CHAPTER VII.

PLOTTING AND PROTRACTING.

Circular Protractors.—Howlett's Semicircular Protractor.— Metcalfe's Protractor.-Laying Down Angles by Chords.Protracting by Northings and Southings, Eastings and Westings: Sines and Cosines.

THERE are several ways of laying down a survey on paper, which is called plotting; the term protracting being applied to setting off angles on paper with an instrument called a protractor.

If the survey has been made entirely by triangulation, we may plot the chain lines by laying down their lengths either with the ordinary or with the beam compasses, or protracting the angles of the triangles, if these have been taken. Where the sides of the triangles are of considerable length, the beam compasses will have to be used to lay down measured lines, or those of which the lengths have been calculated; we have already given some explanation of this under the head of "Chain Surveying," and we shall have an opportunity of saying more upon the subject further on.

To plot a traverse a protractor is required, unless we resort to the system of "Northings and Southings, Eastings and Westings," or of "Latitudes and Departures;" we shall explain the method by the protractor first, being that most usually applied.

Under any circumstances, however, the first thing is to be careful that the sheet of paper is large enough to contain the work; if there be no other means of ascertaining this, plot the survey first to a small scale, which will give the size of the sheet of paper required; when this point is settled, be careful to begin plotting so as to be able to get the whole of the survey into the map without having to make any joints.

PROTRACTORS.

There are numerous kinds of protractors, all constructed differently, but for the same purpose of protracting angles.

The circular protractor is illustrated at Fig. 70, and consists of an entire graduated circle or limb, and four radial bars,

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b, b and c; a piece of the brass metal is removed from the centre, and a circular piece of glass is inserted in its place, on which is marked the centre of the instrument; round the centre is a collar carrying the indices I, I, with verniers; at the end of the index bars are two branches B, B', both of which, when the instrument is in use, are open, as at B, but when packed away are closed, as at B'; these branches carry at their extremities fine steel prickers, the exact centres of which must form one straight line with the centre of the instrument, if correct; by means of the springs 8, 8, &c., these points are kept off the surface of the paper when the arms are moved round; and therefore to prick off an angle when the instrument is in use, a slight pressure upon the buttons, as at B, is required, which leaves a fine puncture on the paper; a line drawn through one of these points and the point on which the centre of the instrument is set, will give a bearing or an angle with any other line previously determined.

Observe that with the circular protractor, if the centre has been correctly set over the angular point from which an angle is being set off, the two punctures from B and B' will form one straight line with the angular point, and not otherwise.

This instrument is provided with clamp and tangent screw motion, T, by means of which the verniers are set to minutes, and as there are two verniers, we have the means of checking the one by the other; either with this instrument or the theodolite we have always the means of ascertaining the reading of the back angle vernier, by adding 180° to the angle read off by the first. The face of the glass centrepiece is placed as nearly even as possible with the under surface of the instrument, so that no parallax may arise from too great a space between the surface of the paper and that of the glass carrying the centre of the instrument.

This instrument, as constructed by Messrs. Elliott, is the most complete we have, and by the fulfilled requirements assimilates the nearest on paper to the conditions of the theodolite in the field.

It is steadied to any position on the paper by means of short points attached to the under surface.

From the description of the theodolite, and of the method of using it, the nicety required in the observations, as the planting over the exact station point, the readings of both verniers, and the repeating of the angles under many circumstances, it will at once be perceived that to make the precautions thus taken in the field of any value in the office, some special means must be taken to lay down the observations on paper with anything like equal fidelity; for otherwise time would be thrown away on the field-work.

To lay off the lengths of long lines, great pains are taken in

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the construction of beam compasses. Similarly with protractors much thought has been devoted at different times to devising an instrument that shall lay down angles with the greatest possible accuracy, when a proper method is applied.

That the reader may appreciate all the difficulties that may arise in protracting the angles of a survey, we will endeavour to go methodically through the process of plotting the traverse at Fig. 67. On the left hand side of the paper draw a straight line, N S, representing the magnetic meridian, and with a fine needle point prick off the station A, at which the work commences; over this set the centre of the protractor with the 360° and 180° divisions coinciding with the meridian; set the zeroes of the verniers to these divisions, and press the buttons at the ends of the arms B B'; the punctures thus made will be exactly on the meridian N S, if the centre of the instrument is correctly placed; if this is so, gently press the protractor on to the paper to secure it. Loosen the clamp, and move the index to the angle NA B, which is the first bearing; clamp and perfect the reading by the tangent screw T, attending to both verniers, and make a puncture, which mark as No. 1; next set off the bearing CBN", and mark it No. 2; then D CN"", which mark No. 3; and so on round the figure; set off at the same time the bearings of Aa, AH, A B, and any others in the field-book; lastly, bring the zeroes of the verniers again to 360° and 180°, and press the buttons; if the instrument has not moved, the points will press into the same punctures as were made at first.

