But sodium sulphate can also exist in the anhydrous form and as the hydrate Na_{2}SO_{4}, 7H_{2}O. In these cases there may {14} be chosen as components Na_{2}SO_{4} and H_{2}O, and Na_{2}SO_{4}, 7H_{2}O and H_{2}O respectively. In both cases, therefore, there are two components. But the two systems (Na_{2}SO_{4}, 10H_{2}O--H_{2}O, and Na_{2}SO_{4}, 7H_{2}O--H_{2}O) can be regarded as special cases of the system Na_{2}SO_{4}--H_{2}O, and these two components will apply to all systems made up of sodium sulphate and water, no matter whether the solid phase is anhydrous salt or one of the hydrates. In all three cases, of course, the _number_ of components is the same; but by choosing Na_{2}SO_{4} and H_{2}O as components, the possible occurrence of negative quantities of components in expressing the composition of the phases is avoided; and, further, these components apply over a much larger range of experimental conditions. Again, therefore, we see that, although the number of the components of a system is definite, a certain amount of liberty is allowed in the choice of the substances; and we also see that the choice will be influenced by the conditions of experiment. Summing up, now, we may say-- (1) The components are to be chosen from among the constituents which are present when the system is in a state of true equilibrium, and which take part in that equilibrium. (2) As components are to be chosen the _smallest number_ of such constituents necessary to express the composition of each phase participating in the equilibrium, zero and negative quantities of the components being permissible. (3) In any given system the _number_ of the components is definite, but may alter with alteration of the conditions of experiment. A certain freedom of choice, however, is allowed in the (qualitative, not quantitative) selection of the components, the choice being influenced by considerations of simplicity, suitability, or generality of application.[17] Degree of Freedom. Variability of a System.--It is well known that in dealing with a certain mass of gas or vapour, _e.g._ water vapour, if only one of the independently variable factors--temperature, pressure, and concentration (or volume)--is fixed, the state of the gas or vapour is undefined; while occupying the same volume (the concentration, therefore, remaining {15} unchanged), the temperature and the pressure may be altered; at a given temperature, a gas can exist under different pressures and occupy different volumes, and under any given pressure the temperature and volume may vary. If, however, two of the factors are arbitrarily fixed, then the third factor can only have a certain definite value; at any given values of temperature and pressure a given mass of gas can occupy only a definite volume.