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SECTION X.

OF THE PROTRACTOR AND PLOTTING.

FOR laying down or protracting angles measured with a theodolite, or other instrument by which they are obtained to minutes, or less, of a degree, a superior kind of protractor becomes necessary; for, as we have already observed, it is of little avail that angles are taken to minutes, unless they can also be laid down on paper with corresponding accuracy. Accordingly, metal protractors of both circular and semicircular forms, and furnished with a vernier, are used.

In Volume I. of Papers on Subjects connected with the Duties of the Royal Engineers, is one on protractors, by Mr. Howlett, which I shall quote at length, as it contains some just observations on them; his method of plotting also deserves to be generally known. He says:

"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 objec

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"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.

"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.

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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 close in a satisfactory manner-and when done, it is little better than a survey plotted by a common protractor, where the degrees and half degrees only are marked.

"The old surveyors of the Ordnance used the semicircular protractor, and transferred the instrument itself to the station, by means of large parallel rulers fixed on the paper; and having set the arm to the required angle, they drew the line against the arm itself, some inch or two of which was made in a line with the centre and zero. This excellent way was, however, rendered inaccurate by the impossibility of preventing the joints of the large three-bar parallel rulers from becoming loose; and much inconvenience was felt in consequence of the rulers, even at a great price, not extending sufficiently wide to carry the protractor over a small sheet of plotting cartridge-paper.

"These methods of plotting a survey to a small scale, where an error of ten minutes is not very striking, may answer, and escape censure; but in making surveys of several thousands of acres for content, to a large scale, I have found all the methods above described exceedingly awkward, and not at all adequate to the plotting of the perfect work done by the theodolite. In making surveys of estates and parishes, while on half-pay, I suffered much

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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 as these do not meet the exigences 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.

"Anxious to discharge the duty confided to me in the most beneficial manner, I have given much study to this as well as to other branches of my duty, and have the honour to submit, at least for trial and discussion, the following very cheap and simple means; which are, in all respects, the nearest approach to perfection that I can contrive :

"The pattern semicircular protractor, at the price of no more than £2 17s., was contrived and made from my drawing and instructions, some few years ago, and must be too well known in the department to need description.

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As, when away from home, it seldom happens that the surveyor can obtain a good drawing-board, or even a table, with a good straight edge, I fix a flat ruler, A, to the table, BBB (plate XI. fig. 1), by means of a pair of clamps, CD, and against this ruler I work the pattern square, E, one side of which has the stock flush with the blade; or, if a straight-edged board be at hand, then the square may be turned over, and used against that edge instead of the ruler, A. Here, then, is the most perfect kind of parallel ruler that art can produce, capable of carrying the protractor over the whole of a sheet of plotting paper of any

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