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. 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 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 LATITUDE 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 Easting or Westing; but if more than 45°, the Easting or Westing will be the greatest. When the Distance exceeds 50, divide it by 2, 3, or 4, that is, take one half, one third or one fourth of it, and multiply the Latitude and Departure by the number by which the Distance was divided: And when the Distance is in Chains and Links, or whole Numbers and Decimals, find the Latitude, &c. for the Chains or whole Numbers, and then for the Links or Decimals, remembering to remove the Decimal Point in the Table further to the Left, according to the given Decimal. EXAMPLES. 1. Required the Latitude and Departure for 45 Rods, on a Course N. 15° 15' W. Under 15° 15' and against 45 is 43.42 for the Northing and 11.84 for the Westing. 2. Required the Latitude and Departure for 120 Rods, on a Course S. 58° 30′ E. Take one third of 120 which is 40; against this number, over 58° 30' is 20.90 for the Latitude and 34.11 for the Departure. These multiplied by 3 give 62.70 for the Southing and 102.33 for the Easting. 3. Required the Latitude and Departure for 37.36 Rods or 37 Chains and 36 Links, on a Course N. 26° 45′ E. Northing 33.36 Easting 16.81 Note. When the Minutes are not 15, 30 or 45, the Northings, &c. must be calculated by Natural Sines, or by Trigonometry. Dist./ 1 2 1.00 0.00 1.00 0.01 1.00 0.01 2.00 0.01 2.00 0.02 2.00 0.03 2 3 3.00 0.01 3.00 4 4.00 0.02 4.00 5 0.03 3.00 0.04 3 0.03 5.00 0.02 5.00 0.04 4.00 0.05 4 5.00 0.07 5 29 29.00 0.13 29.00 30 30.00 0.13 30.00 31 31.00 0.14 31.00 32 32.00 0.14 32.00 33 33.00 0.14 33.00 34 34.00 0.15 34.00 35 35.00 0.15 35.00 36 36.00 0.16 36.00 37 37.00 0.16:37.00 38 38.00 0.17 38.00 39 39.00 0.17 39.00 40 40.00 0.17 40.00 4141.00 0.1841.00 42 42.00 0.18:42.00 43 43.00 0.19 43.00 44 44.00 0.19 44.00 45 45.00 0.20 45.00 46 46.00 0.20 46.00 47 47.00 0.2147.00 48 48.00 0.21 48.00 49 49.00 0.2149.00 50 50.00 0.22 50.00 Dep. Lat 45 0.41 31 0.42|32| 0.43 33 . Lat 0.38 44.00 15 |