The sides are calculated in the following manner :— To find side a g in Triangle I. af: ag sin agf: sin afg = If instead of subtracting the sine of the angle opposite to the given side, its cosecant is added, the result will be as follows: · - In the same way, the lengths of the other sides will be found to be as follows: Triangle III. log b c = log bg+L. sin 85° 49' + L. cosec 57° 24'-20 log ce = log cg+L. sin 56° 42′ + L. cosec 38° 15'-20 log eg = log cg + L. sin 85° 03′ + L. cosec 38° 15'-20 log ef = log eg + L. sin 53° 33' + L. cosec 84° 17' - 20 a result practically the same as that obtained in the solution of triangle I. In some cases the two sides of a triangle and the angle contained between them may be known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added to half their sum will be the greater of the two angles required—that is, the angle opposite to the greater side. Interior Detail of the Triangulation. The triangulation for a survey being completed, the filling-in of the interior detail presents no difficulty. Roads, rivers, woods, &c., may be surveyed by traversing with the theodolite or with the dial. For filling in details, the prismatic compass is of great use. It is a hand instrument consisting of a glass-covered circular brass box, 2 inches in diameter, containing a graduated card or aluminium ring, under or across which a magnetic-needle is fixed. The card or ring is divided to half or one-third of a degree. The needle and card are accurately balanced. Sights are attached to the rim of the box. The farther sight has a fine thread stretched along its opening in the direction of its length. The near sight has a small slit below which is a reflecting magnifying triangular prism, so placed that on looking through the slit the eye sees at the same time the vertical wire of the farther sight and the needlereading, the divisions on the card appearing as a continuation of the wire. The graduation of the ring begins at the south end of the needle, and proceeds towards the right, round to 360°. In this way bearings are shown to the east of north. With this instrument, when held in the hand, bearings may be read to within 30 minutes to 2 degrees. The instrument is thus suitable only for preliminary and unimportant work. Mounted on a stand, the instrument gives more satisfactory results. The plane table is an instrument which may be advantageously used for filling in details where minute accuracy is not required. It consists of a drawing-board mounted on a portable tripod capable of being levelled, like the graduated limb of the theodolite. It must also have a free horizontal angular movement, and be provided with a clamp and tangent screw. The index on the board consists of a flat straight-edge, either with upright sights at its ends or with a telescope for determining the line of sight. The use of the plane table is similar to that of the theodolite. Instead, however, of reading off horizontal angles and afterwards plotting them on paper, the angles are at once laid down in the field on a sheet of paper strained on the top of the table. Before the introduction of the theodolite, the plane table was largely used for mine-surveying in Sweden, where the magnetic nature of the iron ore deposits renders the compass useless for surveying purposes. American Mining Claims.-Prospectors are usually without suitable instruments to lay off their claims on the surface with any degree of accuracy, and consequently the methods they employ are generally very crude. Before the patent or title from the United States can be obtained, a very accurate survey of the claim must be made with the theodolite by a deputy of the United States Surveyor-General of Public Lands. These officers are known as the United States Deputy Mineral Surveyors, and are required to pass an examination. Mining claims are of different dimensions according to the local laws. The length is limited by the United States laws to 1,500 feet in the direction, or along the strike, of the vein. The width varies in the different States; it is usually 300 feet on each side of the middle of the vein at the surface. The end lines of the claims must be parallel, but the side lines need not be so. This prevents more than 1,500 feet of a vein being included in one claim. When mineral discoveries are made on surveyed land, the surveys must be so connected with the public survey that there will be no difficulty in finding some fixed point or corner of that survey. When discoveries are made on unsurveyed land, the survey must be connected with permanent natural objects, such as mountain peaks or rocks. It is frequently found that two or more claims conflict or overlap. In such cases, priority of location determines the ownership of the area in dispute. In making the plan, the United States Deputy-Surveyors must deduct the area in conflict from the subsequent claim. When the survey for patent is completed, the claim must be marked by at least four stakes, one in each corner. According to the instructions issued to the United States Deputy Mineral Surveyors, all mineral surveys must be made with a transit-theodolite with solar attachment, or with some other instrument acting independently of the magnetic meridian. All courses must be referred to the true meridian. The magnetic declination must be noted at each corner of the survey. In case the claim is situated in a district where there are no corners of the public survey within 2 miles, the surveyor must establish a permanent mineral location monument. This should consist of a post 8 feet long and 6 inches square, set 3 feet in the ground, and protected by a well-built conical mound of stone, 3 feet high and 6 feet in diameter at the base. All corners of the claim must be established in a permanent manner, and the corner and survey number must be neatly chiselled on the sides facing the claim. In case the point for the corner is inaccessible, a witness-corner must be established as near as practicable to the true corner, with which it must be connected by course and distance. The claimant is required by law to show that 500 dollars' worth of labour has been expended upon the claim by himself. The surveyor must, therefore, give full details of all improvements made upon the claim. A preliminary plan on a scale of 200 feet to an inch must be filed with the field-notes. With the notes, too, a report must be submitted stating in detail the observations and calculation for the establishment of the meridian from which the courses were deflected, in cases where the solar attachment was not used. If any of the lines of the survey were determined by triangulation or traverse, full details must be given of the calculations whereby the results reported in the field-notes were obtained. The field-notes must be prepared in conformity with the accompanying specimen :— FIELD-NOTES* OF THE SURVEY OF THE CLAIM OF THE 66 ARGENTUM MINING COMPANY" UPON THE SILVER KING AND GOLD QUEEN LODES, AND SILVER KING MILL SITE, IN ALPINE MINING DISTRICT, LAKE COUNTY, COLORADO. Surveyed by G. LIGHTFOOT, April 22 to 24, 1886. Survey No. 4225 A-Silver King Lode.-Beginning at corner No. 1, identical with corner No. 1 of the location. A spruce post, 5 feet long 4 inches square, set 2 feet in the ground, with a mound of stone marked (1) 4225 A, whence the W. corner Section 22, Township 11 S., Range 81 W. of the 6th principal meridian, bears S. 79° 34' W., 1378.2 feet. Corner No. 1, Gottenburg lode (unsurveyed), bears S. 40° 29′ W., 187 67 feet. A pine, 12 inches in diameter, blazed and marked B. T. (bearing-tree) (1) 4225 A, bears S. 7° 25' E., 22 feet. Mount Ouray bears N. 11° E. Hiawatha Peak bears N. 47° 45′ W. Thence S. 24° 45′ W. (variation 15° 12′ E.), 1242 feet to trail coursing N.-W. and S.-E., 1365-28 feet to corner No. 2. A granite stone, 25 by 9 by 6 inches, set 18 inches in the ground, chiselled (2) 4225 A, whence corner No. 2 of the location bears S. 24° 45′ W., 134 72 feet. Corner No. 1, survey No. 2560, Carnarvon lode, bears S. 3° 28' E., 116.6 feet. North end of bridge, over Columbine Creek, bears S. 65° 15' E., 650 feet. Thence N. 65° 15′ W. (variation 15° 20′ E.), 152 feet intersect line 4-1, survey No. 2560, at N. 38° 52′ W., 2312 feet from corner No. 1. 300 feet to corner No. 3. A cross at corner point, and (3) 4225 A chiselled on a granite rock in place, 20 by 14 by 6 feet above the general level, whence *For a copy of these notes, I am indebted to the kindness of Mr. O. Carstarphen, U.S. Surveyor-General, Colorado. |