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346. When the moon is entirely obscured, the eclipse is called total; when only a portion of the disk is concealed partial, and when the disk just touches the edge of the shadow, the phenomenon is termed an appulse.

347. OF THE EARTH'S SHADOW. Since the rays of light move in straight lines, the shadow of a globe illumined by one of greater size is conical, and the length of its shadow will depend upon the size and distance of the illuminating body. For the greater the relative size and the less the distance the shorter will be the shadow, and the smaller the size and the greater the distance the longer the shadow. The sun being vastly greater in magnitude than the earth, the shadow of the latter is accordingly conical.' (Fig. 61,) and though they never vary in size, yet as they vary in their distances from each other, the earth's shadow is changeable in length, being shortest when the sun is in perigee and longest when in apogee.

348. It is by no means a difficult matter to determine the length of the shadow, and by the aid of Fig. 61, we will explain the manner in which the calculation is made. In this figure S represents the centre of the sun, E that of the earth, and AD and PL rays of light from the edges of the sun, touching the earth at D and L, and meeting at B. The lines BD and LB bound the shadow, SEB is a straight line drawn from the centre of the sun through that of the earth, to the extremity of the shadow, and EB is the length of the shadow. Our task is to find how many miles long EB is.

349. We must first direct our attention to the triangle DEB. We know the extent of DE, for it is a radius of the earth, and is 3956.2 miles long; moreover, EDB is a right angle; for if a line (as ADB) touches the surface of a sphere at any point, and a line (as DE) is

1. Strictly speaking the shadow is not an exact cone, the base of which is a circle. It would be a cone if the earth was a perfect sphere but being an ellipsoid the base of the shadow is an ellipse instead of a circle.

When is an eclipse total? When partial? What is an appulse? What is the form of the shadow of a globe illumined by one of a greater size? What does the length of the shadow depend upon? What is the form of the shadow of the earth? When ongest? When shortest? Can its length be calculated ?

drawn from the centre of the sphere to that point, the line drawn from the centre and the touching line always make a right angle with each other. Now join AE, and we thus form two angles; viz., DAE which is the sun's horizontal parallax, (Art. 94,) and AES which is the sun's apparent semi-diameter. In geometrical language AES, is called the exterior angle of the triangle AEB, and is equal to the sum of the two angles ABE and BAE. The angle EBA, is therefore equal to the angle AES, diminished by the angle EAB; or in other words equals the difference between the sun's apparent semi-diameter and his horizontal parallax. The value of the difference at the sun's mean distance is 15'51.4". Therefore, in the triangle DEB, since we know the value of all the angles and the length of one side, we proceed to select from the trigonometrical tables a similar triangle as D'E'B', and institute a proportion as we have before shown between the sides.

350. We thus find, that if the line B'E' represents one mile, D'E1 consists of four thousand six hundred and twelve millionths of a mile; and the proportion runs thus, D'E' (004612ths of a mile): B'E' (one mile): DE (3956.2 miles): BE. Multiplying together the second and third times of the proportion and dividing by the first, we obtain for the value of BE 857,806 miles. The mean or average length of the shadow, is therefore, about 860,000 miles, extending beyond the earth's centre to a distance more than three and a half times that of the

Explain how by Fig. 61. What is the mean length of the earth's shadow in miles?

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moon from the earth. When the sun is at the perigee, the length of the shadow is about 14,400 miles shorter, and when at the apogee, nearly 14,700 miles longer than the mean value.

351. EXTENT OF SHADOW TRAVERSED BY THE MOON. It is proved by mathematical investigations, that the average breadth of the earth's shadow where the moon crosses it, is about three times the diameter of the moon or nearly 6,500 miles. But the length of the moon's path through the shadow is affected by two circumstances; First, the varying distance of the sun from the earth; Secondly, the varying distance of the moon from the earth. For when the sun is in apogee at the time of the eclipse, the breadth of the shadow, at the average distance where the moon crosses it, will be greater than usual; (Art. 350,) and if the moon then happens to be in perigee, she will cross the shadow about 13,000 miles nearer the earth than at her average distance of 240,000 miles, and will consequently traverse a broader part of the shadow.'

But if the reverse happens, the sun being in perigee, and the moon in apogee, the proximity of the sun will narrow the earth's shadow at the average distance where the moon crosses it, while the moon being now farthest from the earth, will pass through the shadow at a still narrower place, nearly 13,000 miles, beyond its average place of crossing.

