84 THE MECHANICS OF THE EARTh's ATMOSPHERE. 



wherein q indicates a constant peculiar to the gas and independent of 

 6 and ^>. Similarly we also have 



and therefore within a stratum of air having a constant 6 and fl we 

 have, according to equations (3a) and {3h), 



1 PJ 

 p^ci.6'7r = -^y~^ ^3^^ 



The very slight deviation of the earth from a spherical form allows 

 us to simplify the computation on the one hand by regarding the 

 earth's surface as a sphere, but on the other hand by giving the 

 potential P an addition, the effect of which is that for the normal 

 velocity of rotation cj,, of the earth, its spherical surface becomes a 

 level surface. To this end we put 



P=— ^. +-,&;(, W^ 



I Where G = normal force of gravity: r=distance from center of 

 gravity" to point or stratum in the actual atmosphere.] 



This gives the component in the direction of x, of the forces acting 

 upon the unit of mass, 



?P_ Gx 



and, for the component in the direction of p, 



-p dP G.p , 



Jp r-* 



If to the latter the centrifugal force -\-cj--ft is also added, there re- 

 mains only one force on the rotating earth and which is directed normal 

 to the spherical surface. Thus the spherical surface becomes the level 

 surface of the combined potential force and centrifugal force, as indeed 

 the surface of the earth really is. 



Thus our equation (3e) becomes 



<I-^-^=-l'^+^-]oj.:'^r+C .... (3/) 



- The function tt which is some power of the pressure jt; with positive 

 exponent, increases and diminishes with p, and remains unchanged 

 when 7? remains unchanged, so that we can determine the direction of 

 the changes ol the pressure easily by the changes of tt. 



Within a uniform stratum and with unchanged r, that is to say, for 





