APPENDIX.

TH

or West.

Of the VARIATION of the COMPASS and ATTRACTION of the Needle. HE Variation of the Compass is the number of Degrees that the Magnetic Needle points from the true North, either East This differs in different places, and in the same place at different times. It is, at present, in Connecticut, a few degrees to the Westward. That is, the Needle points to the Westward of North and is gradually approaching the true North.

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, jun. 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 cannot therefore be due North but 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 being then nearly vertical for some time gives the observer a better opportunity to complete his observation.*

*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.

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 Proportion :

As Co-Sine of the Latitude; Is to Radius; So is Co-Sine of the Declination; to Sine of the Elongation.

From a Table in Blunt's Practical Navigator it appears that the Declination of the North Star, January 1, 1800, was 88° 14′ 32′′, and increasing at the rate of 19.69 Seconds annually. Consequently, January 1, 1805, the Declination will be 88° 16' 10", and the Co-Declination or Polar distance will be 1° 43′ 50′′.

According to the above Proportion, the Elongation, January 1, 1805, in Lat. 41° 30' will be 2° 18" 39", and in Lat. 42° it will be 2° 19' 44".

The following Table shows the Elongation in several different Latitudes for five years successively. It is calculated for the first of January in each year; and in using it, if the time when the Elongation is required, be past the middle of the year, take it for the beginning of the next year.

A Table showing the Elongation of the North Star.

39° 30' 2° 14′ 35" 2° 14' 10" 2° 13′ 44′′ 2° 13′ 19′′ 2° 12′ 53′′

40

2 15 34 2 15 40 30 2 16 34 2 16

8 2 14 43 2 14 17 2 13 52

8 2 15 42 2 15 17 2 14 51

41

2 17 36 2 17 10 12 16 44 2 16 18 2 15 52

41 30 2 18 39 2 18 13 2 17 47 2 17 20 2 16 54

42

2 19 44 2 19 18 2 18 51 2 18 25 2 17 58 42 30 2 20 51 2 20 24 2 19 58 2 19 31 2 19 5

43

2 22 0 2 21 33 2 21

62 20 40 2 20 13

43 30 2 23 10 2 22 43 2 22 16 2 21 49 2 21 22

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 a 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 swing 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, perpendic ular aperture at a convenient height from the ground, say about 2

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 be plainly 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; but if they are both West they must be added, and their difference or sum will be the true Variation.

IT

Of the ATTRACTION of the NEEDLE.

T is well known that any Iron substance has an influence upon the magnetic Needle, attracting it one way or the other from 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 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 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 making mistakes in his Field notes, by 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.

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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 then work by 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 line by the given bearing, the corner is found 20 Links to the left hand; what is the present bearing of this line?

Ch.

Deg.

L.

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.

*57.3 Degrees is the Radius cf a Circle (nearly) in such parts as the Circumference contains 360.

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MATHEMATICAL TABLES.

VIZ.

1. A Traverse Table, or Table of Difference of Latitude and

Departure.

II. A Table of Natural Sines.

III. A Table of Logarithms for Numbers.

IV. A Table of Logarithmic or Artificial Sines, Tangents and Secants.

I. A TRAVERSE TABLE, or TABLE OF DIFFERENCE OF LAT. ITUDE AND DEPARTURE, calculated for Degrees and Quarters of Degrees, and for any Distance up to 50 Rods, Chains, &c; by which the Northings and Southings, Eastings and Westings made in a Survey may be found.

Note. Northings and Southings are called Difference of Latitude, or simply Latitude; Eastings and Westings are called Departure, Meridian Distance, or Longitude.

Explanation of the Table.

To find the Latitude and Departure, or Northing, &c. for any Course and Distance.

If the Course be less than 45°, look for it at the Top, but if more than 45°, at the Bottom of the Page; and look for the Distance in the Right or Left hand Column: Against the Distance, and directly under or over the Course, stand the Northing, &c. in whole Numbers and Decimals.

If the Course be less than 45°, the Northing or Southing will be greater than the Fasting or Westing; but if more than 45°, the Easting or Westing will be the greatest.

L