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towns, villages, &c., carefully noted, and care taken to insure their correct orthography, and to quote the authority upon which it rests when different from that sanctioned by custom.
In measuring long lines between conspicuous objects, marks should be left, to be connected by check lines, or on which to base smaller triangles; where impeded by a house or any obstacle, the means of avoiding it and returning again to the measured line are to be found further on.
Irregular inclosures and roads, even where triangles cannot be measured, can still be surveyed by the chain alone, but of course not so accurately as with the aid of the theodolite.
This method of "traversing" is managed as follows:-Suppose
A B the first line, and B C the direction in which the next is required to be measured, prolong A B to E, make B F equal to B E, and measure the cord E F, from which data the direction of BC can be laid down.
The dimensions in the field-book may be kept either between two parallel lines running up the page, with the offsets written on the right and left of these lines as in the example facing page 36, or on a species of diagram bearing some sort of resemblance to the outline of the ground to be surveyed, which latter method is supposed to assist in the plotting; but if references to the starting points of the different lines, and their junctions with each other, are entered in the field-book kept according to the first system, and the angles forward written on the right or left of the ruled lines according to the direction of the next forward station, there can never be any difficulty in plotting the work, even after a con
atmosphere, it is a good precaution to divide the scale for laying off distances from the fieldbook, on the paper upon which the plot is to be made, as it will then always expand and contract with the outline of the survey; and also to mount the paper before commencing plotting, or not at all.
siderable lapse of time, which however should not be delayed longer than is absolutely necessary. It is customary for land surveyors to compute their work from the plot, adding up the contents of each inclosure for the general total, which is perhaps checked by the calculation of two or three large triangles ruled in pencil so as to correspond nearly to the extreme boundaries, whose lengths are taken from the scale; but if the rigid mode of computing everything from the field-book is deemed too troublesome, still the areas of the large triangles, measured on the ground, should be calculated from their dimensions taken from the field-book, and the contents of the irregular boundaries added to or subtracted from this amount, which constitutes a far more accurate check upon the sum of the contents of the various inclosures than the method in general use. The calculation of irregular portions outside these triangles is much facilitated by the well-known method of reducing irregular polygons to triangles having equivalent areas.
When the contents of fields are to be calculated from the plot, the scale should not be less than twenty, and may be as much as three or four chains to one inch. The former of these two last scales is that on which all plans for railroads submitted to the House of Commons are required to be drawn, and the latter is used for plans of estates, &c.
To return to the second division of this subject, viz. the filling up of the interior, partly by measurement and partly by sketching, which is generally the mode adopted in the construction of topographical maps.
The roads, with occasional check lines, are measured as already described, the field-book being kept in the same method as when the entire county is to be laid down by measurement, excepting that all conspicuous objects some distance to the right and left of the lines are to be fixed by intersections with the theodolite, either from the extremities of these lines or from such intermediate points as appear best adapted for determining their positions. These points when plotted, together with the offsets* from the field-book,
* Mr. Holtzapfell's "Engine-divided Scales," engraved on pasteboard, will be found very useful, and their low price is an additional recommendation. Marquois scales are also adapted for plotting and drawing parallel lines at measured intervals, as well as for other purposes. The offset and plotting scales, introduced by Major Robe on the Ordnance Survey, are as
present so many known fixed stations between the measured lines, and of course facilitate the operation of sketching the boundaries of fields, &c., and also render the work more correct, as the errors inseparable from sketching will be confined within very narrow limits.
In all cases where the compass is used to assist in filling-in the interior (and it should never be trusted in any more important part of the work), it becomes of course necessary to ascertain its variation by one of the methods which will be hereafter explained. Independent of the annual change in its deviation, the horizontal needle is subject to a small daily variation, which is greatest in summer, and least in winter, varying from 15' to 7'. Its maximum on any day is attained to the eastward about 7 A.M., from which time it continues moving west till between 2 and 3 P.M., when it returns again towards the east*; but this oscillation is too small to be appreciable, as the prismatic compass used in the field cannot be read to within one-half, or at the nearest one-quarter, of a degree of the truth. Portions of the work, as plotted from the fieldbook, are then transferred to card-board or drawing-paper, or traced off on thin bank post paper, which latter has the advantage of being capable of folding over a piece of Bristol board fitting into the portfolio, and from its large size, containing on the same sheet distant trigonometrical points which may constantly be of use. It can be folded over the pasteboard, so as to expose any portion that may be required, and when the work is drawing near to the edge, it is only necessary to alter its position. In moist weather, prepared paper, commonly termed asses' skin, is the only thing that can be used, as the rain runs off it immediately, without producing any effect on the sketch.
