The tide is much diminished at promontories under certain circumstances. Thus at the south-east point of Ireland (at Arklow, Glynn, and Cahore) the greatest range is not more than three feet, while at a little distance along the coast each way it becomes twelve or thirteen feet; and his small amount of the tide on one side of the channel is more remarkable, because it is just opposite the enormous range which occurs in the Bristol Channel, amounting at Chepstow to sixty feet. The smallness of the tide in the middle of wide oceans, as at the islands of the Pacific, where it amounts only to two or three feet, affords no proof that this would be the amount on a globe entirely covered with water; for the interruption produced by the continents entirely modifies the direction, height, or other circumstances of the general tide. This interruption will diminish, and in some cases entirely obstruct, the original tide-wave; and when a derivative tide does enter the oceans in question, it is diffused over so wide a space that its height is greatly reduced; so that in the same manner as the tides are augmented by convergence, they are diminished by diffusion.
Mr Lubbock and Mr Whewell seem to have adopted the most promising mode of advancing our knowledge of the tides. This is to examine the laws which can be collected from observations, taking so great a number of these that the effects of all accidental causes may disappear in the average results. The collection registered at the London docks, and first discussed by Mr Dessiou under the direction of Mr Lubbock, afforded an admirable opportunity for such an examination, since it included 13,073 observations, and a period of nineteen years, from January 1, 1808, to December 31, 1826. But it is very unlikely that the discussion, however systematical, of observations at any one place, should exhibit clearly the true principles of the theory; and, besides, with respect to the phenomena of the tides at London, they are in some measure masked by a curious combination of circumstances, namely, by the mouth of its river being in a sort of inland sea, and at a part of an island turned away from the side against which the tide-wave impinges, and so situated, too, that the progress of the tide round the one end of this island occupies about half a day more than that round the other. These two tides, being thus of different ages, and meeting near the mouth of the Thames, must affect the character of the tide at London. It will no doubt require the accumulation and discussion of many large collections of observations at various places to put us in certain possession even of the empirical laws of the phenomena; and whether or not this be the only practicable way of arriving at the true theory, it is at least that by which, founding our expectations on the past history of science, we may look with most hope. When we consider the enormous accumulation of observed phenomena and empirical laws which preceded the discovery of the true principles of the celestial motions, we may reasonably suppose that we are only at the outset of what is requisite to obtain the same success with regard to the tides. It is therefore to be wished that such additional observations may be made and discussed as may most speedily lead to a complete and scientific knowledge of the subject.
The object, in examining a large collection of observations, being to ascertain the manner in which the positions and distances of the heavenly bodies affect the time and height of the tide, the mode of proceeding is to examine how these two quantities depend upon the right ascension, declination, and parallax of the sun and moon, and upon other astronomical elements, should such be required. The mean time of high water will be found to be affected by inequalities depending on the elements just mentioned; and the law and amount of these inequalities for any particular place may be collected from observations made there, without any reference to theory, provided the observations be sufficiently numerous, and their circumstances sufficiently varied. For it was in this manner that the greater inequalities of the moon's motion, the variation, the evction, and annual equation, were detected by observation, long before the celestial motions were referred to their true causes. Indeed, in the history of science, the instances seem to be comparatively few in which the general laws of the phenomena have been pointed out by the theory, before they had been gathered, at least approximately, from observation. The laws thus empirically obtained, besides serving for predicting the tides, may be used either as tests of the existing theories, or as suggestions for the improvements of those portions of mathematical hydraulics on which the true theory may be expected to depend. This, besides, is the way in which we are most likely to discover how the theory must be applied.
