Checking a Spring Scale With What Is at Hand: A Water-Litre Calibration Method and Its Certified Bound

A market vendor who owns no test weights still owns, in effect, a reference mass: a measured litre of water. This paper originates a complete checking procedure based on that reference, and, more importantly, computes an honest bound for what the procedure can certify. Water is not exactly 1,000 g per litre except near 4 °C; at 20 °C a litre has a mass of 998.2 g, at 25 °C 997.04 g, and at 30 °C 995.65 g, so treating a litre as exactly a kilogram introduces an error of 0.18% to 0.435% across that range. That error is small compared with the other errors of a cheap spring scale. Reading resolution contributes 2.5% at a 1 kg load on a typical 5 kg scale with 50 g graduations, tilting the scale or its load by 10 degrees makes it read 1.519% low, and a 20 K temperature shift changes the indication by 0.5%. Adding the controlled error components for the prescribed procedure gives a worst-case bound of 6.23% at a 1 kg load, and a root-sum-square figure of 3.39%. Checking at a 3 kg load, by filling the litre measure three times, tightens the worst-case bound to 3.9%. The water check therefore certifies a spring scale against gross error — the class of error that does the largest season damage — but it does not certify a scale to 1% or 2%. The paper states the procedure, the correction for water temperature, the controls for angle and temperature, and the exact form of words a vendor can honestly use about a scale that passes.