By K. Walters
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12. The thermometer on the left of Fig. 33 cm/◦ C. 3 Static Characteristics of Instruments °C °C 40 200 30 150 20 100 10 50 0 0 B A 33 Fig. 6. Two mercury-in-glass thermometers with different sensitivities. In nonlinear instruments, the sensitivity varies within the measurement range, such as the slope of the curve Z(X). The sensitivity is thus defined as the first derivative dZ/dX. 13. In the semiconductor thermometer of Fig. 18 kΩ/◦ C at 100◦ C. In analog instruments, the display generally consists of a graduated scale.
The different factors that can influence a measure can be classified within three main categories: – – – measurement resolution random fluctuations (or “random errors”) systematic errors These three causes of uncertainty are analyzed separately in the following three sections. A unified procedure for comparing and combining the uncertainties due to different factors is introduced in Sect. 5. It is worth noting that the terms random error and systematic error have here a particular meaning, and should not be confused with trivial mistakes (parasitic errors) that are due to carelessness or inexperience, such as exchanging a mass of 50 g for a mass of 100 g on a two-pan balance, the wrong reading of a display, or a calculus error in an indirect measurement.
Top: two possible inputs. Bottom: the corresponding outputs (continuous lines). 42 3 Measuring Instruments Response to a Step Input Let us consider the simple case of a step input (Fig. 18) and suppose that, for t < 0, the instrument is stabilized at the stationary response Z = (b0 /a0 ) X0 . 28. A mercury thermometer is initially (for t < 0) in equilibrium with the environment at temperature T0 ; at the time t = 0, it is immersed in a fluid at temperature T1 . 29. A spring dynamometer is initially unloaded.
