8 



KNOWLEDGE 



[January 1, 1890. 



trough to creat, was more tlinn twenty-four feet. He, 

 therefore, ventured upon the port paddle-box, wlikh was 

 seven foet higher, giving an eye elevation of thirty feet 

 three inches. This level was maintained during the 

 actual moments of observation, for the whole of tlie ship's 

 length (two hundred and twenty feet) was rlear within the 

 trough Qf the wave when the next following crest was 

 at its greatest apparent height, and the ship at these 

 moments was on an even keel. l'"rom this elevated position 

 quite one-half of the waves which overtook and passed the 

 ship were above the level of the observer's eye. Some- 

 times a crest extending in a ridge one hundred yards long 

 would be from 2" to H"" above the visible horizon, 

 which would give a height from trough to crest of more 

 than forty feet. Sometimes the crossing of two wave- 

 crests would send up a sharp peak of water ten or fifteen 

 feet higher than this, or the crest of a breaking wave 

 would shoot up to similar height. The average height 

 of the waves during the observations of March Tith was 

 thirty feet. On the Gth, at ten a.m., the wind having 

 lulled some hours previously. Dr. Scoresby took up his 

 usual post upon the saloon deck, from which he estimated 

 that the average height of the waves was still as much as 

 twenty-six feet. He then set himself to determine the 

 velocity of the waves, and their length from crest to crest. 

 The ship was travelling at nine knots ; the wave-crests 

 overtook the ship at intervals of sixteen and a half seconds, 

 and each wave travelled the distance of two hundred and 

 twenty feet, from stem to stern, in six seconds. The length 

 from stem to stern would appear, therefore, to have been 

 little more than one-third of the distance from crest to 

 crest. This proportion would give a wave-length of 

 six hundred and five feet, but a necessary correction for 

 the effect of the small angle between the direction of the 

 ship's motion and that of the following waves reduces this 

 to five hmidred and sixty feet for the true wave-length. 

 It follows, therefore, that five hundred and sixty feet of the 

 wave passed the stern of the vessel in sixteen and a half 

 seconds. But the ship dm-ing this time moved two hundred 

 and thirty feet in the direction of the wave's motion. The 

 true distance traversed by the wave in sixteen and a half 

 seconds was therefore seven hundred and ninety feet, which 

 gives a velocity of thirty-two and a half statute miles per 

 hour. 



During the height of the gale the forms of the waves 

 were less regular than after the wind had begun to subside ; 

 the greater waves were chequered with many minor or 

 secondary waves, and the greater waves did not for the 

 most part range themselves in long parallel series, as do the 

 rollers near shore when retarded by the shallowing water. 



Fig. 2 shows an Atlantic wave such as those described 

 by Dr. Scoresby, with a length of about six hundred feet 

 from crest to crest. The wave is travelling from right to 

 left, the right fiank of the crest being that which is exposed 

 to the wind. In judging of the relation of height to length 

 it must be remembered that the view is somewhat fore- 

 shortened. The figure is fi-om a sketch made at sea by 

 Mr. H. Ilohday, who has kindly placed the drawing at our 

 disposal. 



In order to understand waves we must study, not only 

 the motion of the wave, i.e., the steady onward rush of the 

 wave-crest, but also the motion of a particle of surface- 

 water situated in the path of the wave. Some information 

 as to the motion of the water-particle may be gained by 

 watching from a pier the movements of a light floating 

 body outside the line of breakers. When a wave-crest 

 approaches, the body moves upwards and forwards ; then, 

 at the crest of the wave, it is for a moment moving 

 forwards only ; when the crest passes it moves first down- 



wards and forwards, then downwards and backwards, 

 until, in the trough of the wave, the body is again in its 

 first position and is for a moment moving horizontally 

 backwards, i.e., seawards, before rising again as the next 

 wave-crest approaches. More exact observation, agreeing 

 with mathematical calculation, shows that the motion of 

 the particle is, in deep water, almost perfectly circular, the 

 diameter of the circle being in the direction in which the 

 wave is travelling. The particle of water moves with 

 uniform velocity, and the time of one complete swing of 

 the particle round its circle is eq\ial (as follows from what 

 has been already said) to the interval between the passage 

 of succeeding wave -crests. The vertical distance through 

 which the particle moves is equal to the height from 

 trough to crest. Again, from the fact that the motion is 

 circular, it follows that the particle moves through a 

 horizontal distance equal to the height of the wave from 

 trough to crest, mil (be it well understood) equal to the 

 wave-length, or distance from crest to crest. 



The velocity of the particle, it must be remembered, is 

 by no means the velocity of the wave. The particle takes 

 the same time to move uniformly round its small circle 

 that a wave-crest takes to pass over a whole wave-length — 

 say ten times the distance, even in a very rough sea. 



The more rapidly a wave-crest travels the greater will 

 be the distance which separates it from the next wave-crest. 

 This connection between velocity and wave-length is an 

 important property of water waves, which run by the 

 action of gravity. In sound waves, on the other hand, 

 the velocity is independent of wave-length. In order 

 to explain the connection between the wave-length and the 

 velocity of water waves, we cannot do better than adopt 

 the artifice employed by Newton in the second book of the 

 " Principia." He represents the water as contained in a 

 U-tube (see Fig. 3, taken from an edition of 1729). If the 



M 



L N 



Fig. 3. — " If water ascend and descend alternately in the erected legs 

 KL, MN of a canal or pipe ; and a pendulum be constructed, 

 whose length between the jjoint of suspension and the centre of 

 oscillation is equal to half the length of the water in the canal ; 

 I sav, that the water will ascend and descend in the same times 

 in which the pendulum oscillates." — Newton's " Principia," 

 Book II. 



tube be agitated, the level of the water oscillates up and 

 down in the two limbs. The level in one limb being E F, 

 and in the other G H, the uiiijht of so much of the left- 

 hand column as is above E A moves the whole of the 

 liquid. This column of liquid is a falling body, but not a 

 body falling freely. Its descent is retarded by the fact 

 that it has to overcome the inertia of the remainder of the 

 liquid. The oscillations of the liquid in a tube of given 

 length are executed in equal times whether they be great 

 or small, just as are the decreasing oscillations of any 

 pendulum. The time of an oscillation depends upon the 

 length of the whole column of water, in the same way that 

 the time of swing of a pendulum depends upon its length. 

 If the length of the pendulum be doubled the time of one 

 oscillation is increased fourfold ; if the length be tripled 

 the time of oscillation is increased nine times ; and so on, 

 the length of the pendulum being proportional to the square 



