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 is 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. [Bons, and col. 734 of the present article.] In flowing up a river the summit of the tide-wave reaches the different stations lateras these are 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 ricer 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 diminish 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 miles in intervals of time varying from forty-five minutes to one hour, or, at an average, at the rate of miles per hour ; and that the wave of high-water advanced the same distance with a velocity, by an aver age of the observations, of 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 be readily compared together, charts have been constructed, on which are 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 ie 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 wheu high-water takes place. Since, on the first of these days, the moon 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 " Cotidal 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. Whewell's Essay towards an approximation to a Map of Cotidal Lines,' in the Philosophical Transactions' for 1833.
The definition above given of the " Establishment " is only approxi !natively true: it is observed by Dr. Whewell, in the 'Essay,' that it would be correct if the high-tide always occurred when the moon's hour-circle makes equal angles with the meridian; but in fact the hour of tide on any day is reckoned from the time that the sun is on the meridian ; and as the moon changes her right ascension every day by about forty-eight minutes (the observed hour of the tide being given on the day of new or full moon), the moon's hour angle may differ according to the time of the day when the conjunction or opposition takes place, compared with the time of !lay when the high tide is observed. Therefore in observation of the hour of the tide on the day of new or full moon may leave an uncertainty of about lh. Sin. in the time of the " Establishment," unless account is taken whether the morning or afternoon tide was observed, and at what hour the syrygy took place.