The Library of Work and Play: Mechanics, Indoors and Out

by Fred. T. Hodgson

"The tides, then, are not the sole production of the moon, but of the joint forces of the sun and moon together. Or, properly speaking, there are two tides, a solar one and a lunar one, which have a joint or opposite effect, according to the situation of the bodies which produce them. When the actions of the sun and moon conspire together, as at the time of new and full moon, the flow and ebb become more considerable; and these are then called the spring tides. But when one tends to elevate the waters while the other depresses them, as at the moon's first and third quarters, the effect will be exactly the contrary: the flow and ebb, instead of being augmented, as before, will now be diminished; and these are called the neap tides.

"To explain this more completely, let [Fig. 69] represent the sun, Z, H, R, the earth, and F and C the moon at her full and change. Then, because the sun S, and the new moon C, are nearly in the same right line with the centre of the earth O, their actions will conspire together, and raise the water above the zenith Z, or the point immediately under them, to a greater height than if only one of these forces acted alone. But it has been shown that when the ocean is elevated to the zenith Z, it is also elevated to the opposite point, or nadir, at the same time; and therefore in this situation of the sun and moon, the tides will be augmented. And again, whilst the full moon F raises the waters at N and Z, directly under and opposite to her, the sun S, acting in the same right line, will also raise the waters at the same point Z and N, directly under and opposite to him. Therefore, in this situation also, the tides will be augmented; their joint effect being nearly the same at the change as at the full; and in both cases they occasion what are called the spring tides.

Fig. 69. Attractions of the moon

"On this theory, the tides ought to be highest directly under and opposite to the moon; that is, when the moon is due north and south; but we find that in open seas, where the water flows freely, the moon is generally past the north and south meridian of the place where it is high water. The reason is obvious; for though the moon's attraction were to cease altogether when she was past the meridian, the motion of ascent communicated to the water before that time would make it continue to rise for some time after; much more must it do so when the attraction is only diminished. A little impulse given to a moving ball will cause it still to move farther than otherwise it could have done; and experience shows that the day is hotter about three in the afternoon than when the sun is on the meridian, because of the increase made to the heat already imparted.

"Tides do not always answer to the same distance of the moon from the meridian at the same place, but are variously affected by the action of the sun, which brings them on sooner when the moon is in her first and second quarters, and keeps them back later when she is in her third and fourth; because, in the former case, the tide raised by the sun alone would be earlier than the tides raised by the moon; and in the latter case, later.

"The sea, being put in motion, would continue to ebb and flow for several times, even though the sun and moon were annihilated, and their influences at an end, on the same principle that if a basin of water is once agitated, the water will continue to move for some time after the basin is left to stand still. A pendulum, put in motion by the hand, continues to make several vibrations without any new impulse. When the moon is at the equator, the tides are equally high in both parts of the lunar day, or time of the moon's revolving from the meridian to the meridian again, which is 24 hours 50 minutes. But as the moon declines from the equator toward either pole, the tides are alternately higher and lower at places having north or south latitude. One of the highest elevations, which is that under the moon, follows her toward the pole to which she is nearest, and the other declines toward the opposite pole; each elevation describing parallels as far distant from the equator, on opposite sides, as the moon declines from it to either side; and consequently the parallels described by those elevations of the water are twice as many degrees from one another as the moon is from the equator; then increase their distance as the moon increases her declination, till it is at the greatest, when these parallels are, at a mean state, 47 degrees from one another; and on that day the tides are most unequal in their heights. As the moon returns toward the equator, the parallels described by the opposite elevations approach toward each other, until the moon comes to the equator, and then they coincide. As the moon declines toward the opposite pole, at equal distances, each elevation describes the same parallel in the other part of the lunar day which its opposite elevation described before. Whilst the moon has north declination, the great tides in the northern hemisphere are when she is above the horizon; and the reverse whilst her declination is south.

"In open seas, the tides rise to very small heights in proportion to what they do in wide-mouthed rivers, opening in the direction of the stream of tide. In channels growing narrower gradually, the water is accumulated by the opposition of the contracting bank—like a gentle wind, little felt on an open plain, but stronger and brisk in a street; especially if the wider end of the street is next the plain, and in the way of the wind.

"The tides are so retarded in their passage through different shoals and channels, and otherwise so variously affected by striking against capes and headlands, that in different places they happen at all distances of the moon from the meridian, consequently at all hours of the lunar day.