Thermometers and temperature scales reached a certain degree of standardisation only in the late 18th century, more than a century after the invention of the liquid-in-glass thermometer. Until at least the 1770s many thermometers used for meteorological observations had unique characteristics, and even instruments graduated with the same nominal scale could read very different temperatures in the same conditions . Therefore, converting the earliest temperature observations into modern units requires detailed information on the thermometer construction and calibration.

Figure  gives an overview of the scales used in our dataset and the periods in which they were employed. The Réaumur scale, originally defined by René-Antoine Ferchault de Réaumur in 1730, was clearly the dominant scale in Switzerland until the mid-19th century. Today's Celsius scale came into use only in the 1830s and became the prevalent scale by the 1850s.

The history of the Réaumur scale is rather complex as the principles given by Réaumur were very difficult to apply in practice; as a consequence, early Réaumur thermometers were not consistent with each other, and the construction methods changed radically over time . Aside from Réaumur, early instrumental temperature measurements in Switzerland were greatly influenced by two Genevan scientists, Jacques-Barthélemy Micheli du Crest (1690–1766) and Jean-André Deluc (1727–1817). The former proposed in 1741 a “universal” thermometer filled with spirit of wine and graduated according to two fixed points: the temperature of the cellar of the Paris observatory (which Micheli du Crest believed to be more constant than the melting point of ice) and the boiling point of water at an atmospheric pressure of 27.75 Paris inches, corresponding to 0 and 100∘, respectively . The lower fixed point was changed to the melting point of ice in as early as 1742 , but the zero remained at the “temperate” level of the observatory's cellar so that the melting point of ice was defined as -10.4∘. During the following decades, Micheli du Crest's thermometer proved to be very successful, particularly in the German-speaking Swiss cantons (central and eastern Switzerland) and in Bavaria, whereas most French scholars were uncomfortable with Micheli du Crest's disrespect of Réaumur's principles . Seven of the temperature records in our dataset (four in the canton of Zurich and three in the canton of Bern) were originally in Micheli du Crest units (Fig. ). In Schaffhausen, the physician Johann Christoph Schalch read a similar thermometer for over 50 years, between 1794 and 1845.

In 1772, Deluc published a very influential work on meteorological instruments in which he advocated the superiority of mercury as a thermometric liquid and applied Micheli du Crest's ideas to a mercury thermometer. His fixed points were the melting point of ice (0∘) and the boiling point of water at a constant pressure (80∘). Deluc's publication gave a fundamental push to the reformation of the Réaumur thermometer – which used spirit of wine and whose scale was based on one fixed point – into the much better standardised mercury thermometers employed in most of Europe between the late 18th century and the mid-19th century (improperly called “Réaumur thermometers” by contemporaries). We assumed that all records in Réaumur units in our dataset from 1778 onwards were measured with the reformed thermometer.

An additional important source of uncertainty for temperature observations is the exposure of the thermometer. In the 18th century observers were aware that the thermometer should not be exposed to direct or scattered solar radiation or to precipitation, but proper radiation screens came into use only in the second half of the 19th century e.g.. In the first half of the 18th century, the common practice was to measure indoors next to an open window in an unheated room e.g. until comparisons with outdoor thermometers demonstrated the inadequacy of this set-up e.g.. In later years, the most popular solution was to hang the thermometer outside a north-facing window or on a north-facing wall e.g.. Positioning-related biases can reach several degrees Celsius and are usually corrected using a statistical approach e.g.; we plan to address this issue for some of the records in a separate paper.

Air pressure observations involve, to some extent, smaller difficulties than temperature: the liquid used was mercury with very few exceptions, and the problem of the scale definition is much less relevant since pressure is linearly proportional to the height of the mercury column. Moreover, barometers could be kept indoors and were not exposed to solar radiation or precipitation. There are still numerous sources of uncertainty, many depending on the construction of the barometer e.g.. The easiest to address is the expansion of mercury with temperature, which follows a linear equation . Unfortunately, even though Micheli du Crest himself had written about the importance of measuring the temperature of the barometer , it is rare to find an 18th century record with this information. The first Swiss stations to provide an attached temperature were those taking part in the Palatine Meteorological Society's network , namely Gotthard Pass from 1781 and Geneva from 1783. In the 19th century, barometers often came with correction tables, and some observers annotated only the corrected values, while others also reported the raw readings and the attached temperature.

