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Let ${\bf K}$ be a vector field in the neighbourhood of ${\bf p}\in{\mathbb R}^n$, and let ${\bf X}$ and ${\bf Y}$ be two tangent vectors at ${\bf p}$. These two vectors span a parallelogram $P$ with one vertex at ${\bf p}$. The "circulation" of ${\bf K}$ around $P$ computes to $$\int_{\partial P}{\bf K}\bullet d{\bf x}= (L.{\bf X})\bullet{\bf Y}- (L.{\bf Y})\bullet{\bf X} + o(|P|^2)$$ with $L:=d{\bf K}({\bf p})$ and $|P|$:= diam$(P)$. It follows that there is a certain skew bilinear function ${\rm Rot}\thinspace{\bf K}({\bf p}):T_{\bf p}\times T_{\bf p}\to{\mathbb R}$ with $$\int_{\partial P}{\bf K}\bullet d{\bf x}={\rm Rot}\thinspace{\bf K}({\bf p}).({\bf X},{\bf Y})+ o(|P|^2) \ \ \ (|P|\to 0).$$ In the case $n=3$ the bilinear form ${\rm Rot}$ can be represented by the vector ${\rm curl}\thinspace{\bf K}$ in the form $$ {\rm Rot}{\bf K}({\bf p}).({\bf X},{\bf Y}) = {\rm curl}\thinspace{\bf K}({\bf p})\bullet({\bf X}\times{\bf Y}).$$