverse-variance weighted mean of the laboratories' estimates. This method produces adequate results if the data are consistent. However, sometimes a consistency test reveals the possible existence of outliers that nevertheless have to be included in the evaluation task. In this paper the Bayesian understanding of probability is used to derive three methods that may be applied in the case when the data appear to be inconsistent. The performances of these methods are compared through a simulated example.

The author is grateful to Dr Ignacio Lira of the Pontificia Universidad Católica de Chile for noticing the need for the following clarification.

In the absence of informative prior information about the laboratory biases, a restriction in the form is needed to obtain expression (3).

The publishers apologise for an incorrect editing change made to the original manuscript of this paper. The first sentence of section 1.1 should read:

''In 1946 Libby [12, 13] suggested that ¹⁴C should be present at equilibrium concentrations in living matter.''