368-371] Aerostatics 311 



gases is very slow, it follows that the atmosphere is never permitted to 

 assume the equilibrium distribution which has just been discussed. As the 

 density of an element is changed by its enforced motion from one layer of the 

 atmosphere to another, the temperature also tends to change, but before the 

 temperature has adjusted itself by conduction to the temperature of its new 

 surroundings the element finds itself again moved away. Hence it happens 

 that the factor which determines the distribution of the atmosphere is not 

 the equalisation of temperature necessary to a permanent state, but is the 

 condition that an element of gas, on being moved from one place to another, 

 shall take up the requisite pressure and volume in its new position without 

 any loss or gain of heat by conduction taking place. The law connecting the 

 pressure and volume in the atmosphere must accordingly be the adiabatic 

 law found in 230, namely, 



p vv = constant .............................. (748). 



371. The equation of equilibrium of the atmosphere is 



and if, in accordance with the adiabatic law, we write 



p = kpv ................................. (749), 



we obtain kyp y ~ l ^-= gp, 



of which the integral is 



J^L( y-i_ p y-i) = ^ (750), 



7-1 



where p is the density at z = 0. This is the law according to which the 

 density falls off with the height. Since by equation (749), T is proportional 

 to p y ~ 1 , it follows that equation (750) can be expressed in the form 



T -T=cz (751), 



where c is a constant, and T is the temperature at z = 0. Thus the 

 temperature decreases as we move upwards in the atmosphere, the amount 

 of decrease being proportional to the height. 



The process of diffusion, as well as that of conduction, is very slow in 

 gases, and from this it follows that the constituent gases of an atmosphere 

 in convective equilibrium, will be found to occur in approximately the same 

 proportion at all heights. This is found by experiment to be true of the 

 atmosphere of the earth. Frankland* has found that the proportions of 

 nitrogen and oxygen in our atmosphere are the same for all altitudes up to 

 14,000 feet. As has already been remarked, there would be a variation of 

 about one per cent, at this height in an atmosphere in conductive equilibrium. 



* Journ. Chem. Soc. xiu. 22. 



