98 OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 



These equations are equivalent to the equations of the geostrophic wind 

 in the atmosphere. The velocities are expressed here either by the pres- 

 sure gradients, in which case the factor 10 enters because the pressure is 

 measured in decibars, or by the inclination of the isobaric surfaces (VI, 7). 

 It will be shown that the ocean currents can be obtained with sufficient 

 accuracy from these simple equations, and the problem of computing the 

 currents is reduced to a determination of the pressure gradients in the sea 

 or of the inclination of the isobaric surfaces. Thus, if the field of pressure 

 in the sea is known, the corresponding currents can also be approximately 

 known. 



The field of pressure can be fully represented by (1) a series of charts 

 showing isobars in standard level surfaces or (2) a series of charts show- 

 ing the topography of standard isobaric surfaces. 



The term level surface is understood to mean a surface that is every- 

 where normal to the acceleration of gravity — that is, a surface of constant 

 gravity potential. The work required for bringing a unit mass from one 

 level surface to another is independent of the path taken. If the unit 

 mass is moved the distance h along the plumb line, the work is IT = gh^ 

 where g is the acceleration of gravity. The numerical value of this work 

 depends upon the units used for length and time. If length is measured 

 in meters and time in seconds, the unit of work per unit mass is a dynamic 

 decimeter. Thus, differences in geopotentials are in the meter-ton-second 

 system (m.t.s.) measured in dynamic decimeters, but the dynamic meter 

 is the practical unit for measuring geopotential differences and is indicated 

 by the symbol D. The difference in geopotential between the sea surface 

 and a level surface at the geometrical depth, z, is therefore in dynamic 

 meters : 



D^H.f; 



= 10 fi 

 Jo g 



gdz, (VI, 14) 



and similarly the geometric depth of a given level surface is 



dD. (VI, 15) 



Since the acceleration of gravity varies with latitude and depth, the 

 geometric distance between level surfaces is variable, being greater at 

 the Equator than at the poles and being greater near the sea surface than 

 at great depths, but the ''dynamic distance" between two given level 

 surfaces is constant. When the pressure field is represented by the 

 topography of isobaric surfaces, it is of advantage to use ''dynamic" 

 contours — that is, to represent the lines of intersection between the 

 isobaric surfaces and a series of level surfaces. Charts of this character 

 will be called charts of geopotential topography. If the dynamic meter is 

 used as the unit of geopotential, the geopotential slope of an isobaric 



