 Helmholtz, who had formulated a conservation law ten years previously in “On the Conservation of Force,” entered the field at this point. Helmholtz’s own work had concentrated on applying the notion of a potential to fluid movement. But viscous forces do not have potentials. Helmholtz decided to disregard the viscous forces themselves, but also to redefine the problem without appealing to potentials. He defined the “vorticity” of a fluid in a small region as its average rotation or circulation in that region: the rotation at each point on the boundary of the region divided by the area of the region, which is described mathematically as the curl of the velocity of the fluid. (In technical terms, Helmholtz evaluated this as the curl of Euler’s equation.) The vorticity of a fluid at a single point is a vector quantity. Helmholtz introduced two further idealizations. A “vortex line” is the tangent to the vorticity vector of a point in the fluid. If you draw vortex lines on the boundary of a region of the fluid, and then make the region around each line indefinitely small, the lines will converge to “vortex filaments,” now also called “vortices.” 