HYDRAULIC ARCHITECTURE, BOOK III.

until the time of the quadratures The points in the lunar cycle—the first and last quarters—where the moon is at a 90-degree angle relative to the sun as seen from Earth., that is to say, until the time that the moon B is 90 degrees away from the sun D; then the tides are the smallest of all, because in this case they no longer result from the combined actions of the sun and the moon, but rather from the difference of one of these actions upon the other. These weaker tides are called neap tides Original: "mortes eaux," literally "dead waters.", which occur at every quadrature, or seven and a half days after the great spring tides. It has been observed that at these times the sea usually rises one-sixth less than during spring tides Original: "vives eaux," literally "living waters.", and that it also falls one-sixth less, which makes for a difference of nearly one-third.

Calculation by Mr. Newton, by which he finds that the action of the sun on the Ocean is to that of the moon as 2 is to 7.

592. This ratio is not exactly the same in all ports, which arises from the different layout gissement Original: "gissement." An old maritime term referring to the geographical configuration, orientation, or "bearing" of the coastline and seabed. of the land, or the greater or lesser ease with which the sea reaches its level according to the distance it must travel, and whether it passes through openings that are more or less wide. Mr. Newton reports in his book Mathematical Principles of Natural Philosophy Original: "principes mathématiques de la philosophie naturelle," referring to Isaac Newton's seminal work, the Philosophiae Naturalis Principia Mathematica. that below Bristol the sea rises 45 feet during spring tides, and only 25 during the quadratures; he seizes upon this observation to try to discern how much stronger the moon's action is than the sun's by proceeding in this way. Naming L as the first of these actions and S as the second, we have L + S = 45 feet; and as these two actions counteract each other during neap tides, we have instead L - S = 25 feet, from which we deduce S = 10 and L = 35. This shows that the moon, because of its proximity to the earth, can operate three and a half times more powerfully than the sun does in the phenomenon of the tides. So, by adopting 2 and 7 to express the forces with which the sun and the moon each specifically attract the waters of the sea, the high tides will be to the low tides as the sum of these two numbers is to their difference, or roughly as 9 is to 5. Thus, assuming that the sun were capable of attracting the waters alone to a height of two feet, the moon would raise them to 7, and the combined powers of these two planets would make them rise to 9 feet.

The strongest of all tides are those that occur at the time of the equinoxes.

593. It should also be noted that not all spring tides malines Original: "malines." A traditional term for spring tides, particularly the exceptionally high tides occurring twice a month. are equal; those that occur at the time of the equinoxes are much stronger than those that occur three months later, which fall around the solstices. There are roughly the same differences between these spring tides as between the tides of the new...