Pierre Bouguer (1698-1758) royal professor of hydrography at Le Croisic was 23 years old when he was asked to carry out tests on the tonnage of ships following a new method set forth by Pierre Varignon and Jean-Jacques Dortous de Mairan of the Royal Academy of sciences of Paris at the request of the council of the navy. The outcome was in favor of Mairan’s method. The latter then drew up instructions that were to be henceforth applied. The text was read to the Academy on August 30, 1724, before being sent to the naval ports in 1726. Bouguer’s contribution was duly acknowledged. Alongside the procedure of geometric division of the volume sought after into small prismatic elements, he used a new method of calculation, as yet not widespread, namely that of infinitely small quantities in order to compare the two methods. The aim of this study is to examine the role of expertise carried out by the Academy of sciences for the State under the Regency and the beginning of Louis XV’s reign, a mission that it delegated under its supervision to those competent among the King’s men. Furthermore, I show that the Treatise on ships(1746), Bouguer’s major work, was already in preparation during the 1720s.