Lord Bayleigh : H ydrodynamical Notes. 187 



Hence correct to a 4 , 



K.E v =Ja 2 (l + «> (19) 



Again, for the potential energy 



Y.E. = y^fcLc = lcj.c(U 2 + fa' 1 ) ; 



or since £/ = l — a 2 , 



P.E. = ia 2 (l + i« 2 > (20) 



The kinetic energy thus exceeds the potential energy, when 

 a 4 is retained. 



Tide Races. 



It is, I believe, generally recognised that seas are apt to 

 be exceptionally heavy when the tide runs against the wind. 

 An obvious explanation may be founded upon the fact that 

 the relative motion of air and water is then greater than if the 

 latter were not running, but it seems doubtful whether this 

 explanation is adequate. 



It has occurred to me that the cause may be rather in the 

 motion of the stream relatively to itself, e. g. in the more 

 rapid movement of the upper strata. JStokes's theory of the 

 highest possible wave shows that in non-rotating water the 

 angle at the crest is 120° and the height only moderate. 

 In such waves the surface strata have a mean motion 

 forwards. On the other hand, in Gerstner and Rankine's 

 waves the fluid particles retain a mean position, but here 

 there is rotation of such a character that (in the absence of 

 waves) the surface strata have a relative motion backwards, 

 i.e. against the direction of propagation*. It seems pos- 

 sible that waves moving against the tide may approximate 

 more or less to the Gerstner type and thus be capable of 

 acquiring a greater height and a sharper angle than would 

 otherwise be expected. Needless to say, it is the steepness 

 of waves, rather than their mere height, which is a source of 

 inconvenience and even danger to small craft. 



The above is nothing more than a suggestion. I do not 

 know of any detailed account of the special character of these 

 waves, on which perhaps a better opinion might be formed. 



Rotational Fluid Motion in a Corner. 



The motion of incompressible inviscid fluid is here supposed 

 to take place in two dimensions and to be bounded by two 

 fixed planes meeting at an angle a. If there is no rotation, 



* Lamb's Hydrodynamics, § 247. 



