One of the many examinations for which Grassmann sat required that he submit an essay on the theory of the tides. In 1840, he did so, taking the basic theory from Laplace's "Mécanique céleste" and from Lagrange's "Mécanique analytique", but expositing this theory making use of the vector methods he had been mulling over since 1832. This essay, first published in the "Collected Works" of 1894–1911, contains the first known appearance of what is now called linear algebra and the notion of a vector space. He went on to develop those methods in his A1 and A2 (see bibliography).