Internal Waves 551 



system are great. Then the term (2wsin</>) 2 in the equation (XVI. 39) becomes 

 large compared with the second term and the period of the free oscillation 

 of the system on the rotating earth becomes 



Ti = ^— = ¥- = h pendulum day . (XVI.41) 



2(osm(p sinr/> ' 



On a rotating earth the period of a free oscillation of a stationary boundary 

 surface and their related periodical currents approaches the periods of the 

 inertia oscillation provided the dimensions of the oscillating system are 

 great (see vol. I). But in general the period T of the free oscillation of the 

 system is 



T= /r Te ^ . (XVI. 42) 



■l i 



A 



1 + .. 



1 r 



The larger T r is compared to 7), the more T approaches the period of the 

 inertia oscillations T : . Two numerical examples shall illustrate these con- 

 ditions: 



(1) The values in the Baltic (Kattegat) (latitude 57°): q-q' = 2xl0" 3 , 

 h' = 25 m and h = 35 m give as result for the longest oscillation T r = 3-75/ 

 (/ in metres). Assuming T i :T r = 01, one obtains / = 136 km. In a basin 

 of these dimensions the difference between the periods of the free oscillations 

 and the inertia oscillations would be less than 1 %. A disturbance developing 

 motion in the inertia circle would probably start oscillations of the boundary 

 surface. 



(2) As a numerical example for the open ocean (latitude 45°): q—q' 

 = 1 x 10~ 3 , q = 10273, h = 1000 m, g' = 10263, h' = 100 m and / = 150 km, 

 and we obtain for T = 1664 h, and for the inertia period T ( = 16-97 h. The 

 period of the free oscillations in the case of a non-rotating earth would be 

 T r = 89-5 h. 



In the case of deeper basins or basins in lower latitudes the dimensions 

 of the basins must be quite large if the period of the free oscillation is to 

 approach the period of the inertia oscillations. It must be expected that we will 

 find frequently the inertia period in the variations of the oceanographic 

 properties and currents in the open ocean, because this inertia period is so 

 close to the period of the free oscillation of the system. The foregoing de- 

 duction deals only with a two-layer system, but Defant's general result is 

 undoubtedly valid for water-masses where the density increase is continuous. 



A typical example is offered by the oceanographic conditions prevailing 

 at the anchor station of the "Altair" on the northern edge of the main axis of 

 the Gulf Stream north of the Azores (44°33'N., 38°58'W., from 16 to 20 June 

 1938, depth 1110-2390 m), which lasted for 90 h. The current measurements 

 up to 800 m depth showed that the entire water-mass was influenced by the 



