In (2) we see, as 50 seconds of arc represents the distance the earth will rotate in 31⁄3 seconds, a difference of one day will result in 26,000 years. That is since the clock regulated by the stars, or absolute rotations of the earth, would get behind 31⁄3 seconds per year, it would be behind a day in 26,000 years, as compared with a sidereal clock regulated by the Spring equinoctial point.

In (3) we see that as 50 seconds of arc is traversed by the earth, in its annual revolution, in 201⁄3 minutes, a complete circle of the Zodiac will be made in 26,000 years.

In (4) we see that as the difference between the year of the seasons and the Zodiacal year is 31⁄3 seconds of the earth's rotation, it follows that if this is divided by the number of days in a year we have the amount which a sidereal day is less than 4th, or an absolute rotation of the earth. That is, any meridian passes the Spring equinoctial point 1⁄110 of a second sooner than the time of one absolute rotation. These four equations are all founded on the precession of the equinoxes, and are simply different methods of stating it. Absolutely and finally, our time is regulated by the earth's rotation; but strange as it may appear, we do not take one rotation as a unit. As shown above, we take a rotation to a movable point which creeps the 1⁄110 of a second daily. But after all, it is the uniform rotation which governs. This is the one “dependable” motion which has not been found variable, and is the most easily observed. When we remember that the earth is not far from being as heavy as a ball of iron, and that its surface velocity at the equator is about 17 miles per minute, it is easy to form a conception of its uniform motion. Against this, however, we may place the friction of the tides, forcing up of mountain ranges, as well as mining and building skyscrapers—all tending to slow it. Mathematicians moving in the ethereal regions of astronomy lead us to conclude that it must become gradually slower, and that it is slowing; but the amount may be considered a vanishing quantity even compared with the smallest errors of our finest clocks; so for uncounted generations past—and to come—we may consider the earth's rotation uniform. Having now found a uniform motion easily observed and of convenient period, why not adopt it as our time unit? The answer has been partially given above in the fact that we are compelled to use a year, measured from the Spring equinoctial point, so as to keep our seasons in order; and therefore as we must have some point where the sidereal clocks and the meantime clocks coincide, we take the same point, and that point is the Spring equinox. Now we have three days:—

Now, isn't it remarkable that our 24-hour day is purely artificial, and that nothing in nature corresponds to it? Our real day of 24 hours is a theoretical day. Still more remarkable, this theoretical day is the unit by which we express motions in the solar system. A lunar month is days—hours—minutes—and seconds of this theoretical day, and so for planetary motions. And still more remarkable, the earth's rotation which is itself the foundation is expressed in this imaginary time! This looks like involution involved, yet our 24-hour day is as real as reality; and the man has not yet spoken who can tell whether a mathematical conception, sustained in practical life, is less real than a physical fact. Our legal day of practical life is therefore deduced from the day of a fraction less than one earth rotation. In practice, however, the small difference between this and a rotation is often ignored, because as the tenth of a second is about as near as observations can be made it is evident that for single observations 1⁄110 of a second does not count, but for a whole year it does, and amounts to 31⁄3 seconds. Now as to the setting of our clocks. While the time measured by the point of the Spring equinox is what we must find it is found by noting the transits of fixed stars, because the relation of star time to equinoctial time is known and tabulated. Remember we cannot take a transit of the equinoctial point, because there is nothing to see, and that nothing is moving! But it can be observed yearly and astronomers can tell where it is, at any time of the year, by calculation. The stars which are preferred for observation are called “time stars” and are selected as near the celestial equator as possible. The earth's axis has a little wabbling motion called “nutation” which influences the apparent motion of the stars near the pole; but this motion almost disappears as they come near the equator, because nutation gives the plane of the equator only a little “swashplate” motion. The positions of a number of “time stars” with reference to the equinoctial point, are known, and these are observed and the observations averaged. The distance of any time star from the equinoctial point, in time, is called its “right ascension.” Astronomers claim an accuracy to the twentieth part of a second when such transits are carefully taken, but over a long period, greater exactness is obtained. Really, the time at which any given star passes the meridian is taken, in practical life, from astronomical tables in the Nautical Almanacs. Those tables are the result of the labors of generations of mathematicians, are constantly subject to correction, and cannot be made simple. Remember, the Earth's rotation is the only uniform motion, all the others being subject to variations and even compound variations. This very subject is the best example of the broad fact that science is a constant series of approximations; therefore, nothing is exact, and nothing is permanent but change. But you say that mathematics is an exact science. Yes, but it is a logical abstraction, and is therefore only the universal solvent in physical science.

