F(r, t) is a vector field at the spatial position r at time t, Σ is a moving surface in three-space bounded by the closed curve ∂Σ, dA is a vector element of the surface Σ, ds is a vector element of the curve ∂Σ, v is the velocity of movement of the region Σ, ∇⋅ is the vector divergence, × is the vector cross product, The double integrals are surface integrals over the surface Σ, and the line integral is over the bounding curve ∂Σ.