PREDICTION : TIDE-TABLES (22). For many purposes it is of great importance to know in ad vance the times and heights of high water at a particular place on a particular day. Consequently governments and harbour authorities publish, a year or so in advance, tables giving such information for all the principal ports of the world. In a few cases tables are similarly published giving the height of water above datum at every hour of the year, while for a certain number of navigable channels tables of the tides of slack water are also issued. The determination of the information contained in these tables is known as tidal prediction, and obviously de mands a knowledge of the laws of the tides at the place in question, including their correlation with astronomical variables. The standard method of tidal prediction is the harmonic method based on the idea of harmonic constituents (§9), and the necessary information for any particular place is provided by the process of harmonic analysis (§2I). For a number of ports, however, some of which are in British waters, it is found practicable to use the older non-harmonic methods, based on the non-harmonic constants (§9). In any case, the only part of the dynamical theory which is utilized is that which relates to periodicity, at one place, so that the empirical element is still very large.
The process of harmonic prediction consists in the calculation of the value of each harmonic constituent for a given time, and then the ad dition of the values obtained for all the constituents. When this is done for every hour of a year, the compu tational task becomes enormous, and to obviate this a calculating ma chine has been specially designed. Fig. 6 illustrates diagrammatically the nature of the instrument. A cord passes over and under a succession of pulleys, every other pulley being balanced in a fixed position and the alternate ones being movable; the cord is fixed at one end and carries at the other a pen which traces a curve on a revolving drum. In the diagram the instrument possesses
one unit; there are two balanced pulleys and one movable one. If the lowest or movable pulley were made to oscillate up and down with simple harmonic motion the pen would execute the same motion on twice the linear scale. If the instrument possessed two units, i.e., one more movable pulley and one more balanced one, and the second movable pulley also rocked up and down, the pen would add to its previous mo tion that of this second oscillation, again on twice the scale. For any number of additional units the pen would add together all the separate simple oscillations. The rocking motion is communicated to each movable pulley by means of a pin P attached to a fixed point of the wheel of centre C, sliding in a slot attached to the pulley frame. All the wheels C and the drum are geared together so that, as the drum turns, all the movable pulleys rock up and down. The gearing is of such a nature that if one revolution of the drum represents a single day, the rocking motion of each movable pulley corresponds to one harmonic constituent. The nature of the gearing is determined by the relative speeds of the different constituents, but the length of each crank CP and the angle at which it has to be set are derived from the results of harmonic analysis. When the machine has been set appropriately it will run off a complete tide curve for any length of time.
Of course the irregular meteorological effects on sea level cannot be in corporated in a tide-table, and hence any individual prediction is liable to differ considerably from the actual occurrence.