352. OF THE PENUMBRA. On each side of the shadow of the earth there exists, to a certain limit, a space where there is a partial shadow or penumbra.* Outside of this space the moon is illumined by the full orb of the sun, but as she enters the penumbra the dark body of the earth begins to interpose itself, and cuts off a portion of the sun's light. As she continues to ap

1. It will be remembered that the moon in apogee is 26,000 miles farther from the earth than when in perigee (Art. 310.) Her average distance will therefore differ from her apogee and perigee distances by 13,000 miles. 2. See page 133, note 2.

How does it compare in length with the moon's distance from the earth? When the sun is in perigee, how much shorter is the shadow than its mean length? When the sun is in apogee how much longer? What is the average breadth of the earth's shadow where .he moon crosses it? By what two circumstances is the length of the moon's path through he shadow affected? Explain why? What is the penumbra ?

proach the shadow, more and more light is intercepted; and at the moment the earth totally hides the sun from any part of the moon, that part at the same instant passes the inner limit of the penumbra and enters the shadow.

353. The space occupied by the penumbra is determined as follows: Referring to Fig. 61, and supposing the lines ALW and PDU, to be drawn, touching the earth at the points D and L,' the penumbra is found on each side of the shadow bounded by the lines UD, DB and BL, LW. QM represents the path of the moon, and the several small circles.on the line QM, are different positions of the moon at and near the time of an eclipse.

354. It is evident from the slightest glance, that the moon when nearest Q, is exposed to all the light of the solar disk; but that as soon as she passes beyond the line LW, a portion of the sun near A, can not be seen from the moon, on account of the interposition of a portion of the earth at L. More and more of the sun's disk will become invisible at the moon as she advances towards the line LB, and when she has passed this line, the disk of the sun is entirely concealed from a part of her surface, if not from all, by the intervention of the earth.

355. The moon leaves the shadow, re-entering the penumbra on the opposite side, when she has crossed the line DB; for here rays of solar light from the regions about P now shine upon her, and when she has passed the line DU, she emerges from all obscurity and the full light of the sun again illumines her surface. The space DBL therefore comprises the shadow of the earth, while the penumbra is limited as before stated, by the lines UD, DB and BL, LW.

356. DURATION OF A LUNAR ECLIPSE. When a total eclipse occurs, the moon, if she passes centrally through the shadow, may be completely obscured for the space

1. The straight lines PU and AW do not touch the surface of the earth at exactly the same points where AB and PB touch; viz., at D and L, but very near them.

State what changes in illumination the moon undergoes, as she advances from beyond the penumbra into the shadow? Explain from figure. For what space of time is the moon obscured during a total eclipse, when she passes centrally through the shadow ?

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of about two hours, for she moves through a space equal to her own breadth in about an hour, and as the breadth of the earth's shadow where the moon crosses it is nearly three times her diameter, she must traverse two thirds of the breadth of the shadow in obscurity.

357. The duration however of complete eclipse will depend upon the direction of the moon's transit through the shadow, and also upon the varying distances of the sun and moon from the earth, as explained in (Art. 351.) A lunar eclipse may continue for the space of about five and a half hours, counting from the moment the moon enters the penumbra, till the instant she leaves it.

358. RED LIGHT OF THE DISK. During a lunar eclipse the darkened surface of the moon is illumined by a reddish light, a phenomenon resulting from the refraction of the solar rays by the earth's atmosphere. For the solar beams entering our atmosphere are refracted towards the earth, and being thus bent into the shadow pass onward and strike the moon. Being thence reflected to us, they are still sufficiently bright to render her surface, even in shadow, distinctly visible. The color of the light is owing to the same cause that gives rise to the ruddy tints of sunset clouds; the white light of the sun in struggling through the atmosphere loses its feebler rays,' while the red, which possesses the greatest power to overcome any resistance it encounters, emerges, and imparts its own hue to the objects upon which it falls.

This reddish light is of sufficient intensity, to enable observers to detect the obscure regions and spots on the lunar disk. The following facts are stated by Hind. During an eclipse of the moon that occurred on the 23d of July, 1823, M. Gambart saw all the lunar spots distinctly revealed. In an eclipse that happened on the

1. When a sunbeam is refracted, the seven colors of which it is composed; to wit, red, orange, yellow, green, blue, indigo, and violet, are turned out of the course of the original beam. The red deviating the least and the violet the most. The red is therefore least affected by the resistance it meets with.

Why? What does the duration of complete eclipse depend upon? How long may a lunar eclipse last, counting from the time the moon enters to the time she leaves the penumbra ? What phenomenon occurs during a lunar eclipse? How is it caused? To what is the color owing? What can be discerned on the disk of the moon by means of this light?