In January 1875 Cruls was forced to return to Belgium for family reasons. The Commission took Cruls' unexpected return as an opportunity, and assigned him the duty of assisting the Brazilian ambassador in coordinating the receipt and transportation of geodesic instruments that the Commission had previously purchased. While in Europe, published his first major paper, "Discussion of the Methods of Repetition and Reiteration Employed in Geodesy for the Angles". Crul's monograph analyzed the various methods then used to fix geographic points via triangulation. This work won Cruls the respect of Emmanuel Liais, director of the Imperial Observatory in Rio de Janeiro, who would later hire him in 1877. Cruls returned to Brazil in June 1875 and continued his work with the Commission until its dissolution.