Invention of the concept of vector field

Question

I'm very interested to know how the concept of vector field was created. What problems or phenomena led mathematicians to introduce the concept of vector field?

Answer 1

I would point to Euler's Principes généraux du mouvement des fluides, Mém. Acad. Sci. Berlin 11 (1755) (1757) 274-315 for a pretty clear notion of a fluid's velocity field (whose integral curves are the lines of flow, and satisfying what we now call Euler's equations and the continuity equation).

O. Darrigol in Worlds of flow: A history of hydrodynamics from the Bernoullis to Prandtl has some of this anticipated in earlier memoirs of Euler and D'Alembert, but I find the modern concept quite a bit harder to identify there.