VII. PROGRESS OF THE TIDE WAVE OVER THE SEA AND THE TIDES OF THE BRITISH SEAS
40. Meaning of Cotidal Lines
Sufficient tidal data would of course give the state of the tide at every part of the world at the same instant of time, and if we were to follow the successive changes we should be able to picture mentally the motion of the wave over the ocean and the successive changes in its height. The data are, however, as yet very incomplete and only a rough scheme is possible. A map purporting to give the progress of the tide-wave is called a map of cotidal lines. For a perfect representation three series of maps would be required, one for the semi-diurnal tides, a second for the diurnal tides, and a third for the tides of long period. Each class of map would then show the progress of the wave for each configuration of the tide-generators. But as yet the only cotidal maps made are those for the mean semi-diurnal tide, and only for the configuration of new and full moon. The knowledge of the tides is not very accurate throughout the world, and therefore in the maps which we give it is assumed that the same interval elapses at all places between new and full moon and spring tide.
At spring tide, as we have seen in (87) and (88),
since A - μ becomes then equal to - μ. As a rough approximation spring tide occurs when the moons transit is at one oclock at night or in the day. We only assume, however, that it occurs simultaneously everywhere. Now let τ be the Greenwich mean time of high water, and l the E. long. in hours of the place of observation, then, the local time of high water being the time of the moons transit plus the interval, and local time being Greenwich time plus E. long., we have
where μ is in degrees. Therefore, if we draw over the ocean a succession of lines defined by equidistant integral values of the Greenwich time of high water, and if we neglect the separation of the moon from the sun in longitude in twelve hours, the successive lines will give the motion of the semi-diurnal tide-wave in one hour.
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