~Allotropic states or forms of matter.~ Other elements besides oxygen may exist in more than one form. These different forms of the same element are called _allotropic states_ or _forms_ of the element. These forms differ not only in physical properties but also in their energy contents. Elements often exist in a variety of forms which look quite different. These differences may be due to accidental causes, such as the size or shape of the particles or the way in which the element was prepared. Only such forms, however, as have different energy contents are properly called allotropic forms. MEASUREMENT OF GAS VOLUMES ~Standard conditions.~ It is a well-known fact that the volume occupied by a definite weight of any gas can be altered by changing the temperature of the gas or the pressure to which it is subjected. In measuring the volume of gases it is therefore necessary, for the sake of accuracy, to adopt some standard conditions of temperature and pressure. The conditions agreed upon are (1) a temperature of 0 deg., and (2) a pressure equal to the average pressure exerted by the atmosphere at the sea level, that is, 1033.3 g. per square centimeter. These conditions of temperature and pressure are known as the _standard conditions_, and when the volume of a gas is given it is understood that the measurement was made under these conditions, unless it is expressly stated otherwise. For example, the weight of a liter of oxygen has been given as 1.4285 g. This means that one liter of oxygen, measured at a temperature of 0 deg. and under a pressure of 1033.3 g. per square centimeter, weighs 1.4285 g. The conditions which prevail in the laboratory are never the standard conditions. It becomes necessary, therefore, to find a way to calculate the volume which a gas will occupy under standard conditions from the volume which it occupies under any other conditions. This may be done in accordance with the following laws. ~Law of Charles.~ This law expresses the effect which a change in the temperature of a gas has upon its volume. It may be stated as follows: _For every degree the temperature of a gas rises above zero the volume of the gas is increased by 1/273 of the volume which it occupies at zero; likewise for every degree the temperature of the gas falls below zero the volume of the gas is decreased by 1/273 of the volume which it occupies at zero, provided in both cases that the pressure to which the gas is subjected remains constant._ If V represents the volume of gas at 0 deg., then the volume at 1 deg. will be V + 1/273 V; at 2 deg. it will be V + 2/273 V; or, in general, the volume v, at the temperature t, will be expressed by the formula (1) v = V + t/273 V, or (2) v = V(1 + (t/273)). Since 1/273 = 0.00366, the formula may be written (3) v = V(1 + 0.00366t). Since the value of V (volume under standard conditions) is the one usually sought, it is convenient to transpose the equation to the following form: