CHAPTER IV.

ON PLOTTING.

In the execution of extensive Surveys upon scientific principles, the accurate measurement of angles is of the utmost importance, requiring the employment of instruments of a superior construction, as well as considerable care and skill in their management; and one great object of such Surveys, being the correct formation of Maps and Charts, it is no less essential, that the angles, when accurately measured, should be accurately laid down.

As the instruments therefore necessary to be used by the Surveyor in taking dimensions of land, are such wherewith he may measure the length of a side, and the quantity of an angle in the field; so the instruments commonly used in making a plot or draught thereof, are such wherewith he may lay down the length of a side, and the quantity of an angle on paper. They therefore consist in scales of equal parts for laying down the lengths or distances, and protractors for laying down the angles. The various kinds of scales and protractors in general use with Surveyors will be found explained in Part II. of this work.

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 on this line to represent the place where the Survey commenced; lay the edge of the rectangular protractor on this meridian line, and bringing the centre thereof to the point assigned to represent the place of beginning, mark off the degrees and minutes

of the first 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 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, until the whole is laid down.

For Example.-Let it be required to make a plot of the following Field notes:

1st.-Draw any line as NAS to represent the magnetic meridian, and assign any convenient point thereon 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 52° on the limb to the eastward, and draw the line AB through the point so marked off, making the length thereof 9.17 Chains by the scale of equal parts.

2nd.-Draw another meridian line NBS, through the point B, parallel to the former. Lay the edge of the protractor on this second meridian line NBS with the centre thereof at the point B, and mark off 106° 15′ to the eastward, and draw the line BC, through the point so marked off, making the length thereof 12.40 Chains by the scale of equal parts.

3rd.-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 mark off the third bearing 355° 45′ to the westward, making the length of the line CD 14.00 Chains in the same manner as before, and so proceed with all the other lines DE, EF, FG and GA, and if the last line terminates in the place of beginning or at the point A, the work is said to close, 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 Field-notes, or in the protraction of them; in such case therefore, it will be necessary, to go over the protraction again, and if it is not found, the mistake must be in the Field-notes, to correct which, they must be taken again.

This 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.

These inaccuracies or errors of plotting may be partly obviated where the Survey is not very extensive by the use of the circular protractor, and having only one meridian line assigning a point thereon for the beginning of the Survey, all the bearings are laid off at once from this point, and the other points of the Survey fixed, by means of lines drawn parallel to the bearings, as laid off from the first point.

For instance, let it be required to make a plot of the Fieldnotes as given in the last example.

Draw a meridian line NS, and assign thereon a point A, as the beginning of the Survey, on this point A, place the centre of the circular protractor, with 360° exactly to the North, and 180° to the South of this line NS, mark off all the bearings of the lines AB, BC, CD, &c., beginning with the first and numbering it 1, the second 2, and so on. Then laying aside the protractor, cast the eye about the tract traced by the protractor for the bearing marked 1, draw a line from the beginning of the survey or point A, in the direction of the mark 1, and on it, lay off the distance 9.17 Chains, thus fixing the point B. Apply a parallel rule to the point A, and the mark 2, and move its edge up, until it touches the point B, last fixed; draw a line eastward and lay off from the point B, 12.40 Chains, thus fixing the point C.

Again, apply the parallel rule to the point A and mark 3, and move its edge up, until it touches the last point fixed or

C, draw a line thence northward and lay off on it the distance 14.00 fixing the point D.

In the same manner, apply the parallel rule to the point A, and the several other bearings, marked 4, 5, 6 and 7, and lastly, the bearing from the last point fixed, or point G, will fall exactly into the first, which closes the plot; it is almost unnecessary to observe, that the dotted lines in the diagram, are drawn only to illustrate the operation, and that in practice it is only necessary to mark the numbers 1, 2, 3, &c., round the tract traced by the protractor.

This method, now in general use among Surveyors, saves the trouble of shifting the protractor at every bearing and also insures greater accuracy in the plotting, as a great number of bearings being laid down from one meridian, a trifling error in the direction of one line does not affect the next; the accuracy of the plot, however depends much upon using a parallel rule that moves truly parallel, which it is well to look to before proceeding to this mode of plotting.

Triangles are more accurately protracted by means of their sides than by their angles, and one side only, for measures of length can be taken from a scale and transferred to paper with more exactness than an angle can be pricked off from a protractor.

In plotting an extensive survey, it is in most cases requisite to show the direction of the meridian and it therefore becomes

necessary to lay down from one of the principal stations the azimuthal angle subtended by some other station and the meridian: now this angle cannot be laid off from a protractor, even of the most approved construction, so accurately as the plotting of the triangulation may be made from the measured or computed sides of the triangles. To obtain a corresponding degree of exactness, recourse must be had to some other method, and the following described by Mr. Simms* is the best that we have seen practised.

* Treatise on Surveying Instruments, &c.