TBANSACTIONS OF SECTION A. 683 



degree of permanence of the atmospheres of different celestial bodies, the author has 

 calcidated what proportion of the molecules of oxygen and hydrogen at different 

 temperatures have a sufficiently great speed to fly off" from the surfaces of, and 

 never return to, the Moon, Mars, and the Earth. The corresponding results for the 

 Sun are also given, not, hovpever, at its surface, but at the Earth's distance from 

 the Sun's centre, where the critical speed is, of course, V2 x the speed of the 

 Earth's orbital motion. 



The numbers, which are given in Table I., p. 684, represent, in each case, the 

 average number of molecules, among which there is o>ie molecule whose speed 

 exceeds the critical amount. Thus, for oxygen at temperature 0° C. rather over 

 one molecule in every three billwn is moving fast enough to fly off" permanently 

 from the Moon, and only one in every 2'3 x 10^'-^ is moving fast enough to escape 

 from the Earth's atmosphere, while the Sun's attraction, even at the distance of 

 the Earth, prevents more than one in every 2 x 10^"''" from escaping. 



Now it is generally stated that at the Earth's surface there are somewhere 

 about 18 X 10'^ molecules in a cubic centimetre of air. If we suppose the Moon's 

 surface were invested with an atmosphere, say of oxygen, of this density, every 

 cubic centimetre would contain, roughly, about six million molecules moving with 

 suihcient speed to carry them away from the Moon. But the velocity requisite to 

 overcome the Earth's attraction would only be attained by one molecule in a 

 volume of 1'3 x ]0^'° cubic centimetres, that is, in a globe of radius about 2x10^'^ 

 kilometres. In our Earth's atmosphere the acquisition of the requisite speed by 

 a single molecule would only occur once at rare intervals, and would probably be 

 far too rare to affect the permanency of the Earth's atmosphere, even during the 

 long periods of time through which we are wont to trace the history of the solar 

 system. 



In the case of Mars the corresponding figure shows that an atmosphere con- 

 taining oxygen is practically permanent at all ordinary temperatures, but that 

 such an atmosphere could not remain on the planet if its temperature were as high 

 as 819° C. 



If the Earth possessed an atmosphere of hydrogen at temperature 0° C, con- 

 taining 10'^ molecules per cubic centimetre, there would be one molecule in every 

 60 cubic centimetres whose velocity would be sufficient to carry it away perma- 

 nently. Remembering that the Earth at one time was much hotter than at 

 present, we see that the absence of hydrogen from the Earth's atmosphere (except 

 in the form of water) is easily accounted for. In the case of the Sun, a hydrogen 

 atmosphere would be permanent at 0° 0., even as far off as the Earth, as is shown 

 by the number 2-7 x 10^"'. At one-tenth of the Earth's distance from the Sun wo 

 should obtain the same number with an absolute temperature ten times as high, 

 i.e., 2730° absolute, or 2457° C, and so on. A considerably higher temperature 

 would, however, be consistent with peronanency. Thus the kinetic theory quite 

 explains the existence of hydrogen in the Sun's atmosphere at high temperatures. 



The present theory seems to preclude the possibility of the Moon ever having 

 had an atmosphere. If the Moon were formerly much hotter than at present the 

 proportion of gaseous molecules tending to ffy off" would be greater, and such a 

 loss would be exactly the reverse of the process which the nebular hypothesis 

 assumes to be taking place in the solar system. 



But it would seem probable that this flying off of gaseous molecules is not an 

 essential condition in explaining the Moon's absence of atmosphere by means of the 

 kinetic theory. It is only necessary to assume the existence of a distribution of 

 matter of excessive tenuity pervading interplanetary space in order to account for 

 a gradual increase taking place in the atmospheres of all the planets, and such an 

 assumption, taken in conjunction with the kinetic theory, is quite compatible with 

 the absence of a,nj perceptible atmosphere surrounding the Moon, and of any per- 

 ceptible resistance to the motions of the Moon and planets. 



The kinetic theory enables us to compare the densities at different points of a 

 mass of gas in equilibrium under such fixed central forces as the attractions of 

 the celestial bodies. If we apply the theory to the system consisting of the Sim, 

 Moon, and Earth, we shall find the relative densities given in Table II., the density 



