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great distance; and see that the intersection of the cross wires cut it accurately; then loose the clips c, d, that confine the telescope in the Ys, and turn it round on its axis, observing whether the centre of the wires still continue to cut the object, during the whole revolution. If it does, it is in adjustment; if not, the line of collimation, or optical axis of the instrument, is not in the line joining the centres of the eye and objectglasses. To correct this error, turn the telescope on its axis, and by means of the four conjugate screws a, a, &c., that move the cross wires, correct for half the error, alternately loosing one screw and tightening its opposite one, till the cross wires cut the same point of the distant object, during an entire revolution of the telescope round its axis.
2. Adjustment of the horizontal limb.-Set the instrument up as level as you can by the eye, by moving the legs of the stand. Tighten the collar D by the clanıping screw C, and, unclamping the vernier plate, turn it round till the telescope is directly over two of the parallel plate screws. Bring the bubble b of the level ss, beneath the telescope, to the centre of its run, by turning the tangent screw i. Turn the vernier plate half round, bringing the telescope again over the same pair of parallel plate screws; and, if the bubble of the level be not still in the centre of its run, bring it back to the centre, half-way by turning the parallel plate screws, over which it is placed, and half-way by turning the tangent screw i. Repeat this operation till the bubble remains accurately in the centre of its run, in both positions of the telescope; and, then turning the vernier plate round till the telescope is over the other pair of parallel plate screws, bring the bubble again to the centre of its run by these screws. The bubble will now retain its position while the vernier plate is turned completely round, shewing that the internal axis, about which it turns, is completely vertical. The bubbles of the levels on the vernier plate being now, therefore, brought to the centres of their tubes, will be adjusted, and also shew the axis to be vertical. Now, having clamped the vernier plate, loosen the collar D by turning back the screw C, and move the instrument slowly round on the external axis, and, if the bubble of the level ss maintain its position during a complete revolution, the external and internal axes are coincident, both being vertical at the same time; but, if the bubble does not maintain its position, it shews that the two parts of the axis have been inaccurately fitted, and the fault can only be remedied by the instrument-maker.
3. Adjustment of the vertical limb.—The bubble of the level
ss being in the centre of its tube, reverse the telescope end for end in the Ys, and, if the bubble does not remain in the same position, correct for one half of the error by means of the capstan-headed screw at the end of the level, and for the other haif by the vertical tangent screw i. Repeat the operation till the result is perfectly satisfactory. Next turn the telescope round a little both to the right and to the left, and, if the bubble does not remain in the centre of its run, the level s8 must be adjusted laterally by the screw at the other end. This adjustment will probably disturb the first, and the whole operation must be carefully repeated. By means of the small screw, fastening the vernier of the vertical limb to the vernier plate over the compass-box, set the zero of the vernier to the zero of the limb, and the vertical limb will be in perfect adjustment.
Note. The adjustments of the theodolite here given are essentially the same as those given by Heather, in his “Treatise on Mathematical Instruments,' as being adapted to the plate of the instrument, which is taken from his work, though I prefer the concise methods, I have given at page 318 of my Additions to the ninth edition of Nesbit's Surveying.'
TO TAKE A HORIZONTAL ANGLE WITH THE THEODOLITE.
The theodolite being assumed to be in proper adjustment, the bubbles in the two levels B B, by a proper opening of the legs of the instrument should be made nearly central, and the plummet suspended beneath it should also hang over the station at which the angle is to be taken: then unclamp the whole instrument by means of the screw C, keeping the other motions clamped, and set the horizontal limb level, as already shewn in the first adjustment. Now clamp the whole instrument and unclamp the vernier plate; set the arrow of the vernier to 360°, or zero, on the lower plate, adjusting the points carefully by the microscope m, and the adjusting screw i. Again unclamp the whole instrument, turning it to the left of the two stations, between which the angle is to be taken, till the centre of the cross wires in the telescope cut the pole, flag, or other object in the station; then clamp the screw C, and by gently turning the screw T, the most perfect accuracy may be secured. Next unclamp the vernier plate and turn it round till the cross wires cut the object at the second station; then clamp and adjust the vernier plate, as before, and, having obtained perfect accuracy, read off the angle by means of the vernier with the microscope m. Lastly, read off the angle, in the same way, with the other vernier, and the mean, or half sum, of the two angles will be the correct angle.
TO TAKE A VERTICAL ANGLE. Having set the instrument level, as already explained, observe at the same time whether the zero of the vertical limb coincides with that of its vernier, by the microscope attached thereto. These points being found coincident, raise or depress the telescope, till its optical axis, or cross wires, cut the object required; then clamp, and adjust till perfect accuracy be obtained, when the angle may be read off, which will be an angle of depression, if the arrow of the vernier be between the zero of the vertical circle and the object glass of the telescope ; otherwise an angle of elevation.
