42 EKMAN. ON DEAD-WATER. [NORW. POL. EXP. 



oscillations; and if the salt-water has a specific gravity of only l - 02 or l - 03, 

 one can produce even binodal and trinodal oscillations in the boundary, with- 

 out disturbing the upper surface. 



In a basin of larger dimensions, progressive waves, moving in the same 

 manner as ordinary surface waves, may be created in the boundary 1 . The 

 waves in the boundary produce a similar wave-motion in the surface, although 

 of considerably diminished amplitude; the surface has elevations immediately 

 above the depressions in the boundary and vice versa, as is illustrated by 

 Fig. 4, PI. VI. The former places, where the fresh-water layer is thickest, 

 may be called wave-crests, and the latter wave-hollows. The motion of 

 the water particles at the wave-crests and the wave-hollows, is represented 

 in the figure by small arrows, the large arrow denoting the direction of the 

 wave-motion. 



The relative height of the surface waves depends on the difference of 

 density between the two water-strata. If 



q = the density of the fresh-water, 



q -f- Aq = - - - - salt-water, 



I = the wave-length (from crest to crest), 



d = the depth of the fresh-water layer, 



D = - - - - salt-water layer, 



and if D is great compared with d, the ratio of the amplitudes, h and H, of 

 the surface-waves and of the boundary- waves is 



F = f •>-- « 



If the depth of the surface-layer is very small compared with the wave-length, 

 the ratio of the amplitudes is approximately 



H ~q~ (2} 



i. e., there is statical pressure-equilibrium in the salt water. If the depth of the 

 surface-layer is considerable, compared with the wave-length, the ratio h : JET is, 

 according to (1), smaller than Jq : q. 



For the sake of brevity, I shall call the upper water-layer fresh water, and the heavier 

 water below salt water, although, in reality, the two water-layers may consist of salt 

 water of different densities. Likewise by the surface we may always understand the 

 upper, free surface, and by the boundary, the common boundary of salt and fresh 

 water. 



