314 



Forces and their Relationship to the Structure of the Ocean 



ture R) gives a force V^IR away from the centre of curvature; since for an angular 

 velocity Q,V =^ QR the centrifugal force for unit mass will be Q^R. 



Fig. 133. Cross-section through an ocean. A and B are two oceanographic stations. 

 Full lines: isobaric surfaces (p = const.); Dashed lines: surfaces of equal dynamic depth 

 (D = const.); The pressure surface p„ appears in station A at the dynamic depth Da, in 

 station B at the dynamic depth D^ ; L denotes the horizontal distance of both stations 



(schematically). 



(a) All observations on the rotating Earth are usually made with reference to a co- 

 ordinate system rigidly connected with the Earth and therefore rotating with the 

 Earth, although in the classical mechanical sense this is not a permissible reference 

 system. Such a system should not follow the rotation of the Earth, but would for 

 example have to be assumed at rest relative to the fixstars (absolute system). If the 

 basic principles of Galileo-Newton mechanics are used and applied to the rotating 

 Earth, deviations will appear which are due solely to the movement of the reference 

 system imposed by the rotating Earth — a fact which we simply have to accept. These 

 deviations have the character of two apparent forces which are additional to those 

 forces present in the absolute system. 



One of these forces depends only on the geographical location ; this is the ordinary 

 centrifugal force due to the rotation of the Earth ojV (oj is the angular velocity of 

 rotation of the Earth — one total revolution per one sidereal day = (27r)/(86,164 sec) = 

 7-29 X 10~^ sec~^, r is the distance from the axis of rotation of the particle under 

 consideration). Since this additional force acts both on a stationary or on a moving 

 mass particle it can be combined with the gravitational force and becomes in this way 

 part of the force of gravity. 



The second force, however, depends both on the geographical location and on the 

 velocity of the mass particle set in motion on the Earth. This is denoted to CorioUs 

 force and as a vector acting on unit mass has the form 



g = 2[b tu]. 



(X.4) 



Its absolute value is 



C = le| == 2Kcosin(t) to) 



and it is directed at right angles to the direction of the velocity vector b and to the 

 angular vector of the Earth's rotation to, which is in the direction of the Earth's axis, 

 so that I to| = to. It therefore acts at right angles to the tangent to the path of movement 



