SECTION IV. OF FINDING YOUR PLACE IN A SURVEY OR SKETCH WHEN FILLING IN. It is advisable in all kinds of surveying to have few original stations, and these as wide of each other as the nature of the country will allow. The primary points being accurately determined, such intermediate stations as become necessary when filling in, are readily obtained in a very simple manner, by taking the bearings of two stations previously fixed; which has been called finding your station by interpolation, and is a truly useful little problem, that I shall now endeavour to explain. I may mention that there is another method of finding your place on a map or plan, by observing the two angles formed between three fixed points, for which see Geometrical Problems. With respect to the division of the compass card, it will be remembered that I recommend its being divided into twice 180 degrees, instead of carrying the numbers round from 0 to 360 degrees; the advantage of which will be again seen here. Let the circle NESW (plate IV., fig. 1) represent the compass, having a line, HL, passing through its centre: the circle being divided into twice 180°, that is, the semicircle NES is numbered from 0 to 180°, beginning at N; and the other semicircle SWN is numbered in like manner from S. Now, according to this mode of dividing the compass card, the bearing of the object H from C is 130° W., while that of the object L, from the same point C, is 130° E. HCL being a straight line - or it may be expressed thus, NS and HL being two right lines, cutting each other at C, the opposite angles are equal, namely, the angle HCS is equal to the angle N CL. Again, let PH and BL be parallel to the meridian NS; these lines then become the meridians of the objects H and L respectively;* and PH being parallel to BL, the alternate angles PHC and BLC are equal. Hence, if the bearing of the object H taken at L be 130° W., the bearing of L taken at H will be 130° E. For the application of the above to our immediate purpose, namely, to find the place of a third station, by means of two stations already laid down on the paper: Let A and B (plate IV., fig. 2) be two stations, whose places are fixed, and we want to determine the point C. Take the bearing of A, 128° W.: having done which, we know, from the foregoing explanation, that C bears from A, 128° E. Adjust the protractor at A, by means of the east and west parallel lines, and lay off 128° E., the bearing of C; which point. C must, we know, lie somewhere in the line thus obtained. Next, take the bearing of B, 63° E., and having adjusted the protractor at B, lay off 63° W., and where a line drawn from B (to represent this bearing) cuts the line or bearing drawn from A, is the required station C. The above may be put into a short rule: thus-To find your station by observations taken to two points already known, protract from those points the opposite bearings to what you observe, and their intersection fixes the place sought. For example, if the bearing to a point be 20° E., protract from that point 20° W., &c. Observe, that the nearer your two bearings meet at a right * Strictly speaking, meridians are not parallels, but they may be considered as such for surveying purposes. angle, the more correct will the station be determined: and also, that when a third fixed point can be seen, a bearing to it will serve to corroborate your other observations; and a point so obtained, namely, by the exact meeting of three bearings, becomes as good as any other point. The above is a very useful problem-indeed, indispensable when sketching ground and filling in a survey. SECTION V. PROCESS OF A REAL MILITARY SKETCH - SKETCHING FEATURES OF GROUND. LET us now see how a sketch was actually performed upon the plan that I have attempted to describe in the foregoing pages. Our ground (the western part of Hayes common, Kent) having been examined, it appeared that the line A B afforded the most advantageous base; as in most other directions furze bushes rendered it impossible to walk in a direct line. A B measured 400 paces of 30 inches. Bandrols were then planted at each end of the base, and also at such other points (C, D, E) as appeared most favourable for sketching the features of the ground. The prismatic compass gave the bearings as under, from A, namely: Το F 136° 30 W. (F being a remarkable tree.) We then went to B, whence the bearings were— A point on our paper having been chosen for A, the ivory protractor was adjusted (page 5) and the several bearings laid off from it. Along the line representing the bearing of B, the length of the base, 400, was taken from a convenient |