limit, in some measure, the probable magnitude of a resistance varying either accurately, or very nearly in proportion to the square of the velocity; and the chief of these is the time of high water at the spring and neap tides, which must be very differently affected by such a resistance, since it must necessarily cause a much greater acceleration or retardation of the spring tides than of the neap tides. Hitherto it has only been observed, that, in particular parts, the greatest tides have happened the earliest but no accurate comparisons of the time of high and low water have been made in a sufficient variety of circumstances, to authorise our forming any general conclusion of this kind. It might indeed be supposed, that this diversity of the relative time of high water might be modified and concealed by a difference of velocity in the progress of the different tides from their source in the ocean to the places of observation, according to the different degrees of resistance opposed to them: but, if we can depend on a mode of calculation which has occurred to us, the velocity, with which a wave or tide is propagated, is not materially affected by a resistance of any kind, its magnitude only being gradually reduced, and even its form remaining little altered by this cause, when the resistance is nearly proportional to the velocity.

Another limitation of the magnitude of a resistance varying as the square of the velocity is the modification of the apparent proportion of the solar to the lunar force, which must arise from it. In assuming that the comparative magnitudes of the tides in the open sea must be precisely the same with those of the disturbing forces which occasion them, astronomers have hitherto neglected two very material circumstances; one, the effect, that a greater approach of the frequency of the spontaneous oscillations, to the solar or lunar period, must have, in augmenting the respective tide; the other, the greater diminution of the spring than of the neap tides by the operation of a resistance proportional to the square of the velocity, which gives to the lunar tide a greater apparent preponderance. Mr. Laplace is obliged to have recourse to some imaginary peculiarities in the local situation of the port of Brest, in order to explain the existence of lunar and solar tides in the proportion of 3 to 1, while other phenomena, depending on the moo's attraction, make it improbable that the lunar force can be to the solar in a much greater ratio than that of 5 to 2. But, in fact, the proportions of the tides in other ports, very differently situated, for instance at St. Helena, are nearly the same with those which have been observed at Brest; and it is demonstrable, that such a diminution of the apparent solar force must necessarily be the consequence of the operation of any resistance, proportional to the square of the velocity; besides being in part dependent, according to the most probable

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suppositions, upon the actual depth of the sea, as being more favourable to the exhibition of a lunar than of a solar tide.

There remains to be explained the interval which elapses between the time of new or full moon, and the occurrence of the highest tides, amounting at Brest to about a day and a half, and at London bridge probably to two days. The most simple supposition respecting this interval, is that which Mr. Laplace has adopted; as the retardation is greater at London bridge than at Brest, so it may be imagined that there are other places, still more exposed than Brest to the great oceans, at which it will altogether disappear. We cannot, however, discover any thing like a progressive succession of this kind in the tides which are observed at different parts of the continent: nor would so great a time as a day and a half be required for the passage of a tide over more than half the circumference of the globe, upon any probable estimate of the depth of the sea. Another late author has attributed this pheno menon to the different effects produced on the solar and lunar tides by a resistance supposed to vary as the square of the velocity: but in the rapid view which he has taken of this part of the subject, he seems to have omitted the consideration of the modification of the magnitude of the resistance, which must be derived from the combination of the two tides; an omission which appears to us in great measure to invalidate his argument: at the same time, notwithstanding this complication, the cause which he has very ingeniously indicated say possibly be concerned in the phenomenon, although a most intricate calculation is required for determining its effect, nor are we acquainted with any method of obtaining a perfectly correct solution of the problem. It is reduced, indeed, by the analogy of compound vibrations, which we have already mentioned, to the mathematical investigation of a series expressing the actual resistance in terms of the sines of multiple arcs only; but the difficulties attending this investigation appear to be almost insuperable. We have however satisfied ourselves, by an approximation, that upon a moderate estimate of the magnitude of the resistance, it may fairly be inferred, that the tide, which happens half a day after the conjunction, will be greater, even in the ocean in which it originates, than the tide which happens precisely at the time of the conjunction but we doubt whether it is possible to extend the effect of this resistance so far as to account for the excess of the second tide after the conjunction or opposition: and with respect to the third tide, we think that no resistance which can exist in nature could alone retard the maximum of effect so considerably. It may easily be understood, that if the resistances acted separately on the lunar and solar tides, the different degrees of acceleration or retardation, belonging to each, would render it necessary that

the

the luminaries should be at some little distance from each other, in order that the times of high water might coincide: and this effect may be considered as depending simply, at the time of the spring tides, on the excess of the periodical time of the greatest resistance above that of the joint tide. But in the actual circumstances of a resistance proportional to the square of the true velocity, this reason by no means holds good; the period of the greatest resist ance being identical with that of the compound tide; and it requires a very minute investigation to discover, that the periodical changes, derived from the resistance, will tend, in the usual circumstances of the tide, to a recurrence somewhat slower than that of the resistance itself, and that for this reason the effects will be somewhat analogous to those which would be exhibited if the resistance were principally confined to the slower oscillations. In order to complete this investigation, and to confirm it by a comparison with the phenomena, it would be necessary to be furnished with a series of accurate and extensive observations made in different parts of the globe, especially in those ports which are the most exposed to the tides of the great oceans: at present we are obliged to establish our theories on too confined a basis.

