372-375] The Outer Atmosphere 313 



of collision. The majority of these molecules would of course pass outside 

 the free surface predicted by the simpler theory, in a manner somewhat 

 similar to that in which molecules escape from the free surface of a liquid 

 and form a vapour. 



These molecules form what may be described as an " outer " atmosphere. 

 In this atmosphere, the density is very small, so that collisions are rare, 

 and the majority of molecules will simply describe orbits under the earth's 

 gravitation, undisturbed by collisions, and will finally fall back again into 

 the "inner" or adiabatic atmosphere. This at any rate is true of those 

 molecules which start with velocities such that they describe elliptic orbits 

 under the earth's attraction. Others, starting with greater velocities, will 

 describe parabolic or hyperbolic orbits, and these may be regarded as lost 

 altogether to the earth's atmosphere. We shall return to the consideration 

 of these losses later. 



374. In nature it is obvious that there must be a gradual, and not 

 a sudden, transition from the state of things which we have supposed to 

 exist in the. inner atmosphere, to that which has been supposed to exist 

 in the outer. There must, in fact, be an intermediate region, in which 

 neither set of conditions is satisfied with any accuracy. Passing through 

 this layer from inside outwards, we pass from a region at which the mass- 

 agitation is sufficient for the adiabatic law to be obeyed, to a region at which 

 the frequency of collisions is so small that a mass-agitation is impossible. At 

 this outer region conductive equilibrium must clearly obtain. And outside 

 this region, the law of density for gases of type a must be 



v a = Ae- 2h * (752), 



just as if the whole of the atmosphere were in conductive equilibrium, a 

 result which can be deduced either as in equation (165), or as in 178, 

 without making any assumption as to the frequency of collisions in the outer 

 atmosphere. 



375. There is no superior limit to the height of the outer atmosphere 

 which is in conductive equilibrium, since, in equation (752), v a does not vanish 

 at any finite height. It must, however, be remembered that in arriving at 

 equation (752) no account has been taken of the rotation of the planet, 

 and when there is no limit to the height of the atmosphere, the neglect of 

 rotation is inadmissible. 



For a planet rotating about the axis of z with angular velocity &>, the law 

 of density of the atmosphere is found, after the manner of 80, to be 



v a = Ae~ 2h x* +h a <J(x a -+y*) (753), 



and clearly v a not only does not vanish at any Distance, but becomes infinite 

 at infinity. 



