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.

be

Instead of the above system of ruling east and west lines across the paper, lines may 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

necessary to move the protractor, held in this position, slightly up and down upon this line, until its bevelled edge touches the point D; D F is then at once drawn in the required direction. The distances may also be set off from a scale graduated on the edge of the protractor, by merely moving it along this line, DF, until some defined division corresponds with the station D.

By observing with a sextant the angles between three or more known stations, the place of the observer can be ascertained, both instrumentally and by calculation, but not so readily as with the compass. The method of thus determining the position of any point will be explained hereafter.

The plane table is perhaps the best contrivance for sketching in the interior detail of a survey with accuracy, but its size renders it too inconvenient to be termed portable, and its use is now almost universally superseded by the portfolio and compass. The little reflecting semicircle invented by Sir Howard Douglas, is so far an improvement on the sextant that it protracts the angles it observes by means of a contrivance by which the reflected angle is doubled instrumentally, and the angle is protracted upon the paper by means of a bevelled projection of the radius. Other varieties of small reflecting instruments have also been contrived for the same purpose.

The process of sketching between the fixed points plotted on the paper is similar to surveying with the chain and theodolite as far as the natural and artificial boundaries are concerned; the distances being obtained by pacing; the offsets (if small) by estimation; and the bearings of the lines by the compass or sextant*. Everything is, however, here drawn at once upon the paper, instead of being entered in a field-book. The features of the ground are sketched at the same time as the boundaries and other details; and this part of the operation, being less mechanical

* A straight walking-stick will be found very useful in sketching, not only for the purpose of getting in line between two objects, which is easily done by laying the stick on the ground, in the direction of one of them, and observing by looking from the other end to which side of the opposite station it cuts, but also for prolonging a line directed on any known point to the rear. A bush or any other mark, observed in the line of the stick, answers as well as another known point for pacing on.

than the preceding, requires far more practice before anything like facility of execution can be acquired; it is, however, more particularly connected with the subject of the next chapter, where the different methods of delineating ground in the field will be explained.

The following are the best practical methods of passing obstacles met with in surveying, and of determining distances which do not admit of measurement, by means adapted for use in the field, most of them requiring no trigonometrical calculation. Some of these problems are solved without the assistance of any instrument for observing angles; but as a general rule (subject of course to some few exceptions), it is always better to make use of the theodolite, sextant, or other portable instrument, than to endeavour by any circuitous process to manage without angular measurement. The measurement of

the line AD, supposed to be run for the determination of a boundary, is stopped at B by a river or other obstacle.

The point F is taken up in the line at about

A

F F

B

D

the estimated breadth of the obstacle from B; and a mark set up at E at right angles to AD from the point B, and about the same distance as BF. The theodolite being adjusted at E, the angle BEC is made equal to BEF, and a mark put up at C in the line AD; BC is then evidently equal to the measured distance FB.

If the required termination of the line should be at any point C', its distance from B can be determined by merely reversing the order of the operation, and making the angle B E F' equal to BEC', the distance BF' being subsequently measured. There is no occasion in either case to read the angles. The instrument being levelled and clamped at zero, or any other marked division of the limb, is set on B; the upper plate is then unclamped, and the telescope pointed at F, when being again clamped, it is a second time made to bisect B; releasing the plate, the telescope is moved towards D till the vernier indicates zero, or whatever number of degrees it