 For the second term, we note that evolution of the material line element is given by
Hence
The last equality is obtained by applying Stokes theorem.Since both terms are zero, we obtain the result

A similar principle which conserves a quantity can be obtained for the rotating frame also, known as the Poincaré–Bjerknes theorem, named after Henri Poincaré and Vilhelm Bjerknes, who derived the invariant in 1893 and 1898.The theorem can be applied to a rotating frame which is rotating at a constant angular velocity given by the vector formula_17, for the modified circulation

Here formula_19 is the position of the area of fluid.