By the above assumptions the flowfield is Conservative vector field, which means that there 
exists a perturbation velocity potential  such that the total velocity vector  is given by
and that  satisfies Laplace's equation.
Laplace's equation is a second order linear equation, and being so it is subject 
to the principle of superposition. Which means that if  and  are two solutions of
the linear differential equation, then the linear combination  is also a solution for any values of the constants  and . As Anderson put it "A complicated flow pattern 
for an irrotational, incompressible flow can be synthesized by adding together a number of elementary flows, which are also irrotational and incompressible.”. Such elementary flows are the point source or sink, the doublet and the vortex line, each being a solution of Laplace's equation. These may be superposed in many ways to create the formation of line sources, vortex sheets and so on.  In the Vortex Lattice method, each such elementary flow is the velocity field of a horseshoe vortex with some strength .