DYNAMIC METEOROLOGY. 381 



On the otlier liand, atteution 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 inHuence can be taken account of if we imagine at 

 every point of the mass of air a force aj^plied which is perpendicular to 

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

 double angular velocity of the earth, the sine of the latitude, and the 

 velocity of the point. On the northern hemisphere this influence causes 

 a continuous dei)arture of the path towards the right-hand side. Since 

 the movement takes place directly on the earth's surface the direct in- 

 fluence of that surface, namely, the friction, remains to be considered. 

 Its influence diminishes with the distance from the earth's surface. Fur- 

 thermore, it depends on the nature of the eartirs surface, whether sea 

 or lands, plains or wooded mountains. For this com])utation Guldberg 

 and IMohn have made a convenient assumption in that they introduce the 

 friction as a force which opposes the movement and is equal to the pro- 

 duct of a given factor and the velocity. This factor can have different 

 values according to the nature of the earth's surface. 



All these forces are to be introduced into the general equations of 

 motion of the air. If however one desires solutions of these general 

 e(]uations for special cases there is still needed a series of assumptions. 



Let there be ouly one single vertical current of air present. The 

 totality of all the atmospheric movements depending upon this one ver- 

 tical current is called a wind system. If the strength of the ascending 

 current is variable or if the basis itself changes its place then the wind 

 system is variable. In the tirst case the system stands still, in the 

 second case it is movable. 



If, on the other hand, theascendingcurrentof air retains its strength 

 and location without change, or, which is the same, if the isobars for a 

 long time retain their position then the wind sj'stem is invariable. 



It is evident that the last case is by far the most simple. We will 

 therefore begin with its consideration. 



In order to execute the calculation the location of the isobars must be 

 known. Even in this respect also in a preliminary way one must limit 

 himself at first by simple assumptions. Let the isobars be either par- 

 allel straight lines or concentric circles. 



In the first case the computation leads to the following simple results : 



(1) The parallel isobars are equally distant from each other. The 

 gradient is therefore everywhere of equal magnitude. 



(2) The paths of the wind consist of parallel straight lines. The 

 strength of the wind has everywhere the same value. 



(3) The direction of the wind forms an angle with the gradient whose 

 tangent is equal to the quotient of the factor arising from the earth's 

 rotation divided by the friction-constant. 



The deviation of the wind from the gradient is tlierefore greater in 

 proportion as friction is smaller. If the earth's surface were perfectly 

 smooth the wind would blow in the direction of the isobars. 