The best mode of obtaining from a considerable series of tide observations, at the same place, the establishment and of the obliquity of the tide, which are the principal elements necessary for constructing tide-tables of the time for any particular place, appears to be that which was employed by Mr Lubbock and Mr Whewell. The times of high water are arranged according to the half-hour of the moon's transit on the day of the tide. Thus, all those tides which took place when the moon passed the meridian between 0° and 90° apparent time, are put in one class; all those when the moon passed between 90° and 180° in another class, and so on. The mean of all the times of transit in each class is taken, and the mean of the lunitial intervals, or those between the times of transit and high water. We have thus a series of times of transit, with the corresponding lunitial intervals. The interpolation for other times is most easily performed by means of a curve drawn on paper, ruled into small squares. The times of transit being laid down as abscissae, the lunitial intervals are erected as ordinates, and a curve is drawn approximating, as far as a regular form will allow, to the points thus found. This curve gives the intervals for any times of transit, and a table may be constructed by means of it. A similar course is followed for the heights; but for this and various particulars, we beg to refer to the Philosophical Transactions.
It has hitherto been usual, in discussing tide observations for obtaining from them the laws of the phenomena, to proceed upon the supposition that a series of several successive years was requisite, in order that the accidental irregularities might be compensated in the means of the observations, and the effects of the lunar inequalities thus come clearly into view. But in the Phil. Trans., for 1838, p. 291, Mr Whewell has shown that the laws of the phenomena, and the effects of the inequalities, may be deduced with considerable exactness from shorter series of observations; for example, from those of one year. He conceives that such an investigation will be of value in several ways. If the principal elements of tide-tables for each particular place can be obtained with moderate accuracy from short series properly discussed, the formation of such independent tide-tables for different places and times will become far less laborious, and may therefore be expected to be far more commonly practised. This will be a great advantage, not only because the tide-tables will thus become better, but also because several important questions may thus be settled; for instance, whether and how far the laws of tide phenomena change from place to place, and from time to time. But it is besides desirable to compare the results of short series with those of long ones, in order to appreciate the practical accuracy of our tide-tables. If, for instance, the mean of nineteen years gave a very exact rule for the effect of lunar parallax, while each single year deviated widely from this rule, it would be clear that the individual observations must be commonly affected by casual irregularities considerably greater than the parallax. Tides.
correction; and therefore the practical accuracy of the tables would be very little improved by introducing into them the parallax correction. But Mr Whewell has shown that the general law and the approximate amount of the parallax correction may be traced in the observations of a single year; and that thus the tables are rendered practically as well as theoretically better by such a correction being employed. The same is true, though less conspicuously, of the correction for lunar declination.
Although the establishment and mean range of tide were known or given for every several port, yet no general tables have yet been framed, which, even with the help of those data, would equally apply to the computation of the several times and heights of their tides. So extremely imperfect is the present state of the general theory, that each place still requires to have its own particular tables for this purpose. Mr Lubbock has constructed auxiliary tables from which both the times and heights may be computed for Plymouth, Portsmouth, Sheerness, London, Pembroke, Bristol, Liverpool, and Leith, and the times for Brest and Howth. The hydrographer royal, Captain Beaufort, has actually computed and published the tide-tables to that extent for all those places, with the addition of the time for Ramsgate. Mr Lubbock's tables are also used for computing the tide-tables of the British and the Nautical Almanacs. With regard to the accuracy of the tide predictions so computed, Mr Lubbock says they will sometimes, though rarely, deviate an hour from the observed time of high water, owing to accidental causes. Generally, however, they may be depended on to within ten minutes; and it should be recollected that it is difficult to ascertain within five minutes the instant of high water, the fluctuations of height being then so very minute that the water is said to hang. The predicted amount of the height is liable to still greater uncertainties; which is the more to be regretted, because disastrous effects often arise from unexpected and unusually high tides, which are occasioned by storms and reduced atmospheric pressure.
Tolerably accurate tide-tables have long been published annually for London, and still better for Liverpool. But it has been the practice in this country to form tide-tables for other places, merely by taking the time which is stated in the London or Liverpool tables, and, if necessary, to add or subtract some constant quantity, according to the place. Even without this alteration the Liverpool tables have been generally used for the whole of the west coast of England. But tables are published, professing to give the hours at most of the principal ports of England in parallel columns, the times for different places having constant differences. Thus the hour of high water at Plymouth is stated as always 1h. 55m. later than the hour in the same half day at London, although they belong to different transits. The like may be said of the American Almanac, which in a similar manner professes to predict the tides for a great many places. Nor does the British Almanac or Edinburgh Almanac follow a more correct course. Indeed the tides in the latter have as yet been computed from the obsolete rules of Laplace. The assumption of a constant difference in the tide-hours at different places is by no means correct, as we might expect it to be from considering how the tide is transmitted from place to place, and as it appears to be from observation.
