CHAPTER II.

SURVEYING OPERATIONS.

Section 1. METHODS OF PROCEDURE.

THERE are four principal methods of procedure in surveying by which the position of a number of points, requisite to obtain a sufficiently close and adequate representation of the features of the country, and the natural and artificial objects there existing, may be determined for record, and finally reduction to plan.

These modes of procedure may be adopted either severally or in conjunction with each other, whether measurement or calculation or both happen to be the means of carrying out these modes. They are:

1. By distances, or distances and offsets.

2. By triangulation, or a network of triangles.

3. By traversing, or a continuous combination of distances with angles or bearings.

4. By determining the latitudes, longitudes, and azimuths of detached points.

To explain the application of these four methods in their simplest forms, there must necessarily be some starting survey point, and sometimes also some starting direction of some survey line in every survey which may be considered as a relative datum point and datum line of departure. It need not necessarily be the point or line from which the surveying operations commence in order

of time, nor need it always be the most important point or line, as the whole of the results of any complete survey are mutually dependent; but this datum point and datum line may be considered as the starting point and starting line for the purpose immediately under consideration, when the relative position of some single unknown point is required.

FIGURE 8. DISTANCES AND OFFSETS.

1. Adopting the first mode of procedure, let A be the datum point of known or assumed position, and X the unknown or required point; then if AX happen to be in the direction of any datum line of the survey, AB, the distance AX is all that is required to fix the position of X apart from checking; but if X is not in that direction, two distances, or a distance with one rectangular offset, such as AB and BX, become necessary. If, again, the means of setting out a correct right angle are not available, recourse must be had to two distances in the same direction, AD, AC, and two or even three oblique offsets, DX, CX, by which the position of X is determined; but this then becomes a limited case of triangulation combined with distance.

Should I be so far distant from, or so inconveniently placed with regard to A that this mode of procedure cannot be adopted in this the simplest form, it may be arrived at through an intermediate series of distances and offsets on the same principle, or through intermediate steps based on other modes of procedure.

2. The method of triangulation.

X

R

FIGURE 9. TRIANGULATION.

As before, let A be the datum point, and X the point whose relative position is required. If AB is also a datum line, X may be arrived at through one triangle only; in which case either AB, BX, and AX are all measured, or if AB only be measured, and BX and AX be calculated from angular measurements of any two of the three angles, the relative position of X is determined. This may be further checked by measuring a tie-line in the one case, or the third angle in the other.

Should I be so far distant from, or so inconveniently placed with regard to A, that it cannot be arrived at through one triangle, it may be arrived at through a series or network of triangles, or through a combination of triangulation with distances and offsets, as shown in the figure following.

3. The method of traversing.

As before, let A be the datum point, AB the datum line, whose direction is either known or assumed, and X a distant point whose relative position is required. If it happens to be either impracticable or inconvenient to arrive at X by any direct route, and if the method of triangulation be considered too tedious, a

method more circuitous than the former and less tedious than the latter can be adopted. Should there happen to be some road or stretch of open country convenient for measuring operations nearly between A and X, it

may be best to conform partly to that course; supposing this to be the case, let such a course lie to the left of the imaginary line AX. Then if AB be measured, a mark set up at any point C, and the inward angle ABC measured; the distance BC measured, another mark set up at D, the inward angle BCD, and the distance CD measured; and so on, measuring every distance and every inward angle on a route going through a series of points, until the last of them, G, is so placed that GX can be measured, the point X is determined relatively to A. This process is called traversing, and ABCDEFGX is termed an unclosed traverse. If, however, the traverse is continued by some other route XHKLMA back to A, the starting point thus forming a complete irregular polygon, it becomes. a closed traverse; and the correctness of the observed

inward angles may then be checked by the formulæ given at page 48. The correctness of the measured distances, however, can only be checked by check bearings or angles on convenient lateral conspicuous objects, or on traversed points not adjacent

4. The method of latitudes and longitudes is generally adopted as a check on triangulations or on traverses of very large extent, such as the triangulation of a large Topographical Survey, or the route-surveys of travellers and navigators. In the former case the latitudes and longitudes of a certain number of distant points are determined by observation with the zenith sector, and with the aid of sets of chronometers transported from place to place, or simultaneous chronometrical observation of a series of signals. From these, with the aid of any distances and azimuths laid down or obtained in the triangulation work, the latitudes and longitudes of any other intermediate survey points and the azimuths of any other survey lines may be calculated in accordance with the formulæ given in the general collection (page 54). In the latter case, that is, on route-surveys of travellers and navigators, the modes of observation practised are rather different, this observation being much more frequent and less precise. An account of these, with the necessary formulæ of reduction, is given in the Chapter on Astronomical Observation in Route Surveys; while the formulæ for calculating the latitudes and longitudes of intermediate points are rarely necessary; when they are so, the approximations in the general collection (page 54) are sufficiently accurate in most instances.

The above methods are, for brevity, described in a