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DIALS AND CLOCKS. 75
at 5 o'clock, it will then be shown at W, by the shadow on the western side of the dial, and the shadow cannot be observed on the. dial to advantage much later than 5 o'clock, Suppose, then, the dial located, and that when the shadow indicates XII, or apparent noon, a well regulated clock is started, the hands of which also indicate XII, and this on the 24th day of December, for, as we shall soon see, this is one of the four days in the year when the clock and dial agree, then, although for a few days, the clock and dial will appear to indicate the hour of noon together, it will soon be observed, that the clock begins to gain on the dial, and after an interval of one month, the clock will show 12h, 13m, when the dial indicates noon, or 12 o'clock apparent time. This difference will go on increasing, until February 10th, or 11th, when the clock will appear to lose time, and by the 25th of March will be only 6m. faster than the dial, and on the 15th day of April they will again correspond. The clock, after this, will continue, apparently, to lose time until about May 15th, at which time it will only indicate 11h, 56m, when the dial shows noon; after this, its rate seems to increase, and on the 16th day of June they again come together. The clock now continues to gain on the dial until July 25th, when it is about 6m, 4s, faster, after which, its rate apparently decreases, until at August 31, they again coincide. On the 2d of November, the clock shows 11h, 43m, 46s, when the dial says it is noon; this is the greatest difference of all, being 16m, 14s, after this they begin to come together, and on December 24th, again correspond. Now, can it be that the sun’s motion in the heavens, or rather the earth's motion, is thus irregular 7 We might, at first, suspect our clocks, and watches, but the utmost pains have been bestowed on these, and when their rates of going have been ascertained, by means of the stars, and a transit instrument, as already described, they are found to go perfectly uniform, or very nearly so. Hence we are forced to admit, that the discrepancy between the dial and the clock, is to be sought for in the movements of the earth, and we shall fully show, in our next chapter, what these are.
, Thus far we hope we have succeeded in explaining the phemomena of the heavens due to the movements of the earth, and we have, we trust, been sufficiently clear. If, in some parts, we have been tediously minute, the more intelligent reader will remember we are writing for those who may be less expert. Certainly every one must feel interested in understanding the causes of some of the most striking phenomena which are continually occurring. The varying lengths of days, the annual round of seasons, the constant return of day and night, the tides, the winds, and the clouds, all these force themselves upon observation, and demand some attention. To the eonsideration and elucidation of these great phenomena, the wisest men of all ages have devoted their lives, and simple and clear as the illustration of these great natural causes may now appear, they have cost an amount of human labor and severe study, which we might in vain attempt to estimate. We feel not the less satisfaction, that we can look beyond the occurrences of the day and understand the causes which are concealed from careless eyes. The earth is no less beautiful, and beloved by us, because we can look above and see worlds, which we know to be a thousand times larger, and on which, we sometimes fancy, myriads of intelligent beings are existing, all pursuing the same great ends as we. After all, we are well satisfied with the study of our own planet, and find enough upon its surface, or below it, to fill us with admiration and wonder, and see enough in it of beauty, whether glowing in the warm sun-light, 3r reposing in the quiet rays of the moon.
“The Pilots now their rules of art apply,
HITHERTo we have spoken of the earth's orbit as circular, such being its apparent projection upon the celestial sphere, but this is not the actual case, it is elliptical. This is ascertained by the change in the apparent, diameter of the sun, viewed from the earth at different seasons. If the orbit of the earth was a great circle, having the sun in its centre, it is obvious that the angle subtended by his disk would at all times be the same, for his distance from the earth would always be the same. On the contrary, the diameter is observed to increase from the summer solstice to the winter solstice, then to again decrease. It is a proposition established in optics, that the apparent diameter of an object, varies inversely as the distance from the spectator, when the angle is small, hence by observing with great accuracy, the apparent diameter of the sun, at different periods of the year, and actually projecting or calculating the orbit of the earth, it is found to be an ellipse, or oval, as represented in the following diagram. The sun being situated, not in its centre, but nearer one side, in what is called one of the foci of the ellipse. The foci of the ellipse S and C, are so situated on the major, or longer axis, of the ellipse, that the sum of the length of any two lines drawn from the foci to the same point in the circumference of the ellipse is constant. Thus the sum of the lengths C E and S E, are equal to the sum of the lengths CO and SO, or CD, and SD, and al are equal to the
length of the major axis A. B. By placing two pins, one at each focus of the ellipse, and tying a thread around them of such length as will give the requisite major axis, a true ellipse may be described, by stretching the string and moving a pencil around in the angle. In the preceding diagram, we may suppose S E C, SO C, S D C, to be three positions of the string, the pencil being placed in the angles E, O, and D. Such is the peculiar property of the ellipse, and in such an orbit the earth is moving around the sun. Let S be the position of the sun, and A the position of the earth, at the time when nearest the sun, and when, consequently, the sun's diameter appears the largest. This point in the orbit. is called the perihelion point, from two Greek words, which mean near or about the sun. The point B is called the aphelion point, or point away from the sun ; when the earth is in this position, the sun's diameter appears the smallest. The line B.A, is called the line of the apsides, i. e. the line without deviation, or change in length, for we shall show, presently, that whatever changes the earth's orbit may undergo, this line will remain unaltered. In the preceding chapter, we observed that the sun's motion was not uniform in the heavens, or did not correspond with the indications of a well regulated clock. It will not be difficult to understand, that since it is the attraction of the sun which causes the motion of the earth, it will, while approaching the sun, have its motion continually accelerated, or quickened, until it sweeps around the perihelion point A, with its greatest velocity, its motion
will then decrease, and it will move slowest when it passes the aphelion point B. The earth is at the point A, on the 31st of December, and at the point B, six months after, or July 1st. If the inequality between the time indicated by the dial and that by the clock was caused wholly by this change in the velocity of the sun, then the dial and clock should agree exactly when the earth was in these two positions, for the earth occupies just 6 months in moving from A to B, and 6 months in returning from B to A, just what it would if its orbit was a circle, and in which case the dial and clock would agree. But by actual observation, the dial and clock are not together twice in the year, but four times, and then not when the earth is at A and B, December 31, and July 1st, but on December 24th, April 15th, June 16th, and August 31st, as we have already intimated. We must look, therefore, to another source, which, united with the one we have just considered, will fully explain all the observed phenomena, and we find it in the inclination of the sun's apparent path to the equator, As the earth turns on its axis, we may suppose a rod which extends from the centre of the earth, and through its equator to the sky, tracing out a line, or circle, in the heavens, which is called the celestial equator. This circle is, as we have already shown, divided into 24 parts, called hours, each hour comprehending 15°, and all these spaces are exactly equal. If the sun's yearly path in the heavens had corresponded with the equator, or had been in the same plane, then all the difference between the dial and clock would have been simply what was due to his moving sometimes apparently faster than at others, in consequence of the earth’s elliptical orbit, but this is not the case, the plane of the ecliptic, or sun’s path, is inclined to the plane of the equator. Now, on the supposition that the orbit is circular, let us see what effect this would have upon the sun-dial. In the next diagram, the circle 0, 1, 2, 3, 4, 5, &c., which are hour divisions, represents the equator, and I, II, III, IV, V, VI, &c., which are also hour divisions, the ecliptic. Clock time is measured on the former, for this is the circle, or others parallel to it, in which the stars, and other heavenly bodies, seem to move on account of the diurnal rotation of the earth. Dial time is measured on the ecliptic, and