BA,, and in a forward parallel line, and the traces continued as described above. In like manner the obstructions at (3), (4), &c., may be passed, and the trace of the line continued for considerable distances with sufficient accuracy for most practical purposes. The continued parallelism of the lines at the measured distance apart will be a sufficient verification (Smith's Treatise on Land Surveying.)

206. To measure distances by means of the transit.-The cross-wire ring in the telescope of the transit is often fitted with an arrangement called "Stadia," or "Micrometer."

small slides, held apart by a slender brass spring hoop, and actuated by independent screws, dd, by which the distance between the two movable wires can be adjusted to include a given space upon a rod, held perpendicular to the optical axis in front of the object-glass, at a distance from it equal to its principal focal distance.

When the wires are thus adjusted to include a certain space, as two feet for instance, upon a rod placed at a distance of 100 feet from the specified point on the optical axis, it is found that they will cover one foot at half that distance, or four feet at a distance of 200 feet; thus the distance is proportional to the space intercepted upon the rod. By adding to the distance

thus obtained, the principal focal distance of the object-glass,

plus the distance of the object-glass from the middle of the horizontal axis, the distance of the rod from the station can be ascertained without the use of a chain.

The focal distance of the object-glass can be readily obtained by sighting some very distant object, being careful to correct instrumental parallax (Art. 185), and then measuring the distance from the object-glass to the capstan screws of the crosswire ring, which call a; now sight some object, distant about 100 feet, and measure the distance from the object-glass to the horizontal axis, which call b; the sum of these, a+b, will be a constant, sufficiently exact, to be added to all distances obtained by readings on the rod.

The spaces upon the rod used should be equal to that which the instrument intercepts at 100 feet from the point in front of the object-glass, and should be numbered from the bottom up; each space should be subdivided into hundredths. The rod should have two movable targets, like those used upon leveling rods, and should also be furnished with an attached plumb, or level, to insure its vertical position. A distinct mark should be made upon it at the ordinary height of the horizontal axis of the instrument.

In using the micrometer, sight the middle horizontal hair to the height of instrument" mark, and then direct the targets to be moved successively till they coincide with the micrometer wires, the rod being kept vertical. If the telescope has been level during this operation, the distance given by the rod plus the instrument constant, can be recorded; but if the line of sight has been elevated or depressed, then from the distance given by the rod, including the instrument constant, must be subtracted the product of this distance and the square of the sine of the angle of deviation from the horizontal.

If distances greater than 600 feet are to be measured, the

unit of the rod must be less than of the standard distance, to avoid the use of a rod too long for practical management.

If the distances are to be recorded in chains and links, set the stadia staff at 66 feet in order to obtain its unit, and then graduate it to this unit, and subdivide to hundredths.

The stadia staff should be spiked, that it may be thrust into the ground to secure steadiness.

The telescope should be a good one, giving a very sharp, clear definition of objects, and the micrometer wires should be very fine indeed in order to secure close readings.

The degree of accuracy that may be attained is shown by the following table, deduced from that given in "Cours de Topographie, par A. Lehagre, 1881," to which the student is referred for a very full description of the method:

With a telescope of ten inches focal length or over, and within the above limits, the stadia measurements are as reliable as chain measurements on fairly level ground, and are much more accurate than chain measures on bad, broken country. As the use of the micrometer requires care and consumes time, it is not recommended for short distances, except on bad ground, swamps, inaccessible distances, &c.

207. In connection with the chain or tape, the transit is used. to obtain horizontal distances on sloping ground. The chaining is made on the surface of the sloping ground, and not by elevating the chain as described in Art. 71; and the angle of

the slope is taken with the transit, by marking on a rod the vertical distance from the horizontal axis of the telescope to the ground, and sighting to this mark on the rod held vertical at the end of the line measured; the horizontal distance is equal to the measured distance multiplied by the cosine of the angle of the slope.

208. To survey a line, such as a road, boundary of an estate, &c., measure the angle of deviation which each line makes with the preceding line prolonged, or measure the azimuths which each line makes with the first line taken as a meridian (Art. 194), and measure, also, the length of each line and offsets to prominent objects. Care must be taken to centre the instrument exactly over each angular point, as any error in centreing will cause an error in the apparent direction of the object sighted, which will be the greater the nearer the object is to the instrument.

209. To survey the streets of a town or city, place the transit at the intersection of two or more of the principal streets, through which the longest lines of sight can be had; find the angle which each of the streets diverging from this point makes with the principal street, and find, also, the angle of slope of each of the streets at this point; measure, with the chain or stadia-rod, or both as checks one upon the other, the lengths of the lines of sight, and take offsets to the corners of all streets, to public buildings and prominent objects; remove the transit to the next street and take the angles, angle of slope, measurements, and offsets as before, and so continue till the survey is complete.

SECTION IV.

FARM SURVEYING BY TRANSIT.

210. The figure and area of any piece of ground may be found by beginning at any one of the angular points and going entirely around the boundary, measuring the length of the sides by chain or stadia-rod, and the angle which each side makes with the preceding side prolonged, called Angle of Deviation, or the azimuths of the several sides with a given first side as meridian. Let the farm to be surveyed be the one given in Article 123. Let the side AB be taken as the meridian of the survey. Measure with the transit the azimuths of the several successive sides with AB, as directed in Art. 194, and enter them in the notes at the left of the station mark. In the following illustration both the azimuth and the angle of deviation have been entered, though the surveyor would use but one, together with the bearings, which should always be entered as a check:

From the azimuths determine the bearings of the several sides with AB, as directed in Art. 195, and let them be as noted on the following page; complete the table and determine the area as in a compass survey: