44 EKMAN. ON DEAD-WATER. [norw. pol. EXP. 



sion of energy is plotted vertically. The faint curve is valid for waves in 

 shallow water, as well as for boundary-waves when the two water-layers 

 have the same thickness. If the two water-layers are of different thickness, 

 the ratio of transmission of energy becomes somewhat altered, and is repre- 

 sented by the heavy curve, if one of the water-layers — say the salt water — 

 is by comparison, infinitely deep. In either case the curves show that for 

 waves moving with not more than half the maximum wave-velocity, the ratio 

 of transmission of energy is almost exactly V2, just as in deep water. Only 

 when the velocity of the waves is further increased, do their laws of motion 

 begin to be influenced by the shallowness of the water-layers. 



The pressure in the water is, of course, altered by the wave-motion, but 

 differently in the salt and in the fresh water-layer, p may be the pressure 

 when the water-layers are at rest, and p -\- dp when there are waves. Then 

 Jp is positive at the wave-crests and negative at the wave-hollows, in the 

 fresh-water layer, and vice versa in the salt-water (see Fig 4, PI. VI). In 

 the fresh-water layer 



/ 2%-d) _ 2My-d) \ 



4p = %gh'q [el + e l J , 



and in the salt water, when D is infinite, 



dp = — \ gli {q + Jq) el y e 1 — e l J , 



where y is the height of the particular point considered, above the mean level 

 of the boundary {y negative in the salt water), and h' is the height of the 

 water-surface above its mean level, in the same vertical as the considered 

 point. The other symbols have the same signification as before. 



If the wave-length is very great compared with the depth of the surface- 

 layer and with the distance between the boundary and the considered points 



in the water-layers, — =- and — p are small quantities. Then the formulae 



above take the following simple forms; in the fresh-water layer, 



jp = gh'q (5) 



and in the salt-water 



Jp=-gh'(q + Jq)^£ (6) 



