The difference of the velocity of flow of gases also determines the phenomenon cited in the following footnote for demonstrating the existence of an internal motion in gases. If for a certain mass of a gas which fully and exactly follows the laws of Mariotte and Gay-Lussac the temperature _t_ and the pressure _p_ be changed simultaneously, then the entire change would be expressed by the equation _pv_ = _C_(1 + _at_), or, what is the same, _pv_ = _RT_, where _T_ = _t_ + 273 and _C_ and _R_ are constants which vary not only with the units taken but with the nature of the gas and its mass. But as there are discrepancies from both the fundamental laws of gases (which will be discussed in the following chapter), and as, on the one hand, a certain attraction between the gaseous molecules must be admitted, while on the other hand the molecules of gases themselves must occupy a portion of a space, hence for ordinary gases, within any considerable variation of pressure and temperature, recourse should be had to Van der Waal's formula-- (_p_ + _a_/_v_^2)(_v_-_p_) = R(1 + _at_) where _a_ is the true co-efficient of expansion of gases. The formula of Van der Waals has an especially important significance in the case of the passage of a gas into a liquid state, because the fundamental properties of both gases and liquids are equally well expressed by it, although only in their general features. The further development of the questions referring to the subjects here touched on, which are of especial interest for the theory of solutions, must be looked for in special memoirs and works on theoretical and physical chemistry. A small part of this subject will be partially considered in the footnotes of the following chapter.