The Geophysical Structure of the Sea 303 



co-ordinate the potential value gh at the point under consideration (as a positive 

 quantity). In the first case, all points v^^ith the same third co-ordinate will lie on sur- 

 faces of equal geometric depth and in the second case the points of equal third co- 

 ordinate gh will lie on a level surface. The second system of co-ordinates is much 

 more suitable for problems of the statics and dynamics of the ocean, since at every 

 point in such a co-ordinate system the total force of gravity acts in the third direction ; 

 there is no component of gravity acting along the other two. As g is approximately 

 10 m sec-2 the potential gh will change by one unit if the unit mass is lowered by 

 about 1/10 m. that means when the depth is reduced about by 1/10 m. Bjerknes 

 (1910, 1912) has denoted this unit potential the dynamic decimeter (1 dyn.dm). 

 Multiples and fractions of it are the dynamical metre ( 1 dyn .m) or the dynamical centimetre 

 (1 dyn. cm), respectively. By the introduction of this potential quantity as the third 

 co-ordinate the level surfaces become surfaces of equal dynamic depth. 



The dynamic depth has the dimensions [g cm^ sec^^]. The most practical unit of 

 the dynamic depth is the dynamic metre. If /; is expressed in metres then the dynamic 

 depth D in dynamic metres is 



Z) = f^, (IX.3) 



and at this point there is a geopotential 



= -10Z>. (IX.4) 



Since the gravitational acceleration g changes with depth according to (IX. 2) the 

 difference between two dynamic depths in the ocean is given by the relation 



1 



g dh. (IX.5) 



hi 



10 

 As a first approximation (IX. 3) thus gives 



D = 0-98/2 and /; = 1-02Z). (IX.6) 



The numerical difference between a dynamic metre and a geometrical metre is thus 

 about 2%. Tables for converting one unit into the other according to more accurate 

 formulae have been given by Bjerknes and co-workers (1912, 1913). 



3. The Field of Mass 



The mass field is given by the distribution of the density p or its reciprocal, the spe- 

 cific volume a. In the sea it can be represented in a suitable way by surfaces of equal 

 density {isopycnic surfaces) or by surfaces of equal specific volume (isosteric surfaces). 

 The latter are used preferably in oceanography. The field of specific volume a^^, „ can 

 be regarded as made up of two separate fields. The first of these agg, o, p represents the 

 mass field of a homogeneous sea at 0°C and 35%o S (standard ocean) ; it is in this way 

 completely defined and invariable. The second is the field of the specific volume 

 anomaly S and this set of surfaces of equal anomaly 6 is quite sufficient for the charac- 

 terization of the mass field in the total oceanic space. 



In a vertical section of the mass distribution the isosteres and the isopycnals appear 

 as curved or wave-form lines deviating only slightly from the horizontal. A large 



