Porro's principle is adopted, or two readings and a reduced distance when Eckhold's instrument is used; this is exclusive of short distances and offsets less than one chain in length.

Section 4. PLANE-TABLE WORK.

In work of this rather rough description, which is generally confined either to such details or filling in of the triangles of a topographical survey as can bear subsequent considerable reduction in scale, the survey is not recorded in forms, but plotted on the plane table itself in the field while the work is proceeding; angles are not measured, but laid down on the paper with a sighted ruler directed to any object, and thus the principles of triangulation are applied after measuring a single base line to start from, and laying it down to scale on the paper.

As each portion of plane-table work must be comprised within the limits of a sheet of paper of the size of the plane table, and subsequently be joined on to other sheets done in the same way, the errors will be greater at the points of junction farthest from the base line and will increase with the number of intervening sets of triangles; it is hence more usual to limit the sets of triangles on any single sheet either to one or to two, one directly dependent on the base line, the other being secondary, or dependent on the sides of the triangles of the first set.

The plane-table itself consists of a drawing-board, mounted on a light three-legged stand, and capable of motion on a universal joint and of clamping to any position of azimuth or altitude by means of screws. A paper is

strained on the board for scaling distances and ruling. directions, and a ruler with sights is used for laying down the directions of any objects, such as survey marks, corners of buildings, etc.

The mode of using it is thus

A convenient base line AB having been carefully measured is laid down to scale as ab on the paper; the plane-table carefully levelled is then set up at A with the line ab adjusted true to AB, and the directions of any number of points, C, D, E, F, etc., are sighted from A and ruled from a; the plane table is then set up at B with the line ba adjusted true to BA, and the directions of the same points, C, D, E, F, are sighted from B and ruled from b; the intersections of the two sets of ruled lines give the positions, c, d, e, f, on the paper, which can be checked by directions sighted and ruled from other

points subsequently used, or from the same points among themselves.

A needle stuck in the paper and board at the point corresponding to the station of observation is convenient in sighting with the ruler. It is also better to use a distinctive hard pencil for marking these sight lines, and to retain a softer one for the delineation of actual objects and details.

All points thus obtained by observation from the extremities of a measured base line are those of primary triangles; when again the plane-table is moved to any other point C, and ca is used as the fixed direction of departure, the secondary set of points, K, L, M, etc., is obtained in a similar way, but these are less accurately fixed. Smaller details are either measured by offsets and laid down to scale, or as is more frequently the case in work of this sort, guessed and sketched. The closing up of the sheets among themselves on sufficient points common to two of them, and the final closing on important well-defined points laid down in the triangulation of some larger survey, are the matters that demand the most care. The resulting sheets can finally be reduced by the draughtsman with a pantagraph, or otherwise, to any requisite scale, and transferred to a general plan comprising the whole.

The remaining appliances used in such work are mostly the same as those described for chain surveys; the amount of measurement is small, the work can be rapidly carried on by two men, one to set up and remove poles and marks, the other to manage the plane-table; but the results are necessarily rather coarse; in some cases pacing or taping is made to supersede chaining or telemetry, when the results are only suited to military

purposes. As such drawings executed in the field must generally involve some inaccuracy, it is usual to make them to double the scale of the intended final plan or map, and afterwards reduce them to half the scale, so as to entirely eliminate the inaccuracies.

Section 5. COMPASS SURVEYS.

Compass surveys have occasionally been executed on a large scale and with extreme precision, the angular observations in such cases being utilised to an exactitude of one minute, but as it then also becomes necessary to enter into magnetic observations, and verify the compasses used with a very high degree of refinement, such surveys involve particular care and special operations, and are hence comparatively rarely undertaken; their consideration is hence neglected in this work. The generality of compass surveys are very limited in extent, and may be said to be restricted to conditions under which an error of 30 minutes, due to diurnal and annual magnetic changes, or to local attraction, shall not affect the visible accuracy of the survey when delineated to the required scale: the actual compass readings are then taken to 15 minutes, or more frequently only to 20 minutes. (See paragraph on Magnetic Instruments, Chapter I., page 42.) Under these circumstances, as these surveys are based on the principle of triangulation (described in Methods of Procedure, page 72, and more fully explained under the head of Theodolite Surveys), it becomes evident that their extent is dependent on the size of the largest comprehensive triangles that can be used without final appreciable error in the delineation; for the smaller included triangles will be comparatively

free from error, while if an additional set of triangles were subjoined to the primary comprehensive triangles they would be vitiated by a double, or a further amount of error.

For instance, if we suppose that the longest side of one of the comprehensive primary triangles is 1000 feet, and that the liability to error in compass-bearing is 20 minutes; this will then, if roughly represented by its sine at that distance, be equal to about 5.8 feet. If also the scale of representation adopted renders such a distance practically inappreciable, as it would be either with a scale of 400 feet to an inch, or of th, or any smaller scale, then primary triangles of this extent may be correctly adopted; but if a subjoined set of triangles be applied to these, the errors in the second set, if equal in extent to the former, may amount to double those of the first, or may be 116 feet, which becomes appreciable on the scale of th.

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It is hence best to limit such surveys to one set of comprehensive primary triangles, having their angles or extremities visible from each other, or at least from some one or two central points, while the extreme length of any side should be so limited that the error resulting from inaccuracy of chainage of the measured base, and that from angular observation, shall together be an inappreciable quantity on the scale of representation adopted.

It is also evident from the foregoing considerations that it is seldom advisable or possible to include in any such single compass survey an extent of more than half a mile of country: and that such work is best suited to the filling in of details of larger surveys on a comparatively small scale by means of pieces based on inde