134 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



time our knowledge is less detailed. When in spite of this further idealizations have 

 to be performed, great care should be taken, for small irregularities of the bottom 

 may influence the motion of the sea much more than corresponding irregularities 

 of the ground are able to influence the motion of the air.* 



When in the following we speak of the ground, we always mean the ideal 

 surface which is represented by our charts. We shall consider the wind-observations 

 obtained at the meteorological stations as representing the air-motion at this surface 

 itself. This will be perfectly legitimate from a kinematic point of view. But the 

 real removing of all irregularities would of course have great dynamic consequences. 

 We shall therefore be obliged later to consider this ideal surface as offering a frictional 

 resistance which a smooth surface would not offer in reality. 



180. The Motion in the Lowest Surface of Flow. The particles of the moving 

 medium which are in contact with the bounding surface will move tangential to it in 

 virtue of the solenoidal surface-condition. Therefore a hypsometric map represents 

 directly the topography of the lowest surface of flow in the atmosphere ; and in the 

 same manner a bathymetric map represents the topography of the lowest surface 

 of flow in the sea. 



When we shall represent the motion in this lowest surface of flow, we must 

 remember its exceedingly minute inclination. Even on our charts of moderately 

 idealized topography hardly any place will be found where contour-lines correspond- 

 ing to a difference of level of iooo meters approach each other as closely as i mm. 

 On a chart on a scale of i in ten millions, this will give an inclination which is smaller 

 than one in ten. The cosine of the angle of inclination will therefore be greater 

 than 0.995, and when we set this cosine equal to unity, we shall never make errors 

 as great as 0.5 per cent. Such errors will be insignificant compared with the errors 

 of observation. We need therefore make no difference between the numerical values 

 of the horizontal component of the motion and the resultant motion itself which is parallel 

 to the ground. 



For this reason we shall get a representation of the motion along the bounding 

 surface simply by drawing the lines of flow and the curves of equal intensity on 

 outline-maps which contain the contour-lines. The three sets of lines, contour-lines, 

 lines of flow (respective isogonal curves), and intensity-curves give a complete 

 representation of the surface of flow and of the motion in it (compare fig. 43 a and 

 % 45 a). 



181. Charts of Vertical Velocity at the Ground. From a chart containing these 

 three sets of lines we can easily draw a special chart of the vertical component of the 

 motion. When s is a line of flow in the atmosphere and z its height above sea-level 

 its angle of inclination will be 



( N dz 



{a) * = ds 



*Cf. the notes, pp. 58 and 59. 