According to Mr Lubbock, the great obstacle to perfection in calculations or predictions of the tides, consists in the fluctuations of the establishments. Suppose the establishment to change a minute per annum, and that, having determined it from all the observations of twenty-one years, we employ it in calculations of the time of high water for the eleventh year, and compare the calculated times with the observed, they will not be affected with any constant error; but if we calculate for the twenty-first year, the calculated times will have a constant error of ten minutes. Similar remarks apply to the height. If the channel become deeper, the tide-wave travels with greater velocity, and the high water happens sooner. From a very ancient tide-table discovered by Mr Yates, and copied by Mr Lubbock into the Phil. Trans. for 1837, p. 103, it would appear that the tide at London had formerly been fully an hour later than at present. The argument or entry of the table is the day of the moon's age, which runs up to thirty days. The tide-hour on the first day is 3h. 48m.; and with a daily increase of forty-eight minutes, it occurs just at 3h. on the thirtieth day! But Mr Lubbock finds that the establishment of the port of London has been subject to changes even within the present century; and he notices the difficulty of predicting the time of high water with certainty, unless these changes can be accounted for. The high water appears now to be nearly as late as in 1804; in 1821 it was fully ten minutes earlier. The removal of the Old London Bridge appears to have affected neither the time nor the height of high water; but it has made the low water sink about eighteen inches more than formerly. The following table shows the establishment of the port of London, and mean height of tide when the moon's transit occurs at 0°; in other words, the mean time and height of tide at new and full moon from 1802 to 1835; supposing the moon's horizontal parallax 57', and declination 16°.
| Year | Establishment | Height | |------|---------------|--------| | 1802 | 2 59 | 21 90 | | 1803 | 2 61 | 22 14 | | 1804 | 2 74 | 22 42 | | 1805 | 2 45 | 22 17 | | 1806 | 2 63 | 22 11 | | 1807 | 2 09 | 22 15 | | 1808 | 2 47 | 22 07 | | 1809 | 2 44 | 22 39 | | 1810 | 2 42 | 22 21 | | 1811 | 2 08 | 22 43 | | 1812 | 2 00 | 22 48 | | 1813 | 1 58 7 | 22 30 | | 1814 | 1 59 8 | 22 33 | | 1815 | 1 59 6 | 22 19 | | 1816 | 1 58 5 | 22 34 | | 1817 | 1 57 2 | 22 31 | | 1818 | 1 57 0 | 22 40 |
In 1832 none of the lower portions of the Old London Bridge, which obstructed the natural flow of the tidal waters, was removed excepting two piers; and in the following year almost the whole of that structure was cleared away as regarded the masonry and starlings, although the course of the river was far from being completely cleared, many portions still remaining a foot or two above low-water mark, and which were finally removed in 1834.
Hitherto no care has been taken to specify to which transit of the moon the tide at any place is referred, and various mistakes have originated in this want of precision. It seems desirable that some conventional agreement were adopted upon this point. Mr Lubbock has employed the transit which precedes a given high water at London by about two days three hours, and which, according to the notation already described, he terms transit B. If transit A, which occurs about twelve hours and twenty-five minutes sooner,
---
1 On this however we have to remark, that since the mean lunation consists of little more than twenty-nine days and a half, almost half the number of new moons would occur on the thirteenth day; so that, although the table had been in every other respect correct, it would not make the mean time of "flood at London bridge" on the day of new moon to have exceeded 3h. 26m. Flamsteed, in 1683, made it just 3h. His tables were the first which gave the time of the tide for the moon's lower transit, or twice a day.
The preferred, he does not object. This latter transit corresponds in syzygy to the average interval. At this period of the moon's age, the lunital interval changes rapidly, whereas the height of high water is stationary; so that it is impossible to determine directly and with accuracy, how long, after a given transit, the highest tide takes place.
