VALIDITY OF THE -^PRINCIPLE OF LE CHATELIER. 31 



SO that (40) takes the form 



PV = { Ui- 2x) + (.l'i+ 2x) + {A'o-\- x) Rd ..^. 



= \{x + A,+ A\+A'^^Re ^^^' 



In this case it is quite evident that the parameters P, V (correspond- 

 ing to //, G of the general case) have the property defiiifd by (41), 

 which here appears as the characteristic property of the intensity 

 factor and the capacity factor of an energy. 



But for our present purposes we are not concerned with the question 

 whetjier or not the parameters G, H defined for a given system are or 

 are not factors of an energy. We must be prepared to deal with cases 

 where this is either uncertain or actually known not to be true. All 

 we need to know, for our purpose, is that the parameters G, H have 

 the property defined by (41). An example may serve to illustrate the 

 fact that this property may be shared by physical quantities not 

 obviously related to energy. 



Among the parameters on which the rate of increase of a human 

 population depends is the area a occupied by them, since this deter- 

 mines the population density, which in turn influences the death rate 

 in well-known mann^r,^ and. presumably, in some degree the birth 

 rate also. 



Now there is an obvious relation between population density and 

 ground rent. Regulation is effected about as follows: There is a 

 certain demand for space, a desire for expansion, which may be 

 measured by the rent // per unit area that the individual is willing to 

 pay. On the other hand there is a certain market price He which 

 must be paid to obtain accommodatioji. Now \i H > II e, i.e. if, on 

 an average, an individual is willing to pay more than the market price, 

 the population will spread over a greater area by renting more ground. 

 If, on the other hand // < II e the individual is not willing to pay the 

 market price, he will retrench, he will move from a six room apart- 

 ment to a five room apartment say, and the area occupied by the 

 population will contract. The parameter He functions, in fact, much 

 like a "surface pressure," tending to compress the population into a 

 smaller area. The most striking exhibition of this " surface-pressure " 

 is seen in a great metropolis such as New York, where the population, a 

 naturally two-dimensional structure spread like a film over the earth's 

 surface, has been thrown into great creases towering 700 feet and more, 

 50 layers deep, above the street level. 



9 See, for example, Newsholme, Vital Statistics, 1899, p. 154. 



