Hydraulic Architecture, Volume 2, Part 2

CHAP. I. ON THE EBB AND FLOW OF THE SEA.

...of 25 days, one must be satisfied with seeking the delay for 10, following the simple analogy As established on the previous page, "analogy" here refers to the mathematical "Rule of Three" or proportionality. previously mentioned, which will result in 8 hours.

Reasons showing that the cause of the tides depends not only on the action of the moon, but also on that of the sun.

§ 86. This succession and return of the tides, which have been observed throughout all time, show in the most evident manner that the ebb and flow original: "flux & reflux" of the sea depend not only on the action of the moon, but also on that of the sun; for if the tides always arrived at precisely the same hour, one would have to seek the cause solely in the apparent motion of the sun. If, on the other hand, their delay were a bit more significant, and they occurred every 12 hours in 13 and three-quarter days, or about 24 hours in 27 $\frac{1}{2}$ days, one would then be right to say that they depend only on the moon, since the duration of her periodic month A periodic or sidereal month is the time it takes the moon to complete one full orbit around the Earth relative to the stars, roughly 27.3 days. is 27 $\frac{1}{3}$ days, which is the time this planet takes to make one entire revolution around the earth from west to east. But the tides are not regulated in this way, returning to the precisely same hours only at the end of a synodic lunar month A synodic month is the time between two identical lunar phases (e.g., new moon to new moon), averaging about 29.5 days. This is longer than the periodic month because the Earth has also moved along its orbit around the Sun.; that is to say, when the moon finds herself back in the same position relative to the sun. Thus, both planets contribute to this regular movement, although they share in it unequally: this is something that has no longer been doubted since the beginning of this century.

The tides are always subject to the same general law, despite the accidents that sometimes occur to them. Proof of this truth.

§ 87. If the harmony that reigns between the phases of the moon and the ebb and flow of the sea seems to fail sometimes, it is never for more than a few days and is the result of a purely accidental cause; for afterward, the tides resume their former course and once again subject themselves to their ancient rule, which they continue to follow at precisely the same hours, as if they had previously suffered no disturbance. In this, their motion is quite different from that of most machines we build, where it is enough to alter their progress once for them to always feel the effects of the disorder that occurred. We have seen storms suspend the effect of the ebb and flow, and we also have examples to the contrary of two or three high and low tides occurring within 5 or 6 hours; but this irregularity has always been fleeting, because the strong dependence of the tides upon the action of the sun and moon soon restores order by making them arrive at their ordinary hours. The following fact proves the truth of what we are putting forward. It happened once that the persons charged with com—