It is shown that surface tension is not the reason causing minimization of the surface of a liquid pile. It is shown that there exists a pressure inside the liquid arising from the inward intermolecular resultant force on the surface molecules exerted by the liquid molecules adjacent to the surface. We call it as cohesion pressure. A method is presented for measuring the intermolecular attraction which will be also a means for testing the theory in comparison with the current theory of surface tension. It is proven that the surface tension is not what causes the horizontal wire sliding on the two limbs of a U-shaped wire to be in equilibrium in any position when a liquid film forms the area of the U-shaped wire. In a sure manner, incorrectness of both the current relation for the pressure difference between inside and outside of a bubble and the current relation for the pressure difference between inside and outside of a solid drop is proven. It is shown that the adhesion reduces the pressure inside the liquid, because a part of the liquid weight is sustained by the walls of the container. The mechanism of capillarity is discussed in detail in terms of intermolecular attraction and cohesion pressure. Dependence of rise altitude on depth of dipping and dependence of fall depth on depth of dipping are properties in capillarity; this is predicted by the theory presented in this paper and not by the theory of surface tension, and then can be a practical test for the theory.