VI THE TIDES AND THE CHANGES IN THE COURSE OF THE SUN

Son. It was a wise thought, it seems to me, to ask those questions to which I have just received such fair replies; and I am encouraged to inquire into certain other matters, namely the waxing of the sun, the moon, and the streams or tides of the ocean,—how much and how rapidly these things wax and wane. Now these 93things that I have brought up for discussion are subjects which especially touch the welfare of seafaring men, and it looks to me as if they would profit much from a knowledge of these matters, since it gives insight into the right conduct of their profession. And since I intend to labor diligently in the trader’s calling, I should like very much, if it can be done, to have you explain further some of those things that I have just mentioned.

Father. Those things that you have now asked about do not all wax or wane with equal rapidity; for the tide, when it rises, completes its course in seven days plus half an hour of the eighth day; and every seventh day there is flood tide in place of ebb. For the tide rises one seventh part daily from the time when the rise begins; and after it turns and begins to fall, it ebbs in the same way during the next seven days but is retarded as much as half an hour of the eighth day,^[167] which must be added to the seven days. As to how long an hour should be I can give you definite information; for there should be twenty-four hours in two days, that is, a night and a day, while the sun courses through the eight chief points of the sky: and according to right reckoning the sun will pass through each division in three hours of the day. On the other hand, the moon, while it waxes, completes its course in fifteen days less six hours;^[168] and in a like period it wanes until the course is complete and another comes. And it is always true that at this time the flood tide is highest and the ebb strongest. But when the moon has waxed to half, the flood tide is lowest and the ebb, too, 94is quite low. At full moon the flood tide is again very high and the ebb is strong. But when it has waned to half, both ebb and flood are quite low. Merchants are, however, scarcely able to note these changes, as the course is too swift; for the moon takes such long strides both in waxing and waning that men, on that account, find it difficult to determine the divisions of its course. The sun, on the other hand, completes its course more slowly both in ascending and declining, so that one may easily mark all the stages of its course. The sun moves upward one hundred and eighty-two and one-half days and three hours and for a like period it recedes again; it has then completed its entire course, both ascent and decline, in three hundred days, by the twelve-count^[169] {360}, plus five days and six hours. Every fourth year this becomes three hundred by the twelve-count and six days more {366}; this is called leap year, for it has one day more than the preceding twelvemonth, the additional hours being gathered into twenty-four, a night and a day. In Latin all hundreds are counted by tens, and there are, therefore, properly computed three hundred by the ten-count plus sixty-six days whenever leap year occurs, while the intervening years have only five days and six hours with as many additional days by the other reckoning as I have just stated.

But to your question concerning the growth of the sun’s path, how one can most clearly discern it, I can scarcely give an answer so precise as not to be wrong in part; for the sun’s path does not wax at the same 95rate in all parts of the earth. I can, of course, answer according to what I have found in the writings of men who have treated the subject thoroughly, and it is generally believed that their words come very near the truth. I have already told you how many hours there are in a night and day and gave the number as twenty-four.^[170] I have indicated the length of each hour in stating that three hours pass while the sun moves across one division of the sky. Now there are some other little hours called ostensa,^[171] sixty of which make one of those that I mentioned earlier. It seems to me quite likely that, as far north as we are, the sun’s path waxes five of these little hours in a day and as much less than six as a twelfth part of a little hour. And as to the growth of the sun’s path it seems most reasonable to me that it waxes three-fourths of these hours toward the east and the west and the remaining fourth in height toward the zenith. South of us, however, this reckoning will fail; for north of us the increase is greater and to the south less than we have just stated; and the farther south, the greater is the difference, and the sun more nearly overhead.