Troisième Supplément. Application Des Formules Géodésiques De Probabilité a La Méridienne De France

§1. The part of the meridian which extends from Perpignan to Formentera is sup[581] ported on a base measured near Perpignan. Its length is around 466 km, and its last extremity is joined to the base of Perpignan by a chain of twenty-six triangles. We are able to fear that so great a length, which has not been verified at all by the measure of a second base toward its other extremity, is susceptible to a sensible error arising from the errors of the twenty-six triangles employed to measure it. It is therefore interesting to determine the probability that this error not exceed 40m or 50m. Mr. Damoiseau, lieutenant-colonel of the Artillery, who has just gained the prize proposed by the Academy of Turin, on the return of the comet of 1759, has well wished, at my request, to apply to this part of the meridian my formulas of probability. Here the meridian does not cut all the triangles, as we have proposed for more simplicity; but it is easy to see that we are able to apply, to the angles formed by the prolongations of the sides of the triangles with the meridian, that which I have said respecting the angles that these sides would form if they were cut by the meridian. Mr. Damoiseau has found thus that departing from the latitude of the signal of Busgarach, a little more to the north than Perpignan, to Formentera, that which comprehends an arc of the meridian of about 466,006m, and by taking for unity the base of Perpignan, we have (second Supplement, §1) p − pq + q2+p 2 1 − pq + q 2 + · · ·