!73 



WAVES AND TIDES. 



WAVES AND TIDES. 



J74 



cental oscillations by which the water is alternately compressed and 

 ;lilated, let the particles be conceived to ascend and descend alternately 

 in vertical lines, that is, in lines parallel to a! a a'", which is supposed 

 to be perpendicular to a k. Now, at a given instant let the surface of 

 the water have, in a vertical plane, the form abed, &c-, and let the 

 force of ascent cause the particles in the line a b m to be raised up to 

 the line ' 11 m in a portion of time represented by T, that force becom- 

 ing less as it is farther from a horizontally, and ceasing at m. At this 

 place the force of descent commencing, the particles in the line m cdn 

 fall simultaneously with the rise of the particles in abm, and at the 

 end of the same time T, they occupy the line mc'd'n. Here the force 

 of ascent acts, and the particles in n efp at the end of the same time 

 occupy the line ne'f'p, and so on. Thus at the end of the time T the 

 surface of the water has assumed the form a'b'c'd', &c. After this time 

 the force of descent on the particles in the line a'm' causes those par- 

 ticles to fall vertically, during a time equal to T, into the line am' ; at 

 m.' that force ceases, and the force of ascent raises the particles in 

 m'b'c'n' vertically into the line m'k"m', and so on ; thus, at the end of 

 the time 2T from the given instant the surface of the water has the 

 form ab"cd", &c. In like manner, at the end of. the time 3 T the forces 

 of descent and ascent will have brought the particles into the line 

 a.'"b'<J"d', &c. ; and at the end of the time 4 T the particles will be again 

 in the line abed. &c. : so that in this time every particle of fluid has 

 made one complete vibration vertically, as tm'aa"a, and within the 

 name time the top of the wave has assumed successively the positions 

 ''. ' f, y'"> * The horizontal distance from d to A is called the length 

 of a wave ; let it be represented by L, and let ^ express the time 4 T in 



which the summit of a wave has passed from d to h ; then - is called 



the velocity of the wave. On observing the characters of experimental 

 waves in troughs with glass sides, it ia found that, by the combinations 

 of the horizontal and vertical vibrations, the particles of water describe 

 the peripheries of circles or ellipses. In the upper parts of the curves, 

 neau the tops of the waves, the particles move with their greatest 

 velocities in the direction in which the wave is advancing ; in the lower 

 part*, near the bottoms of the waves, they are moving with their 

 greatest velocities backwards ; and at the extremities of the horizontal 

 diameters, about the level of the water's surface when at rest, the 

 motion is almost wholly vertical. 



The varying attraction of the sun or moon on the particles of water 

 in the ocean is alone sufficient to produce the perturbations by which 

 waves are formed ; and if it be assumed that the solid nucleus 

 of the earth is covered entirely with water, both nucleus and water 

 being originally spherical, those perturbations will bring the surface of 

 the water to a spheroidal form, the longer axis being in the direction 

 of a line joining the centres of the earth and luminary ; there will 

 consequently exist, at the same instant, two great waves whose summits 

 are at a distance from one another equal to half the circumference of 

 the earth. But the motion of the water in the tide-wave is totally 

 unlike that in an ordinary surface-wave such as the wind produces ; 

 and while the latter, even in the most violent storms, agitates the sea 

 to a very trifling depth, the tide-wave affects the whole depth of the 

 ocean equally, from the bottom to the surface. 



Very little attention to the phenomena of the tides suffices to show 

 that, in situations where the recurrences of high-water are nearly 

 regular, the greatest elevation of the water takes place at intervals of 

 about 12 hours 25 minutes, and the greatest depressions at the like 

 intervals of time from each other; each greatest depression taking 

 place about 6 hours 12 minutes after the instant of greatest elevation. 

 Now the interval between two successive culminations of the moon on 

 the same side of the geographical meridian of any place varies from 

 about 24 hours 40 minutes to 25 hours ; and thus the intervals between 

 the times of high-tide have evidently a connection with the diurnal 

 revolution of the moon ; moreover, the occurrence of high-water at any 

 place is observed to have a dependence, on the position of the moon 

 with respect to the meridian of the place ; at a few ports it coincides 

 with the time that the moon is on meridian, but in genera! it takes 

 place some time before or after the culmination. The position of the 

 moon at the time ia, however, subject to certain variations even at the 

 same port ; and it differs considerably at diS'erent places. The eleva- 

 tions also of the water with respect to the mean level differ ; in some 

 places, during about half the year, the high-tide which occurs when 

 the moon is above the horizon is greater than that which occurs when 

 the moon is below, and during the other half-year the phenomenon is 

 reversed. In every place, at about the times of new and full moon, 

 the high-tides attain their greatest elevation ; and at about the times 

 of the quadratures, the least : the former are called spring-tidee, and the 

 latter neap-tide*. 



In bays and harbours, the time of high-water coincides with that ai 

 which the current ceases to flow, but this is not the case with the seas 

 which communicate at both extremities with the ocean. For, if it be 

 imagined that a tide-wave flows in at one of the extremities, this will 

 cause an elevation of the waters ; but the waters which are passing oil 

 at the opposite extremity cause, at the same time, a depression, or, at 

 least, a diminution of that elevation ; the surface, therefore, must be 

 the highest when the current flows with equal rapidity at both ex- 

 tremities, and not at the moment preceding the turn of the ti'l". 



