the height of each point being accurately noted. When the height of a sufficient number of points is determined, contour lines are traced with the ground in view. In fact, the ground is practically sketched from nature.

On the United States Coast and Geodetic Survey, the planetable has been exclusively used for making topographical surveys; the stadia, or telemeter as it is called on that service, being used in connection with it. The stadia is graduated experimentally for the particular instrument, and for the eye of the observer who has it in use. It is simply a scale of equal parts painted upon a wooden staff, about 10 feet long, 5 inches wide, and 14 inch thick, so graduated that the number of divisions, as seen between the horizontal wires of the telescope, is equal to the number of metres in the distance between the observer's eye and the staff held perpendicular to the line of sight.

American experience tends to show that the plane-table is adapted to open country and long distances, where no contour lines are to be determined, and where the stations are comparatively few, as well as where a multiplicity of detail is required. Against the advantage of plotting the work in the field may be placed the disadvantages of having no record but the field-sheet, which is liable to be spoiled in a storm.

The Theodolite and Stadia.-The method of surveying with the plane-table and stadia is being superseded in America by the use of the transit-theodolite and stadia, a method introduced in 1864, when it was officially adopted on the United States Lake Survey. All that can be done with the plane-table may also be done with the transit-theodolite. The plane-table can be used only for topographical work, and requires special practice, whilst the theodolite for the stadia survey can be adopted in all cases where a theodolite is required, and but little special training is required in order to use it with the stadia.

The best instrument to employ is a theodolite reading to 30′′. The micrometer wires should be fixed; when adjustable, they are not sufficiently stable to be trustworthy. The stadia is usually a staff, 1 inch thick, 5 inches wide, and 14 feet long. In order to graduate the staff, it is necessary to know what space on it corresponds to 100 feet (or yards, or metres) in distance. To determine this, it is best to measure off c +ƒ in front of the plumbline, and set a point. From this point, accurately measure a base-line of (say) 200 yards, on level ground, and hold the blank staff at the end of this line. Have a fixed mark on the upper portion of the staff, and set the upper wire on this. Then let an assistant at the staff record the position of the lower wire, as he is directed by the observer at the instrument. Repeat the

operation until the mean gives a satisfactory result. If the base was 200 yards long, divide the space intercepted by the two wires into two equal parts, then each of these parts into ten smaller parts, and finally each small space into five equal parts. Each of these last divisions will represent 2 yards. Diagrams are then to be constructed on this scale, in such a way that the number of symbols can be readily estimated at the greatest distance at which the staff is to be held. If, when tested by re-measuring the base-line, the wire interval is found to have changed, the staff must be re-graduated, or a correction must be made to all the readings.

If the wires are adjustable, any unit scale may be selected, and the wires adjusted to this. By this method, distances may be obtained from levelling-staffs, where it is desirable that each foot on the staff should correspond to 100 feet in distance.

In making a survey for the purpose of preparing a contoured plan, a series of points should be determined with reference to each other, both in geographical position and in elevation. These points should not be more than 3 miles apart. The points of elevation, or bench-marks, need not be identical with the points fixed in geographical position. The latter are best determined by triangulation.

A system of triangulation points being established, the angles are observed and the stations plotted on the plan. For small areas the plotting is best done by means of rectangular coordinates. The survey may, however, be plotted directly from the polar co-ordinates (azimuth and distance). For this purpose the plan should have printed upon it a protractor circle, 12 inches in diameter, by means of which the lines can be plotted accurately to 5'.

A line of levels is next run, bench-marks being left at convenient points. The topographical survey is then made, and referred to this system of triangulation points and bench-marks. The surveying party should consist of the observer, a recorder, three staff-holders, and, if necessary, two axe-men.

The record in the field-book consists of (1) a description of the point; (2) the reading of the vernier; (3) the distance; (4) the vertical angle. Two columns are left for reduction; (5) the difference of height corresponding to the given vertical angle and distance; (6) the true height of each point above the datumline. The right-hand page of the field-book is reserved for sketching.

The only calculations necessary are to find the height of all the points taken, with reference to the datum-line, and sometimes to correct the distance read on the staff for inclined sights. These

calculations may be performed by means of tables computed by Mr. A. Winslow, of the State Geological Survey of Pennsylvania, or by means of a diagram prepared by Professor J. B. Johnson, of Washington University.

The only available information as to the accuracy of this method of surveying is given in the report of the United States Lake Survey for 1875. The entire stadia work of that year was co-ordinated, and compared with the corresponding distances obtained by triangulation. In this way 141 lines, on an average 11⁄2 mile in length, were tested, the average error being 1 in 650. The length of sight between the stations averaged 800 to 1,000 feet. The limit of error allowable in closing on a triangulation was 1 in 300. No special pains were taken to make these lines more accurate than others, since it was not known at the time that the results were to be tested. The readings were taken to the nearest metre; the staves were graduated for a single distance; and no corrections were applied when the distance read was greater or less than this. The accuracy thus attained was sufficient for the object of the survey. Had more care been exercised in the work, the readings limited to 1,000 feet, and all corrections applied, it would have been easy to bring the error within 1 in 1,200.

