OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 95 



particle, if it is assumed that the observed motion is characteristic of a 

 considerably extended water mass. 



The curve shows a general motion toward the northwest and later 

 toward the north; superimposed upon this is a turning motion to the right, 

 the amplitude of which first increases and later decreases. This rotation 

 to the right {cum sole) is brought out by means of the inset central vector 

 diagram in which the observed currents between August 21, 6^ and 20^ 

 are represented. The end points of the vectors fall nearly on a circle, as 

 should be expected if the rotation is a phenomenon of inertia, but the 

 center of the circle is displaced to the north-northwest, owing to the char- 

 acter of the main motion. 



The period of one rotation was 14 hours, which corresponds closely to 

 one half pendulum day, the length of which in the latitude of observation 

 is 14 08"°; on an average the periodic motion was nearly in a circle. It is 

 possible that this superimposed motion can be ascribed to the effect of 

 wind squalls, and that the gradual reduction of the radius of the circle 

 of inertia is due either to frictional influence or to a spreading of the 

 original disturbance. According to a theoretical examination by Defant, 

 it is probable that inertia oscillations of this nature are associated with 

 internal waves. 



Simplified Equations of Motion. When the general equations of 

 motion are applied to the ocean, certain simplifications can be made. 

 The vertical acceleration and the frictional term R^, can always be 

 neglected. Similarly, the term depending upon the vertical component 

 of the deflecting force can be neglected. The third equation of motion is 

 therefore reduced to the hydrostatic equation, and the equations can be 

 written in the following form, introducing the abbreviations X = 212 sin (^, 

 Vx = dvx/dt, and Vy = dvy/dt and measuring the pressure in decihars (p. 10) : 



dv 

 Vx = \Vy - 10a -^ + aRx, 

 dx 



Vy = -\Vx- 10a ^ + aRy, (VI, 4) 



dy 



oz 



At perfect hydrostatic equilibrium the isobaric surfaces coincide with 

 level surfaces, but this is no longer the case if motion exists. At any time 

 an isobaric surface is defined by 



From equations (VI, 5) and (VI, 4) one obtains the equation for the 

 isobaric surfaces in a moving system : 



dp = {\pvy -\- Rx — pVx)dx -j- ( — Xp^x + Ry — pVy)dy 



+ gpdz = 0. (VI, 6) 



