A View of Sir Isaac Newton's Philosophy

by Henry Pemberton

27. Moreover the action of the moon being stronger, when near the earth, than when more remote; if the moon, when new suppose, be at its nearest distance from the earth, it shall when at the full be farthest off; whence it is, that two of the very largest spring tides do never immediately succeed each other.

28. Because the sun in its passage from the winter solstice to the summer recedes from the earth, and passing from the summer solstice to the winter approaches it, and is therefore nearer the earth before the vernal equinox than after, but nearer after the autumnal equinox than before; the greatest tides oftner precede the vernal equinox than follow it, and in the autumnal equinox on the contrary they oftner follow it than come before it.

29. The altitude, to which the water is raised in the open ocean, corresponds very well to the forementioned calculations; for as it was shewn, that the water in spring tides should rise to the height of 10 or 11 feet, and the neap tides to 6 or 7; accordingly in the Pacific, Atlantic and Ethiopic oceans in the parts without the tropics, the water is observed to rise about 6, 9, 12 or 15 feet. In the Pacific ocean this elevation is said to be greater than in the other, as it ought to be by reason of the wide extent of that sea. For the same reason in the Ethiopic ocean between the tropics the ascent of the water is less than without, by reason of the narrowness of the sea between the coasts of Africa and the southern parts of America. And islands in such narrow seas, if far from shore, have less tides than the coasts. But now in those ports where the water flows in with great violence upon fords and shoals, the force it acquires by that means will carry it to a much greater height, so as to make it ascend and descend to 30, 40 or even 50 feet and more; instances of which we have at Plymouth, and in the Severn near Chepstow; at St. Michael’s and Auranches in Normandy; at Cambay and Pegu in the East Indies.

30. Again the tides take a considerable time in passing through long straits, and shallow places. Thus the tide, which is made on the west coast of Ireland and on the coast of Spain at the third hour after the moon’s coming to the meridian, in the ports eastward toward the British channel falls out later, and as the flood passes up that channel still later and later, so that the tide takes up full twelve hours in coming up to London bridge.

31. In the last place tides may come to the same port from different seas, and as they may interfere with each other, they will produce particular effects. Suppose the tide from one sea come to a port at the third hour after the moon’s passing the meridian of the place, but from another sea to take up six hours more in its passage. Here one tide will make high water, when by the other it should be lowest; so that when the moon is over the equator, and the two tides are equal, there will be no rising and falling of the water at all; for as much as the water is carried off by one tide, it will be supplied by the other. But when the moon declines from the equator, the same way as the port is situated, we have shewn that of the two tides of the ocean, which are made each day, that tide, which is made when the moon is above the horizon, is greater than the other. Therefore in this case, as four tides come to this port each day the two greatest will come on the third, and on the ninth hour after the moon’s passing the meridian, and the two least at the fifteenth and at the twenty first hour. Thus from the third to the ninth hour more water will be in this port by the two greatest tides than from the ninth to the fifteenth, or from the twenty first to the following third hour, where the water is brought by one great and one small tide; but yet there will be more water brought by these tides, than what will be found between the two least tides, that is, between the fifteenth and twenty first hour. Therefore in the middle between the third and ninth hour, or about the moon’s setting, the water will be at its greatest height; in the middle between the ninth and fifteenth, as also between the twenty first and following third hour it will have its mean height; and be lowest in the middle between the fifteenth and twenty first hour, that is, at the moon’s rising. Thus here the water will have but one flood and one ebb each day. When the moon is on the other side of the equator, the flood will be turned into ebb, and the ebb into flood; the high water falling out at the rising of the moon, and the low water at the setting. Now this is the case of the port of Batsham in the kingdom of Tunquin in the East Indies; to which port there are two inlets, one between the continent and the islands which are called the Manillas, and the other between the continent and Borneo.

