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 sup port 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 21 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 N. E. or N. W. 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, untis, 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 substracted from the latter; and if they are both west, they must be added, and their difference or sum will be the true yariation. * 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 van giation, as synonymous with declination. Variation is properly, how happen that it will point wrong. To ascertain whether this is the case, the surveyor, at each station, should take a hack 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. PRE A RULE TO FIND THE DIFFERENCE BETWEEN THE SENT 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, 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 line by the given bearing, the corner is found 20 links to the left hand; what is the present bearing of this line 2 Ch. Deg. L. 100 20 2000 1146.0 60 2000)68760(34 Minutes. Answer— 34 minutes to the left hand is the allowance re. quired, 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 distance 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. Substract the course from 90°, and the remainder will be the quantity of the angle opposite to the latitude. 40" CASE I. Fig. 1. In the annexed triangle, the side A C, is given N. 400 W. 50 rods. The latitude and departure, or the northing and westing, areC B required. A B is a meridian, or a north and south line. The angle at A contains 40°, and that at C, 509, as appears by their respective arches. B C, is an east and west line, of course the angle at B contains 90°, or it is a right angle. A C is made radius. From the point at A, the arch Ca is described. From the point at C, the arch A z is described. BC is the sine of the angle at A, or of the arch Ca, and A B is the co-sine. A B is the sine of the angle at C, or of the arch A z, and B C is the co-sine. Sines and co-sines lie within their respective arches. Each side is proportioned to its opposite angle, and each angle to its opposite side. TO FIND THE REQUIRED SIDES, TAKE THE FOLLOWING RULE. For the latitude, make radius, the angle at B, the first term,—the logarithm of the side A C 50, the second ; the sine of the angle at C, the third, and the fourth will be the logarithm of the latitude A B. For the departure, take the same first and second terms, the sine of the angle at A for the third, and the fourth will be the logarithm of the departure BC. SEE THEM WORKED: As radius, 10.000000 : side A C, 50 rods, 1.6989701: side A C, 50 rods, 1.698970 :: sine of C, 50°, 9.884254: : sine of A 400, 9.808067 11.583224 11.507037 10.000000 Radius, Required the latitude and departure of S. 28°, W.88 rods. As radius 10.000000 As radius, 10.000000 : distance 88, logarithm, 1.944483: distance, 88 rods, 1.944483 : , cosine of course 28° 9.945935 :: sine of the course 28° 9.671609 Required the latitude and departure of N. 75o, E. 245 rods. As radius, 10.000000 As radius, 10.000000 . distance 245, 2.389166 : distance, 245, 2.389166 »: co-sine of course, 75° 9.412996 :: sine of the course 9.984944 11.802162 12.374110 10.000000 10.000000 : latitude, 63.41, 1.802162 : departure, 236.65, 2.374110 The logarithm of the distance may be set down in two places; and the sine of the course may be placed under one, and the co-sine under the other, and when they are added, the unit at the left hand, in each case, may be cancelled, which will be the same as substracting radius. CASE I I. Fig. 2. In this case, B 150 Suppose you run north from A to B, 220 rods; then east 150 rods to C. What is your course and distance from C to A? First find the course. make the side A B radius. With your dividers on the point at A, describe the arch Ba, a then on the point at C, describe the arch In describing the last arch B C is made radius. Each arch contains as many degrees as its opposite angle. As the sides A B and B C, both lie without their respective arches, they are tangents. B C is the tangent of the angle at A, or of the arch Ba, and A B is the co-tangent. A B is the tangent of the angle at C, or of the archTMB z, and BC is B z. |