The oldest temperature observations that we digitised are those of Johann Jakob Scheuchzer in Zurich, starting in 1718. However, available information on his thermometer was insufficient to attempt a conversion to modern units (he most likely employed an air thermometer; see ).

The next temperature record in chronological order is that of Neuchâtel, started in 1753 by Frédéric Moula, a mathematician who studied under Jean Bernoulli in Basel. He employed a Fahrenheit thermometer, the only one with this scale in our dataset. Moula was a mathematics professor in Berlin and Saint Petersburg before returning to Switzerland in 1752. He probably became familiar with Fahrenheit thermometers while abroad (Fahrenheit thermometers were particularly popular among German scientists in the first half of the 18th century; ). On the first page of the first book of observations (Fig. ), Moula writes, “The thermometer used for the following observations is constructed using the Fahrenheit method. It is with mercury. The point of freezing, or of melting snow, is marked at 32 degrees. That of boiling water at 212” (translated from French by the authors). This description does not correspond to the original method proposed by Fahrenheit, which used the body temperature of a healthy man for the highest fixed point . Clearly, the Fahrenheit scale used by Moula is the reformed one still in use today; hence no special correction was necessary other than the standard conversion to degrees Celsius.

The first record measured on the Réaumur scale is the work of famous polymath Johann Heinrich Lambert. He made regular meteorological observations in Chur (south-eastern Switzerland) between 1750 and 1756, although we could only digitise the observations that he published for 1 year (August 1755 to July 1756; for the previous years Lambert published only monthly extremes). Unfortunately, he did not provide details on the thermometer in that publication. The raw observations for the previous years have been located but have yet to be imaged.

A few years later, in 1760, the Economic Society (Ökonomische Gesellschaft) of Bern started a network of eight meteorological stations, all provided with identical thermometers with the Réaumur scale. According to , these thermometers were made by the French abbé Jean Antoine Nollet, an assistant of Réaumur and his main instrument-maker. However, this information alone is not sufficient to attempt a conversion into modern units, as Nollet himself did not strictly follow Réaumur's principles . In fact, given the general lack of detailed information on how Réaumur thermometers were calibrated, we did not convert temperatures measured in Réaumur degrees before 1778. Luckily, the station of Bern – the only one of the Economic Society's network for which we digitised the data – switched to a Micheli du Crest thermometer in March 1762. The network did not have a long life as observations stopped in 1770.

To convert the Micheli du Crest scale we used the tables published by on the thermal expansion of mercury and the most refined spirit available at the time, which translates into the following equation for values above the freezing point (corresponding to -10.4∘): 1Rd=80110.41.276(DC+10.4)-0.0025(DC+10.4)2, where Rd is the reformed Réaumur scale according to Deluc, and DC is the Micheli du Crest scale. The quadratic term accounts for the deviation from linearity of the thermal expansion of the spirit see also.

For values below the freezing point, the best fit of Deluc's results gives the following equation: 2Rd=80110.41.317(DC+10.4)-0.0018(DC+10.4)2.

We assume that all thermometers with the Micheli du Crest scale underwent the same construction and calibration procedure with one exception: the previously mentioned record of Schaffhausen by Johann Christoph Schalch. Here a thermometer made by the famous Bavarian instrument-maker Georg Friedrich Brander was used. Designated as the “Brander thermometer” by Schalch, this instrument resembled a Micheli du Crest thermometer but was probably filled with mercury instead of spirit.

Schalch's record was analysed before by , who concluded that Schalch's thermometer was a standard Micheli du Crest spirit thermometer. Schalch carried out parallel observations between the Brander thermometer and a thermometer with the Réaumur scale from 1828 to 1842; a scatter plot of these observations is given in Fig. a. According to , “The evaluation of the difference between simultaneous readings of Réaumur and Micheli du Crest thermometers showed clearly that the two thermometers could only be a spirit thermometer, described as a Brander, and a mercury thermometer according to Réaumur” (pp. 36–37, translated from German by the authors). This statement is not supported by any figure or table. By analysing Schalch's parallel observations, we found that the relationship between the two scales is best represented by a linear function: 3Rd=11.00+0.91B, where B is the scale of the Brander thermometer. A nearly identical conversion equation can be found on a loose sheet included in the Schalch papers stored at the Swiss Federal Archives (ref. code E3180-01#2005/90#217*), probably written when the observations were sent to the newly founded NWS in 1864.

