172 THE MECHANICS OF THE EARTh's ATMOSPHERE. 



mass of air will again sink down ; in the reverse case it will rise liigher. 

 Tbe air in these cases is then in stable or unstable equilibrium respec- 

 tively. In the latter case any vertical movement initiated by some acci- 

 dental disturbance will not again disappear, but rapidly assume in- 

 creasing dimensions. The current will also continue uniform for a long 

 time. 



This is the explanation first given by the mathematician Reye,* of 

 Stiasburg, of the ascending air currents in the whirlwinds of the tropics. 



The winds of our (temperate) zone also presup[)Ose such ascending 

 currents whose origin must have been quite similar. The ascending 

 current is in general restricted to a definite region that we can desig- 

 nate as the base. Since the ascending current consists of warmer air, 

 therefore above its base the i)ressure sinks. A barometric depression 

 is inaugurated there. The pressure increases from this region outward 

 in all directions. The isobars therefore surround the region of ascend- 

 ing atmospheric currents in closed curves. At greater heights the up- 

 per cooled air flows away to one side and in other regions gives occasion 

 to descending currents of air. At the earth's surface itself, the air 

 flows towards the depression; its influence thus extends over an area 

 much greater than that of the base. If we neglect the curvature of 

 the earth's surface we find over this larger area only simple horizontal 

 movements. Mathematical computations should now reveal to us the 

 nature of such horizontal movements. To this end all the causes of 

 motion, or the forces that come into consideration, are first to be col- 

 lected. 



The diflerences of pressure have already been several times spoken 

 of. We take as t lie measure of these diflerences, the gradient which gives 

 for any point the direction and amount of the greatest change in pres- 

 sure. In horizontal movements the eflect of gravity can be omitted. 



On the other baud attention must be given to the rotation of the 

 earth on its axis, since we are only interested in the paths of the winds 

 on the rotating earth. This influence can be taken account of if we 

 imagine at every point of the mass of air a force applied which is per- 

 pendicular to the momentary direction of motion and is equal to the 

 product of the double angular velocity of the earth by the sine of the 

 latitude and by the velocity of the point. In the Northern Hemisphere 

 this influence causes a continuous departure of the path towards the 

 right hand side. Since the movement takes place directly on the earth's 

 surface the direct influence of that surface, namely the friction, remains 

 to be considered. Its influence diminishes with the distance from the 

 earth's surface. Furthermore it depends on the nature of the earth's 

 surface, whether sea or land, plains or woorfed mountains. For this 

 computation Guldberg and Mohn have made a convenient assumption 

 in that they introduce the friction as a force which opposes tbe move- 



*[This explanation is oF course much older than Reye (1864), who was preceded by 

 Espy aud Henry in the United States and by Wm. Thomsou iu Great Britain. C. A.J 



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