114 Ratio of the Length and Height of Sea Waves. 



half shapes, viz., i, c, d, e, and i', c', d' e'. The area &, d', h is 

 now equal to area d\ e\ g\ and i', d is the reduced height of 

 the wave, the reduction taking place from both sides of the 

 mean level. The actual quantity of subsidence is measured 

 by the difference between the areas e, i, c, d and e', i', c', d\ 

 or perhaps by the difference of d, h, c and d\ h, c', the 

 change which occurs while the lamina of semi-viscous fluid 

 is sinking into flatness. Whilst the exact expression for the 

 profile curve is undecided — and it is to the determination of 

 this that every inquiry on this subject at present tends — I 

 am not aware so far as my own imperfect knowledge 

 extends of any means of stating such difference: that is, of 

 expressing the actual change in the ratio of height to length 

 in precise terms of the diminution in height (viz., % c 

 -i'. C). 



But whatever be the precise function mathematically, the 

 cause suggested will, I think, sufficiently account for all 

 observed circumstances ; and it will explain also the peculiar 

 difference noted between the easterly and westerly swell on 

 the southern Australian coast in respect of the ratio of 

 height to length. In those parts the south-east winds are 

 known to extend only, and therefore to act on the swell 

 only^ a few hundred miles from the shore; the waves 

 therefore having their genesis within this distance have not 

 space to reach a lengthy decline, or, perhaps, even full 

 maturity. Whereas the south-west winds start from the 

 Pole, and the swell arising therefrom has an unbroken fetch 

 for attainment of the highest possible magnitude, and 

 thousands of miles for the slow process of decline in which 

 it gradually increases its length and diminishes its height. 

 The westerly swell therefore reaches the Australian shore in 

 its declining stage, when the length is great and the height 

 small; the easterly, in its mature or steep stage, when the 

 waves are therefore higher, shorter, and more active, being 

 urged or having been more recently urged by the wind. 



By the fetch of a particular wave at any moment is, of 

 course, meant the distance it has travelled from its genesis 

 as an initial wavelet until then. Let A (Fig. 5) be the 

 point of commencement of the wave (and thence in most 

 cases of the wind also), and A B its path or fetch when it is 

 at the point B. If from points a, h, c, &c., in the fetch 

 ordinates be erected representing the strength or velocity of 

 the wind when the wave was passing those respective 



