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(15) Surveying may also be divided according to the extent of the district surveyed, into Plane and Geodesic. Geodesy takes into account the curvature of the earth, and employs Spherical Trigonometry. Plane Surveying disregards this curvature, as a needless refinement except in very extensive surveys, such as those of a State, and considers the surface of the earth as plane, which may safely be done in surveys of moderate extent.
(16) Land Surveying is the principal subject of this volume; the surface surveyed being regarded as plane; and each of the five Methods being in turn employed. For the purposes of instruction, the subject will be best divided, partly with reference to the Methods employed, and partly to the Instruments used. Accordingly, the First and Second Methods (Diagonal and Perpendic ular Surveying) will be treated of under the title "Chain Surveying," in Part II. The Third Method (Polar Surveying) will be explained under the titles "Compass Surveying," Part III, and "Transit and Theodolite Surveying," Part IV. The Fourth and Fifth Methods will be found under their own names of "Triangular Surveying," and "Trilinear Surveying," in Parts V and VI.
(17) In all the methods of Land Surveying, there are threo stages of operation:
1 Measuring certain lines and angles, and recording them; 2 Drawing them on paper to some suitable scale;
30 Calculating the content of the surface surveyed.
The three following chapters will treat of each of these topics in their turn.
MAKING THE MEASUREMENTS.
(18) THE Measurements which are required in Surveying, may be of lines or of angles, or of both; according to the Method, employed Each will be successively considered.
MEASURING STRAIGHT LINES.
(19) The lines, or distances, which are to be measured, may be either actual or visual.
Actual lines are such as really exist on the surface of the land to be surveyed, either bounding it, or crossing it; such as fences, ditches, roads, streams, &c.
Visual lines are imaginary lines of sight, either temporarily measured on the ground, such as those joining opposite corners of a field; or simply indicated by stakes at their extremities or otherwise. If long, they are "ranged out" by methods to be given. Lines are usually measured with chains, tapes or rods, divided into yards, feet, links, or some other unit of measurement.
(20) Gunter's Chain. used in Land surveying. such chains make one mile.
This is the measure most commonly
It is composed of one hundred pieces of iron wire, or links, each bent at the end into a ring, and connected with the ring at the end of the next piece by another ring. are placed between the links.
Sometimes two or three rings The chain is then less liable to
This length was chosen (by Mr. Edward Gunter) because 10 square chains of 66 feet make one acre, (as will be shown in Chapter IV,) and the computation of areas is thus greatly facilitated. For other Surveying purposes, particularly for Rail-road work, a chain of 100 feet is preferable. On the United States Coast Survey, the unit of measurement (which at some future time will be the universal one) is the French Metre, equal to 3.281 feet, nearly.
twist and get entangled, or "kinked." Two or more swivels are also inserted in the chain, so that it may turn around without twisting. Every tenth link is marked by a piece of brass, having one, two, three, or four points, corresponding to the number of tens which it marks, counting from the nearest end of the chain. The middle or fiftieth link is marked by a round piece of brass.
The hundredth part of a chain is called a link. The great advantage of this is, that since links are decimal parts of a chain, they may be so written down, 5 chains and 43 links being 5.43 chains, and all the calculations respecting chains and links can then be performed by the common rules of decimal Arithmetic. Each link is 7.92 inches long, being = 66 × 12 100. The following Table will be found convenient:
To prevent the very common mistake, of calling forty, sixty; or thirty, seventy, it has been suggested to make the 11th, 21st, 31st and 41st links of brass; which would at once show on which side of the middle of the chain was the doubtful mark. This would be particularly useful in Mining Surveying.
This must not be confounded with the pieces of wire which have the same name, since one of them is shorter than the "link" used in calculation, by half a ring, or more, according to the way in which the chain is made.
To reduce links to feet, subtract from the number of links as many units as it contains hundreds; multiply the remainder by 2 and divide by 3.
To reduce feet to links, add to the given number half of itself, and add one for each hundred (more exactly, for each ninety-nine) in the sum.
The chain is liable to be lengthened by its rings being pulled open, and to be shortened by its links being bent. It should therefore be frequently tested by a carefully-measured length of 66 feet, set out by a standard measure on a flat surface, such as the top of a wall, or on smooth level ground between two stakes, their centres being marked by small nails. It may be left a little longer than the true length, since it can seldom be stretched so as to be perfectly horizontal and not hang in a curve, or be drawn out in a perfectly straight line.* Distances measured with a perfectly accurate chain will always and unavoidably be recorded as longer than they really are. To ensure the chain being always strained with the same force, a spring, like that of a spring-balance, is sometimes placed between one handle and the rest of the chain.
If a line has been measured with an incorrect chain, the true length of the line will be obtained by multiplying the number of chains and links in the measured distance by 100, and dividing by the length of the standard distance, as given by measurement of it with the incorrect chain. The proportion here employed is this: As the length of the standard given by the incorrect chain Is to the true length of the standard, So is the length of the line given by the measurement To the true length. Thus, suppose that a line has been measured with a certain chain, and found by it to be ten chains long, and that the chain is afterwards found to have been so stretched that the standard distance, measured by it, appears to be only 99 links long. The measured line is therefore longer than it had been thought to be, and its true length is obtained by multiplying ten by 100, and dividing by 99.
The chain used by the Government Surveyors of France, which is 10 Metres, or about half a Gunter's chain in length, is made from one-fifth to two-fifths of an inch longer than the standard. An inaccuracy of one five hundredth of its length
13 inches on a Gunter's chain) is the utinost allowed not to vitiate the survey.
(21) Pins. Ten iron pins or "arrows," usually accompany the chain. They are about a foot long, and are made of stout iron wire, sharpened at one end, and bent into a ring at the other. Pieces of red and white cloth should be tied to their heads, so that they can be easily found in grass, dead leaves, &c.
They should be strung on a ring, which has a spring catch to retain them. Their usual form is shown in Fig. 9. Fig. 9. Fig. 10. Fig. 10 shows another form, made very large, and therefore very heavy, near the point, so that when held by the top and dropped, it may fall vertically. The uses of this will be seen presently.
(22) On irregular ground, two stout stakes about six feet long are needed to put the forward chainman in line, and to enable whichever of the two is
lowest, to raise his end of the chain in a truly vertical line, and to strain the chain straight.
A number of long and slender rods are also necessary for "ranging out" lines between distant points, in the manner to be explained hereafter; in Part II, Chapter V.
(23) How to Chain. Two men are required; a forward chainmain, and a hind chain-man; or leader and follower. The latter takes the handles of the chair in his left hand, and the chain itself in his right hand, and throws it out in the direction in which it is to be drawn. The former takes a handle of the chain and one pin in his right hand, and the other pins (and the staff, if used,) in his left hand, and draws out the chain. The follower then walks beside it, examining carefully that it is not twisted or bent. He then returns to its hinder end, which he holds at the beginning of the line to be measured, puts his eye exactly over it, and, by the words "Right," "Left," directs the leader how to put his staff, or the pin which he holds up, "in line," so that it may seem to cover and hide the flag-staff, or other object at the end of the line.
*Eleven pins are sometimes used, one being of brass. Nine of iron, with four or eight of brass, may also be employed. Their uses are explained in Articles (23) and (24).