378 On the Reduction in the Height of Waves 



On the Reduction in the Height of Waves after Passing into 

 Harbours. In a Letter to Professor Jameson. By 

 Thomas Stevenson, Esq., Civil Engineer. 



Edinburgh, 84 George Street, 

 16th March 1853. 



Dear Sir, — In your number for October last I gave an 

 approximate formula for the law of increase in the height of 

 waves due to their distance from the windward shore; and I 

 have now to trouble you with another formula relating to the 

 subject of harbours. 



The great object of constructing harbours is, by lowering 

 the height of the waves to preserve the tranquillity of the 

 area of water which is included by the piers, and this pro- 

 perty is variously possessed by harbours of dhTerent forms, 

 and depends much upon the shape of the entrance and the 

 relation between the direction of its opening and that of the 

 line of maximum exposure. It may here be observed, that 

 when there is an inner harbour, or stilling basin, the ellipti- 

 cal form seems to me the most promising. If one focus be 

 supposed to be on the middle line of the entrance, and to 

 coincide with the point from which the waves radiate, as 

 from a centre, when they expand into the interior of the 

 harbour ; and if the other focus is situated inland of high- 

 water mark, the waves will all tend to reassemble at the 

 landward focus, and on their way will be destroyed by 

 breaking on the beach. For it is a well-known property of 

 the ellipse, that, if two radii vectores be drawn from the two 

 foci to any point in the curve, they will make equal angles 

 with the tangent at that point, and as the angles of incidence 

 and reflection of a wave from any obstacle are practically 

 equal, each wave will obviously be concentrated at the focus 

 opposite to that from which it emanated. 



Irrespective of the considerations mentioned above, the 

 reductive power of a harbour will be dependent on the rela- 

 tion between the breadth and depth of the entrance, and the 

 form and capacity of the area within. Where the piers are 

 high enough to screen the inner area from the wind, where 



