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This inequality holds in all cases, but cannot in general be applied to an irreversible change, because Od4 is not a perfect differential, and cannot be evaluated without a knowledge of the path or process of transformation.
It was further investigated by John Wallis, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).
The above expressions for the capacity of an ellipsoid of three unequal axes are in general elliptic integrals, but they can be evaluated for the reduced cases when the ellipsoid is one of revolution, and hence in the limit either takes the form of a long rod or of a circular disk.
The value of d can be evaluated by considering the combustion of amorphous carbon to carbon monoxide and carbon dioxide.