26 MOLECULAR MOTION AND ITS ENERGY 13 



molecules of the air would disperse into space in conse- 

 quence of their speed. 



A body thrown vertically upward with a speed of 485 

 metres per second would rise to a height of 12,000 metres 

 and then fall back again. A molecule of air, therefore, 

 which moves at the. earth's surface with a calculated mean 

 speed of 485 metres per second, cannot in consequence of 

 this rise higher than 12,000 metres, and remains, therefore, 

 within the much higher atmosphere. Just as little can 

 molecules in higher layers leave the atmosphere, as these 

 layers are colder, and the molecular speed is therefore smaller. 



To entirely escape from the earth without returning, a 

 molecule of air must have at the earth's surface a speed of 

 at least 11,000 metres per second, which is twenty times 

 larger than the mean speed at 0; but we are in a posi- 

 tion l to assume that such a speed can never occur or, at 

 most, only very exceptionally. 



On the moon, whose diameter is four times less than 

 that of the earth, the acceleration of gravity is nearly six 

 times less than on the earth ; consequently a molecule 

 of air with the speed 485 metres per second could rise 

 to a height of 74 kilometres, and to escape entirely from 

 the moon it would require a speed of only 2,400 metres per 

 second. From this we may conclude that if the moon 

 possesses an atmosphere at its general low temperature 

 it can in any case have only a very thin one. 2 



14. Temperature 



The values found for the mean molecular speed are those 

 at C., and it has already been pointed out in 9 that this 

 speed increases with the temperature. To determine in 

 what ratio this increase takes place we have to compare the 

 formula which theoretically expresses the pressure with the 

 laws regarding the pressure that have been deduced from 



1 Compare 24, 26, 28. 



2 Bull,Liveing, and Bryan, Meteorologische Zeitsckrift, xi. 1894, p. 76. 

 G. Johnstone Stoney, Astrophys. Journ. 1898, vii. p. 25 ; Journ. de P/w/s. [3] 

 vii. p. 528. 



