Letters on Astronomy / in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers

by Denison Olmsted

Tides are caused by the unequal attractions of the sun and moon upon different parts of the earth. Suppose the projectile force by which the earth is carried forward in her orbit to be suspended, and the earth to fall towards one of these bodies,—the moon, for example,—in consequence of their mutual attraction. Then, if all parts of the earth fell equally towards the moon, no derangement of its different parts would result, any more than of the particles of a drop of water, in its descent to the ground. But if one part fell faster than another, the different portions would evidently be separated from each other. Now, this is precisely what takes place with respect to the earth, in its fall towards the moon. The portions of the earth in the hemisphere next to the moon, on account of being nearer to the centre of attraction, fall faster than those in the opposite hemisphere, and consequently leave them behind. The solid earth, on account of its cohesion, cannot obey this impulse, since all its different portions constitute one mass, which is acted on in the same manner as though it were all collected in the centre; but the waters on the surface, moving freely under this impulse, endeavor to desert the solid mass and fall towards the moon. For a similar reason, the waters in the opposite hemisphere, falling less towards the moon than the solid earth does, are left behind, or appear to rise.

Fig. 46.

But if the moon draws the waters of the earth into an oval form towards herself, raising them simultaneously on the opposite sides of the earth, they must obviously be drawn away from the intermediate parts of the earth, where it must at the same time be low water. Thus, in Fig. 46, the moon, M, raises the waters beneath itself at Z and N, at which places it is high water, but at the same time depresses the waters at H and R, at which places it is low water. Hence, the interval between the high and low tide, on successive days, is about fifty minutes, corresponding to the progress of the moon in her orbit from west to east, which causes her to come to the meridian about fifty minutes later every day. There occurs, however, an intermediate tide, when the moon is on the lower meridian, so that the interval between two high tides is about twelve hours, and twenty-five minutes.

Were it not for the impediments which prevent the force from producing its full effects, we might expect to see the great tide-wave, as the elevated crest is called, always directly beneath the moon, attending it regularly around the globe. But the inertia of the waters prevents their instantly obeying the moon's attraction, and the friction of the waters on the bottom of the ocean still further retards its progress. It is not, therefore, until several hours (differing at different places) after the moon has passed the meridian of a place, that it is high tide at that place.

The sun has an action similar to that of the moon, but only one third as great. On account of the great mass of the sun, compared with that of the moon, we might suppose that his action in raising the tides would be greater than the moon's; but the nearness of the moon to the earth more than compensates for the sun's greater quantity of matter. As, however, wrong views are frequently entertained on this subject, let us endeavor to form a correct idea of the advantage which the moon derives from her proximity. It is not that her actual amount of attraction is thus rendered greater than that of the sun; but it is that her attraction for the different parts of the earth is very unequal, while that of the sun is nearly uniform. It is the inequality of this action, and not the absolute force, that produces the tides. The sun being ninety-five millions of miles from the earth, while the diameter of the earth is only one twelve thousandth part of this distance, the effects of the sun's attraction will be nearly the same on all parts of the earth, and therefore will not, as was explained of the moon, tend to separate the waters from the earth on the nearest side, or the earth from the waters on the remotest side, but in a degree proportionally smaller. But the diameter of the earth is one thirtieth the distance of the moon, and therefore the moon acts with considerably greater power on one part of the earth than on another.

As the sun and moon both contribute to produce the tides, and as they sometimes act together and sometimes in opposition to each other, so corresponding variations occur in the height of the tide. The spring tides, or those which rise to an unusual height twice a month, are produced by the sun and moon's acting together; and the neap tides, or those which are unusually low twice a month, are produced by the sun and moon's acting in opposition to each other. The spring tides occur at the syzygies: the neap tides at the quadratures. At the time of new moon, the sun and moon both being on the same side of the earth, and acting upon it in the same line, their actions conspire, and the sun may be considered as adding so much to the force of the moon. We have already seen how the moon contributes to raise a tide on the opposite side of the earth. But the sun, as well as the moon, raises its own tide-wave, which at new moon coincides with the lunar tide-wave. This will be plain on inspecting the diagram, Fig. 47, on page 220, where S represents the sun, C, the moon in conjunction, O, the moon in opposition, and Z, N, the tide-wave. Since the sun and moon severally raise a tide-wave, and the two here coincide, it is evident that a peculiarly high tide must occur when the two bodies are in conjunction, or at new moon. At full moon, also, the two luminaries conspire in the same way to raise the tide; for we must recollect that each body contributes to raise a tide on the opposite side. Thus, when the sun is at S and the moon at O, the sun draws the waters on the side next to it away from the earth, and the moon draws the earth away from the waters on that side; their united actions, therefore, conspire, and an unusually high tide is the result. On the side next to O, the two forces likewise conspire: for while the moon draws the waters away from the earth, the sun draws the earth away from the waters. In both cases an unusually low tide is produced; for the more the water is elevated at Z and N, the more it will be depressed at H and R, the places of low tide.

Fig. 47.

Twice a month, also, namely, at the quadratures of the moon, the tides neither rise so high nor fall so low as at other times, because then the sun and moon act against each other. Thus, in Fig. 48, while F tends to raise the water at Z, S tends to depress it, and consequently the high tide is less than usual. Again, while F tends to depress the water at R, S tends to elevate it, and therefore the low tide is less than usual. Hence the difference between high and low water is only half as great at neap as at spring tide. In the diagrams, the elevation and depression of the waters is represented, for the sake of illustration, as far greater than it really is; for you must recollect that the average height of the tides for the whole globe is only about two and a half feet, a quantity so small, in comparison with the diameter of the earth, that were the due proportions preserved in the figures, the effect would be wholly insensible.