After his studies at the Collège de Navarre, Camus continued to work on advanced topics in mathematics aided by Varignon. He :-
... also undertook work in civil and military architecture, mechanics, and astronomy.He first made his name in mathematics when he entered for the Grand Prix of the Académie des Sciences in 1727. The topic for the prize that year was the masts of ships. Both Camus and Bouguer entered memoirs for the competition which were deemed worth of winning the prize and both the prize money and the award was split between the two.
Camus not only won a share of the prize, but he also became known to the Académie as a talented mathematician. On 13 August 1727 he was elected as an assistant in the mechanics division of the Académie on the strength of his memoir. It was the beginning of a long association of Camus with the Académie des Sciences for he served the academy as an administrator for forty years and also took an active scientific role in many of the academy's projects. On the administrative side he was the director of the Académie in 1750 and again in 1761.
Camus went with Maupertuis, Clairaut and Lemonnier to Lapland in 1736 on an expedition to determine the shape of the Earth. Jean Picard had measured the length of the arc of the meridian, the measurements appear in Mesure de la Terre (1671). Camus, Maupertuis, Clairaut and Lemonnier, after their joint work on the Lapland expedition, also worked on measuring the length of the arc of the meridian and examining Jean Picard's work. With Bouguer, Pingré and Cassini de Thury, Camus was involved in another Académie des Sciences project relating to further work on the measurement of the earth.
Camus was involved with cartography helping to produce, again with Bouguer, Pingré and Cassini de Thury, the Carte de la France which the Académie des Sciences published between 1744 and 1787.
Many of Camus's publications appeared in the Mémoires de l'Académie royale des Sciences and they are both on mathematics and mechanics. Discussing some of this work in , Iltis writes:-
Charles-Étienne Camus related the force of rising and falling bodies to Bernoulli's Leibnizian analysis of expanding springs.His other mechanics work includes :-
... treatment of toothed wheels and their use in clocks, studies of the raising of water from wells by buckets and pumps, an evaluation of an alleged solution to the problem of perpetual motion, and works on devices and standards of measurement.The Académie des Sciences was not the only academy which Camus was elected to, and which he served in an administrative capacity. In 1730 he was elected to the Academy of Architecture and served as its secretary. He was then named as Professor of Geometry to the Academy of Architecture and in this capacity he lectured to students of architecture. Camus wrote a Cours de mathématiques for his teaching of the trainee architects. This work was to be in four parts, arithmetic, geometry, mechanics, and hydraulics. Between 1749 and 1751 Camus published the first three parts of his Cours, but despite the fact that he lived for a further seventeen years after this, the fourth part was never published. After Camus's death a work on hydraulics was found among his papers and it is believed that this was intended to be the final part of the Cours.
Perhaps the reason that Camus never published the final part of his Cours was his appointment in 1755 as examiner for artillery schools. As examiner, Camus was able to base his examinations on the three parts of his Cours which were in print and this had, as one might expect, the result that his books sold widely and in great numbers. However, Chapin points out in  that this was:-
... due more to Camus's monopoly on examinations than to its intrinsic merit. In point of fact, the "Cours" came under increasing attack in the 1760s as inappropriate for artillery students and too elementary for those at Mézières.In fairness to Camus, he had never written the Cours for artillery students so one should not hold this against him scientifically but, of course, one can criticise him for using his position as examiner to force his own inappropriate Cours on artillery students.
Article by: J J O'Connor and E F Robertson