With our imaginary—but real—time unit of 24 hours we are now ready to consider “local time.” Keeping the above explanation in mind, we may use the usual language and speak of the earth rotating in 24 hours clock time; and since motion is relative, it is permissible to speak of the motion of the sun. In the matter of the sun's apparent motion we are compelled to speak of his “rising,” “setting,” etc., because language to express the motion in terms of the earth's rotation has not been invented yet. For these reasons we will assume that in [Fig. 47] the sun is moving as per large arrow and also that the annulus, half black and half white, giving the 24 hours, is fastened to the sun by a rigid bar, as shown, and moves around the earth along with him. In such illustrations the sun must always be made small in proportion, but this rather tends to plainness. For simplicity, we assume that the illustration represents an equinox when the sun is on the celestial equator. Imagine your eye in the center of the sun's face at A, and you would be looking on the meridian of Greenwich at 12 noon; then in one hour you would be looking on 15° west at 12 noon; but this would bring 13 o'clock to Greenwich. Continue till you look down on New York at 12 noon, then it is 17 o'clock at Greenwich (leaving out fractions for simplicity) etc. If you will make a simple drawing like [Fig. 47] and cut the earth separate, just around the inside of the annulus, and stick a pin at the North Pole for a center, you may rotate the earth as per small arrow and get the actual motion, but the result will be just the same as if you went by the big arrow. We thus see that every instant of the 24 hours is represented, at some point, on the earth. That is, the earth has an infinity of local times; so it has every conceivable instant of the 24 hours at some place on the circle. Suppose we set up 1,410 clocks at uniform distances on the equator, then they would be about 17 miles apart and differ by minutes. Now make it 86,400 clocks, they would be 1,500 feet apart and differ by seconds. With 864,000 clocks they would be 150 feet apart and vary by tenths of seconds. It is useless to extend this, since you could always imagine more clocks in the circle; thus establishing the fact that there are an infinity of times at an infinity of places always on the earth. It is necessary to ask a little patience here as I shall use this local time and its failure later in our talk. Strictly, local time has never been used, because it has been found impracticable in the affairs of life. This will be plain when we draw attention to the uniform time of London, which is Greenwich time; yet the British Museum is 30 seconds slow of Greenwich, and other places in London even more. This is railroad time for Great Britain; but it is 20 minutes too fast for the west of England. This led to no end of confusion and clocks were often seen with two minute hands, one to local and the other to railroad time. This mixed up method was followed by “standard time,” with which we are all pretty well acquainted. Simply, standard time consists in a uniform time for each 15° of longitude, but this is theoretical to the extreme, and is not even approached in practice. The first zone commences at Greenwich and as that is near the eastern edge of the British Islands, their single zone time is fast at nearly all places, especially the west coast of Ireland. When we follow these zones over to the United States we find an attempt to make the middle of each zone correct to local time, so at the hour jumping points, we pass from half an hour slow to half an hour fast, or the reverse. We thus see that towns about the middle of these four United States zones have sunrise and sunset and their local day correct, but those at the eastern and western edges average half an hour wrong. As a consequence of this disturbance of the working hours depending on the light of the day, many places keep two sets of clocks and great confusion results. Even this is comprehensible; but it is a mere fraction of the trouble and complication, because the hour zones are not separated by meridians in practice, but by zig-zag lines of great irregularity. Look at a time map of the United States and you will see the zones divided by lines of the wildest irregularity. Now question one of the brightest “scientific chaps” you can find in one of the great railroad offices whose lines touch, or enter, Canada and Mexico. Please do not tell me what he said to you! So great is the confusion that no man understands it all. The amount of wealth destroyed in printing time tables, and failing to explain them, is immense. The amount of human life destroyed by premature death, as a result of wear and tear of brain cells is too sad to contemplate. And all by attempting the impossible; for local time, even if it was reduced to hourly periods is not compatible with any continental system of time and matters can only get worse while the attempt continues. For the present, banish this zone system from your mind and let us consider the beginning and ending of a day, using strictly local time.