The portable instruments generally used in sketching between
convenient as any that have been contrived. The plotting scale has one bevelled edge; and the scale, whatever it may be, engraved on each side, is numbered each way from a zero line. The offset scale is separate, and slides along the other, its zero coinciding with the line representing the measured distance; the dimensions are marked on the bevelled edge of this short scale to the right and left of zero, so that offsets on either side of the line can be plotted without moving the scales; and from the two being separate, there is no chance of their being injured, as in those contrivances where the plotting and offset scales are united. * See Colonel Beaufoy's experiments on the variation of the needle. Also the article Observatory (Magnetical), Aide Mémoire.
measured lines and fixed points in the interior, as well as in military sketches made in the exigency of the moment without any measurement whatever, are a small 4-inch, or box sextant (or some small reflecting instrument* as a substitute for it), and the azimuth prismatic compass. Any reflecting instrument is certainly capable of observing angles between objects nearly in the same horizontal plane, with more accuracy than the compass; and from its observations being instantaneous, and not affected by the movement of the hand, it is better adapted for use on horseback, but it is not so generally useful in filling up between roads, or in sketching the course of a ravine or stream, or any continuous line.
Whichever of these instruments is preferred, of course a scale of chains, yards, or paces, and a protractor, are required, for laying off linear and angular distances in the field.
A very convenient method of using the latter for protracting bearings observed with the azimuth compass, is to have lines engraved transversely across the face of the protractor, at about a quarter of an inch apart. The paper upon which the sketch is to be made must also be ruled faintly across in pencil at short unequal distances, at right angles to the meridian, with which lines one or more of those on the protractor can be made to correspond, by merely turning it round on its zero as a pivot, this point being kept in coincidence with the station from whence the bearing is to be drawn. The bevelled edge of the protractor is thus evidently parallel to the meridian, and the observed bearing being marked
* In using reflecting instruments, avoid very acute angles, and do not select any object for observation which is close, on account of the parallax of the instrument. The brightest and best defined of the two objects should be the reflected one; and if they form a very obtuse angle, it is measured more correctly by dividing it into two portions, and observing the angle each of them makes with some intermediate point. Also, if the objects are situated in a plane very oblique to the horizon, an approximation to their horizontal angular distance is obtained by observing each of them with reference to some distant mark considerably to the right or left, and taking the difference of these angles for the one required.
The index error of a sextant must also be frequently ascertained. The measure of the diameter of the sun is the most correct method; but for a box sextant, such as is used for sketching, it is sufficient to bring the direct and reflected image of any well-defined line, such as the angle of a building (not very near) into coincidence—the reading of the graduated line is then the index error. For the adjustment of the box sextant, see Simms on Mathematical Instruments. The less the glasses are moved about the better.
and ruled from this point, is the angle made by the object with the meridian.
For instance, the bearing of a distant object upon which it is required to place, was observed from D to be 30°. The protractor in the sketch is shown in the proper position for laying off this angle, and the dotted line DE is the direction required.
In fixing the position of any point with the compass, by bearings taken from that point to two or three surrounding stations whose places are marked on the paper, the zero of the protractor is made to coincide with one of these stations, and its position being adjusted by means of the lines ruled across its face and on the paper, the observed angle is protracted from this station, and produced through it. The same operation being repeated at the other points, the intersection of these lines gives the re
quired place of observation.
Instead of the above system of ruling east and west lines across the paper, lines may be drawn parallel to the meridian for adjusting the place of the protractor. Thus, suppose from the point D any observed bearing, say 40°, is to be laid down. By placing the zero C of the protractor on any convenient meridian, and turning it upon this point as a pivot until the required angle of 40° at E coincides also with the same meridian NS, it is only