Calibration and instrumental errors in early measurements of air temperature

Calibration and instrumental errors of early thermometers are analysed. The first concepts, the development of scientific ideas, the main problems linked to the construction of early thermometers and the calibration are considered in order to evaluate errors. The operating principle of the `constant-volume' air thermometer is presented and its limits are discussed. The theory shows that for an ideal Amontons' thermometer, only one calibration point is sufficient from which the other can be calculated; it is therefore possible to determine the difference from an ideal instrument. A comparison is made between calibrations and instruments made by G. Amontons (1699), G. Poleni (Venice, 1709; Padova 1725), and J.H. Lambert (1779). Amontons' thermometer needs to be integrated with a barometric reading; an important error arises from the different density of mercury during calibration and usage. The calibration was made in winter and at the upper point the thermometer was at 100 degrees C, while the barometer remained near 0 degrees C. However, field observations were made with both instruments at the same temperature and this caused an error that in the cold season is negligible, but in the hot season reaches 1 degrees C. Problems connected with the calibration and scale linearity are discussed in view of the beliefs of the time and the operative methodologies used in early meteorology. Emphasis is given to comparability of different instruments, thermometric scales and calibration methodologies used in Padova in the 18th century for Amontons', Poleni's, Fahrenheit's, Reaumur's and Delisle's thermometers. The instrument supports and the incision of the scale were subject to expand or contract depending on temperature or humidity changes, and this was a source of error that can be corrected with the help of observed or estimated data. Problems linked to the construction of thermometers have been evaluated, as well as the linearity of displacements of the thermometric liquid, or the drift due to ageing and transformation of the thermometric liquid, the glass or the support. All these errors have been evaluated and some of them have been found negligible, but some are of the order of 0.5 degrees C. The quantitative results obtained here can also be usefully applied to correct and validate other long series.