the second column of radii: the measures of the respective lines of the mearing, viz. AB, BC, CD, DE, &c. being placed in the third column of distances, will complete the field-book. Thus, , If any line of the field be inaccessible, as suppgge CD to be, then by way of proof that the distance CD is true, let the measure of the angle CHD be taken by the line oo, with the chain; if this angle corresponds with its containing sides, the length of the line DC is truly obtained, and the whole work is truly taken. Note. That in setting off an angle, it is necessary to use the largest scale of equal parts, viz. that of the inch, which is diagonally divided into 100 parts, in order that the angle should be accurately laid down; or if two inches were thus divided for angles, it would be the more exact ; for it is by no means necessary that the angles should be laid from the side scale with PROB. III. To take a survey of the chain only, when all the an gles cannot be seen from one point within it. 18. 93 10 B A Let the ground to be surveyed be represented by 1, 2, 3, 4, &c. Since all the angles cannot be seen from one point, let us assume 3 points, as A, B, C, from whence they may be seen: at each of which let a mark be put, and the respective sides of the triangle be measured and set down in the field book ; let the distances from A to 1, and from B to 1, be measured, and these will determine the point 1; let the other lines which flow from A, B, C, as well as the circuit of the ground, be then measured as the figure directs; and thence the map may be easily constructed. There are other methods which may be used; as dividing the ground into triangles, and measuring the 3 sides of each ; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter. PROB. IV. How to take any inaccessible distance by the chain only. Suppose AB to be the breadth of a river, or any other inaccessible distance, which may be required. Let a staff or any other object be set at B, draw yourself backward to any convenient distance C, so that B may cover A: from B, lay off any other distance by the river's side to E, and complete the parallelogram EBCD: stand at D, and cause a mark to be set at F, in the direction of A; measure the distance in links from E to F, and FB will be also given. Wherefore EF: ED ::FB: AB. Since it is plain (from part. 2. theo. 3. sect. 1. and theo. 2. sect. 1.) the triangles EFD BFA, are mutually equi-angular. If part of the chain be drawn from B to C, and the other part from B to E; and if the ends at E and C be kept fast, it will be easy to turn the chain over to D, so as to complete a parallelogram ; by reckoning off the same number of links you had in BC, from OF THE CIRCUMFERENTOR. This instrument is composed of a brass circular box, about five or six inches in diameter within which is a brass ring, divided on the top; into 360 degrees, and numbered 10, 20, 30, &c. to 360 : in the centre of the box is fixed a steel pin finely pointed, called a centre-pin on which is placed a needle touched with a load stone, which always retains the same situation; that is, it always points to the North and South points of the horizon nearly, when the instrument is horizontal, and the needle at rest. The box is covered with a glass lid in a brass rim to prevent the needle being disturbed by wind or rain, at the time of surveying : there is also a brass lid or cover, which is laid over the former to preserve the glass in carrying the instrument. This box is fixed by screws, to a brass index, or ruler, of about 14 or 15 inches in length, to the ends whereof are fixed brass sights, which are screwed to the index, and stand perpendicular thereto : in each sight is a large and a small aperture or slit, one over the other; but these are changed, that is, if the large aperture be uppermost in the one sight, it will be lowest in the other, and so of the small ones : therefore the small aperture in one is opposite to the large one in the other; in the middle of which last, there is placed a horse hair, or fine silk thread. The instrument is then fixed on a ball and socket; by the help of which anri a screw, you can readily fix it horizontally in any given direction; the socket being fixed on the head of a three-legged staff, whose legs when extended, support the instrument, whilst it is used. How to take field notes by the Circumferentor. Let your instrument be fixed at any angle, as A, your first station; and let a person stand at the next angle B, or cause a staff, with a white sheet to be set there perpendicularly for an object to take your view to : then having placed your instrument horizontally (which is easily done by turning the box so, that the ends of the needle may be equidistant from its bottom, and it traverses or plays freely) turn the flower de-luce or north part of the box to your eye, and looking through the small aperture, turn the index about, till you cut the person or object in the next angle B, with the horse hair, or thread of the opposite sight : the degrees then cut by the south end of the needle, will give the number to be placed in the second column of your field-book in a line with station No. 1, and expresses the number of degress the stationary line is from the north, counting quite round with the sun. Most needles are pointed at the south end, and have a small ring at the north : such needles are better than |