The Kinetic Theory of Planetary Atmospheres. 



335 



"The Kinetic Theory of Planetary Atmospheres." By G. H. 

 Bryan, Sc.D., r.E.S. Eeceived March 15, — Eead April 5, 

 1900. 



(Abstract.) 



The appHcation of the kinetic theory to the atmospheres of planets 

 dates from the paper of Waterston, who gave an investigation based 

 on the then only possible assumption of equal velocities for all 

 molecules, an assumption since known as Clausius' law. Of later 

 papers reference is due in especial to Dr. Johnstone Stoney's memoir 

 " Of Atmospheres on Planets and Satellites,""^ in which the test of 

 permanence of a gas in the atmosphere of a planet is made to depend 

 on the ratio of its velocity of mean square to that relative velocity 

 which would enable a suitably projected body to escape from the 

 planet's attraction. If it be admitted, as Dr. Stoney assumes, that 

 helium cannot exist in our atmosphere, it follows that vapour of water 

 cannot exist on M.ars. 



The author's object has been to investigate the logical conclusions 

 obtained by applying the Boltzmann-Maxwell distribution to the- 

 atmospheres of planets. In 1893 calculations were made, having 

 special reference to the absence of atmosphere from the IMoon, but 

 these took no account of axial rotation. When this cause is taken 

 into account, the distribution of co-ordinates and relative velocities of 

 the molecules is found to be the same as if the planet were at rest, 

 and " centrifugal force " applied to the system. The surfaces of equal 

 density are of the forms originally investigated by Edward Eoche, of 

 Montpellier, and they cease to be closed surfaces when passing to the _ 

 outside of the point on the equatorial plane where centrifugal force 

 just balances the planet's attraction. Calling the surface through this 

 point the " critical surface," the density of molecular distribution over 

 this surface must be very small to ensure permanence. The ratio of 

 the density at the planet's surface to the density at the critical surface 

 has been called the " critical density ratio," and the author calculates 

 its logarithm for particular gases at different temperatures on the 

 various planets. The use of this logarithm has the advantage that the 

 calculation can at once be extended to any gas at any temperature. 



The high value obtained in the case of helium considered in reference 

 to the earth, appears to afford abundant proof that if helium existed 

 in our atmosphere it would possess a very high degree of permanence 

 at ordinary temperatures. To test this point further, a calculation is 

 made of the total rate at which molecules would flow across the 

 critical surface, this rate being regarded as a superior limit to the 



* 'Trans. E. Dublin Soc' 



