1 8 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Provisionally we have to do the reverse. The problem to compute the most 

 probable values of the gravity potential from the published heights is therefore of 

 some importance. The method will mainly consist in removing the corrections 

 originally introduced to pass from gravity potentials to heights, and will therefore 

 turn out somewhat differently according as the barometric, the leveling, or trigo- 

 nometric methods have been used. Further, it will differ with the different rules 

 for the reduction used in each of these methods. Thus different methods would 

 have to be used on different occasions, and the data determining the choice of 

 method would not always be at hand. In this state of confusion the normal reduc- 

 tion, which we have developed in the case of points in the free atmosphere (section 

 12), seems to be the most worthy of recommendation, also for the determination of 

 gravity potentials at points on the earth's surface. 



15. Maps of Dynamic Topography. When the gravity potential or the dy- 

 namic height is known for a sufficient number of points of the earth's surface we shall 

 be enabled to draw a new kind of topographic maps, representing not the geometric 

 but the dynamic heights of the country. The curves of these maps would be real 

 level curves, which would represent the coast-lines if the country were partially 

 submerged under the sea. The number of curves between two points would repre- 

 sent the amount of work per unit-mass which had to be performed against the 

 action of gravity, if a body should be moved from the one point to the other. The 

 maps would thus represent the height of a mountain, not by the vertical distance 

 of its summit from sea-level, but by the work required to reach the summit. They 

 would further directly give the amounts of potential energy possessed by the masses 

 of water stored in the lakes and would show how this potential is given up during 

 the flow of the water down the rivers. 



The motion of the air is restricted by the condition of tangential contact with 

 the earth's surface. The knowledge of the topography of the land is therefore 

 indispensable for the study of this motion. Both the geometric and the dynamic 

 topography must be known, but for evident reasons the dynamic topography is of 

 first importance. 



For the construction of these maps the close accordance of the common and the 

 dynamic meter is of great practical value. Especially if the maps should represent 

 large parts of the world on a moderate scale, there will be no visible difference 

 between the course of two curves, one of which represents the height of a certain 

 number of common meters, while the other represents the height of the same number 

 of dynamic meters. To make such maps practically useful in meteorology it will 

 be necessary to simplify the topography, smoothing out all the small irregularities. 

 These maps of idealized topography, drawn on a moderate scale, can therefore, 

 according to circumstances, be considered as representing both the geometric and 

 the dynamic topography. 



If the topography of the earth's surface is of importance for the motion of the 

 air, that of the bottom of the sea is of still higher importance for the motion of the 

 sea. As in the case of the air, the dynamic topography is of the greatest importance, 



