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tion 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 still remain in the center of its run, the level, s s, must be adjusted laterally by means of the screw at its other end. This adjustment will probably disturb the first, and the whole operation must then be carefully repeated. By means of the small screw fastening the vernier of the vertical limb to the vernier plate over the compass box, the zero of this vernier may now be set to the zero of the limb, and the vertical limb will be in perfect adjustment.

The second telescope, placed beneath the horizontal limb, serves to detect any accidental derangement of the instrument during an observation, by noting whether it is directed to the same point of a distant object at the end of the observation to which it has been set at the commencement of the observation. Also the vertical limb admits of an adjustment to make it move accurately in a vertical plane, when the horizontal limb has been first set in perfect adjustment. This adjustment is important, and should be examined with great care; and in the small theodolites, when the verti al limb is permanently fixed to the horizontal limb by the maker, an instrument which will not bear the test of the examination which we proceed to describe must be condemned, till set in better adjustment by the maker. The azimuthal axis having been set truly vertical, direct the telescope to some well-defined angle of a building, and making the intersection of the wires exactly coincide with this angle near the ground, elevate the telescope by giving motion to the vertical limb, and, if the adjustment be perfect, the intersection of the cross wires will move accurately along the angle of the building, still continuing in coincidence with it. A still more perfect test will be to make the intersection of the cross wires coincide with the reflected image of a star in an artificial horizon, and elevating the telescope, if the adjustment be perfect, the direct image of the star itself will again be bisected by the cross wires.

In the conduct of an extensive survey, the two principal desiderata are accuracy and despatch, neither of which should be unduly sacrificed to the other. To obtain both these ends, the principal points of the survey should be determined by a system of triangles proceeding from an accurately-measured base of considerable length. The angles of these triangles should be observed with a large and perfect theodolite con

structed for the purpose, or with an altitude and azimuth instrument; and numerous corrections should be applied for the spherical form of the earth, the refraction of the atmosphere, the errors due to the imperfect graduation of the instrument, &c.

The boundaries of the entire country to be surveyed being thus determined with the greatest possible accuracy, and a series of stations laid down throughout, the spaces included between these stations may be subdivided into spaces of smaller extent, the boundaries of which may be surveyed with considerable despatch by means of the chain, and a portable theodolite, such as we have been describing above, and lastly, the details of the country within these spaces may be sketched with still greater rapidity by means of the prismatic compass.

The boundaries of the spaces to be surveyed by the chain and small theodolite should not exceed three or four miles in extent, and the following is the manner of proceeding.

Let a, b, c, d, e, f, represent the boundary to be surveyed, and let A, B, and c, be three stations which have been accurately laid down by the previous triangulation, of which both B and c can be seen from A, and A can be seen from c. First measure with the chain the lengths of the several lines a b, bc, cd, &c., taking offsets to all remarkable points on either side of these lines in the usual manner, and driving pickets at a, b, c, &c. Measure also the distance from A to a, and from d to c. These measurements having been made, set up the theodolite at A, level it, and clamp the vernier plate to the lower plate of the horizontal limb at zero, or so that the readings of the two verniers may be 360° and 180 respectively, this adjustment being perfected by the slow-motion screw, t. Next move the whole instrument round upon the azimuthal axis, till the object B is accurately bisected by the cross wires, clamp it firmly in this position by the screw c, tightening the collar D, and enter in the field book the reading of the comNow release the vernier plate, and turning it round, bisect the object c, by the cross wires, and enter the readings of both verniers in the field book. Observing, in like manner, the bearings of any other remarkable objects, and, entering the readings in the same way, direct the telescope lastly to a, at which station an assistant must be placed, with a staff held upon the picket there driven into the ground, and, entering the reading of the vernier as before, clamp the vernier plate carefully, and remove the instrument to a. Level the instrument at a, unclamp the collar D, and, turning round the whole in

