Fowler obtained thermodynamic quantities assuming the theory which could be derived by representing the system with microcanonical ensemble, in order to introduce the temperature T of the system proper, he considered the combined systems which are composed of the system proper and another arbitrary system that is in thermal contact with the former, and represented the combined system by a microcanonical ensemble, here, he used the steepest descent method in his calculation. This Fowler's treatment is not only unsatisfactory at the point of theoretical view but also he could not make the formulation of free energy of Helmholtz's so that this formular was forced to be assumed. From the point of Quantum Statistical Mechanical view, the materially closed system which is in an equilibrium state with the temperature T is best represented by canonical ensemble. At the actual derivation of the distribution law and thermodynamic quantities, however, in order to avoid the difficulty of calculation Tolman proceeded his calculation either representing the system proper by the grand-canonical ensemble or adding a certain limitation.