16° from the equinoctial, on the marginal scale south, and from that point, 30 minutes to the left, or just half the distance between the XXI. and XXII. meridian of right ascension, and find that Venus, that day, is within two degrees of Delta Capricorni, near the constellation Aquarius, in the zodiac.

NOTE.-It is to be remembered, that the planets will always be found within the limits of the zodiac, as represented in the maps. By means of Table VII., the pupil can find at any time the situations of all the visible planets, on the maps; and this will enable him to determine their position in the heavens, without a chance of mistake. By this means, too, he can draw for himself the path of the planets from month to month, and trace their course among the stars. This is a pleasant and useful exercise, and is practised extensively in some academies. The pupil draws the map in the first place, or such a portion of it as to include the zodiacal constellations; then, having dotted the position of the planets from day to day, as indicated in Table VII., their path is easily traced with a pen or pencil.

Ex. 2-Mars' right ascension on the 13th of March, 1833, is 5 hours, 1 minute, and his declination 244° north; required his situation on the map?

Solution.-I find the fifth hour line or meridian of right ascension on Plate III., and counting upwards from the equinoctial 244°, I find that Mars is between the horns of Taurus, and about 5° S. W. of Beta Auriga.

Ex 3.-Required the position of Jupiter and Saturn on the 13th of February and the 25th of May ?

When the right ascension and declination of the planets are not given, they are to be sought in Table VII.

PROBLEM VI.

TO FIND AT WHAT MOMENT ANY STAR WILL PASS THE MERIDIAN ON A GIVEN DAY.

RULE.-Subtract the right ascension of the Sun from the star's right ascension, found in the tables: observing to add 24 hours to the star's right ascension, if less than the Sun's, and the difference will show how many hours the star culminates after the Sun.

EXAMPLE 1.-At what time will Procyon pass the meridian on the 24th of February?

Solution.-R. A. of Procyon, 7h. 30m. 33s.+24h.

R. A. of Sun, 24th Feb.

Ans.

31 30' 33'

22 29 1

9 1 32

That is, 1m. 32s. past 9 o'clock in the evening.

Ex. 2.-At what time will Denebola pass the meridian on the first of April?

That is, at 59 minutes, 7 seconds, past 10 in the evening.

Ex. 3.-At what time on the first day of each month, from January to July, will Alcyone, or the Pleiades, pass the meridian?

Ex. 4.-At what time will the Dog-Star, or Sirius, culminate on the first day of January, February, and March?

Ex. 5.-How much earlier will Spica Virginis pass the meridian on the 4th of July, than on the 15th of May ?—Ans. 3 hours, 25 minutes.

PROBLEM VII.

TO FIND WHAT STARS WILL BE ON OR NEAREST THE MERIDIAN AT ANY GIVEN TIME.

RULE. Add the given hour to the Sun's right ascension, found in Table III., and the sum will be the right ascension of the meridian, or mid-heaven; and then find in Table II. what star's right ascension corresponds with, or comes nearest to it, and that will be the star required.

EXAMPLE 1.-What star will be nearest the meridian at 9 o'clock in the evening of the 1st September? Solution.-Sun's right ascension 1st September,

Now all the stars in the heavens which have this right ascension, will be on the meridian at that time. On looking into Table II. the right ascension of Altair, in the Eagle, will be found to be 19h. 40m.; consequently Altair is on the meridian a the time proposed; and Delta, in the Swan, is less than two minutes past the meridian.

Ex. 2.-Walking out in a bright evening on the 4th of September, I saw a very brilliant star almost directly overhead; I looked on my watch, and it wanted 20 minutes of 8; required the name of the star?

Ex. 3. About 8 minutes after 8 in the evening of the 11th of February, I observed a bright star on the meridian, a little north of the equinoctial, and 1 minute before 9 a still brighter one, further south; required the names of the stars?

PROBLEM VIII.

TO FIND WHAT STARS WILL CULMINATE AT NINE O'CLOCK IN THE EVENING OF ANY DAY IN THE YEAR.

RULE.—Against the day of the month in Table IV., find the right ascension of the mid-heaven, and all those stars in Table II. which have the same, or nearly the same right ascension, will culminate at 9 P.M. of the given day.

EXAMPLE 1.-What star will culminate at 9 in the evening of the 26th of March?

Solution. I find the right ascension of the meridian, at 9 o'clock in the evening of the 26th of March, is 9h. 19′ 37′′; and on looking into Table II., I find the right ascension of Alphard, in the heart of Hydra, is 9h. 19′ 23′′. The star is Alphard.

Ex. 2.-What star will culminate at 9 in the evening of the 28th of June? Ans. Aphacca.

PROBLEM IX.

TO FIND THE SUN'S LONGITUDE OR PLACE IN THE ECLIPTIC, ON ANY

GIVEN DAY.