This method was employed by Mr. W. B. Dawson,* for the preparation of a map of the gold-field on the Atlantic Coast of Nova Scotia, on a scale of 2 inches to the mile. The traverse lines ran along the roads and principal streams, forming a network of quadrilaterals, and were plotted by co-ordinates. The instruments used in the survey were a Sopwith levelling-staff, and a 6-inch transit-theodolite with a 4-inch compass-needle. The telescope was fitted with three horizontal spider lines, unequally spaced, the larger interval corresponding to 100 feet of distance for each foot intercepted by the staff. The smaller one was only used for longer sight, and when the view was obstructed. In five months of field work an area of 180 square miles was surveyed, including nearly one hundred lakes from 7 miles long, downwards, all the work being done by Mr. Dawson with one assistant, and one or two men according to circumstances. Wet days were devoted to the reduction of the observations. The total cost of the survey was 16.75 dollars per square mile.

Telescope Measurements in Mine-Surveys. In mine-surveys very accurate readings may be obtained on account of the steadiness of the air. A transit-theodolite magnifying ten times, with adjustable micrometer wires, was used in 1865 with great

* Trans. Amer. Soc. C.E., 1882, p. 397.

success by Mr. B. S. Lyman,* for surveying in an American colliery. It saved much disagreeable groping in the mud to count the links of a chain, and levels were taken at the same time. The wires were placed so far apart that 1 foot of space intercepted on the staff indicated a distance of 100 feet. The figures on the staff were painted with red ink upon thin paper that had been fastened to strips of common window glass by transparent varnish. Then over the paper another coat of varnish was poured, and upon this was placed another strip of glass. The glasses, with the paper between them, were then put into a narrow wooden frame, which formed one side of a long box. This had neither top nor bottom, and its sides were so hinged together that they folded over upon each other when not in use. The back of the box had holes through it to supply air to the lights, and either safety-lamps or candles were fixed to the wood of the back. The box was made 5 feet in length; but for low mines one might be made much shorter. This staff lighted inside makes telescopic measuring and levelling easy underground, where chaining is particularly disagreeable.

To remedy the difficulty of getting sufficient light to read the ordinary staff, Professor Johnson proposes to use two strips, onequarter of an inch wide, one of which is fastened with its top even with the zero of the stadia scale, whilst the other is moved to suit the position of the other wire. The reading of the top edge of the upper strip then gives the distance, which is read off by the staff-holder.

The

Tacheometry is specially adapted for geological-surveys, which have frequently to be made in mountainous districts where chaining is laborious and inaccurate, and where levelling up and down the sides of the mountains is not to be thought of. Geological Survey of Pennsylvania has surveyed some 3,000 square miles by means of the transit-theodolite and stadia. In the vicinity of mines and where land is valuable the work is done with extreme accuracy, the length of the lines being limited to 400 feet.†

* Journ. Franklin Inst., vol. lv., 1868, p. 385.

For further information on this method of surveying, the student is referred to Prof. J. B. Johnson's Manual of the Theory and Practice of Topographical Surveying by Means of the Transit and Stadia, New York, 1885; and to B. H. Brough's paper on "Tacheometry, or Rapid Surveying,' Min. Proc. Inst. C.E., vol. xci., 1888, p. 282, in which a bibliography of the subject is given.

CHAPTER XVI.

SETTING-OUT.

Ranging Straight Lines.-Setting-out, or the location of predetermined points, is defined as that branch of geodetic operations which is the converse of surveying and levelling, the latter consisting in discovering the position of a series of actuallyexisting points.

In ranging and setting-out a base-line for a surface-survey, ranging rods, 5 to 7 feet in length, are used. They are usually circular in section, and painted in lengths of 1 foot or 1 link, black, white, and red alternately. When one colour cannot be clearly seen, one of the other coloured portions can generally be distinguished.

The rods are planted vertically in the ground, the verticality being judged by the eye. When great accuracy is required, a plumb-bob must be used. Its string is turned over the first and second fingers of the hand, so that when it hangs vertically, the rod may be placed parallel to it. The distance apart of the rods varies from 66 feet to 300 feet.

For ranging straight lines of moderate length, the most convenient instrument is the transit-theodolite, because the telescope may be turned completely over about its horizontal axis, so as to range one straight line in two opposite directions from one station. The error with this instrument should not exceed 10 seconds in angular direction—that is, about 3 inches in a distance of a mile.

For straight lines of very great length, the theodolite is not sufficiently exact. It is then advisable to use a transit-instrument. In order that a vertical circle may be correctly described by that instrument, it is necessary that the line of collimation shall be precisely at right angles to the horizontal axis about which it revolves, and that the pivots of that axis shall be pre