20 
DK. C4. H. ORYAX OX THE KINETIC THEORY 
13. Effect of Air Currents in the Lower Regions. 
As previously indicated, one effect of convection currents, or winds, is to produce 
a teniperature-gradient in the lower regions of a planet’s atmosphere, rendering the 
adiabatic law of distrihution a closer aj^proximation than the isothermal. While a 
discussion of the numerical results obtained witli that law must be left for future 
investigation, there appear to be many reasons on general grounds why such a dis¬ 
tribution should not lead to results differing widely from ours, and why these results 
should certainly not be more favourable to the escape of the lighter gases from the 
atmospheres of planets. 
The correction required to take account of the temperature-gradient may be 
roughly estimated in various ways • 
(1) We may calculate the values of the critical density-ratio for the highest and 
lowest temperatures known to exist in the atmosphere, the actual state of affairs 
being intermediate between these extreme cases. 
(2) We may apply a correction to the results above calculated by conq)armg the 
actual gradient of density in the strata of the atmosphere which have been explored 
with the gradient which would exist if the distribution were isothermal. To make 
this correction sufficient, it would be necessary to carry the investigation up to the 
height at which the temperature becomes sensibly constant. 
Now if the density ot' the atmosphere at the assumed iqjper limit be appreciable, 
the factor by whicli the critical density-ratio must be multijDlied in order to apply 
the correction will be finite. Such a correction, then, cannot possibly affect the 
permanence, for example, of helium in the Earth’s atmosphere at ordinary tempera- 
tui'es, where, if the rate of escape were multi|)lied, say, a millionfold, it would still be 
inappreciable. 
But the existence of these air currents has a further infiuence on the distribution 
of the atmosj^here. For, according to the isothermal distribution of the kinetic 
theory, the density of the heavier constituents falls ofi’ much more rapidly with the 
altitude than that of the lighter ones, and we therefore believe that the lighter gases 
extend to altitudes at which the heavier ones have practically ceased to exist. The 
efiect of air currents is to equalise the pei'centage composition of the atmosphere in 
the upper and lower regions ; in this way a greater percentage of the lighter con¬ 
stituents will ])e retained in the lower regions than Avould be the case if e({uilibrium 
were attained by difi’usion. The conditions Avill be more favourable to the escape of 
the heavier constituents, or less fin'orirable to the escape of the lighter ones, or both. 
14. Conclusions. 
Without entering into the debatable question of the “Age of the Earth,” Ave may 
take Lord Kelaun’s estimate of lU® year's as afibrding some indication of the order of 
