CHAPTER X. 



THE FORCED VERTICAL MOTION AT THE BOUNDING SURFACES. 



178. Hypsometric and Bathymetric Maps. Having now developed the mathe- 

 matical methods to be used, we can proceed to the accomplishment of the kinematic 

 diagnosis. Chapters 1 1- VI I gave the direct methods for working out, from the 

 observations, a complete diagnosis of the horizontal motion in atmosphere or hydro- 

 sphere. We shall now see how the correlated diagnosis of the vertical motion should 

 be worked out. 



The vertical motion begins at the bounding surfaces. Here the solenoidal 

 surface-condition, section 115 (), must be fulfilled; i. e., both velocity and specific 

 momentum must be tangential to the surface. The moving masses will be forced 

 up or down according as the motion in horizontal projection goes against the slope 

 or with it. We shall call the vertical motion which is produced in this way the 

 "forced" vertical motion, to distinguish it from the "free" vertical motion to be 

 considered in the next chapter. 



In order to investigate this forced vertical motion, we must have complete 

 topographic charts representing the configuration of the bounding surfaces; i. e., 

 we must have a complete representation of the topography of the world above as 

 well as below sea-level. We have referred to such charts before, using them to 

 define the spaces taken up by atmosphere and sea, and thus to give the extent of 

 the fields representing the atmospheric or oceanic states. But the main influence 

 which the bounding surfaces exert upon the internal structure of these fields comes 

 through the forced vertical motion which arises as a consequence of the boundary 

 condition. In view of this kinematic application we have worked out a representa- 

 tion of the topography of the world which is given on the first twenty-four sheets 

 of the collection of plates which accompanies this work. 



Our knowledge of the configuration of the bottom of the sea is still very 

 incomplete ; but fortunately most of the knowledge acquired has been made ac- 

 cessible by the bathy metrical map on a scale of 1 : 10 000 000 edited by the Prince 

 of Monaco.* This map represents the topography of the earth below sea-level on 

 16 plates in Mercator and 8 in polar projection. We have for the main part copied 

 our bathymetrical curves as well as the coast-lines from this chart, the most im- 

 portant changes being the following : Corrections and completion of the coast-lines 

 in the Arctic and Antarctic regions have been performed according to the results 

 of the well-known later Arctic and Antarctic expeditions. Changes in the course 

 of the bathymetrical lines have been introduced, for the northern Atlantic according 

 to Helland-Hansen and Nansen,f for the eastern Pacific according to the results 



* Carte Generate Bathymetrique des Oceans, dressee par l'ordre de S. A. S. le Prince de Monaco, 

 f B. Helland-Hansen and Fridtjof Nansen: The Norwegian Sea. Christiania, 1909. 



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