300 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



riation and one that varies with locality and with the condition as to 

 cloudiness. It is a question whether the variations of pressure thence 

 resulting are so small iu comparison with the regular variations that 

 they are not very noticeable iu the averages. 



The neglect of the friction and the vertical motion of the air in our 

 last calculations, the assumption of a constant mean temperature for 

 the whole mass of air, and the assumption that for equal latitudes we 

 have equally large ranges of temperature and pressure, allow us to 

 make only the most general application to the case of nature. A more 

 perfect calculatiou, taking account of the actual distribution of laud 

 and water, would be as difficult to execute as would be the computa- 

 tion of the rise and fall of the tides for an ocean of irregulir shape, or 

 even for one bouuded by meridians. 



I. MOVEMENT OF THE AIR IN VERTICAL PLANES. 



Notation, u = horizontal velocity along the axis of x ; w = vertical 

 velocity positive upwards along the axis of z; ju= density; p = pressure 

 T = absolute temperature ; t = time ; g = the acceleration of gravity 

 B = a constant. 



We imagine the earth as an infinite plane above which, iu alJ east 

 west vertical planes, the movement of the air occurs in a similar manner 

 For slight velocities that allow us to neglect terms in the equations of 

 motiou that are of the second degree in u and w, these equations, to 

 gether with the equations of continuity and of elasticity are as follows : * 



du _ _ 1 dp 



dt fX clX 



dw _ 1 dp 



dt '' '' ix dz ) (1) 



dt + dx- + dz 

 p = B pi T. 



If the atmosphere is at rest thenp, ju, T, have the value p , /^ , T 01 

 which are functions of the altitude only, 



1 dp g 



p dz ' ' BT 



1 dfA _g_ l^aZT, > ( 2 ) 



Mo dz - BT ~ T dz 



p = B /u T Q 





[* The expression "Zustands-Gleichung der Oase," which is applied in Germany to 

 the equation p v = RT has, I believe, no single equivalent in ordinary English sci- 

 entific phraseology unless we adopt the very inelegant historical title Bojle-Mari- 

 otte-Gaylussac- Charles-Law. It is the law connecting density, temperature, vol- 

 ume, or pressure, and expresses the simple fact that the substance is truly gaseous. 

 But the characteristic of a gas is its elasticity, and the equation gives the elastic 

 pressure. — C. A.] 



