14 SCIENCE PROGRESS 



d 



The operator -j is defined by 



di " Tt R + s Bd «S^ Sz 



and represents the part of the acceleration which is relative to 

 the moving Earth (the "accelerational" portion). 



The parts involving w arise from the rotation of the Earth 

 (the " rotational " portion). 



These fundamental equations can be simplified in certain 

 cases, but it should be noted that the pressure term must always 

 be important : if this were not the case each portion of the 

 fluid would pursue its path independently, without interference 

 due to impact with surrounding portions. This is never the 

 case in the air below a height of loo kilometres. 



The first stage of the classification is the division of all 

 winds into three main classes, namely : 



Class I. — " Eulerian " winds, where the rotational and 

 frictional terms are small compared with the acceleration 

 terms. The simplified equations were first found by Euler. 

 They are : 



du Zp 



di '^ ~ pRhe 

 dv _ hp 



dt pcbS(j} 



I Sp 

 o = - --f - g. 



p 02 



In these winds each particle of air moves with accelerated 

 velocity corresponding with the horizontal pressure-gradient, 

 as though friction and rotation of the axis were absent. 



Class IL — ^The " geostrophic " winds of Sir Napier Shaw, 

 where the rotational terms far exceed the accelerational and 

 frictional terms. The equations are : 



a I ^P 



2 (o u cos 6 — = — ^ 



pcb oo 

 I hp , 



It should be noted that -^ and ~- are simply the com- 



Koa d)0(p 



ponents of the horizontal pressure gradient. The equations 

 show that the velocity is at right angles to the pressure gradient, 



