310 Planetary Atmospheres [on. xvn 



These equations are independent in the sense that each is concerned with 

 one and only one of the different constituents of the atmosphere. The 

 equations therefore contain the mathematical expression of the law formu- 

 lated by Dalton for an atmosphere in isothermal equilibrium : 



An atmosphere in isothermal equilibrium may be regarded as the 

 aggregate of a number of atmospheres, one for each constituent gas, the law 

 of density in each atmosphere being the same as if it alone was present. 



369. Considering for the sake of simplicity an atmosphere which consists 

 only of two constituents a, (3, the ratio v a /v$ will measure the proportion in 

 which the gases are mixed at any point. From equations (746), 



-"V (747). 



Vf/g 



If the gas of type a. is the heavier of the two, ra a m^ is positive, and 

 therefore v a jvp has its maximum value at z 0. In other words, the heavier 

 gas tends to sink to the bottom. 



To obtain some idea of the magnitude of this imperfection of diffusion, 

 let us make use of the numerical values given in 130. Since 2/m= -^ for 



any gas, we may write the index of the exponential in equation (747) in 

 the form 



If a refers to oxygen and /3 to nitrogen, the value of this quantity at C. is, 

 from the table given on p. 113, found to be 



2gz x 10~ n c. G. s. units. 



If we put g = 981, and z = 5 x 10 6 , corresponding to a height of five kilo- 

 metres, the value of this quantity is found to be "01. Thus the rate at which 

 the proportions of oxygen to nitrogen would change is very small, amounting 

 only to about 1 per cent, in five kilometres. 



Atmosphere in Adiabatic (Convective) Equilibrium. 



370. The atmospheric distribution which has just been investigated, a 

 distribution in which the temperature is constant throughout, while the 

 density of each component gas falls off exponentially with the height above 

 the earth's surface, is the law which would undoubtedly become established if 

 the earth's atmosphere were left at rest for a sufficient time. 



As a matter of fact, however, the earth's atmosphere is incessantly being 

 agitated by currents and storms, so that there is a continual mechanical 

 transference of air from one part of the earth's atmosphere to another. 

 From this consideration, coupled with the fact that the conduction of heat in 



