PAPER BY PROF. OBERBECK. 173 



ment and is equal to the product of a given factor and the velocity. 

 This factor can have different values according to the nature of the 

 earth's surface [and will be called the friction constant]. 



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

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

 equations for special cases there is still needed a series of assumptions. 



Let there be only one single vertical current of air present. The to- 

 tality of all the atmospheric movements depending upon this one verti- 

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

 current is variable or if the base 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 the 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 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 winds 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 velocity 

 of the earth's rotation divided by the friction constant. 



The deviation of the wind from the gradient is therefore 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. 



This result, following directly from the computation and at first sur- 

 prising, finds its confirmation in a variety of observations. For exam- 

 ple, in England we observe a deviation of 61° for land winds, but of 77° 

 for sea breezes. From this it follows that the friction on the land is 

 more than twice as great as on the sea. 



Conditions of pressure like those here considered frequently occur. 

 In the regions of the trade winds and monsoons they ordinarily prevail 

 either during the whole or about the halt of the year. 



The circular isobars to the consideration of which we now pass pro- 

 duce systems of wind that can be considered as the simplest types of 

 cyclones and anticyclones according as the pressure in the interior is 

 a minimum or maximum. We confine ourselves here to the considera- 

 tion of cyclones. 



As alreadv remarked cyclones are not conceivable without an ascend- 



