162 Dr. R. A. Houstoun on the Damping of 



In the coefficient of tanh M, gmVi may be put equal to o- 2 

 since the whole term is small. 'Tanh kh is as usual =1, and 

 the 1/cosh hk term may be neglected as it is very small. 



Substituting from (12) in (20) and writing 



a = p + i/c 

 we get 



P 

 The new term is equal to 



p*U2pK-ghrn*-i2 C ^+gm*\/ J^(l-t) = 0. . (21) 



•o cv 



i2 n 



Hence 



The new surface condition is therefore capable of accounting 

 for the rate of damping. It does not affect the period. 



For h = 5 cms. and a fresh surface c is about 7, i. e., for 

 unit velocity the retarding force/unit area is -^ dyne. We 

 can find the effect of a tangential drag of this magnitude on 

 free waves on deep water very readily by the method of 

 Lamb's ' Hydrodynamics,' 3rd edition, § 331. 



It is only necessary to add a new term — ^r to the dissi- 

 pation function. Then using the notation of that section we 

 have instead of equation (8) 



(\pte**\ = -2/i*»cV- ^ 2 cV. 



Therefore 



<z=oi e 28pJ 



K ~ X 2 7/oX* 



For X = 100 cms., the first term =8 . 10 -5 and the second 

 4 . 10 -3 ; hence there cannot be a tangential drag of this 

 magnitude on free waves on deep water. 



The damping of the waves in the trough seems in some 

 measure to be due to the film being attached to the sides. 

 According to the theory, if the width of the trough were 

 diminished by half, k at the centre should not be altered 

 appreciably. I had a wooden partition made which could be 