From Mr Lubbock's examination of the progress of the tide-wave, the vulgar establishments of the following places are:
| Place | h. m. | |------------------------|-------| | Brest | 3 48, reckoned from transit D | | Plymouth dockyard | 5 33 | | St. Brehat | 5 52 | | Pembroke dockyard | 6 4 | | Bristol, Cumberland Gates | 7 15 | | South harbour | 11 8 | | Liverpool | 11 25 | | Portsmouth dockyard | 11 40 | | Leith | 2 0 | | London docks | 1 57 |
From this it is evident that the establishments of ports as given in various works, often very inaccurately, are besides referred to different transits of the moon without distinction, thereby creating great confusion.
Hence also it is found that the tide arrives at:
| Days h. m. | |------------| | Brest | 1 4 27 | | Portsmouth | 1 12 21 | | Liverpool | 1 12 2 | | Leith | 15 15 | | London Docks | 2 3 16 |
so that the tide takes twenty-three hours forty-nine minutes in travelling from Brest round the north coast of Scotland to the London docks. We are deficient of information with respect to the course of the tide-wave in the Pacific Ocean; and even on our own coasts the number of places of which the establishment is accurately known is probably very small. The tide takes about twelve hours proceeding from the Cape of Good Hope to Cape Blanco; hence it reaches Brest in about four hours. The crest of the tide-wave thus travels over the open ocean with immense rapidity, and gives rise to a slow current, with which, however, it must not be confounded.
At the instance of Mr Whewell, the British Association, with the view of ascertaining what surface ought to be taken as the permanent level of the sea, caused a level line to be carried with great accuracy from the north shore of Somersetshire to the south shore of Devonshire; and the position of this line has been fixed, so as to be recognised at any future time, by means of marks at Axmouth, at East Quantockshead, at Stafford, and at Portishead. This line has also been referred to the sea at its extremes; and the observations show that the mean between the heights of high and low water coincides, at least very nearly, at different places, as well as at the same place at different times. While the difference of the levels of low water at Axmouth in the English Channel, and Wick Rocks on the Bristol Channel, is not less than twelve feet, the mean water at those two places coincides in level within a few inches.
Against these conclusions, Mr Thomas has, in the Philosophical Magazine for August 1840, alleged various facts, which he has no means of testing or deciding upon. To one part of the world there seems a more serious objection than any that he has stated; for though we should think the mean water very likely to be nearly constant everywhere, it cannot be on the same level if there be perpetual high water at some places, as Mr Whewell himself alleges.
From six years' observations made at Plymouth, it appears that the height of mean water is constant from year to year within two or three inches. It appears also that the mean water for each fortnight has a semimensual inequality amounting to six or seven inches, the height of the mean water being greatest when the moon's transit is at 6th and least when it is at 12th. The immediate cause of this is, that the semimensual inequality of low water is greater than that of high water at Plymouth. The result of one year's observations made at Dundee is, that the half-tide level is constant within 1/5 inch, except at eleven and twelve o'clock, when it deviates two inches on a tide of fourteen feet. At any rate, Mr Whewell's scheme of taking the half-tide level as a standard must be an immense improvement on the old system, in which the heights of buildings and mountains are referred to the level of the sea, or to high or low water mark. The heights of spring or neap tides, although not subject to so much uncertainty, are also quantities too vague to be used with propriety as standards of reference.
