LAND SURVEYING.

Part the Third.

THE CIRCUMFERENTOR.

THE Circumferentor is the Mariner's Compass, differently divided, and furnished with sights, standing upon one or three legs, and capable of a horizontal motion, by means of the usual parallel plates, or a ball and socket.

The circumferentor consists of a compass box; divided into degrees, and, by means of a vernier, subdivided into three minutes.

It stands upon three legs, and, by means of a pair of parallel plates, is capable of a truly horizontal position, which is determined by a level, placed, so as not to interfere with the reading under the compass box.

This compass box, has an absolute horizontal motion round its centering, and is fastened by the clamp screw.

When this is clamped, by detaching the pin which passes through the two plates of the compass box, the brass one,

which, with the vernier attached, works round the inner one, on which are divided the degrees, is capable of a relative motion, and thus partakes of the character of the theodolite; this motion is communicated to it by a rack and pinion.

The instrument, also, has other contrivances; the whole instrument can be turned upon its side, and the spirit level at B, being then in a horizontal position, the instrument is made capable of a vertical motion, reading off to three minutes, by means of the vernier.

DIVISION OF THE CIRCUMFERENTOR.

The line of sights is made the north and south end of the instrument, and from each of these the circular rim is graduated toward the east and west points, from 0° to 90°.

On the right of the north of the instrument, looking to the north point of it, should be lettered west, and on the left should be lettered east; and any point between the north and west point of the instrument, read by the north end of the needle, is read north, so many degrees west.

When the needle is released, and is allowed to play freely, it points toward the magnetic north. The north of the instrument points to the object whose bearing is required, the angle made between these two must necessarily give the relative position of the line of the object, and the magnetic north, and the bearing of the object can thus be obtained by reading off the number of degrees to which the needle points on the graduated circular rim.

Definitions.

A meridian line is a line running due north or south.
The distance of a line is its horizontal measurement.

The angle of bearing of any line, is the angle of bearing made between that line and a meridian line running through the point, where the instrument is placed; and is measured always from north or south, eastward or westward.

Thus a line is said to bear magnetically north 16 degrees west, when the needle points to 16 degrees on the graduated circle, and when the direction of the line is to the west of north.

The reverse bearing of a line, is merely the bearing taken in a contrary direction.

The reverse bearing of a line, bearing north 38 degrees east, is south 38 degrees west; that of south 75 degrees west, is north 75 degrees east. The reverse bearing, therefore, is measured by the same angle, as the direct bearing, only taken in opposite directions; from south bearing northward, from east westward.

Difference of latitude, or northing and southing, is the distance that the end of the line is further north or south than the beginning.

The difference of longitude, or departure, is the distance that the end of the line is east or west from the beginning.

In changing our position from one point on the earth's surface to another, in a direction making any angle with the meridian, we at once change our latitude and longitude —the one is the northing and southing, the other the easting and westing.

To obtain the latitude and departure geometrically, when the length and bearing of a line are given.

Draw a meridian line through either end, and let fall a perpendicular from the other. This perpendicular is the departure; and that portion of the meridian line intercepted by it, is the difference of latitude.

The latitude, departure, and distance, form the three sides of a right-angled triangle, whose angle at the vertex is the angle of bearing; whose hypothenuse, or radius, is the distance; the latitude, the cosine; and the departure, the sine of the angle of bearing.

The meridian distance of any station, is the distance of that station from the meridian line passing through the first or any other assumed point, and is equal to the difference between the sums of the eastings and westings from that point; and is, east or west, as the eastings or westings predominate.

EXAMPLES.

Required the difference of latitude and departure of a line, which bears south 16 degrees 30 minutes, east 3 chains 47 links. Answer 3.33 south lat.; 0.98 east dep.

ture.

Given a line, bearing north 13 degrees 30 minutes west, and 6 chains 10 links long, to find the latitude and deparAnswer 5.93 north lat.; 1.42 west dep. What are the latitude and departure of a line bearing north 41 degrees 9 minutes east, 4 chains 47 links?

Answer 3.36 north lat.; 2.95 east dep.

A line bears north 22 degrees 45 minutes west, 27 chains 62 links, required its latitude and departure.

Answer 25-47 north lat.; 10-68 west dep.

To find the bearing of a line by the Circumferentor. Having placed the circumferentor over the station point, release the needle, and then, having unclamped the body of the instrument, by means of the parallel plates, as in the theodolite, make the whole instrument level. Now, turn the whole round until the north end of it lies towards the object, and looking through the sight, at the south end, fix the instrument, so that the fine web-line, in the north sight, exactly covers the object; then, when the needle has perfectly settled (which should be immediately released on setting the instrument), read off, by the north end of the needle, the number of degrees that it points to, from the north or south division line of the compass-box, according as the north end of the needle is in the north or south semicircle of the instrument; the angle measured by these degrees is called the angle of bearing.

Should the needle not point exactly to any degree, but lie between two of them, turn the instrument carefully, so as to make the needle point exactly to the next lower degree, and, clamping the whole head of the instrument, detach, by withdrawing the connecting pin, the two horizontal plates. The instrument having been altered to suit the needle, the flag will be no longer covered by the web. By using the rack and pinion, and carefully bringing the sights back, which are connected with the same plate as the vernier, to cover