RULE. On the lower scale, at the bottom of the Planisphere (Map VIII.) look for the given day of the month; then the sign and degree corresponding to it on the scale immediately above it will show the Sun's place in the ecliptic.

EXAMPLE 1.-Required the Sun's longitude, or place in the ecliptic, the 16th of September.

Solution.-Over the given day of the month, September 16th, stands 5 signs and 23 degrees, nearly, which is the Sun's place in the ecliptic at noon on that day; that is, the Sun is about 23 degrees in the sign Virgo.

N.B.-If the 5 signs be multiplied by 80, and the 23 degrees be added to it, it will give the longitude in degrees, 173.

Ex. 2.-Required the Sun's place in the ecliptic at noon, on the 10th of March.

PROBLEM X.

GIVEN THE SUN'S LONGITUDE, OR PLACE IN THE ECLIPTIC, TO FIND HIS

RIGHT ASCENSION AND DECLINATION.

RULE. Find the Sun's place in the ecliptic (the curved lice which runs through the body of the planisphere), and with a pair of compasses take the nearest distance between it and the nearest meridian, or hour circle, which being applied to the graduated scales at the top or bottom of the planisphere (measuring from the same hour circle), will show the Sun's right ascension. Then take the shortest distance between the Sun's place in the ecliptic and the nearest part of the equinoctial, and apply it to either the east or west marginal scales, and it will give the Sun's declination.

EXAMPLE 1.-The Sun's longitude, September 16th, 1833, is 5 signs, 23 degrees, nearly; required his right ascension, and declination.

Solution. The distance between the Sun's place in the ecliptic and the nearest hour circle being taken in the compasses, and applied to either the top or bottom graduated scales, shows the right ascension to be about 11 hours 35 minutes; and the distance between the Sun's place in the ecliptic, and the nearest part of the equinoctial, being applied to either the east or west marginal scales, shows the declination to be about 2° 45', which is to be called north, because the Sun is to the northward of the equinoctial; hence the Sun's right ascension, on the given day, at noun, is about 11 hours 35 minutes, and his declination 2° 45' N.

Ex. 2.-The Sun's longitude, March 10th, 1833, is 11 signs, 19 degrees, nearly; required his right ascension and declina

tion ?

Ans. R. A. 23h. 21m. Decl. 4° 11′ nearly.

PROBLEM XI.

TO FIND THE RIGHT ASCENSION OF THE MERIDIAN AT ANY GIVEN TIME.

RULE. Find the Sun's place in the ecliptic by Problem IX., and his right ascension by Problem X., to the eastward of

which count off the given time from noon, and it will show the right ascension of the meridian, or mid-heaven.

EXAMPLE 1.-Required the right ascension of the meridian 9 hours, 25 minutes past noon, September 16th, 1833?

Solution.-By Problems IX. and X., the Sun's right ascension at noon of the given day, is 11 hours 35 minutes; to the eastward of which, 9 hours and 25 minutes (the given time) being counted off, shows the right ascension of the meridian to be about 21 hours.

Ex. 2.-Required the right ascension of the meridian at 6 hours past noon, March 10th, 1833?

Solution.-By Problems IX. and X., the Sun's right ascension at noon of the given day, is 23 hours and 21 minutes; to the eastward of which, the given time, 6 hours, being counted off, shows the right ascension of the meridian to be about 5 hours, 21 minutes.

REMARK.-In this example, it may be necessary to observe, that where the eastern, or left-hand extremity of the planisphere leaves off, the western, or right-hand extremity begins; therefore, in counting off the given time on the top or bottom graduated scales, the reckoning is to be transferred from the left, and completed on the right, as if the two outside edges of the planisphere were joined together.

PROBLEM XII.

TO FIND WHAT STARS WILL BE ON OR NEAR THE MERIDIAN, AT ANY GIVEN TIME.

RULE. Find the right ascension of the meridian by Problem XI., over which lay a ruler, and draw a pencil line along its edge from the top to the bottom of the planisphere, and it will show all the stars that are on or near the meridian.

EXAMPLE 1.-Required what stars will be on or near the meridian at 9 hours, 25 minutes past noon, Sept. 16th, 1833 ?

Solution. The right ascension of the meridian by Problem XI. is 21 hours: this hour circle, or the line which passes up and down through the planisphere, shows that no star will be directly on the meridian at the given time; but that Alderamin will be a little to the east, and Deneb Cygni à little to the west of it; also Zeta Cygni, and Gamma and Alpha in the Little Horse, very near it on the east.

PROBLEM XIII.

TO FIND THE EARTH'S MEAN DISTANCE FROM THE SUN.

RULE. As the Sun's horizontal parallax is to radius, so is the semi-diameter of the Earth to its distance from the Sun.