DR. G. H. BRYAN ON THE KINETIC THEORY 
Theory Init various-circumstances have prevented me from following up the line of 
investigation thus started. In the interval, the new elements discovered by Professor 
Hamsay have su 2 :)plied fresh material for discussion, and in 1897 a j^aper “ Of Atmo¬ 
spheres upon Planets and Satellites” was published by Dr. Johxstoxe StoxeavI 
The latter paper, however, does not in any way anticipate the methods that I 
had contemplated using, and there are so many points on vdiich further investigation 
appeared desirable that a continuation of the present work seemed to me fully justified. 
Since the present investigation was completed, I have seen Mr. S. 11. Cook’s jDaper,;}; 
the method of wdiich is closely analogous with that adopted in the calculations of my 
Nc>ttingham j^aper. 
2. Watekston’s Method. 
Waterstox’s investigations take no account of the fact that the molecular 
sj)eeds of the molecules of the gas are distributed about a mean, according to such 
an arrangement as the Boltzmaxx-Maxwell distribution. Hence in dealing with 
planetary atmospheres it is assumed that at any point all the molecules are moving 
with the same sjDeed. On such an assumption the conditions for the existence of an 
atmosphere are very simple, especially if no account is taken of axial rotation. 
For supposing the celestial body under consideration to be a sphere of radius o, and 
that the acceleration of its attraction at distance r is then v being the transla¬ 
tional speed of a molecule at the surface of the body, it is evident that if 
1 
O 
a 
the molecules will describe hyperbolas, and will ultimately fly off to infinity, so that 
the Ijody will lose its atmosphere ; while if 
the atmosphere will not extend Ijeyond a concentric sphere whose radius r is 
given by 
If Waterstox’s hypothesis were correct it would have the following advantages :— 
(i.) It would enable an exact limit to be fixed for the temperature at vliich any 
gas could exist in the atnios])here of a planet. 
(ii.) It would enable an exact limit to be fixed for the height of that atmosphere, 
(iii.) It would account for the decrease of temperature of the atmosphere vith 
increase of height. 
Waterstox concludeil that the Moon was capalile of retaining an atmosphere of 
air })rovided that its temperature was not greater than 2405° F. 
* ‘ British Associiition Report,’ 1894, p. 100. 
t ‘ Trans. Roy. Dublin Soc.,’ vol. 6, p. 305. 
t ‘The Astrophysical Journal,’ vol. 11, 1. 
