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APPENDIX.

OF THE DECLINATION AND VARIATION OF THE MAGNETIC NEEDLE, AND OF THE ATTRACTIONS TO WHICH IT IS SUBJECT.

The declination of the needle is the number of degrees it deviates from the true north, either east or west. This differs in different places, and in the same place at different times. [At Hartford, Conn. the declination was, in 1829, 6° 3' west of the true meridian of the earth; and was increasing by an annual variation of about 3'.]

The following method of ascertaining the variation, by the north star, has been adopted by many surveyors, as the most eligible to be practised on land. It was communicated to the compiler by Moses Warren, Esq., of Lyme, an experienced surveyor, with permission to publish it.

The star commonly called the north star, is not directly north, but revolves round the pole in a small circle, once in 24 hours. It can therefore be due north only twice in that period; and that is within a very few minutes of the time, when a star, called Alioth, in the constellation of Ursa major, or the great bear, is directly over or under it. There is also another star nearly in an opposite direction from the pole, called Gamma, in the constellation of Cassiopeia. When these three stars are vertical, the north star is very near the meridian ; and when they are horizontal, it is at its greatest elongation, that is, at its greatest distance east or west of the pole, and on the same side as the star in Cassiopeia. The variation may be calculated when the star is on the meridian, or when at its greatest elongation; more accurately, however, at the latter period, because its motion be

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* More exactly, 23 hours, 56 minutes and 4 seconds.-Ed.

*

ing then nearly vertical for some time, gives the observer opportunity to complete his observation.

To find the elongation of this star in any latitude, its declination must be known; that is, its distance north of the equator. This being found, institute the following pro portion :

As co-sine of the latitude ; is to radius; so is co-sine of the declination; to sine of the elongation.

The declination of the north star, January 1, 1810, was 88° 17' 28'', and increasing at the rate of about 19 seconds and one half annually.

In the following table, the elongation is calculated for ten successive years, ending with 1840, and for seven different latitudes. The calculation is made for the first of July, and of course gives the mean angle for the year.

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52

12

1831 10 521' 1° 55' 10 581120 11/20 18321 1 54; 1 58 2 1 2 18331 5111 541 1 573 2 0 18341 51 1 531 1 57 1 59 |1835 1 503 1

53

1 563 1 59 2 18361 50 1 521 1 56

1 581 18371 501 152 1

52; 1 551 1 581 18381 50 1 521 1 55 1 58 2 18391 49 1 52 1 54,

54; 1 57 2 18401 49 1 511 1 54 1 57 2

5 20 91 2° 13'
4,2 82 121
4 2 8 2
4 2 7 2 12
3 2 61 2 11

2 6 2 · 10 2

2 10 1] 5 2 91 1 442 9 01 2 4 2

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*The following figure exhibits a view of the relative situation of these stars, as they appear, when in a horizontal position; or when the north star is in its greatest eastern elongation. Tho Great Bear.

Cassiopeia.

*

N. Star.

*

* Alioth

Gamma *

The elongation for the latitude of the observation being calculated, or taken from the above table, proceed to find its range according to the following directions :

Take a pole 18 or 20 feet in length; to the end of it fasten a small line; raise it to an elevation of 45° or 50°; and support it by two crotches of suitable height to keep it firm in its place. At the end of the line near the ground, fasten a weight of half a pound or more, which should swim in water to prevent the air from moving the line. Southward of the line fix a compass sight, or other piece of metal or wood with a narrow, perpendicular aperture at a convenient height from the ground, say about 2 or 2 1-2 feet; and let it be so fixed that it can be moved a small distance east or west at pleasure. Let an assistant hold a light either NE. or NW. of the line, nearly as high as the range from the sight to the north star, in such a position that the line may plainly be seen; then, (the three stars above mentioned being parallel or nearly so with the horizon,) move the sight-vane east or west, until through the aperture, the line is seen to cut the star; and continue to observe, at short intervals, till the star is seen at its greatest elongation. Let a lighted candle be placed in an exact range with the sight-vane and line at the distance of 20 rods or more, which should stand perpendicularly, be made fast, extinguished and left till morning. Then the sight-vane, the line, and the candle, will be the range of elongation, which observe accurately with a compass; and if the elongation be east and the variation west, the former must be subtracted from the latter; and if they are both west they must be added, and their difference or sum will be the true variation.*

OF THE ATTRACTION OF THE NEEDLE.

