to every ten links, or tenths of a chain, which are again subdivided by their respective nonius divisions into single links; the protracting pin is moved with the nonius by means of the screw d, so that the distances may be set off with such great accuracy, as not to err a single link in setting off any extent, which in the scale of four chains in an inch, does not amount to more than the 400th part of an inch.

Fig. IKL, plate 2, answers the same purpose as the foregoing instrument, and may be used as a protractor also.

For Mr. Gale's method of plotting, a method which will recommend itself to every attentive surveyor, two scales should be used, one of about 15 inches long, the other about 10 inches, each divided on the edge from one end to the other; a clasp should be fixed on the shorter scale, whereby it may at pleasure be so fixed to the other scale, as to move along the edge thereof at right angles, for the purpose of laying off perpendicular lines.

this

Fig. FG H, plate 2, represents an instrument for purpose, with different scales on the part FG; both this, and that represented at fig. I KL, form excellent parallel rules. They are also made only with the clasp, if desired.

The protractor is a circle or semicircle of thin brass, divided into degrees, and parts of a degree, on the outer edge.

The common semicircular protractor, fig. 2, plate 3, is of six or eight inches diameter, the limb divided into 180 degrees, and numbered both ways, 10, 20, 30, &c, to 180; each degree is subdivided into two parts. In the middle of the diameter is a small mark, to indicate the centre of the protractor; this mark must be always placed on the given angular point.

The common circular protractor is more useful than the semicircular one; the outside edge is divided into 360 degrees, and numbered 10, 20, 30,

to 360; each degree is subdivided into halves. In the middle of the diameter is a small mark, which is to be placed on the angular point, when an angle is to be protracted; the diameter, representing a meridian, must be placed on the meridian of any plan, where the bearing of any object is to be laid down. The application of this instrument is so easy and simple, that examples of its use are unnecessary here.

OF THE BEST PROTRACTORS.

Fig. 4, plate 17, represents a best kind of circular brass protractor, with a moveable index and nonius scale; it is the kind found most useful and accurate in practice. The circle or limb is generally made about 6 inches in diameter, and divided in the best manner, by the dividing engine into 360°, each degree is subdivided into 3 minutes, or one minute, as may be desired, by the nonius, which with the index is moved round the limb or circle of the protractor on a conical perforated centre. The centre of the protractor is formed by a fine line accurately drawn in the middle of the chamfered edge of a semicircular brass plate fixed in the centre, or by the intersection of two fine lines drawn on a circular glass plate fixed in the centre, see fig, 5, which is considered by some preferable to the brass plate. At the extremity of the index beyond the limb is fixed a fine steel point, in a direct line with the centre of the protractor, and the first division of the nonius: by this point the angles are dotted, precisely on the paper, On the inner circle of the limb there are four fine lines drawn on chamfered edges, which are sometimes used to coincide with two pencil lines drawn at right angles on the paper, in order to determine the central situation of the protractor on the line, in a more ready manner than by the central mark abovementioned, an inspection of the figure will render any further description unnecessary,

Fig. 5, represents the same instrument, but the motion of the index and points by rack work and pinion. There are two protracting points diametrically opposite, which serve to point out any errors in placing the centre, and to save trouble in the operation of protracting. A continued index with double points is often applied to the protractor without rack work, fig. 4.

Fig. 4, plate 11, represents a protractor framed upon a strong and convenient principle, in order to extend its uses. By unscrewing the nut at D, the pointer A may be fixed at any required distance from the centre, and the spring or unsteadiness of the bar is relieved by the friction wheel B. By the rule EF, a tangent or perpendicular line may be drawn at any angle protracted, &c. as will be shewn hereafter.

OF PLOTTING, OR MAKING A DRAUGHT OF THE LAND FROM THE FIELD NOTES.

The common method of plotting is this; take a sheet of paper of convenient size, draw a line thereon, to represent the magnetic meridian, and assign any convenient point therein to represent the place where the survey commenced; lay the edge of the protractor on this meridian line, and bringing the centre thereof to the point so assigned to represent the place of beginning, mark off the degrees and minutes of the first course or bearing by the limb of the protractor, and draw a line from the place of beginning through the point so marked, laying off its proper length or distance by the scale of equal parts; this line will represent the first line of the survey. Through the point or termination of the said first line of the survey, draw another line, representing the magnetic meridian, parallel to the former: and lay off the course or bearing of the second line of the survey by the protractor, and its length by the scale of equal parts, as before;

and so proceed, til. the whole be laid down; and you will have a plot or draught of the survey.

For example. Let it be required to make a plot or draught of the field notes.

18,

1st. Draw any line, as NAS, fig. 1, plate to represent the magnetic meridian, and assign any convenient point therein, as A, to represent the place of beginning the survey; lay the edge of the protractor on the line NAS, with the centre thereof at the point A, and mark off seven degrees on the limb to the westward, or left hand of the north, and draw the line A B through the point so marked off, making the length thereof 21 chains by the scale of equal parts. 2dly. Draw another meridian line NBS, through the point B, parallel to the former*. Lay the edge of the protractor on this second meridian line N BS, with the centre thereof at the point B, and mark off 55° 15' on the limb to the right hand, or eastward of the north; and draw the line BC through the point so marked off, making the length thereof 18 chains 20 links by the scale of equal parts. 3dly. Draw another meridian line NCS, through the point C, parallel to the former ; lay the edge of the protractor to this third meridian line NCS, with the centre thereof at the point C, and lay down the third course and distance CD, in the same manner as before; and so proceed with all the other lines, DE, EF, FG, GA; and if the last line shall terminate in the place of beginning, the work closes, as it is called, and all is right. But if the last line does not terminate in the place of beginning, there must have been a mistake either in taking the notes, or in the protraction of them; in such case, therefore, it will be necessary to go over the protraction again, and if it be not found then, it must of course be in the field notes, to cor

• These parallel lines may be drawn with the least trouble by a parallel rule.

rect which, if the error is material, they must be taken again.

MR. GALE'S METHOD OF PLOTTING.

The foregoing method of plotting is liable to some inaccuracies of practice, on account of having a new meridian for every particular line of the survey, and on account of laying off every new line from the point of termination of the preceding one, whereby any little inaccuracy that may happen in laying down one line is communicated to the rest. But there is a second method of plotting, by which these inconveniences are avoided, and by which also the accuracy or inaccuracy of the field work is decided with precision and certainty; I would, therefore, recommend this second method to the practitioner, as far preferable to any other I have

seen.

2d Method. Take out from the first table in the Appendix to this Work, the northings, southings, eastings, and westings, made on each of the several lines of the survey, placing them in a kind of table in their respective columns; and, if the sum of the northings be equal to the sum of the southings, and the sum of the eastings equal to the sum of the westings, the work is right, otherwise not.*

Then in an additional column put the whole quantity of northing or of southing made at the termination of each of the several lines of the sur

* The truth of this observation cannot but appear self evident to the reader. For the meridians within the limits of an ordinary survey having no sensible difference from parallelism, it must necessarily follow, that if a person travel any way soever with such small limits, and at length come round to the place where he set out, he must have travelled as far to the northward as to the southward, and to the eastward as to the westward, though the practical surveyor will always find it difficult to make his work close with this perfect degree of exactness.