and from thence taking the bearing to the first end which, if both bearings are correct will be the reverse of the former. Note 2.-When there is a fence on the side, or other obstacle in the way, preventing the stake at one end from being seen through the compass sights at the other end, the bearing may be obtained by setting up the compass and stake at small equal distances to the right or left, so that the line joining them may be parallel to the side. Note 3.-The method of obtaining the bearing between two stations when there are obstacles in the way, which also prevent a parallel bearing being readily taken, or when the stations are too distant to be seen from each other, will be noticed in the next chapter. PROBLEM VI. To measure the distance of a line. For convenience in marking the termination of the chain in measuring, ten iron pins should be provided, about a foot in length, and terminated at top by a small ring, to which a piece of red flannel or other conspicuous substance should be tied, in order that the pins may be readily found, when set up among high grass or in other situations where they would not otherwise be easily discovered. Let the person who is to go foremost in carrying the chain, take nine of the pins in his left hand, and one end of the chain and the other pin in his right hand; then he moving on in the direction of the line, let another person take the other end of the chain and hold it at the beginning of the line. When the leader has moved on till the * pendicularly, exactly at the end of the chain, the hinder chain-man taking care that the chain is in the direction of the line; which is readily determined by observing whether it is in a range with a stake previously set up at the far end of the line. When the leader has not his end of the chain in the direction of the line, the hinder chain-man can direct him which way to move, by a motion of his left hand. When the distance of one chain or half chain has been thus determined, the carriers, taking hold of the two ends of the chain, move on till the hinder one comes to the pin which was set up by the other; then the chain being stretched, the person at the fore end of it sets up another pin as before; the hinder chain-man then taking up the pin at his end, they proceed to a third distance of the chain; and so on. When the person at the fore end of the chain has set up all his pins, he still moves on another length of the chain, and then setting his foot on it to keep it in place, he cries "out." The hinder chain man then comes forward, and counts to him the ten pins; and he setting up one of them at the end of the chain, again moves on, dragging the chain after him, till he is checked by the hinder chain-man, who, getting the hind end of the chain, applies it as before to the pin set up. The number of outs should be carefully noticed; each out being ten chains, when a four-pole chain is used, but only five, when the measuring is done, with a two-pole chain. When arrived at the end of the line, the number of pins, which the one at the fore end of the chain has set up since the last out, and the number of links from the last pin to the end of the line, must be carefully noted. From these, and • When a two-pole chain is used, one length of it may properly be called the number of outs, the distance measured is readily determined. All slant or inclined surfaces, as the sides of a hill, should be measured horizontally, and not on the plane or surface of the hill. To effect this, the hind end of the chain, in ascending a hill, should be raised from the ground till it is on a level with the fore end, and, by means of a plummet and line, or when the hill is not very steep. by estimation, should be held perpendicularly above the termination of the preceding chain. In descending a hill, the fore end of the chain should be raised in the same manner, and the plummet being suspended from it will show the commencement of the succeeding chain. PROBLEM VII. To protract a Survey, having the bearings and distances of the sides given. The method of doing this will be best understood by an example. Thus, Suppose the following field-notes to be given, it is re quired to protract the survey. Ch. 1. N. 50° E. 9.60 2. S. 32° E. 16.38 3. S. 41° W. 6.30 5. N. 79° W. 10.92 7. S. 83° E. 6.48 Method 1st. Draw NS, Fig. 75, to represent a meridian line; then N standing for the north and S for the south, the cast NS take any convenient point as A for the place of beginning, and apply the straight edge of the protractor to the line, with the centre to the point A, and the arch turned towards the east, because the first bearing is easterly; then holding the protractor in this position, prick off 50° the first bearing, from the north end, because the bearing is from the north; through this point and the point A, draw the line AB on which lay 9.60 chains, the first distance from A to B. Now apply the centre of the protractor to the point B, with the arch turned toward the east, because the second bearing is easterly, and move it till the line AB produced, cuts the first bearing 50°; the straight edge of the protractor will then be parallel to the meridian NS; hold it in this position, and from the south end prick off the second bearing 32°; draw BC and on it lay the second distance 16.38 chains. Proceed in the same manner at each station, observing always, previous to pricking off the succeeding bearing, to have the arch of the protractor turned easterly or westerly according to that bearing, and to have its straight edge parallel to the meridian; this last may always be done by applying the centre to the station point, and making the preceding distance line produced if necessary, cut the degrees of the preceding bearing. It may also be done by drawing a straight line through each station, parallel to the first meridian. When the survey is correct, and the protraction accurately performed, the end of the last distance will fall on the place of beginning. Method 2nd. With the chord of 60° describe the circle NESW, Fig. ings from the line of chords, and lay them off on the circumference from N or S according as the bearing is northerly or southerly, and towards E or W according as it is easterly or westerly, and number them 1, 2, 3, 4, &c. as in the figure. From A the centre of the circle, to 1 draw A 1, on which lay the first distance from A to B ; parallel to A 2 draw BC, on which lay the second distance from B to C: parallel to A 3 draw CD, on which lay the third distance from C to D; proceed in the same manner with the other bearings and distances. EXAMPLE 2. The following field notes are given, to protract the The bearing of two lines from the same station being given, to find the angle contained between them. RULE. When they run from the same point of the compass, towards the same point, subtract the less from the greater. When they run from the same point, towards different |