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Linearity, Maximum and Minimum Accurate Weighing

An artilce on accuracy and linearity and how to achieve the best results from balances/scales.

The long obsolete beam/apothecary's balance was sensitive and accurate, but painfully slow and complicated to operate; digital balances are near magical, but they have a few peculiarities, and these should be understood by users requiring best accuracy.

Digital scales need to be calibrated to allow for the earth's magnetic field and, when moved, for minor changes in level. Like other analytical instruments they are calibrated, and the recommended accurate standard weight is used to electronically draw a line from zero through the recommended weight to the scale's maximum. From this it is obvious that the longer the range of the scales the less accurate the scales will be furthest from the calibration weight; this is only a minor effect and it only affects critical, very low mass determinations when performed near zero. It should also be obvious that like any other analytical instrument, greatest accuracy is near the calibration standard used.

Linearity is the deviation from a straight line, and that deviation is likely largest near zero and the maximum range of the scales. The implication is that scales with a high maximum range, however desirable that feature is, are a little compromised when minimum weight accuracy is needed. As an example, scales with a maximum range to 3000g and a readability of 0.01g, may only become accurate at around 0.2g; whereas scales with a range to only 600g may become similarly accurate at about 0.10g. When weighing very small quantities it makes more sense to have a 1g weight (or greater) on the weighing pan. Note also that using an arbitrary weight on the pan, and taring this, does not change the basic problem with linearity near zero.

In summary, minimum weight is a somewhat arbitrary figure, because the calibration may have been with a 200g weight, then scales have plotted an electric current sloping down to zero and up to the scales' maximum weight. Further away from the calibration weight the linearity will not be as good, and it is poorest near zero and near the scales' maximum. Some scales give a minimum weight recommendation, but this is arbitrary as is a percentage reliability factor.

The practical solution for weighing very small mass (10 to 20x the minimum reading possible - as a guide) is not to start at zero, but weigh either with the standard calibration weight or with a 1 or 10g weight on the pan, then subtract that to obtain the sample's mass. If small calibration weights are available it would be useful to establish a reliable minimum weight for particular scales.

See also Calibration Weights Classification for Balances.

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