It had been long observed by the people about Stock-Influenceholm, that when the water in the harbour, which is an inlet of the Baltic Sea, subsides so as to allow the waters of pressure on the Mälar Lake, which has almost the mean level of the sea, to have free exit, the air is clear and dry; but when the sea-reverse occurs, or the sea flows into the Mälar, wind and rain are likely soon to follow. This phenomenon was investigated by N. G. Schulten, who, after he had ascertained the truth of the popular belief, and compared it with the corresponding state of the barometer, explained it at considerable length in the Transactions of the Royal Academy of Stockholm for 1806, by referring it to opposite changes taking place simultaneously in the atmospheric pressure at Stockholm and in that at some considerable distance. The increment of pressure at the one place tending to depress the water there, just when the decrement of pressure at the other allows the water to rise, and the total pressure over the whole ocean being supposed constant, a tendency to equilibrium will result. Schulten's explanation, of which we suppose this to be the substance, is embarrassed with some irrelevant considerations; but there can be no doubt that it at the same time involves the true principle. His ideas, although well known at Stockholm, have not in other countries met with the attention they deserve. Some years ago they received a confirmation from M. Daussey, who, without being aware of Schulten's researches, has, from his own observations made at Brest, deduced the effects due to the changes of atmospheric pressure. Some account of these, accompanied by barometric tables, has been published (Connaissance des Temps for 1834, and Annales de Chimie, tome lix.), and clearly exhibits the connection between the phenomena in question.
Mr Lubbock verified the same fact both at Liverpool and at London. At Liverpool he found the water rise eleven times as much as the barometer falls; and therefore the range of the barometer being three inches, the correction due to change in the atmospheric pressure may there amount to thirty-three inches. At London the water rises seven times as much as the mercury falls, and hence the range of the correction there is about twenty-one inches. On the coasts of Cornwall and Devon, Mr Walker found, that in ordinary cases a change of one inch in the barometer corresponds to sixteen on the height of the sea; but that in very sudden changes of pressure, one inch of mercury corresponds to twenty of sea-water. This last has been accounted for by considering that a sudden impulse given to the water would cause a rise or fall in the manner of a wave, beyond that strictly due to mere change of pressure. But this would at best hold good near the time of such change; and Mr Lubbock has remarked that it is sometimes very difficult to distinguish between the effects of pressure and those of the wind. Both wind and pressure may require to be attended to, especially where tide observations are continued during only a limited period. From the facts above stated, it would rather seem that the more confined the situation, Tides.
the less is the effect of change of pressure; though this may, after all, be no general rule. But since the effects of variations of pressure do not accurately follow the inverse ratio of the specific gravities of water and of mercury, it is doubtful if the tides and these effects be independent of each other.
The effects of wind on the level of the sea do not seem to have been much attended to; but Mr Lubbock has collected some important facts regarding its influence on the Thames. During strong north-westerly gales, the tide in the port of London marks high water earlier than otherwise, and does not give so much water, while the ebb tide runs out later, and marks lower; but upon the gales abating and the weather moderating, the tides put in and rise much higher, while they also run longer before high water is marked, and with more velocity of current; nor do they run out so long or so low. The reason assigned for all this is, that the strong north-west winds drive the sea along the Dutch coast, through the Straits of Dover, and consequently away from the mouth of the Thames; so that the tides during north-west winds are always much higher (producing frequently ruinous flooding) on the Dutch than upon the English coast. A south-western gale generally has a contrary effect, and an easterly one gives some water; but the tides in all these cases always improve the moment the weather moderates. This is the opinion of those most competent to form one from their daily experience, and is no doubt correct. The subject is one of considerable importance as regards the accuracy of which tide predictions are susceptible, and merits further inquiry, in order to ascertain if possible the error which may be expected for a wind of a given force and direction.
The progress of the tide-wave in most places must obviously be liable to be disturbed by great storms. Thus, during a violent hurricane, January 8, 1839, there was no tide at Gainsborough, twenty-five miles up the Trent, a circumstance unknown before. At Saltmarsh, only five miles up the Ouse from the Humber, the tide went on ebbing, and never flowed, till the river was dry in some places; while at Ostend, towards which the wind was blowing, contrary effects were observed. It has been supposed, that, owing to the sheltered situation of the port of London, the great undulations produced by the winds will be less sensible there than on the coasts of France, as, for example, at Brest. But it should be recollected, that if the tide at London come from the Atlantic, the irregularities felt at Brest will equally tend to affect it at all those places which it subsequently reaches.
