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obtained from the observation. The great advantage of this method over the preceding is that then the star's motion apparently ceases for a short time.

(304) The following Table gives the







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Jan'y, 027 P.M. 019 A.M. 11 47 A.M. 11 35 P.M. 11 08 A.M.

10 56 P.M.

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230 P.M. 222 A.M.

151 P.M.

143 A.M.

112 P.M.

104 A.M.

Dec'r, The Eastern Elongations from October to March, and the Western Elongations from April to September, occurring in the day time, they will generally not be visible except with the aid of a powerful telescope.

To calculate the times of the greatest elongation of the North Star: Find in one of the Almanacs before referred to, or from the data below, its Polar dis tance at the given time. Add the logarithm of its tangent to the logarithm of the tangent of the Latitude of the place, and the sum will be the logarithm of the cosine of the Hour angle before or after the culmination. Reduce the space to time; correct for sidereal acceleration (3m. 56s. for 24 hours) and subtract the result from the time of the star's passing the meridian on that day, to get the time of the Eastern elongation, or add it to get the Western.

The Polar distance of the North Star, for Jan. 1, 1850, is 1° 29′ 25′′; for 1860, 1°26′ 12.7; for 1870, 1° 23° 01"; for 1880, 1° 19 50".4; for 1890, 1° 16′ 40′′ 7; for 1900, 1' 13' 32".2.

The preceding Table was calculated for Latitude 40°. The Time at which the Elongations occur vary slightly for other Latitudes. In Latitude 50°, the Eastern Elongations occur about 2 minutes later and the Western Elongations about 2 minutes earlier than the times in the Table. In Latitude 26°, precisely the reverse takes place.

The Times of Elongation are continually, though slowly, becoming later. The preceding Table was calculated for July 1st, 1854. In 1860, the times will be nearly 2 minutes later; and in 1900, the Eastern Elongations will be about 15 minutes, and the Western Elongations 17 minutes later than in 1854.

(305) Observations. Knowing from the preceding Table the hour and minute of the extreme Elongation on any day, a little before that time suspend a plumb-line, precisely as in Art. (301), and place yourself south of it as there directed. As the North Star moves one way, move your eye the other, so that the plumbline shall continually seem to cover the star. At last the star will appear to stop moving for a time, and then begin to move backwards. Fix the sight on the board (or the compass, &c.) in the position in which it was when the star ceased moving; for the star was then at its extreme apparent Elongation, East or West, as the case may be.

(306) Azimuths. The angle which the line from the eye to the plumb-line, makes with the True Meridian (i. e. the angle between the meridian plane and the vertical plane passing through the eye and the star) is called the Azimuth of the Star. It is given in the following Table for different Latitudes, and for a number of years to come. For the intermediate Latitudes, it can be obtained by a simple proportion, similar to that explained in detail in Art. (302).*

To calculate this Azimuth: From the logarithm of the sine of the Polar dis tance of the star, subtract the logarithm of the cosine of the Latitude of the place; the remainder will be the logarithm of the sine of the angle required. The Po lar distance can be obtained as directed in the last note.


Latitudes. 1854, 1855 1856 1857 1858 1859 1860 1870

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48 20 1112° 11′ 2° 1012 1012 09/20 091/2009′ 2° 04′ 47° 2° 09′ 2 0812° 08′ 2° 07/20 072 063/20 061/20 013 46° 2° 063 2° 06′2° 05′ 2° 052 05′ 2041 20 041° 591 45° 2° 04'2° 04′ 2 0320 03120 0232 0212° 02′ 1° 57 440 20 0212 02′ 2° 01'20 0112 01 20 00 20 00′ 43° 2° 002° 00′ 1° 59′1° 59′ 10 583/10 581° 58′ 10 531 420 10 5811° 58′ 10 57110 5711° 563/10 5611° 56′ 1° 513′ 41° 1° 563 10 5611° 5531° 55′ 1° 55′ 1° 54′1° 54′ 1° 50′ 40° 1° 55′ 10 5411° 54′ 1° 53′10 531°53′ 10 521 10 481 39 10 53110 52310 5211° 52′ 1° 513 10 511° 51′ 1° 463 38° 1° 51′ 1° 51'1° 51′ 10 501° 50′ 1° 493/10 491 370 10 50110 493 10 4911° 49' 10 483 1 4811° 48′ 360 10 483 10 4811° 48′ 10 471 471 1° 47' 10 46 10 423 350 10 4741° 47′ 10 463 10 461° 46′ 1° 45′ 1° 45′ 1° 41′ 34° 1° 4611° 45'10 451° 45' 10 4431° 44' 1° 44′ 1° 40' 33° 1. 45′ 1° 44′1° 44'10 4331° 4311° 43′ 10 4231° 39′ 1° 423 1° 421 1° 42' 1° 413 10 38' 10 411 10 41 10 403/10 40 10 37' 1° 40110 401 1° 40′ 1° 39'10 36′

