at points far away from the fixed points. For example, the expansion of mercury in a glass thermometer is slightly different from the change in resistance of a platinum resistance thermometer, so these two will disagree slightly at around 50 °C. There may be other causes due to imperfections in the instrument, e.g. in a liquid-in-glass thermometer if the capillary tube varies in diameter. For many purposes reproducibility is important. That is, does the same thermometer give the same reading for the same temperature (or do replacement or multiple thermometers give the same reading)? Reproducible temperature measurement means that comparisons are valid in scientific experiments and industrial processes are consistent. Thus if the same type of thermometer is calibrated in the same way its readings will be valid even if it is slightly inaccurate compared to the absolute scale. An example of a reference thermometer used to check others to industrial standards would be a platinum resistance thermometer with a digital display to 0.1 °C (its precision) which has been calibrated at 5 points against national standards (−18, 0, 40, 70, 100 °C) and which is certified to an accuracy of ±0.2 °C. According to British Standards, correctly calibrated, used and maintained liquid-in-glass thermometers can achieve a measurement uncertainty of ±0.01 °C in the range 0 to 100 °C, and a larger uncertainty outside this range: ±0.05 °C up to 200 or down to −40 °C, ±0.2 °C up to 450 or down to −80 °C. Indirect methods of temperature measurement Thermal expansion Utilizing the property of thermal expansion of various phases of matter. Pairs of solid metals with different expansion coefficients can be used for bi-metal mechanical thermometers. Another design using this principle is Breguet's thermometer. Some liquids possess relatively high expansion coefficients over a useful temperature ranges thus forming the basis for an alcohol or mercury thermometer. Alternative designs using this principle are the reversing thermometer and Beckmann differential thermometer. As with liquids, gases can also be used to form a gas thermometer. Pressure Vapour pressure thermometer Density Galileo thermometer Thermochromism Some compounds exhibit thermochromism at distinct temperature changes. Thus by tuning the phase transition temperatures for a series of substances the temperature can be quantified in discrete increments, a form of digitization. This is the basis for a liquid crystal thermometer. Band edge thermometry (BET) Band edge thermometry (BET) takes advantage of the temperature-dependence of the band