On the Damping of Long Waves. 205 



The formula (p. 709) which the authors quote and use in 

 their calculations is not quite accurate. It should read : — 



J~ 1+ 3 a 45 a 2 945 a s ' 



Schuster gave f 73/53760) (aP/a 3 ) as the fourth term in the 

 expansion of f u when xja is small ; hut I rind by using 

 the Euler-Maclaurin sum formula that the approximate 

 formulae for f\ and / agree, at least as far as the fifth term 

 which is (17/14 175)(# 4 /a 4 ). 



I am, 

 Faraday House, Yours faithfully, 



Nov. 15, 1909. Alexander 1 i essell* 



XX. On the Damping of Long Waves in a. Rectangular 

 Trough. By Egbert A. Houstoun, Ph.l)., D.Sc, Lecturer- 

 on Physical Optics in the University of Glasgow*. 



UXDEB the above title I recently published a paper in 

 this Journal f, in which some experiments on the 

 damping of long waves in a rectangular trough were de- 

 scribed. The observed logarithmic decrement was as a rule 

 more than twice as great as my calculated value, and 1 

 suggested that the difference was mainly due to a film 

 forming on the surface of the water. 



Since then Mr. W. J. Harrison % has attempted to show 

 that the discrepancy is due to the sides. I have delayed 

 replying in the hopes of making further experiment.-, but as 

 that now appear- out of the question, I take this opportunity 

 of stating my views on Mr. Harrison's paper. 



Mr. Harrison finds it impossible to attack the problem in 

 the ordinary way, using the general equations of motion for 

 a viscous fluid and writing down the condition of no motion 

 at a fixed boundary. It was because this method was not 

 possible that I confined myself to long waves. As my trough 

 measured .152*4: cm. by 20*3 cm., and the depths used varied 

 from 1 to 10 cm., this approximation seemed justifiable. 

 Mr. Harrison, on the contrary, abandons the usual boundary 

 conditions, and assumes in their place that the sides are 

 perfectly smooth. On solving and approximating he then 



* Communicated bv the Author. 



f Phil. Mag. [6! vol. xvii. pp. 154-104. 



X Phil. Mag. [6] toI. xviii. pp. 483-491. 



