XVIII. 



ox THE VIBRATIONS OF AN ATMOSPHERE. 



By Lord Rayleigh. 



In order to introduce greater precision into our ideas respecting the 

 behavior of the earth's atmosphere, it seems advisable to solve any 

 problems that may present themselves, even though the search for sim- 

 plicity may lead us to stray rather far from the actual question. It is 

 proposed here to consider the case of an atmosphere composed of gas 

 which obeys Boyle's law, viz, such that the pressure is always propor- 

 tional to the density. And in the first instance we shall neglect the 

 curvature and rotation of the earth, supposing that the strata of equal 

 density are parallel planes perpendicular to the direction in which 

 gravity acts. 



Up, a be the equilibrium pressure and density at the height z, then 



'I^-^^^ <') 



and by Boyle's law, 



P=a?(y, (2) 



where a is the velocity of sound. Hence 



da _ (J 



and 



adz a^' ^^^ 



—qz 



G=a,e «', (4) 



where Co is the density at 2^=0. According to this law, as is well 

 known, there is no limit to the height of the atmosphere. 



Before proceeding further, let us pause for a moment to consider 

 how the density at various heights would be affected by a small change 

 of temperature, altering a for a', the whole quantity of air and there- 



*Froni the London, Efliubnnjh and Dublin rhil. Mag., Feb., 1890, tiftli series, vol. 

 XXIX, pp. 173-180. 



80 A 10 ^^^ 



