details, a number of far more abstruse considerations are requisite to be made out and attended to.

This attraction of the waters towards one part, would then create, as it were, a swelling or protuberance along that meridian of the globe which was at the time under the influence of the cause producing it. Two such ridges, as it were, would exist at opposite sides of the globe. This ridge, or crest of the water, would be simply one enormous wave, extending in length from pole to pole, and in breadth, a quarter of the earth's circumference: this is called the tide-wave. Still, supposing the globe uniformly covered with water, these waves would travel round the globe, each maintaining always the same relative position and direction; or, in other words, any one spot in the ocean would, twice in the twentyfour hours, be elevated to the summit of the ridge, and twice depressed into the bottom of the hollows between the ridges. The tide-wave would move uniformly from east to west; and its direction coincide with the meridian, if the sun and moon were always in the equator. On this hypothesis, the phenomena would present themselves with undeviating regularity. The theory would be easy to investigate upon the principles of gravitation, joined with those of oscillating fluids. But this is manifestly far from the actual condition of things.

The globe is not covered with water; nor are those parts which are so of uniform depth. The sun and moon do not move in the equator; but the former in the ecliptic, and the latter in a plane very little inclined to it. This introduces complexity into the phenomena, and great difficulties into the application of the theory of gravitation to them. Yet a certain modification of the simple conditions will still be preserved. A line drawn through all those points which are on the crest of the tide-wave at the same instant, is named by Mr. Whewell a co-tidal line. In the simple case above supposed, this line is a meridian of the globe; but in the actual case of nature it is broken, contorted, and reflected into a variety of new and irregular directions. Still they will preserve a certain degree of symmetry; in the wide expanse of the ocean something like uniformity will be maintained: but even here, it will be readily seen, that many causes must be taken into account, as operating on the course of the tide, and the form which its ridge will assume in its progress.

"The tide-wave," (as Mr. Whewell has admirably described it,) "by its motion, brings high water and low water to any place at the time when the elevated and depressed parts of the watery surface reach that place. The co-tidal lines, for successive hours, represent the successive positions of the summit of this wave: and if we suppose a spectator detached from the earth, to perceive the summit of the wave, he will see it travelling round the earth in the open ocean once in twenty-four hours, accompanied by another, at twelve hours' distance from it; and both sending branches into the narrower seas: and the manner and velocity of all these motions will be assigned by means of a map of co-tidal lines."

If, for example, we consider the tide-wave advancing from east to west, it will be evident that the continents of Africa and South America will act as immense dams, which will arrest the progress of the tide, and change its direction. Coming directly against those shores, and there

being stopped, it will take a course along their length: it will run round the Capes in which they terminate. These broken streams, as it were, will again meet with others occasioned by the like obstructions of other lands: their combinations, either conspiring, or opposing, will produce a vast variety of irregular and complex effects, often apparently at variance with any uniform law; which will again be still further modified by the extremely different amount of the depth in different parts of the ocean, and the form and structure of the bottom. Similar effects will result, with a much greater degree of complexity, in smaller seas, more broken and interrupted by promontories and islands.

Such would be the first rudiments of the theory; but Newton, in the developement of the vast system of universal gravitation, clearly saw that it would be utterly in vain for him to attempt following out the principle into all the varied and complicated results to which it led. He contented himself, and wisely, with verifying all its great leading points, and leaving the minuter details to his successors. Thus in regard to the Tides, he proceeded only to the general demonstration of their dependence on the attractions of the sun and moon, and showing in a very general way, what course the flow of the tide would take in its daily progress round the globe; but the explanation of all the details of the subject was bequeathed as a legacy of research to his successors. That is to say, all the apparent irregularities in the progress of the tide-wave, all the variations in the time of high water at different places, all the particular effects of the obstructions occasioned by the varied forms of continents, and the changes in the depth of the sea, were to be examined and described; and then again the theory was to be brought to bear upon them, so as to show whether it would afford a satisfactory explanation; and thus the whole series of phenomena, not only in their grander features, but even up to their lesser details, be all susceptible of explanation on the one comprehensive and pervading principle of gravitation. To this task then, Newton's successors addressed themselves. The completion of the Mathematical theory was the first object of their attention. The Academy of Sciences at Paris, proposed a prize on the subject, in 1740. Bernoulli, Euler, and Maclaurin, contended for it; and each produced essays of such singular merit, that the prize was divided between them. They did not succeed, however, in completely delivering the mathematical part of the subject from all its difficulties: but these arose from the imperfection of then existing mathematical processes. At a later period, Laplace applied his gigantic analytical powers to the subject, and in a great degree removed those difficulties. The investigation, however, was not yet strictly complete, or direct, though reduced to a form, in a great measure, applicable to the purposes of comparison with observation. The analysis was carried to greater perfection by MM. Fourier, Poisson, and Cauchy, about the year 1815. And even in 1832, the Academy of Petersburgh proposed as a prize-subject the complete and exact solution.

