Take the Moon's semidiameter, 15'38", in your compasses, from the scale A B, and with that extent, as a radius, upon the points N, T, and P, as centres, describe the circle Q for the Moon at the beginning of the Eclipse, when she touches the Earth's shadow at Y; the circle R for the Moon at the middle of the Eclipse, and the circle S for the Moon at the end of the Eclipse, just leaving the Earth's shadow at W. The point N denotes the instant when the Eclipse begins, mamely, at 25 minutes 30 seconds after XI in the morning: the point T the middle of the Eclipse, at 10 minutes 18 seconds past I o'clock in the afternoon; and the point P the end of the Eclipse, at 58 minutes after II.—Thus it appears, that the Moon was totally eclipsed for the space of 2 hours, 42 minutes, 30 seconds. MORE EXAMPLES. Exr. Let it be required to find the Elements for the Solar Eclipse which happened in April 1764, New Style. 10. Semidiameter of the Penumbra. This Eclipse was nearly central, and annular.* 31 3 *Note. In annular eclipses, the light of the Sun is left all around the Moon in a circulr form Annular, from the Latin annulus, a ring. EXP. Let it be required to find the Elements for the Lunar Eclipse in May, 1762, N. S. 1. True Full Moon in May, 1762. 2. Moon's horizontal parallax 3. Sun's semidiameter. 4. Moon's semidiameter. 5. Semidiameter of Earth's shadow at the Moon. 6. Moon's true Latitude, South descending. 7. Angle of the Moon's visible path with the Ecliptick. 8. Her horary motion from the Sun. Ex. 3. Required the Elements for the Eclipse of the Sun, April 24th, 1819 ? Ex. 4. Required the Elements for the Lunar Eclipse, Oct. 3d, 1819 (total.) Ex. 4. Let it be required to calculate the Elements for the Lunar Eclipse, March 29th, 1820 ? Ex. 6. In the year 1823, there will be four Eclipses; namely, two of the Sun, one February 11th; and the other July the 8th: and two of the Moon, one January 26th, and the other July 23d, (both total.) Let it be required to find the respective Elements for the construction of these Eclipses ? Ex. 7. In the year 1826, there will be two Eclipses of the Moon; viz. May 21st, and November 11th, (both total) What are the Elements belonging to each? Ex. 8. What are the proper Elements for constructing an Eclipse of the Sun, which will happen July 29th, 1980, Oid Style? To find the number of Eclipses there are in any given year, and in what Months they happen. PRECEPT. Enter Table XVIII. and take out the mean Longitude of the Moon's Nodes for the given year; with which enter Table XIX. and find, in that table, when the Sun's Longi. tude will be nearly the same o six signs different; and the day of the month in which these numbers are so found, will be the time required. EXAMPLES. 1. It is required to find the number of Eclipses in the year 1796; and in what months they will happen. The mean Longitude of the Moon's North Node, on the first of January 1796, is 3S 20° 35', of the South Node (it being just six signs distant) 9S 20° 35'; wherefore the Node-months are January, July, and December; consequently there were three Eclipses in that year. 2. Required the number of Eclipses in the year 1800, and in what months they happened. 3. Required the number of Eclipses in the year 1820, and the months in which they happen. To find on what part of the Globe any given Eclipse of the Sun or Moon is visible. This is most readily ascertained by means of an artificial globe; as follows: The day and hour being given when a Solar Eclipse will happen, to find where it will be visible. PRECEPT. Find the Sun's declination, and elevate the pole agreeably to that declination; bring the place, at which the hour is given, to that part of the brass meridian which is numbered from the equator towards the poles, and set the index of the hour circle to twelve; then if the given time be before noon, turn the globe westward till the index has passed over as many hours as the given time wants of noon; if the time be past noon, turn the globe eastward as many hours as it is past noon, and exactly under the degree of the Sun's declination on the brass meridian you will find the place on the globe where the Sun will be vertically eclipsed at all places within 70 degrees of this place, the eclipse may* be visible, especially if it be a total eclipse. Ex. On the 11th of February 1304, at 27 min. past 10 o'clock in the morning at London, there was an eclipse of the sun; where was it visible, supposing the moon's penumbral shadow to extend northward 70 degrees from the place where the sun was vertically eclipsed? Ans. Britain, Ireland, France, Germany, &c. The day and hour being given when a Lunar Eclipse will hapıpen to find where it will be visible. PRECEPT. Find the Sun's declination for the given day, and note whether it be north or south; if it be north, elevate the ,south pole so many degrees above the horizon as are equal to *Note. When the Moon is exactly in the node, and when the axis of the Moon's shadow and penumbra pass through the centre of the earth, the breadth of the earth's surface under the penumbral shadow is 70° 20' ; but the breadth of this shadow is variable; and if it be not accurately determined by calculation, it is impossible to tell by the globe to what extent an eclipse of the sun will be visible. the declination; if it be south, elevate the north pole in a similar manner; bring the place at which the hour is given to that. part of the brass meridian which is numbered from the equator towards the poles, and set the index of the hour circle to twelve; then, if the given time be before noon, turn the globe westward as many hours as it wants of noon; if after noon, turn the globe eastward as many hours as it is past noon; the place exactly under the degree of the Sun's declination will be the antipodes of the place where the Moon is virtically eclipsed. Set the index of the hour circle again to twelve, and turn the globe on its axis till the index has passed over twelve hours; then to all places above the horizon the eclipse will be visible; to those places along the western edge of the horizon the moon will rise eclipsed; to those along the eastern edge she will set eclipsed; and to that place immediately under the Sun's declination the Moon will be virtically eclipsed. EXAMPLE. On the 26th of January 1804, at 58 min. past seven in the afternoon, at London, there was an eclipse of the Moon ; where was it visible? Answer. It was visible to the whole of Europe, Africa, and the continent of Asia. 27 |