|
NAMES. |
LONGITUDE. |
LATITUDE. |
NATURE. |
MAGNITUDE. |
|
Ram's following Horn |
♉ 5° 21' |
9° 57' N. |
♄ ♂ |
SECOND. |
|
The Pleiades |
♉ 26 55 |
4 31 N. |
♂ ☽ |
FIFTH. |
|
The Brightest of the Seven Stars |
♉ 27 50 |
4 2 N. |
♂ ☽ |
THIRD. |
|
Occulus Taurus, or the Bull's North Eye |
♊ 6 11 |
2 36 S. |
♀ |
THIRD. |
|
Aldebaran, or the Bull's South Eye |
♊ 7 31 |
5 29 S. |
♂ |
FIRST. |
|
The Bull's North Horn |
♊ 20 17 |
5 22 N. |
♂ |
SECOND. |
|
Bright Foot of Gemini: |
♋ 6 46 |
6 48 S. |
☿ ♀ |
SECOND. |
|
Castor |
♋ 17 48 |
10 4 N. |
♂ ♀ ♄ |
FIRST. |
|
Pollux |
♋ 20 59 |
6 40 N. |
♂ |
SECOND. |
|
North Assellus |
♌ 4 45 |
3 10 N. |
♂ ☉ |
FOURTH. |
|
Præspe, or the Claw of the Crab |
♌ 5 0 |
1 14 N. |
♂ ☽ |
NEBULOUS |
|
South Assellus |
♌ 6 26 |
0 4 N. |
♂ ☉ |
FOURTH. |
|
Hydra's Heart |
♌ 19 43 |
7 32 S. |
♄ ♀ |
SECOND. |
|
Cor ♌, the Lion's Heart |
♌ 27 33 |
0 27 N. |
♂ |
FIRST. |
|
Vindemiatrix |
♍ 7 38 |
10 15 S. |
♄ ♀ ☿ |
THIRD. |
|
Arista, the Virgin's Spike |
♎ 21 33 |
2 2 S. |
♀ ♂ |
FIRST. |
|
South Scale |
♏ 12 48 |
0 22 N. |
♄ ♀ |
SECOND. |
|
North Scale |
♏ 17 0 |
8 46 N. |
♃ ♂ |
SECOND. |
|
Frons Scorpio |
♐ 0 54 |
1 2 N. |
♄ ♀ |
SECOND. |
|
Antares, or the Scorpion's Heart |
♐ 7 29 |
4 32 S. |
☿ ♂ |
FIRST. |
|
Right Knee of Ophiucus |
♐ 15 41 |
7 18 N. |
♄ ♀ |
THIRD. |
|
Capricorn's Tail |
♒ 21 15 |
2 33 S |
♄ |
THIRD. |
|
Scheat Pegasi |
♓ 26 29 |
1 7 N. |
♄ |
SECOND. |
Rules to find the Zodiacal Latitude and Longitude of a Fixed Star, Comet, Planet, or the ⊕, &c. from the Right Ascension and Declination.
1st. If the right ascension be less than 180°, it is north; and if it be more than 180°, it is south.
2d. To the logarithm co-tangent of the declination add the logarithm sine of the right ascension, measured from ♈ or ♎; but if measured from ♋ or ♑, the logarithm co-sine: the sum (minus 10 in the Index), will be the log. tangent of the angle A.
3d. If the right ascension and declination be both north, or both south, add 23° 28' to angle A, and it will give angle B.
4th. If the right ascension and declination be one north and the other south, the difference between 23° 28' and angle A will give angle B.
Note.--If angle B exceed 90°, the latitude will be of the contrary name to the declination; but if angle B be less than 90°, the latitude will be of the same name as the declination.
To find the Longitude.
To the arithmetical comp. of the log. sine of angle A, and the log. sine of angle B, add the log. tang. of R.A. from ♈ or ♎, (or the log. co-tang of R.A. from ♋ or ♑). The sum will be the log. tang. of the longitude from ♈ or ♎, or the log. co-tang. of the longitude from ♋ or ♑.
To find the Latitude.
To the arithmetical comp. of the log. co-sine of angle A, and the log. co-sine of angle B, add the log. sine of the declination. The sum will be the log. sine of the latitude.
|
N.B. The arithmetical complement of a logarithm is found by subtracting it from |
10.00000 |
|
Example. The log. sine of 13° 10' is |
9.35752 |
|
|
0.64248. |
or it may be found with equal ease, by taking each figure (beginning at the left hand or index), from 9, except the last or right-hand figure, which must be taken from 10.
|
Thus: if from |
9.99990 |
|
we take |
9.35752 |
|
It gives |
0.64248 |
the object of this being to perform each problem by addition, in lieu of the lengthy process otherwise required.
EXAMPLE.--Required the zodiacal longitude and latitude or Halley's comet, at noon, on the 18th October, 1835, Greenwich mean time?
Comet's right ascension, 16h 25.31 equal in degrees to 246° 19', which, being more than 180°, is south. The declination is 0° 35' north.
|
Co-tangent dec. |
|
0° 35 |
= |
11.99219 |
|
Sine R.A. from ♎ |
|
66 19 |
= |
9.96179 |
|
Tang. angle A |
= |
89 22 |
-- |
11.95398 |
|
From angle A take |
|
23 28 |
|
|
|
It gives angle B |
|
65 54 |
|
|
Then for the Longitude.
|
To the sine angle A (arith. comp.) |
|
|
0.00003 |
|
Add the sine angle B |
|
|
9.96039 |
|
And Tang. R. A. from ♎ |
66° 19' |
= |
10.35791 |
|
Tang. longitude from ♎ |
64 20 |
= |
10.31833 |
|
Take the long. of ♎ and ♏ from this |
60 0 |
|
|
|
It leaves |
♐ 4 20, |
the longitude. |
|
Then for the Latitude.
|
To the log. co-sine angle A (arith. comp.) |
|
1.95650 |
|
Add the log. co-sine angle B |
|
9.61101 |
|
And log. sine of the dec |
|
8.00779 |
|
It gives the log. sine of the latitude 22° 6' |
= |
9.57530 |
As angle B is less than 90°, the latitude is of the same name as the declination; which being north, the latitude is north also.
Hence the comet will be, at mean noon, Greenwich time, on the 18th of October, 1835, in; 4° 20', with 22° 6 north latitude.
334:1 These are the principal fixed stars, near the ecliptic, to which only the planets can approach. If the student require the places of the stars for the purpose of bringing them to the midheaven or ascendant in a nativity, he may learn their right ascension and declination in the Nautical Almanac for each year, and he may readily calculate their, longitudes and latitudes therefrom by the rules we have given.
N.B. The longitudes increase about 50" ⅓ each year; the latitudes do not vary.