98 



KNOWLEDGE. 



[May, 1901. 



° iS 



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-^ K 





breakers. The average interval between succeeding 

 breakers was 19.35 seconds, from which it follows that 

 the average wave length in dijep water must have been 

 1918 feet. This is calculated from the formula 



Length of wave in deep water in feet = square of 

 tlie period in seconds x 5'123. 



This formula is derived theoretically from the known 

 behaviour of liquids imder the action of gravity, and 

 has been verified to some extent by observation. Its 

 substantial accuracy when applied to a swell of no great 

 steepness travelling in a fairly calm atmosphere is, I 

 believe, beyond question. The corresponding velocity 

 of the wave is 68.7 statute miles per hour in deep 

 water, which is slightly less than the velocity assigned 

 by Capt. Wilson-Barker to a storm of hurricane force. 

 Sir George Gabriel Stokes has observed breakers with 

 a uniform period of 17 seconds; and I find that a 

 period of 15 seconds is not uncommon with westerly 

 swells on the south coast of England. A 15 second 

 period corresponds to a wave length in deep water of 

 1153 feet. Thus the average interval between the 

 wave crests observed during a storm at sea seldom ex- 

 ceeds 600 feet, although the period of breakers frequently 

 indicates a wave length twice as great. 



I do not know whether attention has been drawn to 

 this anomaly, and I have not met with any published 

 facts which explain it. I propose the following ex- 

 planation : — The swell frequently arrives before the 

 storm ; subsequently when the wind gets up the sea 

 becomes covered with short steep waves ; these 

 grow in length, and gradually the swell be- 

 comes less conspicuous, until at last it is nearly or 

 quite invisible in presence of the storm waves (say be- 

 tween 300 and 600 feet in wavel length). The natural 

 inference would be that the amplitude of the swell 

 must be small as compared with that of the storm wave. 

 This, however, is not necessarily the case, as an examina^ 

 tion of the diagram will show. In looking at this it 

 must be remembered that when waves are observed at 

 sea we have not a fixed platform to observe from, nor 

 can their profile be traced against any fixed structure. 

 The ship rises and falls with the long swell, and the 

 observer has very little notion where the line of mean 

 sea level is ; and for this reason I have not drawn any 

 datum line in the diagram. What he does notice is 

 whether the water siu'face at any place is convex 

 or concave, and, more particularly he notices the 

 advance of the convexities of crests, f Now it is 

 obvious that even though the long swell have an ampli- 

 tude equal to that of the shorter storm wave yet its 

 curvature is less, and therefore it is less potent than the 

 latter in detei'mining the positions of crests, i.e., marked 

 convexities of surface. 



To assume that during storms there is a long swell (say 

 not less than 1100 feet) of an amplitude equal to that 

 of the storm wave would, however, be going somewhat 

 beyond what the facts seem to warrant, but that such 

 invisible swells may have a considerable amplitude 

 seems to me quite possible from what we know of the 

 swell remaining after a storm, of the distances which 

 these swells traverse, and of the size of the breakers 

 which they yield, and finally of the variation of the 

 amplitude of successive waves in a storm. Fig. 1 shows 

 a portion of the actual wave surface due to the simul- 

 taneous existence of two undulations with length 

 600 feet, amplitude 30 feet, and length 1150 feet, ampli- 

 tvide 20 feet. Commencing on the left with the two 

 undidations at the same phase, at mean sea level, and 

 subsiding, there arc shown in the figure five 



t The curvature at the cres); being sharper than in the troughs, a 

 ditTereuce which. howeviM". T have not shown in the ilingrani. 



