94 OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 



-7- = 212 sin ipvy, 



dvy 

 dt 



(VI, 2) 



= — 2fi sin (pVx. 



These equations define motion in a circle of radius r, where 



V 



r = 



212 sin <p 



(VI, 3) 



V being the horizontal velocity. 

 The time of rotation in the in- 

 ertia circle is T = 27r/212 sin <p, 

 which is called ''one half pen- 

 dulum day." Motion of this 

 type has been observed in the 

 sea. The most striking exam- 

 ple is found in a report by 

 Gustafson and Kullenberg, in 

 which are described the results 

 of 162 hours' continuous rec- 

 ord of currents in the Baltic. 

 The measurements were under- 

 taken between the coast of 

 Sweden and the island of Got- 

 land, in a locality where the 

 depth to the bottom was a 

 little over 100 m. On August 

 17, 1933, when the measure- 

 ments began, a well-defined 

 stratification of the water was 

 found. From the surface to a 

 depth of about 24 m the den- 

 sity increased rapidly with 

 depth. Below 30 m a slow in- 

 crease continued toward the 

 bottom. The current meter, 

 a Pettersson photographic re- 

 cording meter, was suspended at a depth of 14 m below the surface, and 

 thus would record the motion of the upper, homogeneous water. 



Gustafson and Kullenberg have represented the results of the records 

 in the form of a ''progressive vector diagram" (fig. 22), which is prepared 

 by successive graphical addition of the hourly displacements as computed 

 from the average hourly velocities. Every twelfth hour is marked on the 

 curve by a short line. The curve represents the path taken by a water 



Fig, 22. Rotating currents of period one 

 half pendulum day observed in the Baltic and 

 represented by a progressive vector diagram 

 for the period, August 17 to August 24, 1933, 

 and by a central vector diagram between G'' 

 and 20'' on August 21 (according to Gustaf- 

 son and Kullenberg). 



