After a visit to the State Library of South Australia, a talk with a very helpful librarian, and an afternoon reading Baudin’s diary (in English translation by Christine Cornell in 1974), I know a bit more.
First, there is a link to Baudin’s chart of this coast here.
I had some difficulty matching it up with a modern map. Of the entire stretch from Cape Jaffa to Encounter Bay (including the Coorong and the mouth of the Murray River), Baudin says only
The entire stretch of coast we have examined since yesterday consists solely of sand-hills and inspires nothing but gloom and disappointment. Quite apart from the unpleasant view that it offers, the sea breaks with extraordinary force all along the shore.
The two capes he named Monge and Fermat seem to be completely imaginary.
Also, as far as I can judge, Cap Bernoulli (actually spelt “Bernoouilli” on the chart) seems to be the modern Cape Jaffa, separating Baie de Guichen from Baie Lacepède. Baudin does have “C. de Jaffa” on his map, but this appears to be the modern site of Beachport, at the northern end of Rivoli Bay (which is “Baie de Rivoli” on Baudin’s chart). I may have been mistaken about Cap Descartes; Baudin’s chart gives “Baie Descartes” further south.
His journal gives very few accounts of his naming things, and none at all of why he chose the names he did.
However, I learnt from the preface to the edition of his diary, written by Jean-Paul Faivre, that he did have a connection with Monge.
It seems that he was a commoner, and his advancement in the French navy was blocked by the nobility, so by various routes he found himself working for the Emperor of Austria. In 1792 he discovered that Austria was at war with France, when an undefended French ship surrendered to him. He immediately tried to rejoin the French navy, but this was impossible. However,
The great mathematician Gaspard Monge, Minister of Marine, could do nothing but grant him the right to continue his voyage without fear of French corsairs, following the custom established by Louis XVI and the American Congress in the case of Captain Cook. “Les savants n’ont aucun ennemi chez un peuple libre.”
Baudin later found favour with scientists in the Muséum National, at the Jardin des Plantes, especially Antoine-Louis de Jussieu, and managed to talk them into sending him on an expedition to explore New Holland. Despite this, according to the preface to his diary, he didn’t have a very high regard for scientists, which makes his choice of names even more puzzling.
For example, when trapped by wintry squalls in the Gulf of St Vincent, he wrote,
The stay of our fore-topmast staysail and its halyard went twice during the night, but the sail was only slightly damaged. The rain-bearing squalls were very cold and sometimes the water was like half-melted snow. We concluded from this that the winter cannot be very agreeable in this climate.
The scientists, however, are of a contrary opinion, because they saw parakeets in D’Entrecasteaux Channel.