# Encyclopædia Britannica, Ninth Edition/Tides/Chapter 7

Chap. VII.—Progress of the Tide Wave over the Sea and the Tides of the British Seas.
* § 40. Meaning of cotidal lines.
* § 41. Cotidal lines of the world.
* § 42. Cotidal lines of the British seas.
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 incom plete and only a rough scheme is possible. A map purporting to Cotidal five the progress of the tide-wave is called a map of cotidal lines, lines. or 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 tidegenerators. 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 - /^ becomes then equal to - fj.. As a rough approximation spring tide occurs when the moon's transit is at one o clock at night or in the day. We only assume, however, that it occurs simultan eously everywhere. Now let T be the Greenwich mean time of high water, and I the E. long, in hours of the place of observation, then, the local time of high water being the time of the moon's transit plus the interval, and local time being Greenwich time plus E. long., we have r fji./(j -&lt;r)-l = FIG. 6. Cotidal lines of the world. where p 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.
§ 41. Cotidal Lines of the World.
No recent revisal of cotidal lines has been made with the aid of the great mass of tidal data which is now being accumulated, and we therefore reproduce (fig. 6) the chart of the world prepared by Sir George Airy for his article on "Tides and Waves." The parts of the world for which data are wanting are omitted. The Roman numerals upon the cotidal lines denote the hour in Greenwich time of high water on the day of new or full moon. Airy remarks ( 575-584) that the cotidal lines of the North Atlantic are ac curately drawn, that those of the South Atlantic are doubtful, and in the Pacific east of New Zealand are almost conjectural. The embodiment of recent observations in a cotidal chart would neces sitate some modification of these statements.
Lines crowded near land.When a free wave runs into shallow water it travels with less velocity and its height is increased. This is observable in the flexure and crowding of the cotidal lines near continents and oceanic islands, as, for example, about the Azores, the Bermudas, and the coast of South America. The velocity of the tide-wave gives good information as to the depth of the sea. In the North Sea it appears to travel at about 45 miles an hour, which corresponds to a depth of 140 feet, and we know that the depth along the deeper channel is greater and along the sides less than this. In the Atlantic the wave passes over 90 of latitude, from the southern to the northern one o'clock line, in twelve hours, that is at the rate of 520 miles an hour. If the Atlantic tide could be considered as a free wave generated by the Pacific tide, this velocity would correspond to a depth of 18,000 feet. Airy considers, however, that the Atlantic forms too large a basin to permit the neglect of the direct tidal action, and thinks that the tides of this ocean derive extremely little of their character from the Pacific.
Sir G. Airy."There is another consideration," he says, "which must not be left out of sight. It is that, supposing the cotidal lines to be accurately what they profess to be—namely, the lines connecting all the points at which high water is simultaneous—they may, nevertheless, with a compound series of tide-waves, not at all represent the ridge of the tide-wave which actually runs over the ocean. Thus an eye at a great distance, capable of observing the swells of the tide-waves, might see one huge longitudinal ridge extending from the mouth of the Amazon to the sea beyond Iceland, making high water at one time from Cape de Verde to the North Cape, and at another time from Florida to Greenland, and another ridge transversal to the former, travelling from the coast of Guiana to the northern sea; and the cotidal lines which we have traced may depend simply on the combination of these waves. It does not appear likely that we can ever ascertain whether it is so or not; but it is certainly possible that the original waves may have these or similar forms; ​and if so it is vain for us to attempt entirely to explain the tides of the Atlantic."
He sums up the discussion of the chart by saying:—
"Upon the whole, therefore, we are driven to the conclusion that we cannot at all explain the cause of the form of the cotidal lines in the ocean, so far as they have been traced with any prob ability. And, supposing us to know with tolerable certainty those corresponding to the semi-diurnal tide, we cannot at all predict those which should hold for the diurnal tide."
§ 42. Cotidal Lines of the British Seas.
Fig. 7 shows the cotidal lines in the seas surrounding the British Islands. Here the lines refer to full moon and change of moon and not to spring tide. The small figures along different parts of the coast denote the extreme range of the tide in yards. This figure is from the same source as the preceding one, and we again, reproduce a portion of Airy's remarks.
"The tides in the English Channel claim notice as having been the subject of careful examination by many persons, English and Fio. 7. Cotidal lines of British seas. French. It appears that in the upper part of the Channel tho water flows up the Channel nearly three hours after high water and runs down nearly three hours after low water (this continuance of the current after high water, if it last three hours, is called by sailors tide-and-half-tide; if it last one hour and a half, it is called tide-and-quar tor-tide). On the English side of the Channel, especi ally opposite the entrance of bays, the directions of the currents turn in twelve hours in the same direction as the hands of a watch; on the French side they turn in the opposite direction. This is entirely in conformity with theory. The same laws are recognized as holding in the British [Bristol?] Channel, and in the German or North Sea near the Scotch and English coasts.
