312 Planetary Atmospheres [cu. xvn 



372. On putting p = in equation (750) we obtain 



" 



0(7-1)' 



from which it appears that there is a superior limit to the height of an 

 atmosphere in convective equilibrium. Since, by equation (749), p = kp y , 

 this limiting height may be written in the form 



where p , p are the pressure and density at the earth's surface. This again 

 can be put in the form 



r 



T 



mg(y~ 

 Substituting numerical values, this height is found to be about 29 kilometres. 



According to Dewar* the greatest height at which clouds have been 

 observed is 17 miles, or 27*37 kilometres. 



Our atmosphere, then, if supposed to be in convective equilibrium 

 throughout, must be regarded as a layer of gas of uniform composition 

 throughout, having a height of about 29 kilometres, the temperature 

 decreasing uniformly as we ascend. 



The rate at which the temperature decreases must be about 10 C. 

 per kilometre, or in English units, about '54 F. per 100 ft. This theoretical 

 estimate of the temperature gradient is approximately confirmed by observa- 

 tion. In practice, however, the problem is one of extreme complexity, owing 

 mainly to the irregularities of the earth's surface which prevent the surfaces 

 of equal temperature from being strictly spherical. Detailed accounts of 

 observations on this point will be found in Meteorological Reports "h 



OUTER ATMOSPHERE. 

 Outer Atmosphere in Conductive Equilibrium. 



373. When, however, we examine in detail the molecular mechanism 

 by which the adiabatic law is maintained in an atmosphere we find that there 

 must be a limit beyond which adiabatic equilibrium is impossible. For at 

 the free surface which is predicted from the supposition that the adiabatic 

 law obtains throughout, the density would be zero, and therefore the mean 

 free path infinite. Hence there would be molecules arriving at this surface 

 from layers of gas inside it, with finite velocities and infinitesimal probabilities 



* Royal Institution Proc. xvn. 1, p. 223. 



t See for example a general discussion in the Report of the Chief of the U.S. Weather 

 Bureau, 1900-1, Vol. n. p. 25. 



