POPULAR SCIENCE 479 



molecules themselves are only slightly compressible, a stage 

 will be reached finally at which it is no longer justifiable to 

 neglect the actual volume occupied by the molecules in com- 

 parison with the total volume. This is particularly the case 

 with liquids, for it is well known that in liquid systems the 

 average distance of the molecules apart is just about the same 

 order of magnitude as the molecular diameter itself. To 

 allow for this effect, van der Waals, many years ago, intro- 

 duced a volume correction term into the gas law, denoting the 

 volume of the molecules when in contact by the term b, so 

 that, if V is the total observed volume of the compressed gas 

 or liquid, the true compressible volume or empty space is 

 (V — b). As a first step in the attempt to modify the gas 

 law, PV = RT, so that it may apply to compressed gases and 

 to liquids, we may write the expression P(V — b) = RT. This, 

 however, is not a sufficient modification. We have still to 

 consider another very important factor which enters into 

 the question, namely, the existence of molecular attractions. 

 As long as the molecules are not very close together this force 

 is negligible. When, however, as a result of compression, the 

 molecules are brought into closer range, mutual attractions 

 must be taken into account, for it is owing to these that the 

 gas possesses less expansive force than it would otherwise have. 

 In other words, a gas becomes too easily compressible and 

 diminishes excessively in volume as the external pressure 

 upon it is increased. The pressure actually exerted by the 

 gas under these conditions is of course P, measured by the 

 manometer. But this value is really smaller, and may be 

 much smaller, than the pressure which the gas would exert 

 if molecular attraction were absent. These attractions act 

 like an additional pressure which we shall denote by the term 

 •7T, so that the total compressing agencies can be represented 

 by the sum of the terms (P + 7r). The modified gas equation 

 may be written, therefore: (P4-7r) (V — b) = RT. This 

 expression is undoubtedly a truer representation of the be- 

 haviour of a compressed gas or liquid than is the simple gas 

 law itself. We have not made much progress, however, until 

 we can express tt in terms of measurable quantities. Van der 

 Waals suggested that it might be written as a/V 2 , where a is 

 regarded as a constant, characteristic of a given substance, 

 whether in the gaseous or liquid state, and V may be taken 



