316 



Forces and their Relationship to the Structure of the Ocean 



radius of this circle follows from the condition that the forces acting on the moving 

 mass particle must balance each other (centrifugal force = Coriolis force). 



so that 



J/2 



'r 



R 



2a>Ksin ^, 

 V 



(X.6) 



2ca sin (j) 



The term "circle of inertia" has been chosen to indicate that relative to the movement 

 of the rotating Earth this circular movement in a certain sense replaces the linear 

 inertia of absolute motion. The radius of the circle of inertia is a function of the latitude 

 and the velocity. Table 112 gives values for this functional relationship. 



Table 1 1 2. Radius of inertia circle as a function of V and </> 

 (V in mm sec-^, cm sec-^, m sec-^: R in m, 10m, km units) 



The time required for one complete rotation on the circle of inertia {inertia period) 

 is given by 



IttR it 1 2 sidereal hours 



T = 



CO sin (f) 



sin <f> 



If the period of rotation of the plane of oscillation of a Foucault pendulum is a pen- 

 dulum day = {2tt)1{o) sin </•), the period of rotation of the circle of inertia will be a 

 half pendulum day whatever the value of the velocity V. Table 1 1 2a shows the time re- 

 quired for one revolution on the inertia circle (the inertia period) at different latitudes 

 (from 5 to 5 degrees). 



Table 112a. The period of rotation of the inertia circle {inertia period). 



In lower latitudes the period may be several days, in middle latitudes 24 h and at 

 high latitudes half a day; here, since it has a similar period as the daily and half-daily 



