396 Prof. H. Lamb on Waves due 



infinitely narrow area. To get anything like a representation 

 of real conditions we must suppose the force to be diffused 

 to some extent. Mathematically, this is most easily attained 

 by introducing a factor e~ kb under the integral signs in (2), 

 and making the consequent changes in the subsequent 

 formulae. The effect is that the pressure is now distributed 

 on each side of a central line according to the law 



7T(h 2 + X 2 ) 



(79) 



the intensity falling to half the maximum when .'6*= ±b. 



In this way we find, for a disturbance advancing along 

 the upper face, 



ge~ 2Klb 



Rl =(?{p-t.(p'-p)e-*<sy (80) 



whilst for a disturbance travelling along the interface 



np -2K l h-2K x b 



2 p'-p2{c-XJ 2 )g{p + ij>'-p)e-^y ' ^°° J 



7. The name "dead-water" is given to a phenomenon 

 occasionally observed in Norwegian fiords, and other similar 

 localities, where the sea is covered by a stratum of fresh 

 water brought down by rivers. It consists in an abnormal 

 resistance experienced by slowly sailing vessels, which 

 disappears if the speed can be raised above a certain limit. 

 The vessel appears to be gripped by some mysterious power, 

 and cannot be properly handled. 



The matter was brought by Nansen to the notice of 

 Y. Bjerknes, who attributed the phenomenon to the inter- 

 facial waves generated at the common boundary of the fresh 

 and salt water. At his suggestion the question was taken 

 up by Ekman, who has devoted a long memoir * to the 

 subject. This includes descriptive accounts from various 



* ' Scientific Results of the Norwegian North Polar Expedition,' 

 1893-96, pt. 15. (Christiania, 1904.) 



