screw the leg of the compasses almost close up to the joint, is beld at Fig. 1, represents these compasses when shut; fig. turned backwards, and the steel To take a distance with them as nearly as you can to the required distance, set the fixed leg on the point from which the distance is to be taken, and make the extremity of the other leg coincide accurately with the other end of the required distance, by turning the screw. NOTE. There are several other kinds of compasses, used for planning; as those with moreable points, for the introduction of black lead pencils or ink points, beam compasses for taking large distances, proportional compasses, &c., the uses of which are sasily learned. (See Heather's Treatise on Mathematical Instruments.) PLOTTING SCALES. Plotting scales, also called feather-edged scales, are straight rulers, usually about 12 inches long. Each ruler has scales of equal parts, decimally divided, placed on its edges, which aru 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 ten links each, the intermediate links being determined by the eye. Plotting scales may be procured in sets, each with a different number of chains to the inch. They are usually made of ivory or box, and each provided with a small scale called an offset scale for laying down the offsets. In using these scales, the first division or zero, on the plotting scale, is placed coincident with the beginning of the line to be plotted, and so as just to touch that line with the feather edge: the end of the offset scale is then placed in contact with the edge of the plotting scale; and thus the offsets may be expeditiously pricked off, for which purpose an instrument called a pricker is used, but a hard black lead pencil with a fine point, is greatly to be preferred, as it does not injure the paper. THE PROTRACTOR. The instrument represented in the annexed figure, is usually supplied with a pocket case of instruments. It is made of ivory, 6 inches long and 13 broad. On the face of the instrument, round three of its edges, which are feathered, the pro tractor is formed for readily setting off angles. In using the protractor, the fourth edge, which is quite plain, with the exception of a single stroke in the middle, is to be made to coincide with the line, from which the angle is to be set off, and the stroke in the middle to coincide with the angular point in the line, at which the angle is to be set off; a mark is then to be made with a fine pointed black lead pencil, or with a pricking point, at the point on the paper which coincides with the stroke on the protractor marked with the number of degrees in the angle required to be drawn; and the protractor being now removed, a straight line is to be drawn from the Angular point in the given line to the point thus marked off. The instrument has, on the same face, two diagonal scales, (which are now little used by surveyors,) and on the opposite face, scales of equal parts, &c. The vernier scale and circular protractor, the uses of which will be hereafter described, are best adapted to laying down extensive surveys, where great accuracy is required. PLANNING SURVEYS. In planning or plotting surveys, the upper part of the paper or book, on which the plan is made, should always, if possible, be the north. The chain lines, buildings, fences, &c., ought first to be drawn with a fine black lead pencil: the first should then be dotted with ink, and the latter neatly drawn. Great care is required in the construction of the plan, when the dimensions are to be measured therefrom with the scale. The scale should never be more than three chains to an inch, for when the parts of a plan are large, the dimensions may be taken with greater accuracy. After having found the content of the field or fields, &c., of which any plan consists, it may be laid down by any scale to give it a more convenient size. THE FIELD BOOK. The method now generally adopted in setting down field notes, and which has long been found to be the best in practice, is to begin at the bottom of the page and write upwards. Each page of the book is usually divided into three columns. The middle column is for distances measured on the chain line, at which hedges are crossed, or offeets, stations, or other marks are made; and in the right and left columns, those offsets, marks, and any other necessary observations thereon, must be entered, according as they are situated on the right or left of the chain line. The crossing of roads, rivers, hedges, &c., are, by some surveyors, shewn in the field book, by lines drawn across the middle column at the distances where they are crossed, and by others these crossings are shewn by lines drawn on part of the right and left hand columns, opposite the distances where they are crossed by the chain line; and buildings, turns of fences, corners of fields, to which offsets are taken, are usually shewn by lines sketched in a similar situation to the middle column, as the fences, buildings, &c., have to the chain line. Thus a representation of the chief objects in the survey may be sketchcd in the field, which will give essential assistance in laying down the plan. The stations are usually numbered, for the sake of reference, and marked thus O. The bearing of the first main line is usually taken by surveyors, from which the posi. tion of the plan with respect to the north is determined. This may be done hy a common pocket compass, where great accuracy is not required: but this will be more fully discussed in treat. ing of surveys by the theodolite, further on. R. of O 2, and L. of O 5, &c., denote that the following lines are measured to the right of station 2, and to the left of station 5, respectively. TO SURVEY WITH THE CHAIN AND Cross, An acre of land is equal to 10 square chains, that is 10 chains in length and one in breadth, or 1000 links in length and 100 in breadth ; an acre, therefore, contains 100,000 square links, as per table of square measure below. Hence the contents in square links are, in the following examples, divided by 100,000, or what is the same thing 5 figures to the right are cut off for decimals, the figures remaining on the left being The decimals are then multiplied by 4 for roods, and again by 40 for poles. The following tables exhibit the number of chains and links in the different units of lineal measure, and the number of square chains and links in the different units of square mea acres. A TABLE OF SQUARE MEASURES. Jor Perches Sq.Chs. 16 Rods. 25,000 10,890 1,210 40 2} 484 Acres. 64,000,000/27,878,400 3,097,600 102,400 6,400 2,560 640 PROBLEM I. SQUARE AND RECTANGULAR FIELDS. Square and rectangular fields seldom occur in the practice of the surveyor; small plots of ground of these forms, however, frequently present themselves. Fix the cross in a corner of the square or rectangular piece UNIVERSITY OF THE of ground, and if the sides be at right angles, measure one of them, and enter its length in the field book. This must be repeated at every side and angle; and if all the angles are found to be right and all the sides equal, the piece of ground is square; but, if only the opposite sides are equal, it is rectangular. TO FIND THE CONTENT. RULE. Multiply the length by the breadth in links, and the product will be the contents in square links, which reduce to acres, rods, and poles by the preceding table for square measure, as in the following examples. If the dimensions be given in yards, divide the product by 4840 for acres, &c. EXAMPLES. 1. What is the area of the square A B C D, whoso side is 478 links? Here the length and breadth are equal, hence 478 5057440 Area 2a. 1r. 5p. 2. The length of the rectangular field ABCD, is 2450, and its breadth 1226 links; required the plan and area. 5.02000 Area 30a. Or. 6p. nearly. |