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 |
|___________|______________|___________|______________|
APPLICATIONS.
In practice to find the true meridian, two observations must be made at intervals of six hours, or they may be made upon different nights. The first is for latitude, the second for azimuth at elongation.
To make either, the surveyor should provide himself with a good transit with vertical arc, a bull's eye, or hand lantern, plumb bobs, stakes, etc.[1] Having "set up" over the point through which it is proposed to establish the meridian, at a time when the line joining Polaris and Alioth is nearly vertical, level the telescope by means of the attached level, which should be in adjustment, set the vernier of the vertical arc at zero, and take the reading. If the pole star is about making its upper transit, it will rise gradually until reaching the meridian as it moves westward, and then as gradually descend. When near the highest part of its orbit point the telescope at the star, having an assistant to hold the "bull's eye" so as to reflect enough light down the tube from the object end to illumine the cross wires but not to obscure the star, or better, use a perforated silvered reflector, clamp the tube in this position, and as the star continues to rise keep the horizontal wire upon it by means of the tangent screw until it "rides" along this wire and finally begins to fall below it. Take the reading of the vertical arc and the result will be the observed altitude.
[Footnote 1: A sextant and artificial horizon may be used to find the altitude of a star. In this case the observed angle must be divided by 2.]
ANOTHER METHOD.
It is a little more accurate to find the altitude by taking the complement of the observed zenith distance, if the vertical arc has sufficient range. This is done by pointing first to Polaris when at its highest (or lowest) point, reading the vertical arc, turning the horizontal limb half way around, and the telescope over to get another reading on the star, when the difference of the two readings will be the double zenith distance, and half of this subtracted from 90° will be the required altitude. The less the time intervening between these two pointings, the more accurate the result will be.
Having now found the altitude, correct it for refraction by subtracting from it the amount opposite the observed altitude, as given in the refraction table, and the result will be the latitude. The observer must now wait about six hours until the star is at its western elongation, or may postpone further operations for some subsequent night. In the meantime he will take from the azimuth table the amount given for his date and latitude, now determined, and if his observation is to be made on the western elongation, he may turn it off on his instrument, so that when moved to zero, after the observation, the telescope will be brought into the meridian or turned to the right, and a stake set by means of a lantern or plummet lamp.