EXAMPLES.

1. At what time were Mars and Venus in conjunction, after the first of January, 1823.

Venus' daily motion is 1,6021-0,5240=1,0781– Mars' longitude for January 1st. 1823, was 311 degrees and 41 minutes: less by 285 degrees, 16 minutes, the longitude of Venus at the same time=26 degrees and 25 minutes. Then as 1,0781: 1 day :: 26 d. 25 m. =24,5, or January 25th, 1823.

TABLE.

The Sun's geocentric longitude for January 1st. 1823,

was,

The heliocentric longitude of Mercu

ry, January 1st. 1823, was

That of Venus, was

The Earth's,

That of Mars,

Jupiter's,

Saturn's,

Herschel's,

Degrees. 280-29 min.

277-25

285-16

100-20

311-41

64-51

38-56

277-30

On what day of the year, 1823, was Venus in conjunction with the earth?

3. When was Jupiter in conjunction with the earth in the year 1824 ?

4. When were Venus and Jupiter in conjunction, in 1825 ?

5. On what day in the year 1832, did Jupiter set; at the moment the Sun arose ?

PROBLEM VII.

When the heliocentric longitude of any planet, for any given day is known, to find it for any required day.

RULE.

Find the number of days between the given, and required day then as one day is to the given planet's daily motion, so are the days so found, to the distance which the planet has revolved during that time. Add this distance to the planet's known longitude, and the sum, if less than 360 degrees, will be the longitude for the required day, but if more than 360 degrees. then subtract 360 degrees from it, and the remainder will be the true longitude,

EXAMPLES.

1. On the first of January, 1823, the heliocentric longitude of Venus was 285 degrees, 16 min.; what was it on the 4th of July, in the same year? Ans. 220 degrees and three minutes.

2. On the first of January, 1823, the earth's longitude was 100 degrees and 20 minutes; what was its longitude on the 4th of July, 1825 ?

PROBLEM VIII.

To determine whether Venus or Jupiter will be the morning or evening star on any given day.

RULE.

Find the longitude of Venus and the longitude of the earth for the given day. If the difference in longitude, counting from the earth's place eastward, be less than 180 degrees, Venus will be east of the Sun, and consequently evening star: but if that difference be greater than 180 degrees, she will be west of the Sun, and therefore morning star.

EXAMPLES.

On the 4th of July, 1823, was Venus a morning or an evening star?

*

The longitude of Venus on the given day, will be found by Problem 7th, to be 220 degrees and 3 minutes, and the earth's longitude, for the same day by the same Problem, 281 degrees and 41 minutes; the difference 61 degrees and 38 minutes; this difference being less than 180 degrees, shows that Venus is east of the Sun, and consequently an evening star.

Did Jupiter rise before, or after the Sun, July 4th, 1832 ?

How many days in succession, can Venus be a morning, or an evening star?

How many days in succession, can Jupiter be a morning or an evening star?

PROBLEM IX.

To determine the day on which any particular planet shall have a given longitude.

RULE.

Subtract the longitude of the given planet found in the preceding table,from the given longitude,if practicable; but if the longitude of the planet found in the Table, be greater than the given longitude, increase the latter by 360 degrees, and then subtract; divide the remainder by the planet's daily motion, as recorded in the Table, and the quotient will show the number of days from the first of January, when the planet will have the given longitude.

EXAMPLES.

1. On what day of the year 1823, did Venus have 220 degrees of heliocentric longitude? Answer-fourth of July.

2. On what days in the year 1825, did each of the planets enter Virgo?

PROBLEM X.

To find whether Venus or Mercury will cross the Sun's disk in any given year,

RULE.

Find by Problem 9th when Venus will pass her node. Find the earth's heliocentric longitude for that day, and if it equals the longitude of Venus' node, there will be a transit of Venus, and in no other case. The same may be said of the planet Mercury.

EXAMPLES.

Were there a transit of Venus in the year 1824, or not ?

The longitude of the ascending node of Venus, is 75 degrees and 8 minutes, which she passed on the 26th of June. The earth's longitude on that day, was 274 degrees and 44 minutes. The longitude of the descending node of Venus, was 258 degrees and 8 minutes, which she passed on the 5th of March. The earth's longitude on that day, was 164 degrees and 55 minutes, consequently there was no transit of Venus in 1824.

PROBLEM XI.

To find when any two given planets shall have a given heliocentric aspect, taking their longitudes as stated in the Table for 1823.

RULE.

Add the degrees in the aspect given to the heliocentric longitude of either given planet. Find the difference between that sum and the heliocentric longitude of the other given planet: Then say, as the difference in the daily motions of the two given planets, is to one day,so is the difference in their longitude found as above to the answer required.

EXAMPLES.

At what time in the year 1824, did the earth and Venus have a trine aspect ?