[LOI]

Fig. 47—Local Time—Standard Time—Beginning and Ending of the Day

A civil, or legal, day ends at the instant of 24 o'clock, midnight, and the next day commences. The time is continuous, the last instant of a day touching the first instant of the next. This is true for all parts of the earth; but something in addition to this happens at a certain meridian called the “date line.” Refer again to [Fig. 47] which is drawn with 24 meridians representing hours. As we are taking Greenwich for our time, the meridians are numbered from 0°, on which the observatory of Greenwich stands. When you visit Greenwich you can have the pleasure of putting your foot on “the first meridian,” as it is cut plainly across the pavement. Degrees of longitude are numbered east and west, meeting just opposite at 180°, which is the “date line.” Our day begins at this line, so far as dates are concerned; but the local day begins everywhere at midnight. Let us start to go around the world from the date line, westward. When we arrive at 90° we are one quarter around and it takes the sun 6 hours longer to reach us. At 0° (Greenwich) we are half around and 12 hours ahead of the sun motion. At 90° west, three quarters, or 18 hours, and when back to 180° we have added to the length of all days of our journey enough to make one day; therefore our date must be one day behind. Try this example to change the wording:—Let us start from an island B, just west of the date line. These islanders have their 24-hour days, commencing at midnight, like all other places. As we move westward our day commences later and later than theirs, as shown above. Suppose we arrive at the eastern edge of the 180° line on Saturday at 12 o'clock, but before we cross it we call over to the islanders,—what day is it? We would get answer, “Sunday;” because all our days have been longer, totalling one day in the circuit of the globe. So if we step over the line at 12 o clock Saturday, presto, it is 12 o'clock Sunday. It looks like throwing out 24 hours, but this is not so, since we have lived exactly the same number of hours and seconds as the islanders. In this supposition we have all the dates, however, but have jumped half of Saturday and half of Sunday, which equals one day. In practice this would not have been the method, for if the ship was to call at the island, the captain would have changed date on Friday night and thrown Saturday out, all in one piece, and would have arrived on their Sunday; so his log for that week would have contained only 6 days. It is not necessary to go over the same ground for a circuit of the globe eastward, but if you do so you will find that you shorten your days and on arriving at the date line would have a day too much; so in this case you would double a date and have 8 days in that week. In both cases this is caused by compounding your motion with that of the sun; going with him westward and lengthening your days, or eastward meeting him and shortening them. [Figure 47] shows Greenwich noon, we will say on Monday, and at that instant, Monday only, exists from 0 to 24 o'clock on the earth; but the next instant, Tuesday begins at 180° B. In one hour it is noon of Monday at 15° West, and midnight at 165° East; so Tuesday is one hour old and there is left 23 hours of Monday. Monday steadily declines to 0 as Tuesday steadily grows to 24 hours; so that, except at the instant of Greenwich noon, there are always two days on the world at once. If we said that there are always two days on the world at once, we could not be contradicted; since there is no conceivable time between Monday and Tuesday; it is an instantaneous change. As we cannot conceive of no time, the statement that there is only one day on the earth at Greenwich noon is not strictly permissible. Since there are always two days on the world at once let us suppose that these two are December 31st and January 1st; then we have two years on the world at once for a period of 24 hours. Nine years ago we had the 19th and 20th centuries on the world at once, etc. As a mental exercise, you may carry this as far as you please. Suppose there was an impassable sea wall built on the 180° meridian, then there would be two days on the world, just as explained above; but, practically, there would be no date line, since in sailing west to this wall we would “lengthen our days,” and then shorten them the same amount coming around east to the other side of the wall, but would never jump or double a date. This explanation is founded, as it ought to be, on uniform local time, and is the simplest I can give. The date line is fundamentally simple, but is difficult to explain. When it is complicated by the standard time—or jumping hour system—and also with the fact that some islands count their dates from the wrong side of the line for their longitudes, scientific paradoxes arise, such as having three dates on the world at once, etc.; but as these things are of no more value than wasting time solving Chinese puzzles, they are left out. Ships change date on the nearest night to the date line; but if they are to call at some island port in the Pacific, they may change either sooner or later to correspond with its date. Here is a little Irish date line wit printed for the first time,—I was telling my bright friend about turning in on Saturday night and getting up for breakfast on Monday morning. “Oh,” said he, “I have known gentlemen to do as good as that without leaving New York City!”