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strument upon the azimuthal axis, direct the telescope to the last station A, tighten the collar D, and perfect the adjustment, if necessary, by the slow-motion screw T. Now release the vernier plate, and, bringing it back to zero, if the reading of the compass be the same as the reading previously entered in the field book, we assume our work, as far as it has gone, to be correct; but, if not, we must go back to A, and go over the work again. Next release the vernier plate, and enter the readings, when the telescope is directed to the several remarkable points visible from a, and lastly direct the telescope to the next forward

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time, the reading of the vernier will now be the same as when the telescope was directed to c from the point a. If then we have not been able to make all the compass readings agree at the previous stations, after going twice over the work at such stations we may now consider that our work was correct, and that the error in the compass reading arose from some local attraction, or extraordinary variation of the needle. This verification of the work at c is called closing the work. We now come back again to d, and proceed from d to e, and so on, as before, till we come to some other station, which has been observed either from a or c, and which we again close upon, and at last arriving at f, if the readings agree within a minute or two with the readings for ƒ, previously observed at

* If the same result is again arrived at, we may presume that the com pass is acted on by some local attraction, and proceed with the work; and the accuracy of this presumption will be further tested as we go on.

a, the whole work may be considered to have been performed with a sufficient degree of accuracy; but, if the error amount to more than a minute or two, we must proceed back again from f to e, and so on till we find out the station at which the error has occurred. If the ground along any of the lines a b, bc, &c., rise or fall, suppose, for instance, along bc, then we must direct the telescope from b, so as to make the cross wires bisect upon the staff, held upon the picket at c, a point at the same distance from the ground as the center of the telescope, and then upon one side of the vertical limb is pointed out the number of links to be deducted for each chain from the measured distance b c, to reduce it to the required horizontal distance. This reduction is then to be entered in the field book*

INSTRUMENTS FOR PLOTTING THE SURVEY.

In plotting the survey, as in taking it, due regard must be had to both accuracy and despatch, and we should aim to lay down the various points observed with an accuracy proportionate to the accuracy of the survey itself. To this end the principal points should be laid down by setting off with the beam compasses the computed sides of the triangles, the angles of which have been accurately observed with the large theodolite; and the direction of the meridian is to be laid down from an observation of the angle which it makes, with a side of one of these triangles, by means of the computed chords +, which chord is also to be set off with the beam compasses.

THE CIRCULAR PROTRACTOR.

The principal points having thus been laid down, the boundaries observed by the small theodolite may be put in by first laying down upon the paper a large circular protractor. This protractor may be pricked off by means of the circular metallic protractor represented in the accompanying figure, and the lines can then be transferred to any part of the paper by means of a large ruler and triangle, or by any parallel ruler. The circular protractor is a complete circle, A A, connected with its center by four radii, a a a a. The center is left open, and surrounded by a concentric ring, or collar, b, which carries

The method of surveying with the chain and theodolite, explained above, is called surveying by a traverse.

+ If a table of chords be not at hand, take out the sine of half the angle from a table of natural sines, and, reckoning the first figure as integral, this will be the chord of the whole angle to radius 5, or, reckoning the first two figures integral, it will be the chord to radius 50.

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two radial bars, c c. To 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, c, is fixed a vernier, which subdivides the primary divisions on the protractor to single minutes, and by estimation to 30 seconds. This vernier, as may readily be understood from the engraving, is carried round the protractor by turning the pinion d. Upon each radial bar, cc, is placed a branch e e, carying at its extremity a fine steel pricker, whose point is kept above the surface of the paper by a spring placed

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under its support, which gives way when the branch is pressed downwards, and allows the point to make the necessary puncture in the paper. The branches e e are attached 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 center 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 center, 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 center of the instrument, as denoted by the before-mentioned intersection of the cross-lines upon the glass, which, it may be observed, are drawn so nearly level with the under surface of the instrument as to do away with any serious amount of parallax, when setting the instrument over a point from which any angular lines are intended to be drawn. In using this instrument the ver

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