﻿CGC) Mr. C. G. Darwin on the Effects of the 



Thus collisions in the lower atmosphere are sufficient to 

 reduce the upper regions to the state they would have if 

 they were subject to collisions. 



These facts may be deduced directly from the general 

 kinetic theory of gases. For suppose that a smooth spherical 

 envelope is placed at a considerable distance outside the 

 eaith. In this case, if sufficient time were allowed, the gas 

 would ultimately attain accurately its normal distribution, 

 while most of the molecules in the outer regions would be 

 describing parts of orbits, having come from collision near 

 perigee. The distribution of molecules will be given by (A), 

 the assumption that all values of YOcj) are possible being 

 equivalent to the assumption of an envelope which returns 

 molecules describing hyperbolic orbits, and the assumption 

 of infinite time being equivalent to the assumption that the 

 free orbits which never go inside r are properly distributed. 

 Thus the lagging effect, which at first sight was expected, 

 is entirely absent. This may be seen physically from the 

 fact that the molecules projected eastwards from r Q have, in 

 genera], greater velocities than those projected westwards, 

 and so will tend to go higher. Thus, though every molecule 

 has less velocity at r, the ratio of the number of molecules 

 moving eastwards to those moving westwards is just so much 

 greater than at r that the mean angular velocity about the 

 earth's axis is unaltered. 



It has been stated that this result is subject to two 

 corrections; one for hyperbolic orbits which cause permanent 

 loss to the atmosphere, and the other for molecules describing 

 free elliptic orbits which never cut r . The first correction 

 is known to be very small. Its general effect would be to 

 impart an infinitesimal upward motion to the air. The 

 second correction is subject to an essential uncertainty. 

 For there must certainly be some molecules describing 

 " external " orbits which do not cut r . Originally each of 

 these must have been caused by a collision outside r , but as 

 soon as we admit the existence of such collisions, the region 

 at once becomes subject to the normal law of distribution. 

 This correction is thus only needful at such heights that 

 there have been very few collisions since the time when the 

 angular velocity and temperature of the earth were markedly 

 different. Considering how vague is our information of the 

 state of the present atmosphere, it seems hopeless to estimate 

 at all any effects remaining in it from the remote past. It 

 is very doubtful also if such external orbits could persist 

 for any long time. I am informed that up to a distance of 

 about 1<» earth's radii the orbits would be stable, but 



