5S8 NORMAN LOCKYER LECTURE 



In a simple gas, at a uniform temperature, the velocities of the mole- 

 cules are distributed according to a law, discovered by Maxwell, which he 

 first announced at the meeting of the British Association in 1859. The 

 mean velocity of the molecules increases with the temperature, being 

 proportional to \/T ; the number of fast-moving molecules with velocities 

 much in excess of the mean velocity falls off very rapidly with increase of 

 velocity. In a mixture of gases, the average energy of each type of mole- 

 cule is the same ; the lighter the molecules the faster they move in the mean. 



There are definite proportions of molecules with speeds of 10, 20 or 

 100 times the mean speed, so that there must be a progressive loss of fast 

 moving molecules from the upper layers of the atmosphere of any planet. 

 The rate at which this loss takes place depends upon the relative magni- 

 tudes of the velocity of escape and of the mean velocity of the molecules. 

 The rates of escape were calculated by Jeans. He found that if the 

 velocity of escape is four times the mean molecular velocity, the atmosphere 

 would be practically completely lost in fifty thousand years ; if the velocity 

 of escape is four and a half times the mean molecular velocity, the atmo- 

 sphere would be lost in thirty million years ; whilst if the velocity of escape 

 is five times the mean molecular velocity, twenty-five thousand million 

 years would be required for the loss to be almost complete. The age of 

 the planets is believed to be of the order of three or four thousand million 

 years, so that if the velocity of escape is as great as five times the mean 

 molecular velocity of hydrogen the atmosphere will be practically immune 

 from loss. 



The mean molecular velocity of hydrogen at 0° C is 1-84 km. /sec. 

 At the observed maximum temperature of the Moon, 120° C, it is 

 2-21 km. /sec. The escape velocity from the Moon is only 2-4 km./sec, 

 so that an atmosphere of hydrogen would be lost from the Moon almost 

 instantly. Similarly for Mercury ; the temperature of the sunlit face is 

 found by measurement to be about 400° c. and at this temperature the 

 mean molecular velocity of hydrogen is 2-9 km./sec, whilst the escape 

 velocity from Mercury is 3-6 km./sec. ; a hydrogen atmosphere would 

 again be lost almost instantly. It appears that the Moon, if it had never 

 been hotter than at present, would have lost water-vapour, nitrogen, and 

 oxygen completely, but would have retained carbon dioxide and heavier 

 gases ; Mercury, under the same supposition, would have lost almost all 

 its water-vapour and nitrogen and most of its oxygen, but would have 

 retained heavier gases to a large extent. The rates of loss are likely to be 

 underestimated because, as we shall see later, it is probable that when 

 these bodies were young and had temperatures much higher than they 

 now have, the loss of atmosphere during the period of rapid cooling must 

 have been considerable. It is certain that the Moon has no atmosphere 

 now and this is fully in accordance with expectations. The evidence of 

 an atmosphere on Mercury is not fully conclusive, but faint and transient 

 shadings on the planet have been interpreted by Antoniadi as indications 

 of an atmosphere. The observations are naturally difficult, but the con- 

 clusion of Antoniadi that Mercury may possess a very tenuous atmosphere 

 is not in conflict with the theoretical evidence. It is certain, howevef, 

 that most of the original atmosphere must have been lost. 



Coming to the Earth, the escape velocity is 11 -2 km./sec, which is 



