On Inquiries as to the Escape of Gases from Atmospheres. 287 



particles whose speed lies between v and v + dv, in a system of colliding 

 particles intended to represent an isotropic portion of gas. 



Professor Bryan's investigation* is based on the investigations made 

 since 1866 into the way in which energy tends ultimately to be par- 

 titioned among the various motions possible within a self-contained 

 dynamical system of bodies. The system need not be isotropic, since 

 the bodies may be moving in a constant field of force. 



An inquiry by the present writer into Mr. Cook's method of dealing 

 with the problem is attempted in the May and June numbers of the 

 'Astrophysical Journal' for 1900, and in the present paper a similar 

 attempt is made with reference to Professor Bryan's. 



Both Mr. Cook and Professor Bryan predict the proportion of mole- 

 cules which can escape from an atmosphere by deducing the proportion 

 from its supposed causes, and in this respect are in contrast with an 

 investigation previously published, which sought to ascertain from the 

 observed effects of escape where and on what scale it has in fact taken 

 place. (See memoir by the present writer in the ' Scientific Transactions 

 of the Royal Dublin Society,' vol. 6, Part 13, or in the 'Astrophysical 

 Journal' for January, 1898. And for further evidence that helium is 

 escaping from the earth, see 'Nature' of the 24th May, 1900, p. 78.) 



Where, as in the present instance, the a priori and a posteriori 

 methods have led to inconsistent numerical results, there must be a 

 mistake or mistakes somewhere, and it is incumbent upon us to search 

 till these are detected. If they can be. found and corrected an 

 important advantage will be gained. Professor Bryan, at the end of 

 his letter in 'Nature ' of the 7th June, 1900, indicated one place where 

 a mistake may have been made, viz., in the assumed relation between 

 temperature and the kinetic energy of the translational motions. 

 Another mistake may perhaps have been made in assuming the legiti- 

 macy of treating the partition of energy when molecules move in a 

 field of force, as though the only partition to be considered is between 

 these molecules, whereas no field of force can exist unless it has been 

 produced by some physical agent, upon which every motion that goes 

 on within the field must react. In consequence of these reactions no 

 field of force in which any motion occurs can be accurately constant, 

 and a partition of energy based upon the supposition of its constancy 

 is a theorem in rational dynamics, but has no counterpart in nature. 



Thus, in the case of the earth's atmosphere, the anisotropic condition 

 of its outer layers is due to the field of force which exists in the neigh- 

 bourhood of the earth ; and when we are obliged to take into account 

 this anisotropic condition, as we must when dealing with the escape of gases 

 from atmospheres, this is to be done (when we are treating the problem 

 as one of partition of energy) by including as molecules between which 

 the partition has to take effect not only the gaseous molecules, 

 * ' Roy. Soc. Proc.,' April, 5, 1900, p. 835. 



