Long Waves in a Rectangular Trough. 



161 



h. 



Observed 

 period. 



T - 



Difference. 



*T 2 

 2ir ' 



cms. 

 •5 



sees. 

 1671 



sees. 

 13-76 



sees. 

 295 



sees. 

 1-45 



1-0 



10-57 



9-75 



•82 



•45 



20 



7'18~ 



6-89 



•29 



•23 



3-0 



5-79 



5-62 



•17 



•14 



5-0 



4-425 



4-35 



■07 



•09 



7-0 



3-70 



3-68 



•02 



•02 



100 



3085 



3-08 



•00 



•01 



The agreement is not good, but it ought to be stated that 

 (18) is hardly applicable to such small values of h as l'O or 

 0*5 cms. 



If we calculate T by the general formula for surface-waves 

 instead of by the formula for long waves, no difference is 

 made, except in the case of h = 10 cms. The value for the 

 latter becomes 3*10 sees. 



The calming effect of oil on a stormy sea is explained by 

 supposing that the oil floats as a membrane on the surface of 

 the water and hampers its motion by offering resistance to 

 extension. The surface- film here seemed to be easily exten- 

 sible. To explain the dissipation of energy it is necessary to 

 assume that the membrane opposes the extension with a force 

 proportional to the velocity. The tangential stress on the 

 surface of the water is proportional to and opposed to the 

 velocity there. 



We thus have to solve (7) with the conditions 

 3Z 



=£— = — en, z = h. 

 0~ 



We find 



Z = 0, 



0. 



Z= [cosh kh -cosh k(h— '*)] - - [sinh hz— sinh hh + sinh k(h— z)] 



Neglecting the term in which n 2 is a factor, we find that 

 (12) still holds ; but in place of (13) we have 

 2c 



la 2 — ghm?+-^gm*} 



gm\l-c7i) + co* , _ Zcgm* I _ 



Phil. Mag. S. 6. Vol. 17. No. 97. Jan. 1909. 



M 



