His earliest mathematical work was the *Exercitationes* (*Mathematical Exercises*), published in 1724 with the help of Goldbach. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. His chief work is *Hydrodynamica*, published in 1738; it resembles Joseph Louis Lagrange's *Mécanique Analytique* in being arranged so that all the results are consequences of a single principle, namely, conservation of Energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's *Philosophiae Naturalis Principia Mathematica* and the investigations of Pierre-Simon Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by Jean le Rond d'Alembert.