We have however assigned abundant reasons for the diversity which occurs in the time of high water at any given period of the moon's revolution in places differently situated: and this time being once ascertained for any one tide, we may easily infer by calculation the time at which every other tide will occur: and we shall find in this sequence the most perfect coincidence between theory and observation. Thus if the high water of the spring tides, derived from the coincidence of the solar and lunar high waters, soon after the new or full moon, happen at any port precisely at noon; the next time of the high water belonging to the solar tide would of course be at midnight, and that of the lunar high water 25 minutes later; and the true time of high water will divide this interval nearly in proportion to the apparent forces, and will occur about 18 minutes after midnight: and the next day it will be high water about 36 minutes after 12. This retardation will increase from day to day, since its mean daily value is about 50 minutes: and at the neap tides, following the moon's quadratures, it will become about twice as great as at the syzygies, its different values, in these cases, being nearly proportional to the magnitude of the spring and neap tides: so that Bernoulli has considered them as affording the most correct estimate of the comparative magnitude of the solar and lunar forces: although they are probably less capable of being correctly determined by observation than the different elevations and depressions. We can scarcely imagine it possible that any individual, acquainted with these simple facts alone, to say nothing of many others,

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equally well established, could for a moment entertain the slightest doubt of the real and immediate dependence of the tides on a combination of the solar and lunar attractions.

When a regular tide moves continually forwards in an open ocean, the progressive motion of the fluid is the greatest, or in other words, the flood is the strongest, where the elevation is greatest, and the motion is retrograde, constituting the ebb, whereever there is a depression. In a river, the effect of a stream would only so far modify this velocity as to make it proportional to the elevation above or the depression below a different level: but if a river or channel of any kind terminated abruptly, so as to cause a reflection, the progressive velocity would commence from the time of low water, and continue till that of high water ouly, or even be counteracted by the motion of the current, so as to cease still earlier, and to commence later. The rivers, in which our tides are commonly observed, seem to hold a middle place between these two cases at Lambeth, for instance, the flow of the tide is continued, not during the whole time that the water remains elevated above a certain level, but about three quarters of an hour after the time of high water, at which it would cease near the end of a channel terminating abruptly. And it is probable that by similar considerations the course of the ebb and flood tides might be explained in many other cases.

In the diurnal and annual variations of the height of the tides, there is no peculiar difficulty. The declinations and distances of the luminaries modify their forces in a manner which is easily determined and the periods of these changes being much greater than the times of spontaneous oscillation in any of the seas concerned, the effects directly follow their causes, almost in the simple proportion of the intensity of the forces concerned. Mr. Laplace has calculated, that in an ocean of equable depth, the difference between the heights of the morning and evening tides, depending on the declination of the luminary, must wholly disappear: but we cannot help suspecting that there must be an imperfection in some of the many steps of his investigation. The depth would be equable if the whole sphere were fluid: and it will not be denied, tha in this case there would be a difference in the morning and evening tides, very nearly coinciding with that of the primitive variations of the figure affording an equilibrium: nor can we discover any imperfection in the method, which Mr. Laplace himself has sometimes adopted, of considering the difference of the two tides as a separate diurnal tide, and determining its magnitude precisely in the same manner as if it existed alone.

If we apply a similar mode of calculation to the tides of the atmosphere, they will appear to be subject to some very singular

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modifications. At the poles they must be very small; at the equator moderate; but at the latitude of about 42, where the rotatory velocity of the earth's surface is equal to the velocity with which any impression is transmitted by the atmosphere, or at about 40° for the lunar tide, the height of the oscillations will only be limited by the resistances, the greatest elevation occurring about three hours after the transit of the luminary; nearer the pole they will occur earlier than this, and nearer the equator later: but perhaps the oblique situation of such a tide might be expected to tend in some measure to equalise its height. It seems, however, to be a mistake to suppose that the effects of the atmospherical tides must be more perceptible near the equator than in temperate climates: and the variations of the barometer, which have been observed between the tropics, are manifestly independent of the lunar attraction, occurring regularly at certain hours of the day or night; as indeed the tides of the ocean might have been expected to occur, if they had really been derived from the causes to which Mr. Ross Cuthbert has chosen to attribute them.

ART. V. A History of the Colleges, Halls, and Public Buildings attached to the University of Oxford, including the Lives of the Founders. By Alexander Chalmers, F.S.A. 2 vols. 8vo. Longman, London. Parker, Oxford.

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N this age of antiquarian research, when every village has produced its historian, and ponderous volumes are compiled from the scanty records of a parish register, it is not a little surprising that a subject so generally interesting, and apparently so rich in matter as the history of our English Universities, should have hitherto remained unnoticed. It would be difficult, perhaps, to find any other corporate institution, whose antiquities could be more regularly developed, whose magnificence remains so entire, and whose learning admits of such ample illustration in the biography of the eminent characters educated in those classic abodes. Yet, with all these inducements, the antiquities of Cambridge have never, we believe, been investigated by any writer of note; at least with that copiousness which the interesting and important nature of the subject so justly deserves.

The University of Oxford happily produced a man whose whole life seems to have been devoted antiquam exquirere matrem,' to investigate and preserve the history and antiquities of his native place. Such was the patient industry of Authony Wood, and such the ardent enthusiasm which he displayed in pursuit of