the eclipse. From the centre S, with the radius equal to the minutes contained in the sun's semidiameter, describe the circle A B C for the sun. And from the centre P, with the radius equal to the moon's semidiameter, describe the circle AOCD for the moon. If these circles do not intersect, there will be no eclipse. But if they intersect, an eclipse must necessarily happen. 736. 5. Then P is the place of the moon in the middle of the eclipse.. Make SI and SK equal to the sum of the semidiameters of the sun and moon; and the moon's centre will be at I when the moon first touches the sun, or at the moon's centre, at the end of it. In the triangle PSI, there is given SI, SP; to find PIPK, which reduced to time by help of the moon's apparent horary motion, shews half the duration of the eclipse; and consequently we shall have the beginning and end. 737. 6. And to find the quantity no, or the digits eclipsed; we have no Sn+ Po-SP, The 739. 1. By the tables the mean time of the conJunction is found to be June 2d. 20h. 41m. And hence, the true time of conjunction is June 3d. 20h. 27m. 43s. And their places are 2° 13° 51 25". And the moon's lat. 55.32 north. moon's motion from the sun 35′ 47′′. 2. In fig. 5 and 6, Plate IX. the angle AMS 84° 47'. Z SM 35° 20′. CSF 5° 18′ SBM 43° 49'. SF 42° 16', CF3° 34'. CS 42° 24'. = The angle QMI = 8° 25′. SMQ 92° 52'. MN or IQ = =6° 38′. MQ 31° 20′. Also The moon's horizontal parallax . Her horary motion . 60′ 58′′ . 33 32 38 10 31 41 2 23 3. In fig. 4, the moon's parallax in altitude Mm is 45' 09"; her parallax in latitude Mn, 38′ 05′′; her remaining latitude Sn, 17′ 26′′; her parallax in longitude Ss, 24′ 13′′; which is increased so much. 4. Draw SL for the ecliptic, as in fig. 10, at any point S, erect the perp. M S equal to 17' 26′′, the moon's apparent latitude; through M draw the moon's way 8 M R, making the angle SMR = 92° 52'. Draw SP perp. MR, which here falls very near M. From the centre S, with the radius SA = 15′ 50′′, describe the circle ABC for the sun. And with the radius MD = 16′ 46′′, and centre P, describe the circle ADCO for the moon. of 31′ 20′′ an hour, is 52′ 45′′ for the semiduration. By reason of the parallax (24′ 13′′), she is past the apparent conjunction; the difference being what the parallax causes, which comes to 47′ 23". Therefore the middle of the eclipse is so much sooner, being at 3d. 19h. 41m. 20s. This reduced to apparent time is 3d. 19h. 43m. 27s. for the middle. 6. The digits eclipsed are 5, nearly. 740. In this example, the concave side of the sphere is projected, which suits best to the appearance of the heavens. And the figures are drawn upon that supposition. It appears from the process, that the moon is advancing to her descending node, and therefore has north latitude. And by the position of that part of the ecliptic, her parallax in longitude, advances her so much forward, viz. 24′ 13′′. And therefore she is so much past the apparent conjunction. Hence we gain these several particulars, as to the eclipse: D. H. 6 53 42 741. 1. The begin. June, morn. 4 middle end total duration 22285 4 8 46 12 1 45 30 digits eclipsed 51, on the upper side of the sun, towards the left; as appears by the figure. 742. 2. Hence the position of the horns at C and A, are easily found in the middle of the eclipse. For they are in a position parallel to RI, the moon's way. 743. 3. The middle of the eclipse will not be at the same time in all places of the same longitude; for the parallax of longitude will be different in different places. 744. No eclipse of the sun can last above two hours. For SI or SA +MD= : 32′ 26′′ = 32.6 and the horary motion = 34′ 47′′ 35.78. And 32.6 35.78 duration. = ='91 = 54 minutes, for the semi 745. If it were not for the parallax, eclipses of the sun would be as easily calculated as those of the moon. And in order to get the parallax, the angle ZSM and SP must be known, fig. 2, which occasions the resolving several spherical triangles before they can be had. Likewise it may be observed, that the apparent way of the moon is strictly curve line, concave towards S, which arises from the parallel of latitude being a curve, and the moon being out of its plane. Likewise the moon's apparent velocity is something greater at the beginning than at the end. VI.-RULES FOR CALCULATING A GENERAL ECLIPSE OF THE SUN. 746. The elements necessary for this are: 1. The sun and moon's place, and the time at the true conjunction; 2. The moon's latitude, horizontal parallax, diameter, and horary motions; 3. The sun's declination, diameter, and horary motion; and 4, the angle the moon's way makes with a circle of latitude. 747. 2. From a large scale of minutes, take the moon's horizontal parallax in the compasses, and at any point C, in the right line B D, (which represents the ecliptic in plate XI. fig. 6), describe the circle ABED, for the earth's disk, or the earth's flat face as it appears at a distance, in a line drawn to the sun. Draw CM perpendicular to CD, and equal to the latitude of the moon upwards, if north. Make the angle C MG equal to that which the moon's way makes with a circle of latitude; acute to the right hand, if she tend to the node; or obtuse, if she be past it; and drawing FM G, it will be the way of the centre of the moon's shadow upon the earth. From C let fall C H perpendicular to FG. Then at H will be the middle of the earth's eclipse. 748. 