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EXPLANATIONS AND PROBLEMS

meridian; the hours and minutes opposite the arrow, reading from 12 o'clock, noon, to 24 hours.

What is the right ascension and declination of the sun on the 20th of March? (616.) Ans. 0.

What is the right ascension and declination of the sun on the 21st of June? Ans. 90 deg. or 6 hours right ascension, 23 deg. north declination.

What is the right ascension and declination of the sun on the 21st of December? Ans. 270 deg. or 18 hours right ascension, and 23 deg. south declination.

On what day of the month does the sun enter each of the signs? (618.) Solution: The day of the month is marked opposite each sign on the ecliptic.

What is the declination and right ascension of the sun on the 5th of June? Ans. 224 deg. north declination, 734 deg. or 4 hours 55 minutes right ascension.

CHANGE OF SEASONS-DIFFERENT LENGTHS OF DAYS AND NIGHTS.

Bring March 20th on the ecliptic to the east horizon; at March 20th on the outer circle, will be the mean time of the sun's rising. Bring March 20th to west horizon, and see at March 20, outside, the mean time of the sun's setting. The rising and setting will be later every day until the 21st of June, when the days decrease until December 21st. (616 and 617.)

AMONG ALL THE STARS VISIBLE ON A CLEAR EVENING, WHICH IS JUPITER? WHICH IS SATURN, or any other oF THE PLANETS, or THE MOON?

Find in the almanac the time at which the given planet rises, souths, or sets. Bring that time to the day of the month; if rising, its place will be where the eastern horizon meets the ecliptic; if southing, where the meridian meets the ecliptic; if setting, where the western horizon meets the ecliptic. Notice its place among the stars, and then bring the time of observation to the day of the month, and the position of the planet in the heavens will be shown. Or, find in the almanac the nearest day upon which the planet is in conjunction with the moon; and find the POSITION OF THE MOON on that day in like manner, which will be nearly the place of the planet on the given day.

EXAMPLE.-Where was the moon at 74 o'clock on the evening of August 18th, 1863?

Solution. We see by almanac that the moon southed at 2 hours 58 minutes P. M. Bring this time to the 18th of August, and under the meridian on the ecliptic 12 deg. in the sign Libra, constellation Virgo, will be the moon's place on the 18th of August. To find its position in the heavens, bring 77 o'clock P. M. to August 18th, and 12 deg. Virgo (the moon's place) will be about an hour above the W. S. W. horizon.

EXAMPLE.-Where were Saturn and Venus at the above time? Ans. By referring to the almanac, we see that they were in conjunction with the

moon.

SIDEREAL TIME.

Bring the given mean (clock) time to the day of the month; the corresponding sidereal time will be found opposite the arrow. (392.)

EXAMPLE.-August 18, 1863, when the moon is on the meridian at 2 hours 58 minutes P. M., what is the sidereal time? Ans. 12 hours 46 minutes. The right ascension.

EXAMPLE.-When the sun is on the meridian December 22d, what is the sidereal time? Ans. 18 hours 2m. R. A. of the sun.

EQUATION OF TIME. TO FIND HOW MUCH THE SUN IS FAST OR SLOW.

Bring the meridian to the given day on the ecliptic; opposite the same day, on the outer circle, will be the time the sun is on the meridian; if before 12 o'clock, the sun is fast; if after 12 o'clock, the sun is slow. (397.)

EXAMPLE. Bring the meridian to November 10th, on the ecliptic; opposite that date will be found 11 hours 44 minutes, the sun being 16 minutes fast.

EXAMPLE. Is the sun fast or slow September 1st? how much? (397.) Ans. Sun and clock agree.

EXAMPLE.-How many minutes is the sun slow or fast on the 10th of February? Ans. 14 minutes slow.

EXAMPLE.-When the sun is on the meridian July 31st, what is the true clock time? Ans. 6 minutes past 12.

EXAMPLE.-How shall we get a meridian line to-day at noon? Ans. When the sun is on the meridian, mark its shadow for the meridian.

TO FIND THE VARIATION OF THE MAGNETIC NEEDLE, OR TO GET A

MERIDIAN LINE. (46, 192-194.)

Bring the meridian to 171° on the equator, the arrow will point a 1 hour 9 minutes, the right ascension of the north pole star·

EXPLANATIONS AND PROBLEMS.

opposite the day of every month will be found the time the north pole star is on the meridian; a correct range at that time will be a true meridian. Six hours after, it will be at its greatest elongation west; and six hours later, on the meridian below the pole; and six hours later, at its greatest elongation east.

EXAMPLE.-At what time can we get a meridian line December 10th? Ans. 7 hours 50 minutes, evening.

EXAMPLE.—At what minute, February 20th, can we get the variation of the compass? Ans. 6 minutes past 3 in the morning.

EXAMPLE.-When will the polar star be at its greatest elongation east August 23d? Ans. At 9 in the evening.

ΤΟ TELL THE COURSE AND POSITION OF THE MILKY WAY ANY

GIVEN TIME.

Bring the given time to the day of the month; the course and position can be readily traced on the Planisphere. (256–260.)