A linear relationship suggests that both thermometers were filled with the same liquid – most likely mercury. However, as the Brander thermometer was likely calibrated against an original Micheli du Crest thermometer, Eq. () gives very similar results to Eq. (), aside from a constant shift (Fig. ). In fact, Eq. () also implies that the zero of the Brander scale is at 11∘ Réaumur, 1.4∘ higher than defined in the Micheli du Crest scale. A possible explanation for this shift is that the zero of the Brander thermometer had risen over time because of the gradual contraction of the glass, a well-known source of systematic error particularly in mercury thermometers .

Brander was a correspondent of Micheli du Crest and had started to make thermometers with the Micheli du Crest scale in as early as 1757 ; it is possible that he decided at some later point to use mercury instead of spirit, especially after Deluc's publication and Micheli du Crest's death. It is also likely that the thermometer was already rather old when Schalch started to make regular observations in 1794 given that Brander died in 1783. In fact, in 1782 a newspaper based in Augsburg (Augsburgische Ordinari Postzeitung n. 178, 26 July 1782) published a short piece about an earthquake in Schaffhausen, reporting a temperature measured in that city with a “Brander thermometer”, perhaps the same thermometer used by Schalch 12 years later. If so, most of the rise of the zero had probably already occurred when Schalch started his observations, meaning that Eq. () can be used for the entire record.

If, on the other hand, we use Eqs. () and () and correct for the shifted zero, we obtain an average underestimation of about 1 ∘C at low and high temperatures when comparing to the parallel observations in Réaumur (Fig. c). Equation () also produces a slightly lower root mean square error for the whole temperature range. Given these considerations, we adopted Eq. () for the conversion of the Brander scale.

Schalch's parallel record actually continues until 1845 but shows a large inhomogeneity in 1842 (Fig. c): in that year, between August and September, Schalch observed only one thermometer at a time, probably because he moved them apart. He usually read the Brander thermometer at noon and the other thermometer in the morning and in the evening. In October he resumed the parallel observations, but from that moment a seasonal cycle with an amplitude of about 2 ∘C appears in the bias, confirming that the two thermometers were no longer next to each other.

Conversion from Deluc's (or reformed) Réaumur scale is made by multiplying by a factor of 1.25. However, one must always keep in mind that the accuracy of the calibration and its stability over time probably varied among different instrument-makers. In particular, we did not apply any correction for the contraction of the glass as we rarely know the age of the instrument and its origin.

Table  gives an overview of the conversions applied to the different instruments mentioned in this section.

Our strategy for the temperature correction of barometer readings was to prefer a modern correction over the corrected values provided by the observers. The latter was used only if the attached temperature was not provided. The converted data are accompanied by metadata that indicate for each observation whether the pressure was reduced to 0 ∘C, the original pressure reading, and the attached temperature in the original units. In addition, we applied a gravity correction to all pressure observations .

Before the introduction of the metric system, the standard unit for barometers in Switzerland was the Paris inch (pouce), corresponding to 27.07 mmHg, and the Paris line (ligne), corresponding to 1/12 of a Paris inch. The oldest record of Scheuchzer was reported in British imperial inches (Fig. ), corresponding to 25.4 mmHg, because it had been converted for publication in a British journal . Furthermore, a few years (1839–1843) of the record of Marschlins are compatible with a scale in British inches, although we did not find any metadata about the barometer. A few more records in the 1830s and 1840s (Einsiedeln, Gottstatt, and Utzenstorf; the latter two by the same observer) have unrealistically high pressure values, possibly because an unknown length unit different from the Paris inch was used.

The conversion from millimetres to hectopascals follows from the hydrostatic equation .

Precipitation was measured by only a small fraction of observers in the early instrumental era. Even though the oldest record of Scheuchzer dates back to 1708, there are never more than two stations measuring precipitation at the same time before the 1860s (Fig. ). The units adopted were Paris lines and, more recently, millimetres (Scheuchzer's earliest record was published in British inches).

The time of observation usually refers to local solar time. In the common data format all times are converted to Greenwich mean time (GMT). Some observers, particularly in remote locations, continued to use sundials after a standard time (Bern time, GMT+00:30) was introduced in Switzerland in 1848 . Given that the difference between mean local solar time and Bern time is less than 12 min anywhere in Switzerland, we assumed mean local solar time for every record.

Qualitative time entries such as “afternoon” were not converted. In this case, the time is missing in the data files and the original time entry is provided in a designated column. Times given as “sunrise” or “sunset” were converted using the R package suncalc version 0.5.0 .