Ordinary Tides

Tidal currents have mostly been measured by noting the dis tance moved by a floating log in a definite interval of time. But series of observations at frequent intervals, especially of currents below the surface, are usually made by current-meters. One of the commonest of these, the Ekman meter, registers the mean speed and direction of the current during the interval of time it is in operation, the former by a small propeller actuating a revolution-counting apparatus, and the latter by a vane attached to an apparatus dropping shot into sectorial boxes on a compass card. Owing chiefly to the difficulty of keeping a meter fixed relatively to the sea-floor, the accurate measurement of currents is a matter of great difficulty.

Astronomical Correlation.

(4). The times of high water are found to bear an intimate relation to the positions of the moon and sun. The period of 12 hr. 25 min. is half that of the moon's apparent revolution round the earth. The length of time between the moon's crossing of the meridian of a place and the next high water at that place is known as the lunitidal interval, or the high water interval, for the place. Similarly, the length of time between the moon's crossing of the meridian and the next low water is called the low water interval. For London Bridge the average value of the lunitidal interval is r hr. 31 min. In many cases, including those of British waters, the chief variation in the lunitidal interval is associated with the phase of the moon. The average value of the lunitidal interval on the days of new and full moon is known as the establishment of the port. For London Bridge the establishment is i hr. 58 min.

The range of tide may be similarly correlated. In British waters it reaches its maximum a day or so after new and full moon and its minimum a day or so after the quarters. In these circumstances the maximum tides are known as spring tides and the minimum tides as neap tides. About the time of the equinoxes spring tides are generally larger and about the time of the solstices they are generally smaller than usual. The average interval between new or full moon and the next following spring tide is known as the age of the tide at the place in question. At certain places in Canadian waters the chief variation in the range of tide is associated with the varying distance of the moon from the earth, while at others it is associated with the varying declination of the moon. The diurnal inequality is always asso ciated with the declination of the moon or sun. But the most complete correlation between the tides and astronomical variables is provided by the harmonic methods.

qr. The moon attracts every particle of the earth and ocean. By the law of gravitation the force acting on any particle is directed towards the moon's centre, and is jointly proportional to the masses of the particle and of the moon, and inversely proportional to the square of the distance between the particle and the moon's centre. If we imagine the earth and ocean subdivided into a number of small particles of equal mass, then the average, both as to direction and intensity, of the forces acting on these particles, is equal to the force acting on that particle which is at the earth's centre. If every particle of the earth and ocean were being urged by equal and parallel forces there would be no cause for relative motion between the ocean and the earth. Hence it is the departure of the force acting on any particle from the average which constitutes the tide generating force. Now it is obvious that on the side of the earth towards the moon the departure from the average is a small force directed towards the moon; and on the side of the earth away from the moon the departure is a small force directed away from the moon. All round the sides of the earth along a great circle perpendicular to the line joining the moon and earth the departure is a force directed inwards towards the earth's centre. Thus we see that the tidal forces tend to pull the water towards and away from the moon, and to depress the water at right angles to that direction. In fig. I this distribution of forces is illustrated graphically. The relative ratio of 27000,00o to i.e. -46o or 1/2.17. This means that at cor responding points of the two spheroids representing the lunar and solar equilibrium-forms the tidal elevations on the average will be in the ratio of 2.17 to I.

Harmonic Constituents.—Dynamical considerations make it impor tant to analyse the tide-generating forces into the sum of a number of constituent distributions, each of which is a harmonic function of the time. This means that at any point of the earth's surface we must represent the sum of the two varying elevations due to the two moving equilibrium-spheroids as the sum of a number of terms of the form — To), where t denotes the time, n is an angular speed, a length and a constant. The quantity n is called the speed of the corresponding constituent; it is the same for all points of the earth's surface. The length is called the amplitude of the constituent; and are con stant at any one place but vary over the earth's surface. The angle n (t 0) is called the phase of the constituent at time t.