The outward circle is numbered from the right to the lefthand, with 10, 20, 30, &c. to 180 degrees; the middlemost the same way, from 180 to 360 degrees; and the innermost from the upper edge of the scale both ways, from 10, 20, 30, &c. to 90 degrees.

It is easy to conceive that the protractor, though a semicircle, may be made to supply the place of a whole circle; for if a line be drawn, and the centre-hole of the protractor be laid on any point in that line, the upper edge of the scale corresponding with that line, the divisions on the edge of the semicircle will run from 0 to 180, from right to left: again, if it be turned the other way, or downwards, keeping the centre-hole thereof on the aforesaid point in the line, then the divisions will run from 180 to 360, and so complete an entire circle with the former semicircle.

The use of the protractor is to lay off angles, and to delineate or draw a map or plan of any ground from the fieldnotes; and is performed in the following manner.

To protract a field-book, when the angles are taken from the meridian.

PL. 6. fig. 9.

On your paper rule lines parallel to each other, at an inch asunder (being most usual), or at any other convenient distance; on the left end of the parallels put N for north, and on the right S for south; put E at the top for east, and W at the bottom of your paper for west.

Then let the following field-book be that which is to be protracted, the bearings being taken from the meridian, whether by a circumferentor, theodolite, or semicircle, and measured with a two-pole chain.

Pitch upon any convenient point on your paper for your first station, as at 1, on which lay the centre-hole of your pro

1

tractor with a protracting-pin; then, if the degrees be less than 180, turn the arc of your protractor downwards, or towards the west, but if more than 180 upwards or towards the east.

Or, if the right-hand be made the north and the left the south, the west will be then up and the east down.

In this case, if the degree be less than 180, turn the arc of your protractor upwards, or towards the west; and if more, downwards, or towards the east.

By the foregoing field-book the first bearing is 2831; turn the arc of your protractor upwards, keeping the pin in the centrehole, move the protractor so that the parallel lines may cut opposite divisions either on the ends of the scale or on the degrees, and then it is parallel. This must be always first done, before you lay off your degrees.

Then by the edge of the semicircle, keeping the protractor steady, with the pin prick the first bearing 283, and from the centre-point, through that point or prick, draw a blank line with the pin, on which, from a scale of equal parts or from the scale's edge of the protractor, lay off the distance 55ch. 201.; so is that station protracted.

At the end of the first station, or at 2, which is the beginning of the second, with the pin place the centre of the protractor, turning the arc up, because the bearing of the second station is more than 180, viz. 3483. Place your protractor parallel, as before, and, by the edge of the semicircle, with the pin prick at that degree, through which and the end of the foregoing station draw a blank line, and on it set the distance of that station.

In the like manner proceed through the whole, only observe to turn the arc of your protractor down when the degrees are less than 180.

If you lay off the stationary distances by the edge of the protractor, it is necessary to observe, that if your map is to be laid down by a scale of 40 perches to an inch, every division on the protractor's edge will be one two-pole chain; of a division will be 25 links, and of a division will be 12 links.

If your map is to be laid down by a scale of 20 perches to an inch, two divisions will be one two-pole chain; one division will be 25 links; a division 12 links; and of a division will be 6 links.

In general, if 25 links be multiplied by the number of perches, to an inch the map is to be laid down by, and the product be divided by 20 (or, which is the same thing, if you cut off one and take the half), you will have the value of one division on the protractor's edge in links and parts.

EXAMPLES.

1. How many links in a division, if a map be laid down by a scale of 8 perches to an inch?

25

8

210)2010

10 links, Answer.

2. How many links in a division, if a map be laid down by a scale of 10 perches to an inch?

25
10

And so of any other.

210)2510

12.5 or 12 links, Answer.

To protract a field-book taken by the angles of the field. Note. We here suppose the land surveyed is kept on the right-hand as you survey.

Draw a blank line with a ruler of a length greater than the diameter of the protractor; pitch upon any convenient point therein, to which apply the centre-hole of your protractor with your pin, turning the arc upwards if the angle be less than 180, and downwards if more; and observe to keep the upper edge of the scale, or 180 and 0 degrees, upon the line: then prick off the number of degrees contained in the given angle, and draw a line from the first point through the point at the degrees, upon which lay the stationary distance. Let this line be lengthened forwards and backwards, keeping your first station to the right and second to the left, and lay the centre of your protractor over the second station, with your pin turning the arc upwards if the angle be less than 180, and downwards if more; and keeping the 180 and 0 degrees on the line, prick off the number of degrees contained in the given angle, and through that point and the last station draw a line, on which lay the stationary distance; and in like manner proceed through the whole.

In all protractions, if the end of the last station falls exactly in the point you began at, the field-work and protraction are truly

taken and performed; if not, an error must have been committed in one of them: in such case, make a second protraction; if this agrees with the former, and neither meet nor close, the fault is in the field-work and not in the protraction and then a resurvey must be taken.

REMARKS.

The accuracy of geometrical and trigonometrical mensuration depends in a great degree on the exactness and perfection of the instruments made use of; if these are defective in construction or difficult in use the surveyor will either be subject to error or embarrassed with continual obstacles. If the adjustments by which they are to be rendered fit for observation be troublesome and inconvenient, they will be taken upon trust, and the instrument will be used without examination, and thus subject the surveyor to errors that he can neither account for nor

correct.

In the present state of science it may be laid down as a maxim, that every instrument should be so contrived that the observer may easily examine and rectify the principal parts; for however careful the instrument-maker may be, however perfect the execution thereof, it is not possible that any instrument should long remain accurately fixed in the position in which it came out of the maker's hand, and therefore the principal parts should be moveable, to be rectified occasionally by the observer.

An enumeration of Instruments useful to a Surveyor,

Fewer or more of which will be wanted, according to the extent of his work and the accuracy required.

A case of good pocket instruments.

A pair of beam compasses.

A set of feather-edged plotting scales.

Three or four parallel rules.

A pair of proportional compasses.
A pair of triangular ditto.

A pentagraph.

A cross-staff.

A circumferentor.

A Hadley's sextant.

An artificial horizon.

A theodolite.

A surveying compass.

Measuring chains and measuring tapes.

King's surveying quadrant.

A perambulator, or measuring wheel.
A spirit-level with telescope.
Station staves used with the level.

A protractor, with or without a nonius.

To be added for County and Marine Surveying.

An astronomical quadrant, or circular instrument.
A good refracting and reflecting telescope.

Besides these, a number of measuring rods, iron pins, or arrows, &c. will be found very convenient, and two or three offset staves, which are straight pieces of wood six feet seven inches long, and about an inch and a quarter square: they should be accurately divided into ten equal parts, each of which will be equal to one link. These are used for measuring offsets and to examine and adjust the chain.

Five or six staves, of about five feet in length and one inch and a half in diameter, the upper part painted white, the lower end shod with iron, to be struck into the ground, as marks.

Twenty or more iron arrows, ten of which are always wanted to use with the chain, to count the number of links, and preserve the direction of the chain, so that the distance measured may be really in a straight line.

The pocket measuring tapes, in leather boxes, are often very convenient and useful. They are made to the different lengths of one, two, three, four poles, or sixty-six feet and one hundred feet: divided on one side into feet and inches, and on the other into links of the chain. Instead of the latter are sometimes placed the centesimals of a yard, or three feet into 100 equal parts.