Lithium be cut with a knife. When cut, it possesses a silvery-white color that quickly changes to gray as it oxidizes to lithium oxide. While it has one of the lowest melting points among all metals (180 °C), it has the highest melting and boiling points of the alkali metals. Lithium has a very low density (0.534 g/cm), comparable with pine wood. It is the least dense of all elements that are solids at room temperature; the next lightest solid element (potassium, at 0.862 g/cm) is more than 60% denser. Furthermore, apart from helium and hydrogen, it is less dense than
Gauss's principle of least constraint is equivalent to D'Alembert's principle. The principle of least constraint is qualitatively similar to Hamilton's principle, which states that the true path taken by a mechanical system is an extremum of the action. However, Gauss's principle is a true (local) "minimal" principle, whereas the other is an "extremal" principle. Hertz's principle of least curvature is a special case of Gauss's principle, restricted by the two conditions that there be no applied forces and that all masses are identical. (Without loss of generality, the masses may be set equal to one.) Under these conditions, Gauss's minimized quantity can be written The