DYNAMIC METEOROLOGY. 381 



On tbe other hand, attention must be given to the rotation of the earth 

 on its axis, since we are only interested in the i)aths of the winds on the 

 rotating" earth. This influence can be taken account of if we imagine at 

 <'very point of the mass of air a force a])plied whi(5h is perpendicular to 

 tlu' momentary direction of motion and is Cipial 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 departure of the path towards the right-hand side. Since 

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

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

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

 Ihermore, it depends on the nature of the earth's surface, whether sea 

 or lauds, plains or wooded mountains. For this computation Guldberg 

 ami iMolm have made a convenient assumption in that they introduce the 

 lVi(;tion as a force whi(;h opposes the movenuMit and is ecpial to the i)ro- 

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

 values a(;cording to the nature of the earth's surface. 



All these forces are to be introduced into the general eiiuafions 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 oidy 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 strengthof the ascending 

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

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

 second case it is movable. 



If, on the other hand, the ascending current of air retains its strength 

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

 long time retain their position then tiie wind system 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 assuini)tions. 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 eacli 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) Tlie 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. 



Tlie (leviation of the wind from the gradient is therefor*^ greater in 

 ])roi)ortion as friction is smallei'. if the eartli's surface were perfee^tly 

 .smooth llie wiiid would blow in tlic direction of the isQbiu\s, 



