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