MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 



I«I 



the motion. We shall in the following chapter consider some special 

 cases of interior friction. However, the absence of observations on 

 the variation of the velocity with the altitude prevents the applica- 

 tion of the exact theory to the winds in general. We shall consider 

 friction as an exterior force acting along the surface of the earth. 

 Denoting the components of the friction by X t and Y v we write 

 (see §7): 



X, = — k u ) 



i .... (5) 



Y t k v J 



in which k denotes the coefficient of friction. 



By introducing the preceding values of the components of the 

 exterior and interior forces and noticing that the velocities and the 

 density are functions of the four variables x, y, z and /, the equations 

 of motion are written as follows: 



1 dp ,, „ du du du du 



- — = X + X 1 — — — u — v — w 

 p dx dt dx dy dz 



1 dp T . .. dv dv dv dv 



= Y + Y l — ~ — u — — v - - — w 

 p dy dt dx dy dz 



1 dp 



p dz 



„ dw dw dw dw 



-- Z — g — — u — — v — — w — 



dt dx dy dz 



d A + u d P- + v d E- + w d A + p A^Q . 



dt dx dy dz 



. .(6) 



(7) 



The trajectory of a particle of air is determined by the equations 



dx 



= t 

 dt 



dy 



dt 



dz 



dt 



v \ 



= w 



(8) 



§20. Classification of the systems of wind 



Each disturbance of the eqtiilibrium of the atmosphere produces 

 a motion of the air or what we in general call a system of winds. 

 Considering the forces which act during the motion, we divide the 