3. With the centre H, and radius HO, equal to the sum of the semidiameters of the sun and moon, describe the circle QOR, which will be the moon's penumbra. Also describe a small circle round the centre H, whose radius is the difference of the sun and moon's semidiameters, that little circle will be the dark shadow of the moon. Then all the countries of the earth contained in the segment V A W will be successively eclipsed by the penumbra, as the shadow moves along the tract FG; while the other segment VEW suffers no eclipse at all. All places in the line st will be totally eclipsed, as the dark shadow, or the small circle at H passes successively over them. But this circle, or dark shadow, being very small, a total eclipse at any place continues but a small time. Sometimes the sun's semidiameter exceeds the moon's; and then there will be no dark circle, or total eclipse, but a lucid ring will appear about the moon in these places, and this is called an annular eclipse. The difference between the semidiameters of the sun and moon is so little, that no total eclipse lasts above four minutes. 749. 4. Draw CF, CG sum of the semidiameters of the sun and moon, and the moon's parallax; then the moon's shadow will touch the earth at L and K, where the eclipse begins and ends. In the triangle CF H, there is given C F, CH; to find F H = HG, which, converted into time, gives half the duration, or half the time that the moon's shadow is upon the earth. Also NO measured, shews how far the eclipse reaches; or C O measured, does the same. It may be sufficient to measure all these by the scale with out calculation. 750 5. To find the pole. Draw the arch A P, making the angle KAP equal to the sun's longitude, and AP the distance of the poles of the equator and ecliptic, 23°; then P is the pole. For A P is a part of the solstitial colure, and passes through Cancer and Capricorn. And CAP is what the sun wants of Cancer, therefore PAK is what it is past Aries. Through P draw CP T. And here we may suppose that the pole P is fixed during the time of an eclipse. Then in the right angled spherical triangle APT, there is given AP and the angle A, to find AT or angle ACP. In this triangle PT is the sun's declination, and APT or CPK his right ascension from Cancer. Here note, that any place in the line CT is in the sun's meridian; and C is the place where the sun is vertical at the time of the eclipse. 751. 6. To find the situation of any given place, at a given hour. Make the angle CPX (with the sun's meridian), equal to the time from noon; on the left hand, if it is before noon. And make P Z the complement of the latitude; then Z is the place required. And if it falls in the penumbra, it is eclipsed; or anywhere in the segment VAW; if its motion in the parallel circle does not carry it out, before the penumbra reaches it. 752. 7. To find the place which is first or last touched by the penumbra, as K. Draw the arch PK. In the triangle GCA, there are given CG and CH, to find the angle GCH, from which subtract HCP which is known, gives the angle PC K or TK. Then in the right-angled spherical triangle PTK, there is given T K, and PT the sun's declination; to find P K the complement of the latitude of K, and T P K or C PK the difference of longitude of K, and the sun.Therefore its longitude and latitude is obtained. In the same manner may be found that of L. And by the same method the latitude and longitude of the places s and t may be found, where the dark shadow first enters the earth's disk, or quite leaves it. Thus also may be found the place which is in the line FH, at any point of time: or if the place be given, what the time will be; and that by help of the horary motion, with other particulars of like nature. 753. 8. The part of the sun's diameter eclipsed by the moon, is known by the situation of the place within the penumbra, or its distance from the centre of the penumbra. And the phasis of the eclipse, as seen from any place Z, upon the disk, will be found thus, for any time. Find the centre of the shadow for that time, as suppose at H. Describe about H, a circle, whose radius is the moon's radius, and about Z, a circle with the sun's radius. Then the part cut off the sun's circle will be the part obscured. SECT. VIII. REMARKS ON ECLIPSES IN GENERAL. 754. In eclipses of the moon, even when she is near the centre of the earth's shadow, her body is still visible, and appears of a tarnished copper color. This seems to be occasioned by the rays of light which come from the sun, and which, passing near the earth, are inflected from their rectilinear course by our atmosphere; so that they enter the earth's conical shadow, thus producing that faint illumination on the surface of the moon, which some have supposed to be her own native light; but there seems to be no just ground for such a conjecture. 755. In most solar eclipses, the moon's disk is covered with a faint light, which is attributed to the reflection of the light from the illuminated part of the earth; and in total eclipses, the moon's limb is seen surrounded by a pale circle of light: which some astronomers consider as an indication of a lunar atmosphere, but others as the atmosphere of the sun; because it is observed to move equally with the sun, but not with the moon. 756. Eclipses have in all ages greatly attracted the attention of mankind. The ignorant and superstitious have viewed them with terror, and in former ages they were often considered as the forerunners of national calamities. The Chinese, even at the present day, upon their appearance, perform the most absurd and superstitious ceremonies, although they are so far acquainted with their nature, as to be able to predict them. See CHINA. But true philosophy has taught us, that instead of these appearances being portentous of evil to mankind, they may, by proper observations upon them, be made of great advantage to the sciences, and to some of the arts of life. 757. We have already shewn, that, by eclipses of the moon, the earth is demonstrated to be a globular figure. The longitudes of places on the earth are also determined by observations on solar and lunar eclipses; as will appear by consulting the articles GEOGRAPHY, LONGITUDE, NAVIGATION, &c. Eclipses are also of great importance in CHRONOLOGY, (which see), as by them we are enabled to determine exactly the time when events recorded in history happened. 