Example 4. Elevation at A+ 94.0; AB 1 in 100; BC, AH, level; A D, BC, each 150 feet, divided into 50-feet spaces, the points of division corresponding therefore to ordinates 8 and 4 of the initial diagram C H = 1 X 1.5 = 1.5. Descent from A to C along chord A C = CH÷6 = 0.25. The elevations then along the chord A C, descending at the rate of 0.25 per 50 feet, will be: Α 8 4 0 4 8 C From which deduct the ordinates just found, 0.0 0.21 0.33 0.37 0.33 0.21 And the grade elevations on the curve will be: 0.0 94.0 93.54 93.17 92.88 92.67 92.54 92.5 The figures are drawn much distorted, in order to make the illustration clear. 2. With profile paper at hand, a convenient and quite suf ficient determination of the grade elevations on a vertical curve may be made by drawing the gradients to a scale of 2 feet to an inch vertical, and 50 feet to an inch horizontal. By means of the curve protractor (Art. XXV. 1) a suitable arc may XIV. THE TRANSIT. 1. Should the vernier and circle plates be out of parallel, should one or the other be sprung, a defect shown by a slight rocking motion when the rims are pinched alternately on opposite sides, the instrument must be sent to the shop for repair. This is a common disease of transits in their old age: instrument-makers need to study its cause and cure. 2. TO ADJUST THE LEVEL TUBES. Bring the bubbles to the middle of them by means of the levelling screws. Turn the top of the instrument horizontally half way round. If the bubbles then err, reduce the error onehalf with the small adjusting screws attached to the tubes, and one-half with the levelling screws. Repeat until the adjustment is perfect. 3. TO ADJUST THE VERTICAL HAIR SO THAT IT SHALL REVOLVE IN A PLANE, AND MARK BACKSIGHT AND FORESIGHT POINTS IN THE SAME STRAIGHT LINE. Try, first, by reference to the corner of a well-built house, or to a plumb-line, whether the hair be truly vertical. If it is not, loosen the four small capstan head screws on the outside of the barrel slightly, and gently tap the topmost one right or left, until the adjustment is effected. 4. Then, after bringing the four screws to a snug bearing again, direct the cross-hair to the edge of some well-defined object, as a chain pin, or stake, placed 400 or 600 feet distant. Upset the telescope, and place a like mark at about the same distance, and level in the opposite direction. Unclamp. Revolve the instrument horizontally on its spindle half way round, and direct the cross-hair to the point first observed. Again upset the telescope. If the cross-hair now strikes aside from the second mark, correct one-quarter of the error by one-quarter with the tangent screw. Repeat until the adjustment is effected. An experienced transitman will generally prefer to make this adjustment without aid, points in range being readily found. 5. Having thus brought the cross-hair to revolve in a plane, it is next to be seen whether the plane in which it revolves is truly vertical. To do so, set the instrument near the base of some lofty point, as a church spire or chimney, on which point lirect the cross-hair, and then, tilting the object end of the telescope downwards, set a pin, or make a pencil dot in line. Unclamp the spindle; turn the instrument horizontally halfway round; clamp fast; fix the cross-hair again on the lower point, and try it on the upper one. If it misses, correct half the error by means of the adjusting screws now usually provided, at one of the bearings of the cross-bar; or, if these be lacking, by filing off the feet of the standard which supports the higher end of the cross-bar. 6. TO ADJUST THE NEEDLE. Having removed the cap, and placed the instrument conveniently in a still room, push one end of the needle a little aside from the point where it tends to settle, and exactly to some figured division line on the graduated circle. There gently stay it in position by means of a small wooden block, an ivory die, or the like. Observe where the opposite end strikes. If between graduation lines, mark the precise spot with a sharp pencil. Turn the needle end for end, and stay the reverse point at the division line first observed. Again spot with the pencil where the opposite end stakes. Midway of these two pencil spots make another. Take the needle off the pivot, and bend it this way, or that, until, by repeated trials, when replaced with one end stayed at the division line first observed, the other shall cut the midway pencil spot. 7. The needle being thus straightened, proceed to rectify the position of the centre pin, if necessary, by bending it with nippers so that the needle shall cut opposite degrees at the quarter points of the circle. XV. MISCELLANEOUS. THE VERNIER. 1. The vernier in the transit is a short graduated arc, movable around the graduated circle of the instrument, by means of which subdivisions of the circle graduation can be read. There are many varieties of the vernier; but a knowledge of the principle upon which one is made introduces the student to an easy acquaintance with all. 2. Suppose the tenth part of a foot to be marked off on a straight edge into ten equal parts, and that on another straight edge a space equal in length to nine of these parts is divided also into ten equal parts. The subdivisions of the latter scale will then each be nine-tenths as large as the subdivisions of the former; and if the graduated edges are placed together, with the zero marks in both exactly lined, the first mark of the latter, or vernier, scale will fall short of the first mark of the former, or limb, so to speak, by one-tenth part of the first space on the limb; that is to say, by one-tenth part of one-hundredth of a foot, or one-thousandth of a foot. The second mark of the vernier will fall short of the second mark of the limb by two-thousandths of a foot, and so on. If, therefore, the vernier scale be moved slowly forward, the successive oppositions of the scale marks will indicate successive advances of the vernier, each equal to the one-thousandth part of a foot. The marginal example reads 6.217=six feet, two-tenths, one-hundredth, and seventhousandths. vernier, together with a part of the graduated circle. The vernier is a double one, for convenience in reading angles right or left. It will be observed that a space, equal to twenty-nine half degrees on the limb, is laid off from zero each way on the vernier, and there subdivided, on both sides of zero, into thirty equal parts. If now the zeros are brought into line, the first marks of the vernier right and left will fall one-thirtieth part of a half degree short of the first, or half-degree marks on the limb; that is to say, one minute short. The vernier, therefore, is scaled to read minutes; and, if its zero mark be moved slowly half a degree on the limb, its several subdivision marks, one after another in arithmetical succession, will be seen to line with marks of the limb until the thirtieth is reached, when zero will be found to have traversed the half degree space. 4. TO READ AN ANGLE. First note whether the vernier has been moved right or left; then observe on the limb the number of full degrees, and the half-degree, if any, which zero of the vernier has passed; next, look along the vernier from its zero towards the right, if the movement has been towards the right, and from zero towards the left, if the movement has been 20 20 ΟΙ ΟΙ 30 25 20 C 01 10 155 20 towards the left, until a "minute" mark is found exactly in |
