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I, &c., thus indicated on the paper, and the centre of the circle A, draw the hour-lines A F, A G, A H, &c., extending, however, only to the circumference of the circle, and we have a dial ready for use, after adding the figures. Of course the little circle must be so adjusted that when the line is passed by some one of its graduations, it will reach the horizontal plane at a point in the meridian line A C. Instead of a wire for the gnomon, we may use an inclined plane, so that our dial will now be not unlike this

figure. In order to use it, we must next determine the north and south line, or a meridian line, and place the line on our dial which marks XII, to correspond therewith. This may be ascertained by means of a surveyor's compass, provided the variation of the needle from true north is known; or, at the time of the solstices, mid-summer or mid-winter, when the sun's declination is changing very slowly, a number of circles may be traced upon a horizontal plane, having a common centre, over which centre a plumb-line must be suspended, having two or three knots tied in it. Upon marking where the shadow of these knots falls, successively, on the circles, in the forenoon and afternoon, and then bisecting the space so measured on each circle, and drawing a line through the centre and these points of bisection, a pretty exact meridian line may be laid down. The use of several circles, is simply to ensure greater accuracy in the result. We will now suppose the dial constructed, and located in a window facing to the south. We may here observe, that there will be no use in graduating the dial all the way round, as that portion only can be used over which the shadow passes during the day, say from 5 o'clock to 5 o'clock, on each side, viz: from V, on the western side, through VI, VII, VIII, IX, X, XI, to XII, and from XII, to V, on the eastern side. When the sun rises before 6 o'clock, say

DIALS AND CLOCKS.

75 at 5 o'clock, it will then be shown at V, 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? 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 phenomena 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 consideration 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, or reposing in the quiet rays of the moon.

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ORBIT OF THE EARTH.

CHAPTER VII.

Measurement of Time.

"The Pilots now their rules of art apply,
The mystic needle's devious aim to try;
Along the arch the gradual index slides,
While Phœbus down the vertic circle glides,
Now, seen on ocean's utmost verge to swim,
He sweeps it vibrant with his nether limb.
Their sage experience thus explores the height
And polar distance of the source of light."

Falconer.

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

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the lengths C O and S O, or C D, and S D, and all are equal to the

E

B

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 EC, SO C, SD 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

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