Now with a straight rule draw in the bearing A B, through the point A, and that marked No. 1; on this line set off the length of the chain line; next place the edge of a parallel rule on A and No. 2, and parallel to this line through the point B last marked off as the length of the chain line, draw the line B C, and placing zero of your scale at B, make BC equal to the second chain line; now place the rule on A and No. 3, and parallel to it draw CD, and make this also equal to the length of the chain line; proceed thus until you have completed the sides of your traverse; if all is correct, not only the last chain line, OA, will measure on paper as in the field, but the bearings of A H and A E will pass directly through the stations H and E.

We may now observe, that the degree of accuracy to be attained will much depend on the extent of the traverse; if small, and the work is fairly done, it will "close" easily enough; but the difficulties will increase with long lines, when parallel rulers become next to useless, and another system has to be adopted; as also with a great number of angles, when we must endeavour

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to subdivide minutes into seconds by means of the two verniers; that is if seconds be entered in the field-book. It will be evident that if the chain lines are long the traverse will be of corresponding extent, and that the difficulties of working the parallel rulers over it will be in proportion; in the same manner, if the angles are numerous and carefully taken, seconds in several instances will probably have been read off, which, if repeatedly neglected, and on long chain lines, may involve an actually practical error. One way of overcoming these difficulties, may be by carefully drawing a parallel to the first meridian line through every third or fourth angle, and protracting the angles from the last angular bearing found; but considerable care must be observed in drawing the parallels; we shall, however, presently describe a more easily practicable method, known as Howlett's, and which, on extensive traverses, may be resorted to jointly with the method just described, the one checking the other. On the other hand, the traverse may be so small and so easily plotted, that even the paper protractor we have described in another place may be sufficient to close the work correctly; between such a simple case and one with numerous difficulties, the reader must apply a discerning intelligence according to the circumstances and magnitude of the case.

It is now some years since Mr. Howlett, chief draughtsman to the Ordnance, made the following observations on the circular protractor, which are deserving of the greatest attention, but which he himself probably never intended to be followed blindfold.

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"The circular protractor, at the price of from four to eight guineas,* is generally considered the most perfect kind of instrument for plotting the angles of a survey; but against this instrument there are the five following objections:

"It is only steadied by being attached to the paper by pins; and in moving the arm it is liable to shift.+

"As the vernier has to be set while the protractor is fixed on the paper, and cannot be held to the light, it is next to impossible in some positions to see the divisions ;§ or if the protractor be taken from the paper, time is lost and error is caused by having to replace it on the working meridian,

*Elliott's eight-inch circular protractor is 77. 17s. 6d.

We have had this instrument in use for many years without meeting with this accident, which must arise from not pressing down the instrument when fixed in its place, or from the map laying loose and unevenly, in which condition it is not fit to be plotted on.

When several angles are protracted from the same point this must be

the case either with the circular or semicircular protractor.

This inconvenience will not occur with a seven or eight-inch instrument and such defect applies equally to the semicircular instrument.

"When the whole set of angles required are set off and numbered, they have to be transferred to the station, one after the other, with parallel rulers, in doing which much error creeps in, both while setting the edge of the ruler against the points, and then in shifting the ruler along to a distant part of the paper.*

"It is a very delicate instrument, liable to be soon strained and rendered unfit for use.†

"Lastly, the general inaccuracy of the method which this instrument implies-for the sources of error are so many that the work cannot be brought to a close in a satisfactory mannerand when done, it is little better than a survey plotted by a common protractor, where the degrees and half-degrees only are marked."

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"In making surveys of estates and parishes, while on halfpay, I suffered much for want of a better system of plotting than any I could find after making every inquiry, and searching books on the subject. Such methods do not meet the exigencies of practical men, and hence it is usual to employ the chain alone. The theodolite is very little used among private surveyors: they reject the system altogether; and, indeed, many use the chain so skilfully that, under ordinary circumstances, it leaves nothing better to be desired. The theodolite is, however, an invaluable instrument; and if the proper use of it, together with a more satisfactory method of plotting, were more generally known among private surveyors, much of this prejudice would certainly give way."

Mr. Howlett then goes on to mention his pattern semicircular instrument, which is well known in the profession as "Howlett's Protractor," and of which an illustration will be found at Fig. 71; he then goes on to make the following very just observations :

*This defect entirely applies to the method of using, and not to the construction of the instrument itself.

The branches of the arms, as will be seen in the drawing, are liable to be strained if the instrument is not taken care of; but there is no reason whatever why the arms should not be constructed the same as those of the semicircular protractor.

This is a very strong and sweeping charge, and must be taken not only cùm grano, but cùm granis.

This will not by any means be found the case at present, and there are now few surveyors without a theodolite, and cases constantly occur where it is next to impossible to produce a good survey with the chain alone; for engineering field-work a theodolite is constantly in requisition.