In the execution of the field work the pro cedure has conformed to the general methods employed in accurate trigonometrical surveys; but the enormous extent of the territory sur veyed; the great diversity and the peculiar ar rangement of the natural features of the coun try, and the necessity for executing the work as expeditiously as possible, and yet consistent with all the requirements of thorough accuracy, have tended to develop methods which are not only specially applicable to the work of the Survey, but also form a group of comparatively new methods available for any other line of topo graphical work. These methods may be briefly outlined as follows: The surveying and mapping operations con form to the general plan which divides the whole area of the country into a series of quadrangles each of which is equal to a square degree, that is, each quadrangle is bounded on the east and the west by a degree of longitude, and on the north and the south by a degree of latitude.
The surveying operations consist in the ex tension of a system of primary and secondary triangles with tertiary triangulation points over the whole country, accompanied by three sys tems of level lines, supplemented by a system of road and stadia traverse.
The primary triangulation Las been planned for the control of the work over the whole country, thus insuring the accurate ultimate meeting of fragmentary surveys which may be initiated a hundred or even a thousand miles apart. In this work, the triangles are ex panded from accurately measured base lines, and connect various points of reference the geographical positions of which have been ac curately determined by the most approved astronomical methods. The astronomical work consists of (1) the measurement of the zenith distances of stars by means of delicate zenith telescopes, for the determination of latitude; (2) the exchange of telegraphic time signals between unknown astronomical positions and a known astronomical position, such as a first class observatory, for the determination of the differences of longitude; and (3) the observa tion of circumpolar stars for the determination of the azimuth of a line,.such as a base line, or the side of a primary triangle. The base lines are measured by means of base bars, iced bars, or steel tapes, proper allowances being made for sag, pull, etc., and the measurements repeated several times in order to reduce the probable error to a minimum of less than one in 1,000,000. The elevations of the various stations are' established by lines of precise levels run from the datum of mean sea level determined by means of accurate tide gauges. The angles of the triangles connecting these stations are measured by means of theodolites equipped with high power terrestrial telescopes. From the data thus obtained, the lengths of the sides of the various triangles are computed and the entire system of triangulation plotted on the map to furnish the primary control for the secondary detail.
The secondary triangulation is usually exe- • cuted by means of the plane table, and new points located so as to give from one to three good tertiary triangulation points per square mile. The elevations of these points, usually hill summits, are determined by the measure ment of vertical angles of elevation and depres sion, depending upon spirit levelling, while the lower relief of the country is determined by lines of secondary spirit levels run six miles apart with intermediate lines of flying levels run three miles apart with sufficient accuracy to allow them to close on the secondary levels within the limits of one or two feet.
Traverse Lines.— Where the country is covered with dense forests, or where the sur face relief is insufficient for triangulation pur poses, both the primary and secondary control consists of a system of primary traverses checked by primary triangulation locations„ or by astronomically determined positions. These traverses are run by compass and plane table, and a secondary system traverse lines con sisting of and stadia measurements of i roads is interwoven with the plane table work. The data obtained from the secondary traverses is plotted upon the plane table sheets during the progress of the work, and is subsequently ad lusted upon the final map between the check points established by the primary traverse, or by the plane-table triangulation, the distances between which are so short — one to four miles — that errors of location are scarcely percepti ble upon map scales of one inch to one or two miles.
The work of primary triangulation and pre _ cise levelling is usually executed a season in advance of the topographic sketching, while the secondary triangulation, traverse work and lines of flying levels are immediately followed by the topographic sketching, both classes of work being done by members of the same party. The data obtained from the secondary triangulation and traverses is then plotted upon a sketch sheet. This data is of such a character that each sheet includes from two to five trigono metric locations; from four to eight inches of road traverse; and one or more instrumental elevations, per square inch. Equipped with a sketch sheet thus prepared, the topographer places himself at a point of known elevation and sketches on the sheet by eye with the aid of a hand level the plan of the contour line which passes through his positron. In open country, the contours may be located in this manner quite accurately for a distance of half a mile in either direction from his position, corresponding to a total distance of an inch upon the sketch sheet. In wooded country where the figure of the contour cannot be seen beyond his immediate position, he proceeds by road carefully observing the variations of the slope, and determines the differences of eleva tion for short distances between check points by means of the aneroid, and sketches in the plan of the contour according to the data thus obtained. In cases where the number of ac curately determined elevations are insufficient, more locations are fixed by vertical angulation, or by flying levels as the work of sketching progresses. In this manner a system of con tours is built up along the roads and water courses, and if the lines do not practically fill up the entire sheet, the topographer walks into the spaces within the road circuits, and by means of stadia lines for long distances, or by pacing for short distances, determines the posi tions of the contours required to complete the sheet. The sketches thus obtained are inked in, either in the field or at the office, and are then reduced to the scale of the final map by photog raphy and form the copy for the engravers.