In the Phil. Trans. for 1838, p. 249, there is a particular description of a very complete machine, by Mr Bunt, for registering, in a continuous form, the rises and falls of the tides, or their height for any instant of time. The principal parts are, an eight-day clock, which turns a vertical cylinder revolving once in twenty-four hours; a wheel, to which an alternate motion is communicated by a float rising and falling with the tide, in an almost close chamber, and connected by a wire with the wheel, which is kept constantly strained by a counterpoise; and a small drum, on the same axis with the wheel, which by a suspending wire communicates one eighteenth of the vertical motion of the float to a bar carrying a pencil, which marks a curve on the cylinder, or on a sheet of paper wrapped round it. The leading principle is obviously the same with that which Mr Keith first applied to the register thermometers and barometers. Various tide-gauges on similar principles have been constructed by others, particularly by Captain Lloyd, Mr Mitchell, and Mr Palmer, and are described in previous volumes of the Philosophical Transactions.
Hitherto the phenomena of the tides have to a certain extent been referred to the equilibrium theory, the actual elevation of the waters being compared with the elevation which the moon would produce if the earth and moon were both at rest. But on account of the interruption of the land, the general motion of the waters of the ocean cannot conform to this theory, or admit of a fluid elevation resembling that of the equilibrium spheroid following the moon from east to west, except in some parts of the southern hemisphere. The Pacific, the largest ocean of all, has very small tides in its central parts; and at its eastern shore, near Cape Horn, the tide-wave runs from west to east, although there is apparently nothing to prevent its following the usual course. From such considerations, viewed in connection with various tide observations on the eastern and western sides of the Pacific and of the Atlantic, Captain Fitzroy (Voyage of the Adventure and Beagle, vol. ii. appendix, p. 279) has been led to propose a considerably different theory, in which the tide of each large ocean is considered to be nearly as independent of the tides of other waters as if it were a lake. The central area of each ocean is further supposed to be occupied by a lunar wave oscillating so as to keep time with the moon's transits, and having its motion kept up by the attraction of that luminary acting at each return. From the skirts of this oscillating central area, tides are supposed to be carried on all sides by free waves, the velocity of which would depend upon the depth and local circumstances of the sea; and thus the littoral tides may travel in any direction, while the oceanic tides near the centre of the oscillating area may be small, or may altogether vanish. Such we take to be the substance of this theory, as explained, with some improvements, to the Cambridge Philosophical Society, by Mr Whewell. Single observations, as that gentleman has remarked, can be of little use in deciding upon such a theory. More light would be thrown upon it if the real forms and positions of the cotidal lines could be ascertained for the shores of the Pacific. With this view it is desirable that numerous and connected observations were made on the eastern shores of Australia, the Indian Archipelago, the Philippine Isles, the Loo Choo Isles, and those of Japan. But we suspect that the magnitude and peculiarities of the diurnal inequality in some of those regions would throw great difficulties in the way of determining the cotidal lines, if they even admit of them at all.
Some of the facts which Captain Fitzroy considers most difficult to be reconciled with the theory which deduces tides in the Northern Atlantic from the movement of a tide-wave originating in the Southern Ocean are, 1st, the comparative narrowness of the space between Africa and America, with the certainty, that the sea is neither uniformly nor excessively deep in that space, and the trifling rise of the tide, not only upon each nearest shore (where it does not exceed four or five feet), but at Ascension Island, where the highest rise is not quite two feet; 2dly, the absence of any regular tide about the wide estuary of the river Plata, the situation and shape of which seem so well disposed for receiving an immense tide; 3dly, the flood-tide moving towards the west and south along the coast of Brazil, from near Pernambuco, to the vicinity of the river Plata; and, lastly, the almost uniformity of the time of high water along that extent of the coast of Africa which reaches from near the Cape of Good Hope to the neighbourhood of the Congo.
Against the supposition that a tide-wave travels southward along the west coast of America, are the facts, that the flood-tide impinges upon Chilié and the adjacent outer coast from the southward of west; that it is high water within half an hour of the same time at Cape Pillar and at Chilié, including the intermediate coast; that from Valdivia to the Bay of Mexillones (differing 18° in latitude), there is not an hour's difference in the time of high water; that from Africa to Payta, and from Panama to California, the times change gradually as the coast trends westward; and