758. From the observations made upon the ancient eclipses, it appears that the period of the that occasioned by a secondary planet. If we suppose the primary planet and comet to be moving both the same way, the duration of such an eclipse would be prodigiously lengthened; and thus, instead of four minutes, the sun might be totally darkened to the inhabitants of certain places for as many hours: and, from this cause, some account for that prodigious darkness, which we sometimes read of in history, at times when no eclipse of the sun by the moon could possibly happen. PART V. ASTRONOMICAL MACHINERY AND IN- MACHINERY INVENTED FOR ILLUSTRATING moon is now shorter, and consequently that her SECT. I.-DESCRIPTION OF THE ASTRONOMICAL distance from the earth is now less, than in former ages; and this has been considered as an argument against those who assert, that the world may have existed from eternity; for it was hence inferred, that the moon moves in a resisting medium, and therefore that her motion must by degrees be all destroyed, in which case she must at last come to the earth. But M. de La Place has shewn, that this acceleration of the moon's period is a necessary consequence of universal gravitation, and that it arises from the action of the planets upon the moon. He has also shewn that this acceleration will go on, till it arrive at a certain limit, when it will be changed into a retardation; or in other words, that there are two limits, between which the lunar period fluctuates, but neither of which it can pass. 759. M. de La Grange has also discovered, that all the seeming irregularities in the motions of our system are periodical; so that although the obliquity of the ecliptic, the eccentricities of the planetary orbits, the precession of the equinoxes, the length of the year, &c. may change, yet these changes will not pass certain limits, and after stated periods, they will return precisely to what they had formerly been. Some of these periods, however, may be very long. The acceleration of the moon, for example, has been going on from the earliest ages of astronomy to the present day. 760. We cannot close this section, without obscrving, that eclipses happen very frequently to all the satellites of Jupiter; and, as they are of great service in determining the longitude of places on the earth, astronomers have been at pains to calculate tables for the eclipses of these satellites by their primary; for the satellites themselves have never been observed to eclipse one another. But this falls more properly to be considered under the articles GEOGRAPHY, and LONGITUDE, to which the reader is therefore referred. 761. The primary planets would also eclipse one another, were it not for their great distances; but, as the comets are not subject to the same laws with the planets, it is possible they may sometimes approach so near to the primary planets, as to cause an eclipse of the sun to those planets; and as the body of a comet bears a much larger proportion to the bulk of a primary planet than any secondary, it is plain, that a cometary eclipse would both be of much longer continuance, and attended with greater darkness, than 762. The Grand Orrery, a very magnificent machine, first made in this kingdom, by Mr. Rowley, for king George I. is represented in plate XII. fig. 1. The frame of it, which contains the wheel-work, &c. and regulates the whole machine, is made of ebony, and about four feet in diameter. Above the frame is a broad ring, supported with twelve pillars, which represents the plane of the ecliptic. Above the ecliptic, stand some of the principal circles of the sphere, viz. No. 10, are the two colures divided into degrees, and half degrees; No. 11, is one half of the equinoctial circle, making an angle of 233°. The tropic of Cancer, and the arctic circle, are each fixed parallel, at their proper distance from the equinoctial. On the northern half of the ecliptic, is a brass semicircle, movable upon two points, fixed in and, representing the movable horizon to be put to any degree of latitude upon the north part of the meridian, and the whole machine may be set to any latitude, without disturbing any of the internal motions, by two strong hinges, (No. 13.) fixed to the bottom-frame, upon which the instrument moves, and a strong brass arch, having holes at every degree, through which a strong pin is put at every elevation. This arch, and the two hinges, support the whole machine, when it is lifted up, according to any latitude; and the arch, at other times, lies conveniently under the bottom frame. 763. The sun, (No. 1.) stands in the middle of the whole system, upon a wire, making an angle with the ecliptic, of about 82°. Next the sun is a small ball, (2), representing Mercury. Next to Mercury is Venus, (3), represented by a larger ball. The earth is represented (No. 4), by an ivory ball, having some circles and a map sketched upon it. The wire which supports the earth, makes an angle with the ecliptic, of 66°, the inclination of the earth's axis to the ecliptic. Near the bottom of the earth's axis is a dial plate, (No. 9.) having an index, pointing to the hours of the day, as the earth turns round its axis. Round the earth is a ring supported by two small pillars, representing the orbit of the moon; and the divisions upon it answer to the moon's latitude. The motion of this ring represents the motion of the moon's orbit, according to that of the nodes. Within this ring is the moon, (No. 5), having a black cap or case, by |