several divisions on the external quadrant, 12 VI, and where it cuts the quadrant il mark, and thus divide it into six equal parts. Or it may be divided by stepping the dividers. Through the points of division in the small quadrant, draw lines parallel to the line VI k VI, till they intersect the hour lines on each side of the axis. Through the points, where these lines meet the hour lines, 6, 7, &e. from VI, on one side to VI, on the other, draw with a pen or pencil an elliptic curve. This will represent the path of the place over the earth's disk, as seen from the moon on the day of the eclipse. When the sun is in south declination, the ` elliptic curve, representing the path of the place, must be drawn on the upper side of the line VI k VI. The order must be reversed in drawing for places in the south latitude.

The ellipse representing the path of the place on the earth's disk may be more easily, and perhaps more elegantly delineated by considering VI k VI as the transverse, and ij as the conjugate. The mean proportional between the sum and difference of these is the distance of the foci. At the place of the hours, however, unless drawn with great attention, it might not be so accurate, as the method used in the diagram. Set the degrees and minutes in the angle of the moon's path with the ecliptic, 5° 39', from D to M, her latitude being north descending. Draw the line C M for the axis of the moon's orbit. When the moon's latitude is north or south ascending, the axis of her orbit must be represented on the left hand of the axis of the ecliptic; but when her latitude is north or south descending, the axis of her orbit must be on the right hand of the axis of the ecliptic. Bisect the angle D C M by the line C m. Take the moon's latitude CM it from the line A CB to n

31′ 55′′ from your scale, and set on the bisecting line C m, as the line n o parallel to C L.Through n at right angles to the axis C M draw N O for the path of the moon's shadow over the earth at the time of the eclipse.

7

Take from your scale the moon's horary motion from the sun 33′ 25′′, and making it equal to QR, (Plate IX. Fig. 2.)

divide it into 60 equal parts for minutes; or it may be divided into larger parts of two, three, five, or ten minutes each, at pleasure. Set the true time of new moon on the line N O at n, where it intersect the line C m. Then from QR, the line of horary motion, take the minutes and seconds passed after the hour preceding the conjunction, and set them from n, backwards on the path of the shadow towards N. Thus 39m. 46s. will extend from n to IX. on that path. Take the whole extent of QR, and set it each way from IX, to the different hour marks as on the line NO. The marks will show the centre of the moon's shadow at the times specified. The spaces may be subdivided into quarters, five minutes, or minutes, as may be convenient.

Apply the side of a square to the path of the moon's shadow, and, as you move it along, observe, when the other side cuts the same time in that path and in the path of the place over the earth's disk. This time is the instant of greatest obscuration. From the scale take the sun's semi-diameter, and setting one foot of the dividers in the path of the place at the point of greatest obscuration, draw a circle to represent the sun, as seen at the centre of the eclipse. With the moon's semi-diameter, taken from the scale, as a radius, make a circle on the path of her shadow, the centre at the point, where the centre of her shadow is at the greatest obscuration, representing her disk at the same time. The circle of the moon being shaded with ink or paint, the appearance of the sun at the centre of the eclipse will be represented. The part only of the sun covered by the moon may be shaded, if preferred.

From the scale take the semi-diameter of the penumbra, and setting one foot of the dividers backwards, on the path of the shadow, N O, the other on the path of the place, observe when each is at the same instant. Note this is as the beginning of the eclipse. With the dividers at the same extent, and one foot in each path, after the greatest obscuration, note the point, where each is at the same instant by the marks, as the end of the eclipse. Thus we find that the

eclipse of July 18th, 1860, at Boston, beginning at Th. 22m. middle 8h. 28m. end 9h. 37m. A. M.

With a ruler laid over the centres of the sun and moon, as represented, draw the diameter of the sun's disk, and divide it into 12 equal parts. The number of these within the moon's disk, are the digits eclipsed.

Most of this operation supposes the projector to stand at the moon, or in the ecliptic opposite, looking down upon the earth. To find the duration of complete darkness in a total eclipse of the sun, subtract the apparent semi-diameter of the sun from that of the moon, take in the dividers the minutes of the difference from the scale, making allowance for seconds; place one foot of the dividers in the path of the moon's shadow, the other in the path of the place, and proceed in the same manner in finding the beginning and end of total darkness, as in finding the beginning and end of the eclipse by the semi-diameter of the penumbra.