When the stream continues to flow up for three hours after it is high- 

 water, it is said to make tide and half-tide ; if it continues to flow 

 during one hour and a half, it ia said to make tide and quarter-tide, 

 and so on. Near the shores of the British Channel, probably in con- 

 sequence of the obstructions caused by the land, or the disturbances 

 at the mouths of rivers, the progressive movement of the tide-wave is 

 more retarded than in the middle ; and in some places the current has 

 curvilinear motions, which on the French and English sides are in 

 opposite directions. The race of Portland is a current produced by 

 ihe tide-wave, while advancing along the shore ; being arrested by the 

 promontory till it attains a height which allows it to flow of obliquely 

 ith considerable velocity. 



The rise of a tide-wave near the mouth of a river takes place 

 rapidly by the shoaling of the sea and the confinement of the wave 

 between the banks ; for the motion of a body of water is capable of 

 raising the particles to the heights through which they must fall to 

 acquire their actual velocities ; and if the same motion is employed 

 in raising a smaller quantity of water, it is evidently capable of 

 raising it higher : thus, when the contraction ia considerable, as in 

 the Bay of Fundy, the Bristol Channel, and other places, the elevation 

 becomes very great ; at Chepstow it amounts to 60 feet. When, at the 

 mouth of a river, the bed has a long and gentle slope on each side, 

 the waves, becoming high and steep, fall over, and flow up rapidly with 

 a surf, constituting what is called a bore : the bore-wave which enters 

 the Severn is 9 feet high, and that which occurs in the Amazonas is 

 said to be from 12 to 15 feet in height. [BoKE, and col. 784 of the 

 present article. ] In flowing up a river the summit of the tide-wave 

 reaches the different stations later as these arc farther from the mouth; 

 and in the Thames it advances from Margate to London, a distance of 

 70 miles, in three hours. It is observed also that the current of a river 

 runs upward during some time after the summit has passed any station, 

 and downwards for some time after the surface of the water is at the 

 lowest ; the intervals between the times of low and high water, more- 

 over, gradually dimmish as the stations are farther up, while the 

 intervals between high and low water increase. 



From the observations made by the committee of the British 

 Association in 1836, on the tide-waves of the river Dee in Cheshire, 

 it was found that the first wave of flood-tide advanced 5'275 miles in 

 intervals of time varying from forty-five minutes to one hour, or, at 

 an average, at the rate of 6'4 miles per hour ; and that the wave o 

 high-water advanced the same distance with a velocity, by an aver- 

 age of the observations, of 1 4'6 miles per hour. It is said however to 

 have been impossible to determine whether the wave which carried the 

 flood-tide to the lower station was the same as that which carried it 

 to the higher. It is thought probable that the wave which passed the 

 lower station was diffused in the spaces between certain projections 

 from the bank on one side of the channel, and was overtaken by a sub- 

 sequent wave from the sea. The wave of high-water, being above 

 those obstructions, flowed up more regularly, and the observed height 

 of the wave approached very nearly to that which is due to its observed 

 velocity : it being understood that the velocity of a wave is that which 

 would be produced by a body falling from rest through half the height 

 of the wave. 



In order that the phenomena of the tides at different places may bo 

 readily compared together, charts have been constructed, on which aro 

 drawn curve-lines joining the points at which high-water takes place at 

 the same times. Now, since the heights of the wave and the times of 

 its greatest elevation vary at every place from day to day, it is neces- 

 sary to fix on the height attained at a particular time ; and on this 

 account, by general agreement, the time of high-water at every seaport 

 on the days of full and change of the moon is chosen. This is called 

 the " Establishment of the Port ;" and an extensive table of " Esta- 

 blishments " for the ports of Great Britain and Ireland is given in the 

 ' Nautical Almanac ;' the hours and minutes indicating the time from 

 apparent noon on the days of new and full moon when high-water 

 takes place. Since, on the first of these days, the moun passes the 

 meridian with the sun, the time of high-water on any other day may 

 be found from the table by merely adding the " Establishment " to 

 the time at which the moon comes on the meridian on the given day. 

 Finding upon the surface of the earth and sea any number of points at 

 which the " Establishment," when reckoned according to Greenwich 

 time, is the same, a line drawn through all the points will indicate the 

 summit of a great tide-wave at that time : drawing a curve in like 

 manner through all the points at which the " Establishment " in 

 Greenwich time is an hour later, there is obtained a new position of 

 the summit ; and it must then be understood that the wave has 

 travelled, in the sense above explained, from the first line to the next 

 in one hour. These are called " C'otidal lines ;" they were first indi- 

 cated on a chart of the world by Mr. (now Sir John W.) Lubbock, in 

 the ' Philosophical Transactions ' for 1831, and an extensive series of 

 such lines is traced on the chart which accompanies Dr. Whcwell's 

 ' Essay towards an approximation to a Map of Cotidal Lines,' in the 

 ' Philosophical Transactions ' for 1833. 



In the ' Naatical Almanac ' this information is now given in tables of the 

 " Time of High Water on the Full and Cimnge of the Moon," not only at ports 

 and places in the British itlnd, but on the neighbouring shores of foreign 

 countries. 



