Scientific American Supplement, No. 360, November 25, 1882

by Various

TO FIND THE AZIMUTH OF POLARIS.

As we have shown the azimuth of Polaris to be a function of the latitude, and as the latitude is now known, we may proceed to find the required azimuth. For this purpose we have a right-angled spherical triangle, Z S P, Fig. 4, in which Z is the place of observation, P the north pole, and S is Polaris. In this triangle we have given the polar distance, P S = 10° 19' 13"; the angle at S = 90°; and the distance Z P, being the complement of the latitude as found above, or 90°--L. Substituting these in the formula for the azimuth, we will have sin. Z = sin. P S / sin P Z or sin. of Polar distance / sin. of co-latitude, from which, by assuming different values for the co-latitude, we compute the following table:

AZIMUTH TABLE FOR POINTS BETWEEN 26° and 50° N. LAT.
LATTITUDES
___________________________________________________________________
| | | | | | | |
| Year | 26° | 28° | 30° | 32° | 34° | 36° |
|______|_________|__________|_________|_________|_________|_________|
| | | | | | | |
| | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " |
| 1882 | 1 28 05 | 1 29 40 | 1 31 25 | 1 33 22 | 1 35 30 | 1 37 52 |
| 1883 | 1 27 45 | 1 29 20 | 1 31 04 | 1 33 00 | 1 35 08 | 1 37 30 |
| 1884 | 1 27 23 | 1 28 57 | 1 30 41 | 1 32 37 | 1 34 45 | 1 37 05 |
| 1885 | 1 27 01 | 1 28 35½ | 1 30 19 | 1 32 14 | 1 34 22 | 1 36 41 |
| 1886 | 1 26 39 | 1 28 13 | 1 29 56 | 1 31 51 | 1 33 57 | 1 36 17 |
|______|_________|__________|_________|_________|_________|_________|
| | | | | | | |
| Year | 38° | 40° | 42° | 44° | 46° | 48° |
|______|_________|__________|_________|_________|_________|_________|
| | | | | | | |
| | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " | ° ' " |
| 1882 | 1 40 29 | 1 43 21 | 1 46 33 | 1 50 05 | 1 53 59 | 1 58 20 |
| 1883 | 1 40 07 | 1 42 58 | 1 46 08 | 1 49 39 | 1 53 34 | 1 57 53 |
| 1884 | 1 39 40 | 1 42 31 | 1 45 41 | 1 49 11 | 1 53 05 | 1 57 23 |
| 1885 | 1 39 16 | 1 42 07 | 1 45 16 | 1 48 45 | 1 52 37 | 1 56 54 |
| 1886 | 1 38 51 | 1 41 41 | 1 44 49 | 1 48 17 | 1 52 09 | 1 56 24 |
|______|_________|__________|_________|_________|_________|_________|
| | |
| Year | 50° |
|______|_________|
| | |
| | ° ' " |
| 1882 | 2 03 11 |
| 1883 | 2 02 42 |
| 1884 | 2 02 11 |
| 1885 | 2 01 42 |
| 1886 | 2 01 11 |
|______|_________|

An analysis of this table shows that the azimuth this year (1882) increases with the latitude from 1° 28' 05" at 26° north, to 2° 3' 11" at 50° north, or 35' 06". It also shows that the azimuth of Polaris at any one point of observation decreases slightly from year to year. This is due to the increase in declination, or decrease in the star's polar distance. At 26° north latitude, this annual decrease in the azimuth is about 22", while at 50° north, it is about 30". As the variation in azimuth for each degree of latitude is small, the table is only computed for the even numbered degrees; the intermediate values being readily obtained by interpolation. We see also that an error of a few minutes of latitude will not affect the result in finding the meridian, e.g., the azimuth at 40° north latitude is 1° 43' 21", that at 41° would be 1° 44' 56", the difference (01' 35") being the correction for one degree of latitude between 40° and 41°. Or, in other words, an error of one degree in finding one's latitude would only introduce an error in the azimuth of one and a half minutes. With ordinary care the probable error of the latitude as determined from the method already described need not exceed a few minutes, making the error in azimuth as laid off on the arc of an ordinary transit graduated to single minutes, practically zero.

REFRACTION TABLE FOR ANY ALTITUDE WITHIN THE LATITUDE OF THE UNITED STATES.

_____________________________________________________
| | | | |
| Apparent | Refraction | Apparent | Refraction |
| Altitude. | _minus_. | Altitude. | _minus_. |
|___________|______________|___________|______________|
| | | | |
| 25° | 0° 2' 4.2" | 38° | 0° 1' 14.4" |
| 26 | 1 58.8 | 39 | 1 11.8 |
| 27 | 1 53.8 | 40 | 1 9.3 |
| 28 | 1 49.1 | 41 | 1 6.9 |
| 29 | 1 44.7 | 42 | 1 4.6 |
| 30 | 1 40.5 | 43 | 1 2.4 |
| 31 | 1 36.6 | 44 | 0 0.3 |
| 32 | 1 33.0 | 45 | 0 58.1 |
| 33 | 1 29.5 | 46 | 0 56.1 |
| 34 | 1 26.1 | 47 | 0 54.2 |
| 35 | 1 23.0 | 48 | 0 52.3 |
| 36 | 1 20.0 | 49 | 0 50.5 |
| 37 | 1 17.1 | 50 | 0 48.8 |
|___________|______________|___________|______________|