We have accounted for the time when they occur in the fact that the water attempts to follow the moon, but this does not account for the gradual changes in the amount of fluctuation from day to day. The problem is complicated by the fact that the sun also has an attraction for the earth as well as the moon. But from the fact that the sun is something like 400 times further from the earth than the moon is, and also the fact that the attraction of one body for another varies inversely as the square of the distance, the moon has an immense advantage over the sun, although so much smaller. If the power of the moon were entirely suspended, or if the moon were blotted out of existence, there would still be a tide. The fluctuation between high and low tide would not be nearly so great as it is at present, but it would occur at the same time each day, because it would be wholly a product of the sun.
It will be easily seen that these two forces acting upon the water at the same time will cause a complicated condition in the movement of the waters of the ocean. There will come a time once in twenty-eight days when the sun and the moon will act conjointly, and both will pull in the same direction at the same time upon the water. This joint action of the sun and moon produces the highest tide, which is called the "spring" tide. From this point, however, the tides will grow less each day, because the relation of the sun and moon is constantly changing, owing to the fact that it requires 365 days for the sun to complete his apparent revolution around the earth, while the moon does her actual course in twenty-eight days. When the sun and moon have changed their relative positions so that they are at right angles to each other with reference to the earth—at a quarter-circle apart—the sun and moon will be pulling against each other; at least this is the point where the moon is at the greatest disadvantage with reference to its ability to attract the water.
Because one-quarter around the earth the sun is creating his own tide, which to that extent counteracts the effect produced by the moon, the tide under the moon at this point is at its lowest point and is called the "neap" tide. When the moon has passed on around the earth to a point where it is opposite to that of the sun—at a half-circle apart—there will be another spring tide, and then another neap tide when it is on the last quarter, and from that point the tide will increase daily until it reaches the point where the sun and moon are in exact line with reference to the earth's center, when another spring tide occurs. From this it will be seen that there are two spring tides and two neap tides in each twenty-eight days. This is the fundamental law governing tides.
There are many other conditions that modify tidal effects. Neither the sun nor the moon is always at the same distance from the earth. So that there will be a variation at times in high and low tides. For instance, it will happen sometimes that when both the sun and moon are acting conjointly they will both be at their nearest point to the earth, and when this is the case the spring tide will be much higher than usual.
For many years the writer has observed that artesian wells, made by deep borings of small diameter into the earth to a water supply, have a daily period of ebb and flow, as well as a neap and spring tide, the same as the tides of the ocean, except that the process is reversed. The time of greatest flow of an artesian well will occur at low tide in the ocean. This might be accounted for from the fact that when the tide is at its height the moon is also pulling upon the crust of the earth, which would tend to take the pressure off the sand rock which lies one or two thousand feet below the surface and through which the flow of water comes, and thus slacken the flow. When the moon is in position for low tide, the crust of the earth would settle back and thus produce a greater pressure upon the water-bearing rock. This is the only theory that has suggested itself to the writer that would seem to account for these phenomena.
Looked at from one standpoint, it is easy to account for tidal action. But when we attempt to make up a table giving the hour and minute as well as the height of the tide at that particular time we find that we have a very complicated mathematical problem. However, tables are made out so that we know at just what time in the day a tide will occur every day in the year.