Among the instruments with which Borda’s name remains closely associated is the reflection circle, developed from a device devised by the German astronomer Tobias Mayer and perfected by Borda in the 1770s. Intended primarily for observations at sea, it enabled angular distances to be measured with great precision, particularly the altitude of a celestial body above the horizon or the angular distance between the Moon and another celestial body. Its limb was graduated from 0 to 720°. One of its principal advantages lay in the possibility of repeating the same measurement several times before taking a reading, thereby reducing the effect of certain instrumental and observational errors.
The repeating circle, also associated with Borda’s name, was a distinct instrument, intended chiefly for astronomical observations and terrestrial geodetic operations. It too relied on the principle of repetition: the same angle could be measured successively without resetting the instrument to zero, after which the accumulated value was divided by the number of repetitions. Instruments constructed by Étienne Lenoir were notably used by Jean-Baptiste Delambre and Pierre Méchain during the measurement of the meridian arc between Dunkirk and Barcelona, an undertaking fundamental to the determination of the metre.
These two instruments illustrate the central place occupied by precision measurement in Borda’s work. The reflection circle played an important role in late eighteenth-century navigation, particularly in astronomical observations used to determine latitude and, through the lunar-distance method, longitude. Borda also took an interest in marine timekeepers and in the growing importance of chronometric methods for determining longitude.
His work formed part of the broader transformation of the sciences of measurement in the late eighteenth century. Borda participated in the commissions responsible for defining the new units of the metric system and advocated their decimal division. The instruments and methods he helped to develop were closely connected with the geodetic operations of Delambre and Méchain, who were charged with measuring the meridian arc used to determine the length of the metre. Borda was also among the first members of the Bureau des longitudes, established in 1795 and entrusted, among other responsibilities, with improving navigational methods, astronomical tables and the determination of longitude.
The instruments designed or perfected under his influence remained fully relevant at the time of the Baudin expedition. An episode recorded by Louis de Freycinet at Port Jackson in November 1802 provides a particularly concrete illustration. It shows both the importance attached to the reflection circle in hydrographic work and the difficulties involved in distributing a limited supply of scientific instruments among the expedition’s different vessels.
As he prepared the Casuarina for departure, having recently received command of the schooner, Freycinet sent Baudin a further request for equipment on 22 Brumaire Year XI (13 November 1802). In addition to cordage, tools, a larger steering compass and paper for drawing charts, he requested two instruments he considered indispensable to his work:
“the reflection circle and the marine timekeeper which you have assigned to the Casuarina”.
Their appearance together in the same request is revealing of contemporary hydrographic practice: the circle provided the angular measurements required for astronomical observations and coastal survey work, while the marine timekeeper supplied the time reference essential for determining longitude.
The following day, the discussion with Baudin became particularly tense. According to Freycinet’s account, the commander informed him that he would receive only one of the requested items. Freycinet pressed his case:
“Would you have the kindness [...] to give me the marine timekeeper and the circle which I need.”
Baudin nevertheless refused to part with either of the two timekeepers that remained to him. He argued that Freycinet would not have to work in isolation, since the geographer Charles-Pierre Boullanger was to take part in the hydrographic operations of the Casuarina: “by not separating yourself from the geographer, you will make use of our observations.”
This remark is best understood in the context of the scientific organisation being put in place at Port Jackson. Boullanger, who had until then served aboard the Géographe, was assigned to work with Freycinet during several of the surveys carried out from the Casuarina. Baudin therefore considered that the observations made by the geographer and, more generally, the data collected by the different components of the expedition could be shared. Freycinet, by contrast, believed that he needed direct access to the instruments required to carry out accurately the surveys entrusted to him.
Unable to obtain the marine timekeeper, Freycinet asked at least for one of the “two reflection circles which were aboard the Naturaliste”, noting that the other was out of service. He justified his request by the demands of his mission itself: whenever he was instructed to survey a section of coast, he explained to Baudin, he would be unable to “carry out this work with accuracy without the instruments” he was requesting.
The continuation of his journal shows that the disagreement had by then extended beyond the reflection circle alone. Freycinet recorded that several of his other requests were also refused, including those for a larger steering compass, cordage and paper. He even gave up asking for the Connaissance des temps, an essential work for astronomical calculations, since he considered it useless without the instruments required for observation: “this book was becoming useless to me since I could not obtain an instrument with which to observe.”
Freycinet clearly interpreted the situation as inconsistent with the hydrographic mission entrusted to him. Reflecting on his “last conference” with Baudin, he asked in his journal:
“Why did Mr Baudin not tell me, in the letter setting out the conditions which he wrote to me, that he would not give me the instruments most indispensable to the kind of navigation we were about to undertake?”
He then went to Jacques-Félix-Emmanuel Hamelin, commander of the Naturaliste, told him of the conversation and asked him to intervene with Baudin on his behalf.
The episode thus provides particularly concrete evidence of the material conditions of hydrographic work during the voyage. Astronomical observations could not be separated from the instruments used to make them, the tables required for their calculation, and the marine timekeepers that supplied a time reference. Reflection circles, chronometers, compasses and astronomical publications formed a technical system whose individual components were complementary.
The passage also bears witness to the highly strained relations then existing between Freycinet and Baudin. In Freycinet’s journal, the conflict over the instruments reveals a broader disagreement concerning the organisation of hydrographic work, the resources to be placed at the disposal of the Casuarina, and the degree of autonomy its commander should enjoy. Baudin appears to have favoured the sharing of observations and resources across the expedition, whereas Freycinet believed that he needed direct access to the instruments required to carry out accurately the surveys entrusted to him.
The reflection circle therefore appears here not merely as one item of scientific equipment, but as one of the fundamental tools of practical hydrography. The exchange gives a concrete sense of the value attached, at the beginning of the nineteenth century, to the precision instruments associated with Borda’s work: access to them directly conditioned the ability to observe, calculate positions, survey coastlines and produce charts.