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 things 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, is 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 rate 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.
VII
THE SUBJECT OF THE SUN’S COURSE CONTINUED
Son. With your permission I wish to inquire somewhat more fully into this subject, for I do not quite understand it. You have said that the sun’s ascent is more rapid to the north of us, where summer is almost wanting, while the strength of winter is so overpowering that summer seems like a mere shadow, and where in many places both snow and ice lie all through summer just as in winter, as is true of Iceland and particularly of Greenland. But I have heard that in the southlands there are no severe winters, the sun being as hot in winter as it is with us in summer; and that in winter, when the sun has less power, both grain and other crops grow, while in summer the earth cannot endure the fervent heat of the sun and consequently yields neither grass nor grain; so that in regions like Apulia and even more so in the land of Jerusalem the heat of summer causes as great distress as the cold of winter with us. Now when you tell me that the sun’s path waxes faster here in the north than yonder in the south, I cannot see the reason why; for there the sun’s heat is as great in winter as it is with us in summer; and it is so much greater in summer that all vegetation on the earth is scorched by it. Therefore it seems to me more likely that the sun’s path waxes most rapidly where the heat is most intense. Now if you can and will clear this up for me so that I can grasp it, I shall listen gladly and attentively.
Father. I shall begin my talk on the subject that I am now to take up with a little illustration, which may help you to a clearer insight, since you find it so difficult to believe the facts as stated. If you take a lighted candle and set it in a room, you may expect it to light up the entire interior, unless something should hinder, though the room be quite large. But if you take an apple and hang it close to the flame, so near that it is heated, the apple will darken nearly half the room or even more. However, if you hang the apple near the wall, it will not get hot; the candle will light up the whole house; and the shadow on the wall where the apple hangs will be scarcely half as large as the apple itself. From this you may infer that the earth-circle is round like a ball and not equally near the sun at every point. But where the curved surface lies nearest the sun’s path, there will the greatest heat be; and some of the lands that lie continuously under the unbroken rays cannot be inhabited. On the other hand, those lands which the sun approaches with slanting rays may readily be occupied; and yet, some of these are hotter than others according as they lie nearer the sun’s path. But when the curved and steep slope of the sphere-shaped wheel moves up before the light and the beams of the sun, it will cast the deepest shadow where its curved surface lies nearest the sun; and yet, the lands nearest the sun are always hottest.[[172]] Now I agree with you that Apulia and Jerusalem are hotter than our own country; but you must know that there are places where the heat is greater than in either of those just mentioned, for some countries are uninhabitable on account of the heat. And I have heard it stated as a fact, that even when the sun mounts highest, the night in those regions is very dark and quite long. From this you must conclude that where the strength and power of the sun are greater, since it is nearer, it must ascend and decline more slowly; for the night is long in summer when the sun mounts highest, and the day is long in winter when it sinks lowest. Now I shall explain this so clearly that you will understand it fully.
You know that here with us in winter the day and the course of the sun are brief; for so short is the sun’s path that it passes through but a single region of the sky, and then only where the sun has considerable strength. But in many places the sun is not to be seen during a large part of winter, for example in Halogaland,[[173]] as we have not only heard tell but have often and constantly learned and observed with our own eyes. For we know definitely that from about November 10 to January 10 there never comes a day so bright up north in Vaag or at Andenes[[174]] in Halogaland but that the stars in the sky are visible at midday as at midnight. And although the days have so much light that the stars cannot be seen, nevertheless, in most of the places that we have mentioned the sun remains invisible till January 23. But after that date the days lengthen and the sun mounts so rapidly, that beginning with April 6 daylight does not disappear before September 17, all the intervening time being one continuous day, for daylight never fails in all that while. From this you may safely conclude that, though the sun is hotter in the southern lands that we spoke of earlier, its course waxes and mounts more slowly where the night, even at mid-summer, is deep and long and dark, and where there is never a time in the whole twelvemonth when day does not fail. But in Halogaland, as I have just said, there is no day in winter and stars are visible at midday when the day should be brightest; later, however, when the days begin to lengthen, they grow so rapidly that early in spring daylight begins to tarry all the night and continues till much of the autumn is past.
There remains one more proof which will seem very clear to you. You know that in those localities in Halogaland that we have just mentioned the sun about May 15 begins to shine with the same brightness by night as by day, never setting either at night or during the day but shining continuously in this manner and with this brightness, except when its light is obscured by clouds, even to July 25. Now you know that the sun is only moderately warm in Halogaland, and that there is but a little time in summer when it gives sufficient warmth. Still, there it is with its blazing disk about as long as we have just stated, and it maintains the daylight about as long as we have just computed. But neither fact is true of the southlands, though the sun is hotter there. Now these facts give evidence that the sun is more distant here, for it gives less heat. They also testify to the waxing of its course, for, since its light is as bright by night as by day, its path must lengthen more rapidly here. But yonder it waxes less and more slowly, for there the night has its prescribed period both for length and darkness in summer as well as in winter.