ATOM. 453 



particle greater than that of the neighbouring parts. Indeed, we should arrive 

 at the conclusion that the pressure depends not only on the density of the air 

 but on the form and dimensions of the vessel which contains it, which we 

 know not to be the case. 



If, on the other hand, we suppose the pressure to arise entirely from the 

 motion of the molecules of the gas, the interpretation of Boyle's law becomes 

 very simple. For, in this case 



The first term is the product of the pressure and the volume, which ac- 

 cording to Boyle's law is constant for the same quantity of gas at the same 

 temperature. The second term is two-thirds of the kinetic energy of the system, 

 and we have every reason to believe that in gases when the temperature is 

 constant the kinetic energy of unit of mass is also constant. If we admit 

 that the kinetic energy of unit of mass is in a given gas proportional to the 

 absolute temperature, this equation is the expression of the law of Charles as 

 well as of that of Boyle, and may be written 



pV=Rd, 



where is the temperature reckoned from absolute zero, and R is a constant. 

 The fact that this equation expresses with considerable accuracy the relation 

 between the volume, pressure, and temperature of a gas when in an extremely 

 rarified state, and that as the gas is more and more compressed the deviation 

 from this equation becomes more apparent, shews that the pressure of a gas is 

 due almost entirely to the motion of its molecules when the gas is rare, and 

 that it is only when the density of the gas is considerably increased that the 

 effect of direct action between the molecules becomes apparent. 



The effect of the direct action of the molecules on each other depends on 

 the number of pairs of molecules which at a given instant are near enough to 

 act on one another. The number of such pairs is proportional to the square 

 of the number of molecules in unit of volume, that is, to the square of the 

 density of the gas. Hence, as long as the medium is so rare that the encounter 

 between two molecules is not affected by the presence of others, the deviation 

 from Boyle's law will be proportional to the square of the density. If the 

 action between the molecules is on the whole repulsive, the pressure will be 

 greater than that given by Boyle's law. If it is, on the whole, attractive, the 

 pressure will be less than that given by Boyle's law. It appears, by the ex- 



