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nier should first be set to zero (or the division marked 360) on the divided limb, and then placed on the paper, so that the two fine steel points may be on the given line (from whence other and angular lines are to be drawn), and the center of the instrument coincide with the given angular point on such line. This done, press the protractor gently down, which will fix it in position by means of very fine points on the under side. It is now ready to lay off the given angle, or any number of angles that may be required, which is done by turning the pinion d till the opposite vernier reads the required angle. Then press downwards the branches e e, which will cause the points to make punctures in the paper at opposite sides of the circle; which being afterwards connected, the line will pass through the given angular point, if the instrument was first correctly set. In this manner, at one setting of the instru ment, a great number of angles, or a complete circular protractor, may be laid off from the same point.

THE T SQUARE AND SEMICIRCULAR PROTRACTOR.

We cannot speak too highly of a method by which a tra verse can be most expeditiously as well as accurately plotted,

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by means of the T square and semicircular protractor, the manner of using which is thus described by Mr. Howlett, chief draughtsman, Royal Ordnance Office, in vol. i of Papers

on Subjects connected with the Duties of the Royal Engineers:

"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 B B B, by means of a pair of clamps, O D, 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 size, and may be used upon a table of any form. It is convenient to suppose the north on the left hand, and the upper edge of the blade to represent the meridian of the station.

"This protractor is held in the hand while the vernier is set, which is an immense comfort to the sight; and it will be seen that, as both sides of the arm are parallel with the zero and center, the angle may be drawn on the paper against either side, as the light or other circumstances may render desirable."

From this description and a mere glance at the engraving, it is clear that angles taken with the theodolite can be transferred to the plot as accurately as the protractor can be set, namely, to a single minute, and that, too, in a rapid and pleasant

manner.

Another most admirable and expeditious method of plotting, especially useful when it is a principal point to obtain the area of an estate or parish, &c., is to procure or form a table of northings, southings, eastings, and westings *, for all angles made with a meridian line, and for all distances from 1 to 100. These distances may be either links, feet, chains, or estimated in any denomination whatever, and the corresponding northings, southings, eastings, and westings will be in the same denomination. This table is in fact nothing more than the products of the sines and cosines of the angles, made with the meridian line, multiplied by the several distances, and the following is the method of using it. Take out from this table the northings, southings, eastings, and westings made on each of the lines of the survey, the line from which the angles have been measured being for this purpose assumed as the meridian, no matter in what direction it may lie, and place them in a table, which we may call a traverse table, in four separate columns, being the third, fourth, fifth, and sixth columns of the table †, headed

* This table is the same as the table given in books on navigation, and then called a table of latitude and departure.

The first and second columns of the traverse table contain the course and distances,

N., S., E., and W. respectively. Add up these several columns, and, if the work is so far correct, the sum of the northings will equal the sum of the southings, and the sum of the eastings will equal the sum of the westings. Then in two additional columns enter the whole quantities of northing and easting, made at the termination of each of the several bounding lines of the survey; which quantities will be determined by putting zero for the greatest southing, and adding or subtracting the northing or southing made on each particular line to or from the whole quantity of northing made at the beginning of this line, or at the termination of the preceding line; and again, by putting zero for the greatest westing, and adding or subtracting the easting or westing made on each line to or from the whole quantity of easting at the beginning of the line.

This preparatory table having been formed, the plot may be laid down with great ease and accuracy by means of a plotting scale, formed of two ivory graduated rules, one of which, n n, represents the assumed meridian along which the northings

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are to be measured, and the other, e e, represents the east and west line, and serves to set off the eastings. The rule, n n, is perforated throughout nearly its whole length with a dovetail groove, receiving an accurately fitted sliding piece, to which the rule, ee, is fixed

by the screw s, so as to slide along, and always have its edges at right angles to the edges of the rule n n. The rule, nn, is to be placed on the paper with its zero division opposite that point of the line assumed as a meridian, at which the plotting is to be commenced, and with its edges parallel to this line, and at such distance from it, that the zero division on the rule, ee, may be upon the assumed meridian. The rule, n n, is then to be fixed by placing weights upon its extremities, or by clamps. The scale, e e, being now slid along till either of its edges coincides with the divisions upon the scale, n n, answering to the whole quantities of northing at the termination of each line of the survey, the divisions upon the scale, e e, answering to the

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whole quantities of easting, will give the terminations of these lines, which, being pricked off, have only afterwards to be joined, and the plot will be completed.

To compute the Area of the Plot.-Rule six additional columns. In the first of these, or ninth column of the traverse table, set the sums of the total northings, and in the tenth, the sums of the total eastings at the beginning and end of each line in the survey, which sums will be found by adding together each pair of succeeding numbers in the two preceding columns. In the eleventh column set the products of the eastings made on the respective lines of the survey, found in the fifth column, multiplied by the corresponding sums of the total northings in the ninth column; and in the twelfth column set the products of the westings found in the sixth column, and the corresponding sums of the total northings in the ninth column. Sum up the eleventh and twelfth columns, and the difference of the totals thus found will be twice the area of the plot. Again in the thirteenth and fourteenth columns set the products of the northings and southings in the third and fourth columns, multiplied by the corresponding sums of the total eastings in the tenth column, and the difference of the sums of the thirteenth and fourteenth columns will again be twice the area of the plot, and, if agreeing nearly with the double area before found, shows the calculations to have been correctly performed. (We give an example in the opposite page.)

The near agreement of the sums of the third and fourth, and of the fifth and sixth columns is a test of the accuracy of the survey; in columns 7 and 8 we have the distances to be set off by the plotting scale; in column 9 we have the multipliers by which the east and west products in columns 11 and 12 are found; and in column 10 we have the multipliers for finding the north and south products in columns 13 and 14. The difference of the sums of the eleventh and twelfth columns gives double the area, the difference of the sums of the thirteenth and fourteenth gives again double the area, and, taking the mean of these results, by adding them together and dividing by 4, we obtain the area most probably to within a quarter of a perch, since the two double areas differ by less than a perch.

THE STATION POINTER.

When the principal features of a country have been laid down by the methods already pointed out, the details may be

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