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).*

AZIMUTHS OF THE NORTH STAR.

4

2

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Latitudes. 1854 1855 1856 1857 1858 1859 1860 1870 50° 2°16′2016112° 16′ 2° 15′ 2° 15′ 2° 14′2° 141 2009 49° 2° 14′ 20 1312° 131 2012 201212°12′ 2°11′ 2°06′ 48° 2° 11′2° 11′ 2°10′2010 2009 2009′2°09′ 2°04′ 47° 2°09′ 2° 08′2°08′ 2007 2007 2006 2006 2° 01' 460 2006 2006 2005 2° 05′2°05′ 2°04′2°04′1°59′ 45° 2° 04′2°04′ 2° 03′2° 03′2°02′ 2°02′2°02′ 1°57′ 44° 2° 02′2002′ 2°01′2°01′2°01′ 2°00′ 2°00′ 1°55′ 43° 2° 00′2°00′ 1°59′1°59′ 1°58′1°58′1°58′ 1°53′ 42° 1°58′1°58′ 1°57′105711°56′1°56′ 1°56′ 1°51′ 41° 1°56′105611°55′1°55′ 1°55′ 1°54′1°54′1° 50′ 40° 1°55′ 1°54′1°54′ 1°53′10531°53′ 1°52′1°48 39° 1°5311°52′ 105211°52′ 1° 51 105111° 51′ 1° 46 38° 1051 105111°51′ 1° 50′ 1°50′ 1° 49′1°49′1°45 37° 1°50′1°49′1° 49′1°49′ 1° 48′1°48′1° 48′ 1° 44′ 36° 1°48′104811°48′ 1°47′1°47′1°47′ 1°461°42′ 35° 1° 47′1° 47′ 1° 46′1° 4611° 46′ 1°45′1°45′1°41′ 34° 1°46′1°45′1°45′1° 45′ 1° 44′1°44′1° 44′ 1° 40′ 330 1° 45′ 1° 44′1° 44′1° 43′ 1° 4311° 43′ 1°42′1°39′ 32° 1° 44′ 1° 43′1° 43′ 1° 42′1° 4211° 42′ 1° 41′1° 38′ 31° 1°42′1°42′1°42′ 104211° 42′ 1°41′ 1° 41′ 1° 40′ 1° 40′ 1° 37' 30° 1° 411° 4111° 41' 41′ 1° 40′ 1° 40′ 1° 40′ 1° 39

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12/12/1

1°37′

1°40′ 1°39′1° 36′

P S ★

(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. CH B

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.

A

1

(308) Determining the Variation. The variation would of course be given by taking the Bearing of the Meridian thus obtained, but it 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 NPN 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 PZS, 2o 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.

Z

N

Suppose the needle to point to N', and the bearing of the star, i. e. N'ZS, to be 14° 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.

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° = 7o East. In the second case, the Variation = +2°-(+14°) ३० = 4o East. In the third case, the Variation = +2°-(+10°) = (+100) 8° 8° West.

= +

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 astronomical 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 variation in any part of the United States, east of the Territories, 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 1840,† 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-Easterly 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 situated to the West of this line (including the Western and Southern States) the Variation is easterly, i. e. the North end of the needle points to the East of the true North. This variation increases in proportion to the distance of the place on either side of the line of no variation, reaching 21° of Easterly Variation in Oregon, and 18° of Westerly Variation in Maine.

Lines of equal Variation are lines drawn through all the places which have the same variation. On the map they are drawn for each degree. All the places situated on the line marked 1o, East or West, have 1o Variation; those on the 2o line, have 2o Variation, &c. The variation at the intermediate places can be approximately estimated by the eye. These lines all refer to 1840.

The lines of equal Variation, if continued Northward, would all meet in a certain point called the Magnetic Pole, and situated in the neighborhood of 96° West Longitude from Greenwich, and 70° of North Latitude. Towards this pole the needle tends to point.

Another Magnetic pole is found in the Southern hemisphere; but the farther development of this subject belongs to a treatise on Natural Philosophy.

The Variation on the Pacific slope of this country has been very imperfectly ascertained. A few leading points are as below. California; Point Conception,

Sept. 1850, 13° 49′ E.

(311) To correct Magnetic Bearings. The Variation at any place and time being known, the Magnetic, Bearings taken there and then, may be reduced to their true Bearings, by these Rules. RULE 1. When the Variation is West, as it is in the NorthEastern States, the true Bearing will be the sum of the Variation and a Bearing which is North and West, or South and East; and the difference of the Variation and a Bearing which is North and East, or South and West. To apply this to the cardinal points, a