30 MAXWELL'S LAW 63 



theory forms the true explanation of the constancy of the 

 chemical equivalents, since a molecule can contain only an 

 integral and not a fractional number of atoms. 



The relations considered above may be made useful in 

 theoretical chemistry in two ways. We may either, with 

 Gay-Lussac, calculate by means of the given propor- 

 tion the unknown density of a gas or vapour from its 

 chemical equivalent which has been determined from its 

 chemical action ; or, inversely, from its observed density 

 we may deduce its chemical equivalent. For this purpose 

 Avogadro's law, which is discussed in the next para- 

 graph, is of service. 



31. Avogadro's Law 

 The proportion deduced from Maxwell's theory, viz. 



or the theorem that the densities p^ /o 2 of two gases at the 

 same temperature and under the same pressure are in the 

 ratio of their molecular masses m t , w 2 in the gaseous state, 

 is capable of a very simple interpretation, which is, there- 

 fore, the more important. 



In the meaning assigned in 13 to the idea of density, 

 p is nothing else than the mass of all the N molecules con- 

 tained in unit volume, or 



p = Nm. 



For two different gases we must write 

 P! = N l m l and /o 2 = Nrfn z , 



where the meaning of the symbols is plain. If we sub- 

 stitute these values of the densities in the above proportion 

 we obtain the equation 



N, = N v 



which, expressed in words, gives the theorem that two 

 different gases, when they are at the same temperature and 

 under the same pressure, contain equal numbers of molecules 

 in equal volumes. 



This is called Avogadro's law, after its discoverer. 



