December 8, 1893.] 



SCIENCE. 



311 



SCIENCE: 



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THE ATMOSPHERES OF THE MOON, PLANETS AND 



SUN. 



BY G. H. BRYAN, M. A., CAMBKIDSE, ENGLAND. 



It was only a week or two before reading Professor 

 Liveing's interesting communication in Science that I had 

 made some calculations which led me to adopt the same 

 theory which he has advocated. The object of my inves- 

 tigations was, in fact, to show that we could not regard 

 the atmospheres of the different members of the solar sys- 

 tem as isolated masses of gas, from which molecules 

 might fly off if their si^eeds were to become sufficiently 

 great, but that, to account for the very existence of plane- 

 tary atmosi)heres at all, it would be necessary to adopt 

 the hyijothesis of an atmosphere of excessive tenuity per- 

 vading both interplanetary and interstellar space. 



It is unfortunate that Mr. Howard did not apply the 

 principle of conservation of energy to the arguments con- 

 tained in his letter in the issue of April 28. Had he done 

 so he would have realized that the question as to whether 

 a molecule will permanently leave the atmosphere of the 

 Moon or a planet depends only on its speed, irrespective 

 of direction, and does APt in any way depend on whether 

 the motion takes place in a vertical direction. In fact, if 

 the kinetic energy of a molecule is greater than the work 

 required to be done against the planet's attraction in or- 

 der to remove the molecule to an infinite distance, the 

 molecule will describe a hyperbola, and will fly off never 

 to return again, no matter what be its direction of motion, 

 provided that it does not come into collision with any 

 other molecule or with the planet itself. 



Again, the speed requii-ed to leave the Earth is about 

 five times as great as that required to leave the Moon; 

 but this is not because the earth's attraction is five times 

 as great as the Moon's, but because the Earth's potential 

 is about twenty-five times as great as the Moon's, conse- 

 quently, in order to leave the Earth, a particle would re- 

 quire to have twenty-five times the kinetic energy, or five 

 times the speed, which it would require to leave the Moon. 



According to the well-known "error law" of distribu- 

 tion of speed among the molecules of a gas, which forms 

 the basis of calculations connected with the kinetic the- 

 orj', there must always be .some molecules moving with 

 sufficiently great sjjeeds to overcome the attraction of any 

 body, however powerful, and .<ome whose speed is too 

 small to enable them to escape from the attraction of any 

 body, however feeb e. On this assumption no planet can 

 have an absolutely permanent atmosphere, and no planet 



or satellite which has ever had an atmosj'herc could get 

 rid of that atmosphere entirely. If, however, the propor- 

 tion of molecules which escape is relatively exceedingly 

 small, any changes which occur in the nature of the at- 

 mosphere of the planet will take place so slowly that 

 countless ages will have to elapse before they make them- 

 selves felt. In order, therefore, to test the relative de- 

 gree of permanence of the atmospheres of different celes- 

 tial bodies, I have calculated what proportion of the mole- 

 cules of oxygen and hydrogen at different temperatures 

 have a sufficiently great speed to fly oft' from the surfaces 

 of, and never return to, the Moon, Mars and the Earth. I 

 have also given the corresponding results for the Sun, 

 not, however, at its surface, but at the Earth's distance 

 from the Sun's centre, where the critical speed is, of 

 course, square root of two times the speed of the Earth's 

 orbital motion. 



The numbers, which are given in Table 1 below, repre- 

 sent in each case the average number of molecules, among 

 which there is one molecule whose speed exceeds the crit- 

 ical amount. Thus, for oxygen at temperature 0°C, 

 rather over one molecule in every three billion is moving 

 fast enough to fly off permanently from the Moon, and 

 only one in every 2 3x10''"'' is moving fast enough to es- 

 cape from the Earth's atmosphere, while the Sun's attrac- 

 tion, even at the distance of the Earth, prevents more 

 than one in every 2x10""" from escaping. 



When we arrive at such vast numbers as this, it might 

 be reasonable to object that we have pushed the kinetic 

 theory a great deal further than it will go. The assump- 

 tions made in many proofs of the "error" law of distribu- 

 tion certainly preclude its application to high speeds that 

 are so rarely attained. Still there is no physical limit to the 

 speed which any individual molecule might acquire in the 

 course of colliding with other molecules. As Professor 

 Liveing has pointed out, all that would be necessary 

 would be a sufficiently long run of collisions, in each of 

 which the line of impact happened to be nearly perpen- 

 dicular to the direction in which the molecule in question 

 was previously moving, so that each impinging molecule 

 should transfer the greater portion of its energy to that 

 one molecule. 



And theory j)oints to the conclusion that whenever 

 there is any law of permanent distribution of the mole- 

 cules of a gas, that law must be the "error" law. Hence 

 the calculations may be reasonably expected to give a cor- 

 rect estimate of the proportion of molecules whose speed 

 exceeds the critical speed, provided that the mass of gas 

 under consideration is so large that the total number of 

 such molecules is great, however small their relative pro- 

 portion maj' be. Thus we are at least justified in regard- 

 ing the figures as affording indications of the relative 

 permanency or otherwise of the gaseous envelopes sur- 

 rounding dift'erent bodies of the solar system. 



One great difficulty presented by the theory is that oe 

 taking account of the differences of temperature of the 

 atmosjsheres of the different bodies. There seems to be 

 good reason for believing that the Moon's temperaturf 

 may fall below — 200'^C , in which case only one molecule 

 in 7x10'" will be able to escape. And generallj' the 

 larger members of the solar system ai e the hotter, and 

 this would cause them to part with their atmospheres more 

 readily in jjroportion than they would if all the bodies 

 were at one common temperature. If the absolute tem- 

 2)eratures of different bodies were proportional to their 

 gravitation potentials, the proportion of molecules jjos- 

 sessing the speed requisite to carry them off would be 

 the same for aJl. This condition would require the 

 Earth's atmosphere to have an absolute temjoerature 

 roughly twenty-five times as high as that of the Moon's. 

 Even supposing this were the case, it does not necessarily 



