By 1789 the French had made three measurements of arcs along the meridian passing through Paris. The earliest, made by Jean Picard between 1668 and 1670, on an arc of about 1°20', gave a value for the length of a degree of latitude near Paris that differed by less than three parts in ten thousand from what the metric measurers later obtained with much greater labor and much better instruments. The second arc, extending over 8°30' from Dunkirk to Perpignan and completed under Jacques Cassini in 1718, authorized a new Atlantic coastline that brought some French towns a hundred or more kilometers East of their previous positions. Louis XV lost more land to his cartographers than his successors have to the Germans. The measurements were not accurate enough, however, to settle the much agitated question of the shape of the earth. In the 1730s, the Paris Academy sent out its expeditions to Peru and to Lapland to measure arcs far enough apart to reveal the departure of the earth's profile from perfect sphericity. Their results, which confirmed Newton's conclusion that mechanics required the equatorial axis to exceed the polar, agreed with the third measurement along the Paris meridian, made during 1739 and 1740 by the Abbé Nicolas-Louis de Lacaille.
As the general shape of the earth came into view, its finer features loomed ever larger in academic minds. Lacaille contributed another data point by measuring an arc at the Cape of Good Hope. The Pope, the Austrian-Hungarian Empress, and the King of Sardinia commissioned surveys of meridians traversing their domains, with the consequence, as one of the surveyors put it, that the more the earth
was measured, the more uncertain its shape became. The British then ran an arc through Greenwich, to serve as the backbone for a military map of Scotland. The Paris academicians looked upon it rather as an opportunity to improve geodesy, and in 1783 they proposed a linking of the Paris and Greenwich observatories by triangles based on the meridians already determined. The proposal had a sporting side. The linking would pit the small repeating circle then recently invented by Charles Borda, a prominent academician and a former naval officer, against the large theodolite built by the world's leading instrument-maker, Jesse Ramsden, for the triangulations in England.
Jean Dominique Cassini (Cassini IV), who took nominal charge of the French party, retrospectively threw down the challenge: "we dared to flatter ourselves that we had on our side an instrument that yielded nothing to the English in point of precision." The showdown took place in the late summer of 1787. The British turned their great theodolite toward Calais; the French aimed their delicate circle at Dover. The British took their single observations quickly; the French multiplied their repetitions slowly. The season grew late. Fog descended. The weather did not remit long enough to permit the full circle of French measurements, and the contest between the repeater and the theodolite ended indecisively. As Delambre wrote much later, however, "a more important occasion soon presented itself to demonstrate the advantages of the new instrument."