What will be the course of the Milky Way on the 5th of September, at 6, 9, 14 and 6 o'clock? Ans. At 6 o'clock evening, starting from northern horizon to east of zenith, to southern horizon. At 9 o'clock it appears in the N. E., in zenith, to S. W. At 14 o'clock it appears in the east, passes the meridian at 60 deg. north, to the west. At 6 o'clock morning, it appears in the S. E., passes the zenith to the N. W.

TO EXPLAIN THAT IN SUMMER, WHEN THE SUN RUNS HIGHEST, THE FULL MOON RUNS LOWEST; AND IN WINTER, WHEN THE SUN RUNS LOWEST, THE FULL moon runs highEST. (421.)

Bring the graduated side of the meridian to the 21st of June on the ecliptic, the sun's place among the stars at his greatest distance north; should the moon full on that day, she will be at her greatest distance south, in the opposite part of the sky; shown by bringing the meridian to the 21st of December on the ecliptic, at her greatest distance south. Bring the first date to the W. N. W. horizon, and the second date will be near the E. S. E.; when the sun sets at his greatest distance north in summer, the full moon will rise at her greatest distance south.

For winter, reverse the above, by bringing the second date near the W. S. W., showing the sun's setting at his greatest distance south, while the full moon can be rising in the E. N. E., at her greatest distance north.

EXAMPLE 2.-(Page 328.) If it is 12 o'clock at this place, what is the time 20 deg. east of us? Bring the meridian to 20 deg. on the equinoctial, and opposite the arrow read 1 hour 20 minutes past 12.

EXAMPLE 4.-(Page 329.) A vessel leaves Boston, and having been tossed about in foul weather for some days, finds, that when it is 12 o'clock by the sun, it is only 11 o'clock and 50 minutes by the watch; is the vessel east or west of Boston; and how many degrees? Ans. 2 deg. 30m. east. TO FIND THE AZIMUTH, AMPLITUDE, ZENITH DISTANCE, AND VERTI CAL CIRCLE OF A STAR AT ANY TIME.

Bring the given time to the day of the month; lay a straight edge on the zenith; let it pass through the star to meet the horizon; that line will be a quarter of a vertical circle. From the east or west which is nearest to the line, will be the amplitude; from the horizon to the star, measured on the vertical line, will be the altitude; from the star to the zenith, will be the zenith distance.

[To measure the azimuth in degrees, we know that a circle is 360 deg.: from N. to S. will be 180 deg., from S. to E. 90 deg., from S. to S. E. 45 deg., from S. to S. S. E. 221 deg., from S. to S. by E. 114.]

TO FIND AT WHAT TIME ANY STAR WILL COME TO THE MERIDIAN, OR RISE, OR SET, ON ANY GIVEN DAY OF THE MONTH.

Turn the graduated side of the meridian, or the eastern or western horizon, to the center of the star; opposite the day of the month will be found the time required.

EXAMPLE.-At what time will a Gemini (Castor) culminate, on the 24th of February? (95.) Ans. About 9 o'clock.

TO FIND ON WHAT DAY OF THE YEAR ANY STAR PASSES THE MERIDIAN, OR RISES, OR SETS, AT ANY GIVEN TIME.

Bring the meridian, or the eastern or western horizon, to the centre of the star; opposite the given time will be found the day required.

EXAMPLE-On what day will a Leo (Reg'-u-lus) be on the meridian about 9 o'clock? (124.) Ans April 6th.

ADAPTED TO WHITALL'S PLANISPHERE.

By the almanac, see when the moon is full, and the time sne is south, by which find her place on the Planisphere.

Where will the full moon of June be found? Ans. At her greatest distance south.

Where will the full moon in December be found? Ans. At her greatest distance north.

The Harvest-Moon (626-635), so called in some parts of Europe, is of great benefit to the husbandman, by lengthening the day while gathering the fruits of the earth, and takes place at the full moon in September, when the moon rises for several evenings near the same hour. Shown on the Planisphere by bringing 6 o'clock, evening, to the 20th day of September. The eastern horizon, first meridian, ecliptic, and equator, meet at the vernal equinox. Should the moon be full on that day, and rise at the vernal equinox at 6, on the following evening she will have moved eastward about 13 deg. ; then turn the horizon until 13 deg. on the ecliptic rises, opposite the 21st day of September, will be found the time of the moon's rising to be about 28 minutes later. Bring 13 deg. more above the horizon, opposite the 22d of September, will be found the time of the moon's rising to be about 28 minutes later. The ecliptic being nearly parallel to the horizon, it changes less than half an hour per night. Now turn 6 o'clock, evening, to March 22d, the eastern horizon meets the autumnal equinox. Bring 13 deg. of the ecliptic up, and opposite March 23d will be found 7 o'clock, making more difference in one day than there was before shown in two days; the ecliptic being now nearly perpendicular to the horizon.

See in the almanac the day the moon fulls in September; by her southing locate her on the Planisphere; and by bringing her place to the eastern horizon, the time of rising can be seen opposite the day of the month. Locate the moon for the next day and note the difference in time of rising, to see the Harvest-Moon illustrated.

TO CONVERT TIME INTO DEGREES, OR DEGREES INTO TIME.

Bring the meridian to the center of the star. The degrees of right ascension will be read on the equator or equinoctial opposite 0 on the meridian. The arrow, at March 22d, will point at the hour and minute of R. A., reading from 12 noon around to 12 noon, counting 24 hours.

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