SECTION VI.

PROJECTION OF LUNAR ECLIPSES.

By page 96, we find, that when the moon is within about 11° of either of her nodes, she may be eclipsed.

The elements for projecting a lunar eclipse are 8.

1. The true time of full moon.

2. The moon's horizontal parallax.

3. The sun's semi-diameter.

4. The moon's semi-diameter.

5. The semi-diameter of the earth's shadow at the moon.

6. The moon's latitude.

7. The angle of the moon's visible path with the ecliptic.

8. The moon's horary motion from the sun.

1. To find the true time of full moon, see preceding directions, page 117.

All the other elements for projecting a lunar eclipse, may be found by the directions for the same in solar eclipses, except the fifth.

To find the semi-diameter of the earth's shadow at the moon, add the horizontal parallax of the moon to that of the sun; from the sum subtract the apparent semi-diameter of the sun.

The eclipse of the moon in November, 1808, as seen at the Capitol, is represented in the following delineation, for an example of lunar projection. (Plate VIII. Fig. 1.) The student, who acquaints himself with the course of the moon, and with the tables, will be able to vary the position of the axis, so as to project other eclipses of the moon from this example. The axis of the moon's orbit is usually placed as in solar eclipses, and when the moon is in south latitude, her course is marked from the right to the left, considering the upper part of the plate north. The representation, however, would correspond better to the real appearance, if, when the moon is south descending, the axis of her orbit be laid on the left hand, when she is south ascending, on the right; and her path marked from the left to the right.

At the time of full moon, in November, 1808, the sun's anomaly was 4' 3° 3' 6"; the moon's, 11° 27° 21' 51"; the sun's equated distance from the moon's ascending node 11' 28° 25′ 53′′. To this, if 6 signs be added, it gives the moon's place 5$ 28° 25′ 53", bringing her within 1° 34′ 7′′ of her descending node.

38' 24"

8' 14 north des.

50

45/

27/ 40"

5. The semi-diameter of the earth's shadow at the moon,

7. The angle of the moon's visible path,

8. The moon's horary motion from the sun,

Draw the line A C B at random, (Plate VIII. Fig. 1.) From a diagonal scale, or a scale made for the purpose, take as many parts, as the moon's semi-diameter added to the semi-diameter of the earth's shadow, at the moon, contains

With

53′ 18′′. above the line A

minutes of a degree, 14' 54" + 38' 24" this extent draw the semi-circle, A D B, C B, the moon's latitude being north. For south latitude, the semi-circle must be drawn on the other side. When it may be necessary for representing the whole eclipse, a segment greater than a semi-circle may be drawn, and the figure extended, as in the diagram to I K and i k. Divide one quadrant of this into degrees. Take D M, 5° 45', the angle of the moon's visible path, and draw the line C M for the axis of the moon's orbit, on the right hand, the latitude of the moon being north descending. With the semi-diameter of the earth's shadow at the moon, 38′ 24′′, from the centre C draw the semi-circle c d e, for the northern half of that shadow. Bisect D M in a, and draw the occult line, Ca. Set the moon's latitude, 8′ 14′′, perpendicularly from the line A C B to b on the line Ca. Through b and perpendicular to the axis C M, draw the line E F for the path of the moon through the earth's shadow. Make the line GH, Fig. 2, equal to the horary motion of the moon from the sun, and divide it into 60 equal parts for minutes. Or it may be divided into larger parts of 3, 5, or 10 minutes each. Place the true time of full moon at b where the line E F intersects the line Ca; and set 22 minutes, taken from the line, G H backward on the line E F from b to 1. With the whole line, G H, mark the line, E F, each way from III. The dots at I, II, III, IV, V, show the moon's place at those hours. The spaces between the hour marks may be divided into minutes, or five minutes, as may be thought requisite.

With the semi-dianter of the moon as a radius, draw circles at f, g, and h.--ƒ will represent the moon's place at the beginning, g at the middle, and h at the end of the eclipse.

"

The disk of the moon, like that of the sun, may be divided into 12 equal parts for digits, and the amount of the eclipse ascertained. Where great accuracy is required, each digit may be divided into 60 equal parts for minutes.

Plate IX, Fig. 3 and 4, are projections of the lunar eclipse, as seen at the Capitol, January 16, 1824. It will appear,