It is well known that any iron substance has an influence upon the magnetic needle, attracting it one way or the other upon the point where it would settle, were there no such attraction. A surveyor should therefore be careful to see that no iron is near the compass when taking a bearing. But as the earth in certain spots contains, near its surface, iron or other minerals, which attract the needle, it will frequently

* The author, in common with many writers, employs the term variation, as synonymous with declination. Variation is properly, however, the happen that it will point wrong. To ascertain whether this is the case, the surveyor, at each station, should take a back view of the one last left; and if he finds that the compass does not reverse truly, he may be sure, provided the compass be accurately graduated and placed horizontally, that he either made a mistake at the last station, or that in one or the other or both of the stations, the needle was attracted from the true point. When he finds a place where he suspects there is an attraction, he should go a few rods backward or forward, and see whether the needle points differently. In this way he may prevent mistakes in his field notes, which would arise from putting down a wrong course.

To take back sights is particularly necessary in running long lines, and laying out new lands, where the needle is the only thing to guide the surveyor.

By practice and experience a knowledge will be acquired on this subject, and with regard to many other things in surveying, which cannot be taught by books; and after all the directions which can be written, the practitioner will frequently find occasion for the exercise of his own judgment.

A RULE TO FIND THE DIFFERENCE BETWEEN THE PRESENT VARIATION OF THE COMPASS, AND THAT AT A TIME WHEN A TRACT WAS FORMERLY SURVEYED, IN ORDER TO TRACE OR RUN OUT THE ORIGINAL LINES.

Go to any part of the premises where any two adjacent corners are known; and if one can be seen from the other, take their bearing; which compared with that of the same line in the former survey, shows the difference.

But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run, and the corner; and then work the following proportion :

AS THE LENGTH OF THE WHOLE LINE,
Is To 57.3 DEGREES,
So is THE SAID DISTANCE,
TO THE DIFFERENCE OF VARIATION REQUIRED.

*

EXAMPLE.

Suppose it be required to run a line, which, some years ago, bore N. 45° E., distance 20 chains, and in running this

*57.3 degrees is the radius of a circle (nearly) in such parts that the cirfine by the given bearing, the corner is found 20 links to the left hand; what is the present bearing of this line ?

Ch.

L.
As 20 57.3 : : 20

100 20

Deg:

:

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2000)68760(34 Minutes. Answer-34 minutes to the left hand is the allowance required, and the line in question bears N. 44° 26' E.

The compiler of this work acknowledges himself under obligations to George Gillet, Esq., Surveyor General of the state of Connecticut, for the following illustrations, remarks, and miscellaneous questions, considering them calculated to be useful to the learner, and the practical surveyor.

PRACTICAL TRIGONOMETRY.

The learner must understand decimals and the nature and use of logarithms, before he can make any proficiency in this branch. Difference of latitude is the distance between the parallels of the beginning and of the terminating point of a line, or of any number of lines, whether northerly or southerly. Departure is the distance between the meridians of the beginning and of the terminating point, or the dis tance made either east or west from any particular meridian on any course.

These distances are also called northings or southings, eastings or westings, as different cases may happen.

When a course and distance are given, the distance is the hypothenuse of a right angled triangle, of which, the latitude and departure are the legs. The angle which the course makes with the meridian, is opposite to the departure. Subtract the course from 900, and the remainder will be the quantity of the angle opposite to the latitude.

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