THE CIRCULAR PROTRACTOR. This instrument is a complete circle A A, connected with its centre by four radii a, a, a, a, The centre is left open and surrounded by a concentric ring, or collar, b, which carries two radial bars c c. At the extremity of one bar is a pinion d, working in a toothed rack quite round the outer circumference of the protractor. To the opposite extremity of the other bar is fixed a vernier, which subdivides the primary divisions op
the protractor to single minutes, and by estimation to 30 seconds. This vernier, as may be readily seen from the engraving, is carried round the protractor by turning the pinion d. Upon each radial bar c, c is placed a branch e, e, each branch carrying at its extremity a fine steel pricker, whose points are kept above the surface of the paper by springs placed under their supports, which give way when the branches are pressed downwards, and allow
the points to make the necessary puncture on the paper. The branches e, e are attached do away
to the bars c, c with a joint, which admits of their being folded backwards over the instrument, when not in use, and for packing in its case. The centre of the instrument is represented by the intersection of two lines, drawn at right angles to each other, on a piece of plate glass, which enables the person using it to place it so that the centre, or intersection of the cross lines, may coincide with any given point on the plan. If the instrument is in correct order, a line connecting the fine pricking points with each other would pass through the centre of the instrument, as shewn by the intersection of the cross lines on the glass; which it may be observed, are drawn so nearly level with the under surface of the instrument as to
any serious amount of parallax, when setting the instrument over a point, from which any regular lines are to be drawn. In using this protractor the vernier should first be set to zero, or the division marked 360, on the divided limb, and then placed on the paper, so that the fine steel points may be on the given line, from whence the angular lines are to be drawn, and that the centre of the instrument may coincide with the giver angular point in the same line. This done, press the protractor gently down, which will fix it in position by means of very fine points on its under side. It is now ready to lay off the given angle, or any number of angles, that may be required from the given point, which is done by turning the pinion d till the opposite vernier reads the required angle. Then press the branches ee gently down, and they will cause their points to make the punctures in the paper, at opposite sides of the circle; which being afterwards connected, the line will pass through the given angular point, if the instrument was first correctly set. In this manner, at one setting of the instrument, any proposed number of angles may be laid off from the same point.
PLANNING EXTENSIVE SURVEYS, IMPROVED
FORM OF THE FIELD BOOK, &c. GENERAL DIRECTIONS FOR PLANNING EXTENSIVE SURVEYS.
Provide a sheet of paper, mounted on canvass of the proper size to contain the survey. This may be easily ascertained from the lengths of the longest lines in the survey, and the scale to which it is intended to be laid down. Draw the first line with the proper bearing, which may be determined by the compass of the theodolite, making proper allowance for the vari. ation, as alrendy noticed in the description of surveying instruments. If the survey has been made by the chain only, the bear.
ing may be found by a common pocket compass, or by tying a line to the first or base line in the direction of the sun at 12 o'clock.
If the first or base line be a very long one, a straight-edge should be provided of equal length, for repeatedly splicing the line, as it is termed, with a short straight-edge will almost invariably throw it out of the right direction, and if the first line be longer than any straight-edge that can be procured, (the author has had lines in maps of his surveys nearly 20 feet in length), in this case, stretch a strong silken thread in the proper direction of the line, and carefully puncture the drawing paper in several places, in the exact direction of the thread, the line may then be correctly drawn, with a short straight-edge, from one point or puncture to another.
The first line being laid down, by one or other of these methods, the stations, crossings, &c., marked thereon, take separately, (in the beam-compasses if the extent of survey require them), the second and third lines, or any other two convenient lines that form a triangle with the line already laid down, and, from the proper stations as centres, describe arcs intersecting each other; thus giving the position of the first triangle, which must now be proved by drawing one or more of the secondary lines from their proper stations therein. In the same manner proceed with the other triangles, formed on the first and other lines, till all the lines are laid down.
If the surveys have been made with the help of an angular instrument, as the theodolite, &c., the angles must be laid off at their proper stations, proving the work as it proceeds.
It may here be proper to observe, that in extensive surveys, the lines measured each day must be laid down, and proved at night, that any error that may have occurred may be corrected before the work has proceeded too far; otherwise the correction will involve greater trouble.—The lines of the survey being thus laid down, all the fences, roads, footpaths, rivers, brooks, ponds, bridges, towns, villages, and detached buildings of every kind, as well as every remakable object, must next be laid down in pencil, and the fences and outlines of buildings, roads, rivers, &c., drawn with Indian ink; thus finishing what is called the rough plan.
MR. RODHAM'S IMPROVED FORM OF THE FIELD BOOK. As an example for practice, a plan with the form of the field book, as given by the late Mr. Rodham, of Richmond, Yorkshire, is presented in the plate facing page 82. This form of the field book was first published by Dr. Hutton, above 50 years ago was then generally adopted, and has not since