180 to 360, and so completes 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 ound from the field notes; and is performed in the following manner.

gr

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. i.

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 protractor, 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, turù 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 283, turn the arc of your protractor upwards, keeping the pin in the centre-hole, 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 55C. 20L. 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; 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 twopole 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?

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 fieldwork 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 re-survey must be taken.

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