TIDES 739 16 bay runs upward for some time after high rater, and after changing its direction con- inues to run downward for some time after >w water, when it again changes its direction, id runs upward. If we further examine the of the tide in different parts of the same river, or in a bay of great length as compared rith its breadth, as for instance Chesapeake ay, we shall find that near the mouth there very little difference between the interval )m high to low water and that from low to ligh water ; also that the current runs up the "lannel for a long time (sometimes approach- to three hours) after high water, and runs lown the channel for as long a time after low rater. In going up the bay we find that the ligh water occurs later and later, but the velocity with which the high water travels is great as entirely to preclude the idea of ex-, plaining the tide by supposing the same mass water to have been moved all the way up bay. Thus, high water is 13 hours in welling from Cape Henry to the head of Chesapeake bay, 190 m., moving with an av- rage velocity of 15 m. an hour, while the reatest observed current is less than one mile an hour. High water takes place simul- taneously near the head and the mouth of the bay, *while it is low water at the same time near the middle. The interval from low water to high water diminishes as we go up the bay, as also the difference be- tween the stand and slack water. At the en- rance of the bay the ebb current begins three >urs after the high water stand ; in the vicin- ity of Annapolis it is but one hour, and at the head of the bay there is only half an hour between the high water stand and the com- lencement of the ebb current. Herodotus )eaks of the tides in the Red sea. Plutarch says that Pytheas of Massilia, who had ob- served them in Britain, ascribed them to the moon. Csesar, in his account of the invasion of Britain, refers to the nature of spring tides well understood in connection with the moon's age. Pliny explains the phenomena at some lengfh, and ascribes them to the sun and moon dragging the waters along with them. Kepler in accounting for the tides was evi- dently aware of the principle of gravitation, but not of the law. Newton laid hold of this class of phenomena as the most incontestable proof of universal gravitation, and showed that according to its law just such periodic fluctuations in the fluid covering of the earth must take place as are actually exhibited by the tides of the ocean. If we conceive the earth to be wholly or in a great degree covered with water, and subject to the attraction of the sun, the force of which is inversely as the square of the distance, it will be obvious that while the whole earth will fall toward the sun with a velocity proportioned to the aggregate attrac- tion upon its solid portions (which is the same as if all the matter were collected at its centre), the water nearest to the sun, being accelerated a greater force, and being fluid, will ap- proach the sun more rapidly than the solid core. It will thus run from all sides into a protuberance beyond the form of equilibrium of the earth's attraction and rotation, until the pressure of the elevated mass equals the differ- ence in the attraction of the sun. Moreover, a similar protuberance will be formed on the side opposite to the sun, since the particles of water, being solicited by a less force than the solid core, will fall more slowly toward the sun, and as it were remain behind. Nor does the fact that, on the average, the earth does not lessen its distance from the sun, in the least invalidate the force of this reasoning ; for the deviations from the tangential motion of the earth in its orbit are precisely those which the earth would move through if falling toward the sun unaffected by any other impulse. The same considerations hold good in regard to the attraction of the moon upon the earth and the waters surrounding it ; for although we are in the habit of considering the moon as simply revolving about the earth, it must be remem- bered that the attraction is mutual, that both bodies describe orbits about their common cen- tre of gravity, and that while the moon obeys the attractive force of the earth, the latter equal- ly follows that of the former, by which it is at every instant of time drawn from the path which it would pursue if that influence did not exist, by an amount precisely equal to the fall corresponding to the moon's attractive force. As a necessary consequence of the elevation of the water in the regions nearest to and most remote from the attracting body, there must be a corresponding depression below the mean level of the sea at points distant 90 from the vertices of the protuberances, or at the sides of the earth as seen from the sun or moon. If the latter bodies maintained a constant posi- tion with respect to the earth, the effect would therefore be to produce a distortion of figure in the ocean surface (assumed to cover the whole earth) having the form of a slightly elongated ellipsoid, the two vertices of which would be, the one precisely under, the other precisely opposite to the points at which the disturbing body is vertical. But this is not the case ; for by the rotation of the earth and the motion of earth and moon in their orbits, the direction of the disturbing forces is constantly changing with respect to any point on the earth's surface. New points arrive at every instant under the zenith and nadir of either luminary, and thus waves are produced which follow them round the globe. The highest points of these waves will remain far behind the verticals of the disturbing bodies, because the inertia and friction of the water prevent the instantaneous change of form required, and because, although the elevating force is greatest under the vertical, it continues to act in the same direction for some hours after the passage of the luminary, with but little dimin- ished force. This retardation, which would be
