Molecules, on this supposition, may consist of single atoms, or they may consist of pairs of such atoms, joined in some fashion like the bulged ends of a dumb-bell; or lastly, they may consist of greater numbers of atoms arranged in some different manner, the arrangement depending on their relative size and attraction for each other. It must be clearly understood, however, that such mental pictures are not to be taken as actually representing the true constitution of matter, but merely as attempts to picture such forms as will allow of our drawing conclusions regarding their behaviour from known configurations of large masses. The molecules of gases are imagined to be in a state of continual motion, up and down, backwards and forwards, and from side to side. It is true that they must also move in directions which cannot be described by any of these expressions, but such other directions may be conceived as partaking more or less of motions in the three directions specified; _i.e._ in being resolvable into these. To these motions have been applied the term “degrees of freedom.” Such motions through space, in which the molecule is transported from one position in space to another, form three of the possible six degrees of freedom which a molecule may possess, and the molecules are said to possess “energy of translation” in virtue of this motion. The other three consist in rotations in three planes at right angles to each other. Now, it can be shown that the product of pressure and volume of a gas, _pv_, is equal to ⅔rds of the energy of translation of all molecules of the gas, or _pv_ = ⅔(NR), where N stands for the number of molecules in unit volume, and R for their energy of translation; inasmuch as a pressure diminishing a volume is of the nature of work, or energy. For one gram of air at O° C. and 76 cms. pressure (normal temperature and pressure), the pressure (_p_), measured in grams per square centimetre, is 1033, and the volume (_v_) is 773·3 cubic centimetres; and the raising of the temperature through 1°, as was shown before, requires 2927 gram-centimetres of work. Further, since the product of pressure into volume is equal to ⅔rds of the energy due to motion, or the translational energy of the gas, NR = 3/2_pv_ = 3/2 × 2927 = 4391 gram-centimetres. Dividing this number by 42,380, the mechanical equivalent of heat, or the number of gram-centimetres corresponding to one calory, the quotient is 0·1040 calory. If the energy of the air were due to the translational motion of its molecules, we should expect this number, 0·1040, to stand for the specific heat of air at constant volume; but it has been found equal to 0·1683, as already shown.