[32.] The next thing to be considered is the effect, which these fluids of the planets have upon the solid part of the bodies to which they belong. And in the first place I shall shew, that it was necessary upon account of these fluid parts to form the bodies of the planets into a figure something different from that of a perfect globe. Because the diurnal rotation, which our earth performs about its axis, and the like motion we see in some of the other planets, (which is an ample conviction that they all do the like) will diminish the force, with which bodies are attracted upon all the parts of their surfaces, except at the very poles, upon which they turn. Thus a stone or other weighty substance resting upon the surface of the earth, by the force which it receives from the motion communicated to it by the earth, if its weight prevented not, would continue that motion in a straight line from the point where it received it, and according to the direction, in which it was given, that is, in a line which touches the surface at that point; insomuch that it would move off from the earth in the same manner, as a weight fasten’d to a string and whirled about endeavours continually to recede from the center of motion, and would forthwith remove it self to a greater distance from it, if loosed from the string which retains it. And farther, as the centrifugal force, with which such a weight presses from the center of its motion, is greater, by how much greater the velocity is, with which it moves; so such a body, as I have been supposing to lie on the earth, would recede from it with the greater force, the greater the velocity is, with which the part of the earth’s surface it rests upon is moved, that is, the farther distant it is from the poles. But now the power of gravity is great enough to prevent bodies in any part of the earth from being carried off from it by this means; however it is plain that bodies having an effort contrary to that of gravity, though much weaker than it, their weight, that is, the degree of force, with which they are pressed to the earth, will be diminished thereby, and be the more diminished, the greater this contrary effort is; or in other words, the same body will weigh heavier at either of the poles, than upon any other part of the earth; and if any body be removed from the pole towards the equator, it will lose of its weight more and more, and be lightest of all at the equator, that is, in the middle between the poles.

33. This now is easily applied to the waters of the seas, and shews that the water under the poles will press more forcibly to the earth, than at or near the equator: and consequently that which presses least, must give place, till by ascending it makes room for receiving a greater quantity, which by its additional weight may place the whole upon a ballance. To illustrate this more particularly I shall make use of fig. 116 In which let A C B D be a circle, by whose revolution about the diameter A B a globe should be formed, representing a globe of solid earth. Suppose this globe covered on all sides with water to the same height, suppose that of E A or B F, at which distance the circle E G F H surrounds the circle A C B D; then it is evident, if the globe of earth be at rest, the water which surrounds it will rest in that situation. But if the globe be turned incessantly about its axis A B, and the water have likewise the same motion, it is also evident, from what has been explained, that the water between the circles E H F G and A D B C will remain no longer in the present situation, the parts of it between H and D, and between G and C being by this rotation become lighter, than the parts between E and A and between B and F; so that the water over the poles A and B must of necessity subside, and the water be accumulated over D and C, till the greater quantity in these latter places supply the defect of its weight. This would be the case, were the globe all covered with water. And the same figure of the surface would also be preserved, if some part of the water adjoining to the globe in any part of it were turned into solid earth, as is too evident to need any proof; because the parts of the water remaining at rest, it is the same thing, whether they continue in the state of being easily separable, which denominates them fluid, or were to be consolidated together, so as to make a hard body: and this, though the water should in some places be thus consolidated, even to the surface of it. Which shews that the form of the solid part of the earth makes no alteration in the figure the water will take: and by consequence in order to the preventing some parts of the earth from being entirely overflowed, and other parts quite deserted, the solid parts of the earth must have given them much the same figure, as if the whole earth were covered on all sides with water.

34. Farther, I say, this figure of the earth is the same, as it would receive, were it entirely a globe of water, provided that water were of the same density as the substance of the globe. For suppose the globe A C B D to be liquified, and that the globe E H F G, now entirely water, by its rotation about its axis should receive such a figure as we have been describing, and then the globe A C B D should be consolidated again, the figure of the water would plainly not be altered, by such a consolidation.

35. But from this last observation our author is enabled to determine the proportion between the axis of the earth drawn from pole to pole, and the diameter of the equator, upon the supposition that all the parts of the earth are of equal density; which he does by computing in the first place the proportion of the centrifugal force of the parts under the equator to the power of gravity; and then by considering the earth as a spheroid, made by the revolution of an ellipsis about its lesser axis, that is, supposing the line M I L K to be an exact ellipsis, from which it can differ but little, by reason that the difference between the lesser axis M L and the greater I K is but very small. From this supposition, and what was proved before, that all the particles which compose the earth have the attracting power explained in the preceding chapter, he finds at what distance the parts under the equator ought to be removed from the center, that the force, with which they shall be attracted to the center, diminished by their centrifugal force, shall be sufficient to keep those parts in a ballance with those which lie under the poles. And upon the supposition of all the parts of the earth having the same degree of density, the earth’s surface at the equator must be above 17 miles more distant from the center, than at the poles[275].