320 10 44 10 4311° 43′ 310 10 42310 4211° 42′ 30 10 411 411° 41′

10 451

1° 44′


(307) Setting out a Meridian. When two points in the direction of the North Star at its extreme elongation have been Fig. 204. obtained, as in Art. (305), the True Meridian can be found thus. Let A and B be the two points. Multiply the natural tangent of the Azimuth given in the Table, by the distance AB. The product will be the length of a line which is to be set off from B, perpendicular to AB, to some point C. A and C will then be points in the True Meridian. This operation may be postponed till morning. If the directions of both the extreme Eastern and extreme Western elongations be set out, the line lying midway between them will be the True Meridian.


(308) Determining the Variation. The variation would of course be given by taking the Bearing of the Meridian thus obtained, but i can also be determined by taking the Bearing of the star at the time of the extreme elongation, and applying the following rules.

When the Azimuth of the star and its magnetic bearing are one East and the other West, the sum of the two is the Magnetic Varition, which is of the same name as the Azimuth; i. e. East, if that be East, and West, if it be West.

When the Azimuth of the star and its Magnetic Bearing are both East, or both West, their difference is the Variation, which will be of the same name as the Azimuth and Bearing, if the Azimuth be the greater of the two, or of the contrary name if the Azimuth be the smaller. Fig. 205.

All these cases are presented together in the NPNS N figure, in which P is the North Pole; Z the place of the observer; ZP the True Meridian; S the star at its greatest Eastern elongation; and ZN, ZN', ZN", various supposed directions of the needle. Call the Azimuth of the star, i. e. the angle 1ZS, 2° East.

Suppose the needle to point to N, and the Bearing of the star, i. e. SZN, to be 5° West of Magnetic North. The variation PZN will evidently be 7° East of true North.


Suppose the needle to point to N', and the bearing of the star, i. e. N'ZS, to be 11° East of Magnetic North. The Variation will be East of true North, and of the same name as the Azimuth, because that is greater than the bearing.

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Suppose the needle to point to N" and the bearing of the star, i. e. N'ZS, to be 10° East of Magnetic North. The Variation will be 8° West of true North, of the contrary name to the Azimuth, because that is the smaller of the two.*


Algebraically, always subtract the Bearing from the Azimuth, and give the remainder its proper resulting algebraic sign. It will be the Variation; East if plus, and West, if minus. Thus in the first case above, the Variation +2° (-5)=7° 7° East. In the second case, the Variation = +2°—(+14°) °°East. In the third case, the Variation 80: 8° West.


+2° - (+100)

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If the star was on the other side of the Pole, the rules would apply likewise.

(309) Other Methods. Many other methods of determining the true Meridian are employed; such as by equal altitudes and azimuths of the sun, or of a star; by one azimuth, knowing the time; by observations of circumpolar stars at equal times before and after their culmination, or before and after their greatest elongation, &c

All these methods however require some degree of astronomica knowledge; and those which have been explained are abundantly sufficient for all the purposes of the ordinary Land-Surveyor.

"Burt's Solar Compass" is an instrument by which, "when adjusted for the Sun's declination, and the Latitude of the place, the azimuth of any line from the true North and South can be read off, and the difference between it and the Bearing by the compass will then be the variation."

(310) Magnetic variation in the United States. The vari ation of the Magnetic needle in any part of the United States, can be approximately obtained by mere inspection of the map at the beginning of this volume.* Through all the places at which the needle in 1850,† pointed to the true North, a line is drawn on the map, and called the Line of no Variation. It will be seen to be nearly straight, and to pass in a N.N.W. direction from a little west of Cape Hatteras, N. C. through the middle of Virginia, about midway between Cleveland, (Ohio), and Erie, (Pa.), and through the middle of Lake Erie and Lake Huron. If followed South-Easter.y it would be found to touch the most Easterly point of South America. It is now slowly moving Westward.

At all places situated to the East of this line (including the New-England States, New-York,New-Jersey, Delaware, Maryland, nearly all of Pennsylvania, and the Eastern half of Virginia and North Carolina) the Variation is Westerly, i. e. the north end of the needle points to the west of the true North. At all places

* Copied (by permission) from one prepared in 1856, by Prof. A. D. Bache, Supt. U. 8. Coast Survey, from the U. S. C. S. Observations. The dotted portions of the lines are interpolations due to the kindness of J. E. Hilgard, Assist. U. S. Coast Survey.

+ A gradual change in the Variation is going on from year to year, as will be explained in the next Chapter.

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