HYDRAULIC ARCHITECTURE; BOOK III.

...consecutive high tides, as well as between two low tides. For example, if it is high tide in a certain port on a given day after 9 o'clock in the morning, it will also be high tide in the evening shortly after 9 o'clock, and between the two there will be a low tide around 3 o'clock in the afternoon.

§ 84. The short amount of time that the sea remains in the same state, high or low, combined with the extra time beyond the 6 hours it takes to rise or fall, together make 48 minutes at the end of 24 hours. That is to say, high and low tides occur consecutively each day 48 minutes later; thus, in the port where we assumed it was high tide at 9 o'clock in the morning, it must also be high tide the next morning, but at 9:48. The following day it will again be 48 minutes later than the previous one, and so on. It is true that winds and other causes can disrupt the regularity of this daily machine original: "machine journaliere." Bélidor uses this term to describe the mechanical, clock-like regularity of the Earth's natural systems., but its average amount will always be very nearly 48 minutes, which produces a 4-hour delay over 5 days. From this, the method is deduced for finding how much the tides are delayed proportionally in any other interval of time, since for that one needs only a simple analogy In this context, "analogy" refers to a mathematical proportion or the "Rule of Three" used to calculate an unknown value from three known values. to perform, by saying: if 5 days produce a 4-hour delay in the tides, how much will another number produce? For example, if we are dealing with 8 days, one must multiply the second term, 4, by the third, 8, and divide the product, 32, by the first, 5; this will result in 6 hours and 24 minutes, which show that in 8 days the tides must be delayed by that much. That is to say, if it is high tide on a certain day at 9 o'clock in the morning in the port of which we speak, after 8 days it will be high tide in the same port 6 hours and 24 minutes later; thus, high tide will arrive at 3:24 in the afternoon.

§ 85. The average delay of 48 minutes per day, or 4 hours in 5 days, producing—by repeating itself—a delay of 12 hours in 15 days, one sees that the tides must return to the same hours every 15 days, with the only difference being that the morning tides correspond to those of the evening, and conversely, those of the evening correspond to those of the morning.

It follows from this that when one wants to find how much the tide is delayed during a greater number of days than 15, one only has to take the remainder; thus, assuming we are dealing with...

Vocabulary: Hydraulic Architecture, tides, delay, high tide, low tide, analogy (proportion), time interval.