379, 380] The Outer Atmosphere 317 



17 absolute ( 256 C.), we may say that the temperature of the outer 

 atmosphere would be less than 17 absolute. In this case an atmosphere of 

 hydrogen only would be reached at a height of about 53 kilometres from the 

 adiabatic atmosphere say 80 kilometres from the earth's surface. Any 

 numerical estimate must, however, be very uncertain. 



Collisions in the Outer Atmosphere. 



380. It is not possible to form an exact estimate of the frequency of 

 collisions in the outer atmosphere, for the obvious reason that we know 

 hardly anything as to the actual value of the absolute density of the gas at 

 this height. We can, however, easily obtain an upper limit to the collision- 

 frequency. As we shall find that this leads, at a certain height, to a mean 

 free path many times greater than the earth's diameter, the information 

 obtained will be sufficient for our purpose. 



Throughout that part of the atmosphere which is in adiabatic equilibrium, 

 the density falls off more rapidly than it would if the equilibrium were 

 isothermal throughout, and hence the density at any point is less, for the 

 same value at the earth's surface, than it would be if the atmosphere were in 

 isothermal equilibrium. On this latter hypothesis, the density at height z 



would be 



v = v e- 2h *, 



where % is the difference of potential of a molecule between a height z and 

 the earth's surface. We accordingly have 



r = a+z 



gtf j 



y dr 



yJ 



= mqa? ( ) 



\a a + zj 



_ mgaz 

 ~ a + z' 



as in 377 and hence the density at a height z is 



(758), 



in which the variations in gravity are now taken" into account, but not the 

 planetary rotation. 



We shall consider a height z = a, at which, it must be noticed, the 

 apparent centrifugal force is still small compared with gravity, the ratio 

 being about 1 to 37. At such a height, even assuming a temperature as 