Before this time, the subject had attracted the attention of that eminent mathematician and zealous cultivator of Physical Astronomy, Mr. Lubbock; and at the meeting of the British Association for the Advancement of Science, in 1832, that gentleman produced, at the request of the association, a masterly report on the present state of our knowledge on this VOL. I.

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1

has improved the calculations an inclined orbit, which had

igh mathematical ability, and the most general views of the ace,) had, at the same time ts to the subject of the Tides. ry of the Tides is now in the resented about a century ago; ade, it may so continue for

planets have only acquired ral encouragement of learned of Europe: nor can tables of f Science be now constructed, urred from the immense labour

he systems of observations which orthy diligence for securing the ground these calculations and animated a number of other e, to the circulation of notices, tleman, and the stimulus and he subject at the meetings of the umber of able labourers are now a in different places, which will of accurate tables, and enabling on, the indications of theory.

1833, Part I., appeared Mr.Wheation to a Map of Co-tidal Lines.” this kind had been given by Mr. ince that time, however, so much that Mr. Whewell found himself ete and accurate map of the actual ariety of irregular curves, yet all y and dependence upon each other xtending up into the lesser seas, points at which it is high water at

2, &c., o'clock; a distinct line rms which these lines assume, then it were, by the continuous crest

it is impossible to inspect Mr. conveyed to the mind a far more which this striking effect is propapossibly be done by any verbal or, with that caution which dishas only ventured to call it a first and more extensive observations details.

be evident that in the varied courses of the Tide, there must be great

The

curious and important subject. He found that theory, though, as we have stated, not brought to a state of absolute mathematical completeness, was much further advanced than our knowledge of the facts from observation. In this, indeed, the deficiency was great and singular. question had suggested itself to the penetrating mind of Bacon:-What was the connexion between the tides in different parts of the world? and, in particular, whether the high-water extends across the Atlantic, so as to affect, contemporaneously, the shores of America and Africa? or whether it is high-water on one side of this ocean, when it is low on the other? Even at the present day we are hardly able to answer this question with accuracy: but it seems probable that the former idea is near the truth.

The extreme practical importance of a correct knowledge of the tides on coasts and in harbours has, in many places, led to the prosecution of some sort of regular observations, though mostly of a very rude kind, to determine what is called the establishment of particular ports. This means the interval of time after the new and full moon passing the meridian, at which it is high water there; from this the time of high water on other days is known from the age of the moon. At most ports, in commercial countries, some rude data of this kind have been long determined; and it is a singular circumstance, that even up to a very late period, determinations of this kind, and rules for the calculations deduced from them, should have been jealously guarded as secrets by the persons connected with the respective harbours; though it is manifest that any observer who chose, might easily put himself in possession of the information. But their secrets were very safe: for the attention of scientific men had scarcely been at all directed to the comparison of theory and observation. It deserves to be recorded, that in this country, Flamsteed (the father of British Astronomy) was one of the first to attempt to obtain something like accurate observations of the times of high water in the Thames. Observations have been regularly kept at Liverpool and some other ports for a number of years. Since the establishment of the London-Docks, in 1804, a regular system of observations has been carried on there. These have been investigated by Mr. Lubbock, who, with the assistance of M. Dessiou, went through a laborious series of computations upon the data thus obtained, and found some remarkable coincidences with the mathematical theory. A full account of these researches appeared in the Philosophical Transactions for 1831, Part II. He also compared one year's observations at the East India Docks, made with great accuracy by Captain Eastfield. But one of the most valuable and interesting features of that paper is the collection of such data, as to the time of high water at different parts of the world, as could be collected from different voyagers and other sources, and which are laid down in large charts; thus presenting to the eye a sort of map of the actual course of the tides.

Again, in the Philosophical Transactions for 1832, Part II., a further comparison was made of theory with some observations at St. Katherine's Docks, by the same gentleman; and in Part I. for 1833, at Portsmouth, Plymouth, and Sheerness; and in another paper in the same collection for 1834, Part I., this indefatigable and skilful investigator has given a number of highly interesting details on the variations due to the influence