Note. The natural scale may be used advantageously in setting off the distances in a drawing, and the corresponding artificial scale in drawing parallels at required distances.

To draw a Line perpendicular to a given Line from a given point in it. 1st. Make the shortest side of the triangle coincide with the given line, and apply the rule closely against the hypothenuse. 2nd. Slide the triangle along the rule until a line drawn along the sloped edge passes through the given point; and the line so drawn will be the line required.

The advantages of Marquois' scales are: 1st, that the sight is greatly assisted by the divisions on the artifical scale being so much larger than those of the natural scale to which the drawing is constructed: 2nd, that any error in the setting of the index produces an error of but one-third the amount in the drawing.

If the triangle be accurately constructed, these scales may be advantageously used for dividing lines with accuracy and despatch.

PLOTTING SCALES.

PLOTTING Scales, also called feather-edge scales, are straight rules, usually about ten or twelve inches long. Each rule has scales of equal parts, decimally divided, placed upon its edges, which are made sloping, so that the extremities of the strokes marking the divisions lie close to the paper. The primary divisions represent chains and the subdivisions, consequently, ten links each, as there are 100 links on the surveying chain. Plotting scales may be procured in sets, each with a different number of chains to the inch.

The advantages of this arrangement are, that the distances required can be transferred with great expedition from the scale to the paper by the aid of the pricking point alone, and the marks denoting the divisions are in no danger of becoming defaced, as upon the plain scale, by the frequent application of the compasses.

For plotting offsets, measured to the right and left of station lines, ivory or brass scales with fiducial edges may be employed.

The above diagram represents an ingenious contrivance for an offset scale; the graduated scale, A, A, is perforated nearly its whole length by a dovetail-shaped groove, for the reception of a sliding piece which is fastened to the cross scale, B, B, by the screw, C. It will readily be understood from an inspection of the figure, that the cross scale, B, slides along the scale, A, the whole length of the groove, and at right angles to it. The graduations on both the scales represent either feet or links, &c., or whatever length may have been assumed as the unit in the operation of measuring. The mode of its application is simply this: place the scale, A, A, on the paper, parallel to the line on which the offsets are to be plotted, and at such a distance, that the zero division on the cross scale, B, (which is placed about its middle) may coincide with it as the scale slides along, and also that the zero of the scale, A, may be exactly opposite that end of the line at which the measurement commenced; then, in sliding the scale, B, from the beginning of the line, stop it at every divisional line on A, corresponding to the distance on the station line at which an

off-set was taken, and lay off the exact length of the off-set from the edge of the scale, B, either to the right or left of the station line, to which it will be at right angles as taken in the field; the instrument thus gives both dimensions at the same time. It is perhaps needless to add, that the extremities of the off-sets being connected, will represent the curved line, &c. to which they were measured; weights may be placed at the two ends of the scale, A, A, to keep it steadily in its position. In our figure, the instrument is represented as in the act of plotting off-sets upon a station line.

It may be useful here to add a few remarks on the scales used in plotting a survey.

One Chain to an inch (80 inches to 1 mile) is perhaps the largest scale used in plans of land and road surveys, and is adopted only where great clearness is required, and when the work is of limited extent. It is a very useful scale for plans of building or pleasure grounds.

Two Chains to an inch (40 inches to 1 mile) is a very clear scale for land surveys, the extent of which is not very great. It may likewise be used with advantage for gardens and building grounds.

Three Chains to an inch (26 inches to 1 mile) has hitherto not been in very general use, it is, however, the smallest scale that can with safety be used in all cases for plans, from which the contents are to be computed.

Four Chains to an inch (20 inches to 1 mile) is a scale frequently employed in plotting surveys of estates, and is very convenient for either enlargement or reduction.

Smaller scales are usually employed in extensive operations: 6 inches to 1 mile is a large scale for the survey of a district, 4 inches to 1 mile is the scale used on the Revenue surveys for Village maps; 1 inch to 1 mile for Pergunnah maps, and in the Revenue Surveyor General's Office, in the compilation of the Geographical maps, 4 miles to 1 inch is made use of.

CHAPTER IX.

INSTRUMENTS FOR PLOTTING A SURVEY.

IN plotting a Survey, as in taking it, due regard must be had to both accuracy and despatch, and we should aim to lay down the various points observed with an accuracy proportionate to the accuracy of the survey itself. For this purpose certain instruments are used, a short description of which we will here give.

OF THE PROTRACTOR.

THIS is an instrument used to protract, or lay down an angle containing any number of degrees, or to find how many degrees are contained in any given angle. There are two kinds put into cases of mathematical drawing instruments, one in the form of a semicircle, the other in the form of a parallelogram. The circle is undoubtedly the only natural measure of angles; when a straight line is therefore used, the divisions thereon are derived from a circle, or its properties, and the straight line is made use of for some relative convenience: it is thus the parallelogram is often used as a protractor, instead of the semicircle, because it is in some cases more convenient, and that other scales, &c., may be placed upon it.

THE SEMICIRCULAR PROTRACTOR.

THIS instrument is divided into 180 equal parts or degrees which are numbered at every tenth degree each way, for the convenience of reckoning either from the right towards the left or from the left towards the right; or the more easily to lay down an angle from either end of the line, beginning at each end with 10, 20, &c., and proceeding to 180 degrees. The edge is the diameter of the semicircle, and the mark in the middle points out the centre.

THE RECTANGULAR PROTRACTOR.

THE divisions are here as in the semicircular one numbered both ways; the blank side represents the diameter of a circle. The side of the protractor to be applied to the paper is made flat, and that whereon the degrees are marked, is chamfered or sloped away to the edge, that an angle may be more easily measured, and the divisions set off with greater exactness.