412 VAN DEB WAALS ON THB CONTINUITY 



aft the square of the density, and since, in the case of carbonic acid, it 

 dimmudu* Ue pressure, it must be of the positive sign, that is, it roust arise 

 from at I ruction between the molecules. 



Hut if the volume is still further diminished, at a certain point lique- 

 faction begins, and from this point till the gas is all liquefied no increase of 

 measure takes place. As soon, however, as the whole substance is in the liquid 

 condition, any further diminution of volume produces a great rise of pressure, so 

 that the product of pressure and volume increases rapidly. This indicates negative 

 vi rial, and shews that the molecules are now acting on each other by repulsion. 



This is what takes place in carbonic acid below the temperature of 30'92C. 

 Above that temperature there is first a positive and then a negative virial, 

 but no sudden liquefaction. 



Similar phenomena occur in all the liquefiable gases. In other gases we are 

 able to trace the existence of attractive force at ordinary pressures, though the 

 compression has not yet been carried so far as to shew any repulsive force. 

 In hydrogen the repulsive force seems to prevail even at ordinary pressures. 

 This gas has never been liquefied, and it is probable that it never will be 

 liquefied, as the attractive force is so weak. 



We have thus evidence that the molecules of gases attract each other at 

 a certain small distance, but when they are brought still nearer they repel 

 each other. This is quite in accordance with Boscovich's theory of atoms as 

 massive centres of force, the force being a function of the distance, and 

 changing from attractive to repulsive, and back again several times, as the 

 distance diminishes. If we suppose that when the force begins to be repulsive 

 it increases very rapidly as the distance diminishes, so as to become enormous 

 if the distance is less by a very small quantity than that at which the force 

 first begins to be repulsive, the phenomena will be precisely the same as those 

 of smooth elastic spheres. 



M. Van der Waals makes his molecules elastic spheres, which, when not in 

 contact, attract each other. His treatment of the "molecular pressure" arising 

 from their attraction seems ingenious, and on the whole satisfactory, though he 

 has not attempted a complete calculation of the attractive virial in terms of 

 the law of force. 



His treatment of the repulsive virial, however, shews a departure from the 

 principles on which his investigation is founded. He considers the effect of the 

 size of the molecules in diminishing the length of their "free paths," and he 



