THE COMPOSITION OF WATER, HYDK< Kil-N IB'J 



Although a substance which passes with great difficulty into a 

 liquid state by the action of physico-mechanical forces, hydrogen loses 



while a third class of investigators (Van der Waals, Clausius, and others ), starting from the 

 already generally-accepted principles of the mechanical theory of heat and the kinetic 

 theory of gases, and having made the self-evident proposition of the existence in jj 

 of those forces which clearly act in liquids, deduced the connection between the properties 

 of one and the other. It would be out of place in an elementary handbook like the 

 present to enunciate the whole mass of conclusions arrived at by this method, but it is 

 necessary to give an idea of the results of Van der Waals' considerations, for they explain 

 the gradual uninterrupted passage from a liquid into a gaseous state in the simplest 

 form, and, although the deduction cannot be considered as complete and decisive (see 

 note 25), nevertheless it penetrates so deeply into the essence of the matter that its 

 signification is not only reflected in a great number of physical investigations, but also in 

 the province of chemistry, where instances of the passage of substances from a gaseous 

 to a liquid state are so common, and where the very processes of dissociation, decomposi- 

 tion, and combination must be identified with a change of physical state of the partici- 

 pating substances. 



For a given quantity (weight, mass) of a definite substance, its state is expressed 

 by three variables volume v, pressure (elasticity, tension) p, and temperature t. 

 Although the compressibility [i.e., d(v)d(p)] of liquids is small, still it is clearly ex- 

 pressed, and varies not only with the nature of liquids but also with their pressure and 

 temperature (at tc the compressibility of liquids is very considerable). Although gases, 

 according to Mariotte's law, with small variations of pressure, are uniformly compressed, 

 nevertheless the dependence of their volume v on t and p is very complex. The same 

 applies to the coefficient of expansion [ = d(v)d(t), or d(p)d(t)], which also varies with 

 t and_p, both for gases (see Note 26), and for liquids (at tc it is very considerable, and 

 often exceeds that of gases, 0'00367). Hence the equation of state must include three 

 variables v, p, and t. For a so-called perfect (ideal) gas, or for inconsiderable variation 

 of density, the elementary expression pv = Ra(t + at), or pv R (273 + 2) should be 

 accepted, where R is a constant varying with the mass and nature of a gas, as expressing 

 this dependence, because it includes in itself the laws of Gay-Lussac and Mariotte, for at 

 a constant pressure the volume varies proportionally to 1 + at, and when t is constant 

 the product of tv is constant. In its simplest form the equation may be expressed thus : 



where T denotes what is termed the absolute temperature, or the ordinary temperature 

 + 273- that is, T-2 + 273. 



Starting from the supposition of the existence of an attraction or internal pressure 

 (expressed by a) proportional to the square of the density (or inversely proportional to 

 the square of the volume), and of the existence of a volume or length of path (expressed 

 by b) of gaseous molecules, Van der Waals gives for gases the following more complex 

 equation of state : 



(p+ a } (v -6) = 1+0-003672 ; 

 V 9* J 



if at under a pressure ^ = 1 (for instance, under the atmospheric pressure), the volume 

 (for instance, a litre) of a gas or vapour be taken as 1, and therefore v and b be expressed 

 by the same units as p and a. The deviations from both the laws of Mariotte and Gay- 

 Lussac are expressed by the above equation. Thus, for hydrogen a must be taken as 

 infinitely small, and 6 = 0'0009, judging by the data for 1000 and 2500 metres pressure 

 (Note 28). For other permanent gases, for which (Note 28) I showed (about 1870) from 

 Regnault's and Natterer's data, a decrement of pv, followed by an increment, which was . 

 confirmed (about 1880) by fresh determinations made by Amagat, this phenomena may 

 be expressed in definite magnitudes of a and b (although Van der Waals' formula is not 

 applicable for minimum pressures) with sufficient accuracy for contemporary require- 

 ments. It is evident that Van der Waals' formula can also express the difference of the 



