584 Dr. Harold Jeffreys on 



it would have proved possible to interpolate at all in such a 

 way as to secure even approximate agreement between the 

 two estimates of k obtained for any depth, and perhaps as it 

 is a considerably different distribution of turbulence would 

 satisfy the data equally well. It will be noted that k is 

 comparatively small near the surface, increases downwards 

 to 100 metres, and then diminishes again. Now the results 

 obtained for oceanic currents suggest that in mid-ocean, so 

 far down as they extend, the turbulence is comparatively 

 constant. Their vertical extent is of order (k/co)*, according 

 to the theory already developed, which in this case is about 

 1-2 metres. For the greater turbulence in mid- ocean the 

 vertical extent of the currents is, of course, greater. The 

 variation in turbulence found does not therefore invalidate 

 the assumption of its constancy in the theory of ocean 

 currents; but if the results just obtained are substantially 

 correct they require an explanation. It is possible that near 

 the Sognefjord the surface water is largely river water, and 

 therefore lighter than that below. The greater density 

 below would have a stabilising effect, tending to reduce 

 turbulence in the surface layers. The Norwegian Oyster- 

 basins, described by Murray and Hjort, afford an extreme 

 example of such an effect ; the low temperature above 

 hinders the heat absorbed in the salt water below from being' 

 conveyed away, with the result that the deep water there is 

 several degrees hotter than elsewhere. If turbulence can 

 be largely attributed to wave-motion, the way it dies down 

 at great depths is readily accounted for ; for wave-motion 

 diminishes as the depth increases, and at a depth equal to 

 the wave-length it has practically ceased. This suggestion 

 is confirmed by the fact that the depth where turbulence 

 shows marked diminution is actually of the same order of 

 magnitude as the length of Atlantic waves. 



III. Friction on the Ocean Bottom. 



The ocean currents driven by the trade winds are seen 

 from the discussion in the first section of this paper to have 

 a comparatively small vertical range. Even if the eddy- 

 viscosity is as high as 1000 cm. 2 /sec. and the latitude as low 

 as 10°, the depth through which the current is considerable^ 

 being of order (k/w)i, is only about 4000 centimetres, an 

 insignificant fraction of the depth of the ocean. If the 

 theory that the main ocean currents are caused by the skin 

 friction of the wind on the surface is correct, they must 

 therefore be practically confined to the upper layers. The 