"With regard to the Irish Channel we have only to remark that there is a very great difference in the height of the tide on the different sides, the tide on the east side being considerably the greater. They are also greater in the northern part (north of Wicklow on one side, and of Bardsey Island on the other side) than in the southern part. Between Wexford and Wicklow they are very small.
"The tides of the German Sea present a very remarkable peculiar ity. Along the eastern coast of England, as far as the mouth of the Thames, the tide-wave, coming from the Atlantic round the Orkney Islands, flows towards the south. Thus, on a certain day, it is high water in the Murray [Moray] Firth at eleven o clock, at Berwick at two o clock, at Flamborough Head at five o clock, and so on to the entrance of the Thames. But on the Belgian and Dutch coasts immediately opposite, the tide-wave flows from the south towards the north. Thus, on the day that we have sup posed, it will be high water off the Thames at eleven o clock (the tide having travelled in twelve hours from the Murray Firth) and at Calais nearly at the same time; but at Ostend it will be at twelve, off The Hague at two, off the Helder at six, and so on.
"We believe that a complete explanation may be found in tho arrangement of the great shoals of the North Sea. It must be remarked that (except within a very small distance of Norway) the North Sea is considerably deeper on the English side than on the German side; so much so that the tide-wave coming from the north runs into a deep bay of deep water, bounded on the west side by the Scotch and English coasts as far as Newcastle, and on the east side by the great Dogger Bank. As far as the latitude of Hull, the English side is still the deep one; and, though a species of channel through the shoal there allows an opening to the east, yet immediately on the south of it is the Wells Bank, which again contracts the deep channel to the English side. After this (that is, in the latitude of Yarmouth) the deep channel expands equally to both sides. It seems reasonable to conclude from this that the great set of north tide is on the English side of the North Sea, both between the Dogger Bank and England and between the Wells Bank and England (a branch stream of tide having been given off to the east between these two banks), and that any passage of tidewave over these banks may be neglected. Now this view is sup ported in a remarkable degree by the tidal observations on two dangerous shoals called the Ower and Leman, lying between Cromer and the Wells Bank, but nearer to the latter. It appears that on these shoals the direction of the tide-current revolves in the same manner as the hands of a watch, proving conclusively that the Ower and Leman are on the left hand of the main stream of tide (supposing the face turned in the direction in which the tide pro ceeds), or are on its eastern border, and therefore that the central stream is still nearer to the coast of Norfolk. From a point not far south of this we may suppose the tide to diverge in a fan-shaped form over the uniformly deep Belgian Sea. Along the English coast the wave will flow to the south; but it will reach the whole of the Belgian and Dutch coast at the same instant; and, if this tide alone existed, we doubt not that the time of high water would be sensibly the same along the whole of that coast.
"But there is another tide of great magnitude, namely, that which comes from the English Channel through the Straits of Dover. This also diverges, we conceive, in a fan form, affecting the whole Belgian Sea: the western part turns into the estuary of the Thames; the eastern part runs along the Dutch coast, producing at successive times high water (even as combined with the North Sea tide) along successive points of that coast from Calais towards the Helder. And this we believe to be the complete explanation of the apparently opposite tide-currents. The branch tide of the North Sea running between the Dogger Bank and the Wells Bank will assist in propa gating the tide along the German coast from the Helder towards the mouth of the Elbe. We have gone into some detail in this explanation for the purpose of showing the importance of consider ing the form of the bottom in explanations of specific tides.
"A set of observations has been made by Captain Hewett (at the point A, fig. 7) on the depth and motion of the water at a strictly definite point a few miles south of the Wells Bank, near the middle of the Belgian Sea. The result was that the change of elevation of the surface was insensible, but that there was a considerable stream of tide alternately north-east and south-west (magnetic). The point in question corresponds pretty well to the intersection of the cotidal lines of nine o clock of the North Sea tide and three o clock of the English Channel tide (ordinary establishment), and these tides would therefore wholly or partially destroy each other as regards elevation. As regards the compound tide-stream, the greatest positive current from one tide will be combined with the greatest negative current of the other, and this will produce a stream whose direction agrees well with observation. At 3$^h$ on the day of new moon, the North Sea tide would be running north (magnetic), and the English Channel tide would be running east, and therefore the compound current would be running north-east; at 9 h it would be running south-west. Both currents, and consequently the com pound current, would cease at about O h, 6 h, &c., on the day of new moon; and, as the observations were made rather more than a day before new moon, the slack water would occur an hour or more before noon. The whole of this agrees well with the observations."